Session.name = Ergodic_Theory
Loading theory "SG_Library_Complement"
loading_theory = SG_Library_Complement
ML_statistics = :now=1489705505.03tasks_ready=0tasks_pending=8tasks_running=1tasks_passive=0tasks_urgent=0workers_total=4workers_active=1workers_waiting=0full_GCs=0partial_GCs=0size_allocation=273678336size_allocation_free=273357400size_heap=273678336size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=0threads_total=7threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=0.008time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=89name=theoryelapsed=0.280
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=699name=abbreviationelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1072name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1185name=applyelapsed=0.081
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1258name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=5431name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=20830name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=18140name=byelapsed=0.030
ML_statistics = :now=1489705505.53tasks_ready=36tasks_pending=8tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=0size_allocation=735051776size_allocation_free=82765560size_heap=735051776size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=8.708time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=18019name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=17656name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=25108name=lemmaelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=17333name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=28443name=lemmaelapsed=0.010
### Rule already declared as introduction (intro)
### open {}
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; open ?T\<rbrakk> \<Longrightarrow> open (?S \<union> ?T)
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. open (?B x) \<Longrightarrow>
### open (\<Union>x\<in>?A. ?B x)
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=28883name=lemmaelapsed=0.010
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. open T\<rbrakk>
### \<Longrightarrow> open (\<Inter>?S)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. open (?B x)\<rbrakk>
### \<Longrightarrow> open (\<Inter>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### closed {}
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<union> ?T)
### Rule already declared as introduction (intro)
### closed UNIV
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<inter> ?T)
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. closed (?B x) \<Longrightarrow>
### closed (\<Inter>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### \<forall>S\<in>?K. closed S \<Longrightarrow> closed (\<Inter>?K)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. closed T\<rbrakk>
### \<Longrightarrow> closed (\<Union>?S)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. closed (?B x)\<rbrakk>
### \<Longrightarrow> closed (\<Union>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; closed ?T\<rbrakk> \<Longrightarrow> open (?S - ?T)
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; open ?T\<rbrakk> \<Longrightarrow> closed (?S - ?T)
### Rule already declared as introduction (intro)
### closed ?S \<Longrightarrow> open (- ?S)
### Rule already declared as introduction (intro)
### open ?S \<Longrightarrow> closed (- ?S)
### Rule already declared as introduction (intro)
### continuous_on ?s (linepath ?a ?b)
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=29348name=lemmaelapsed=0.016
### Rule already declared as introduction (intro)
### (\<And>i. continuous_on UNIV (\<lambda>x. ?f x i)) \<Longrightarrow>
### continuous_on UNIV ?f
### theory "SG_Library_Complement"
### 0.764s elapsed time, 1.336s cpu time, 0.000s GC time
Loading theory "Banach_Density"
loading_theory = Banach_Density
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=17096name=byelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16871name=applyelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16970name=byelapsed=0.010
### Rule already declared as introduction (intro)
### ((\<lambda>x. x) \<longlongrightarrow> ?a) (at ?a within ?s)
### Rule already declared as introduction (intro)
### ((\<lambda>x. ?k) \<longlongrightarrow> ?k) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. ereal (?f x)) \<longlongrightarrow> ereal ?x) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. - ?f x) \<longlongrightarrow> - ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?c\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?x \<noteq> 0; (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?y \<noteq> - \<infinity>; ?x \<noteq> - \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?y\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=11876name=applyelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=10426name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=11612name=byelapsed=0.030
### Rule already declared as introduction (intro)
### ((\<lambda>x. x) \<longlongrightarrow> ?a) (at ?a within ?s)
### Rule already declared as introduction (intro)
### ((\<lambda>x. ?k) \<longlongrightarrow> ?k) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. ereal (?f x)) \<longlongrightarrow> ereal ?x) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. - ?f x) \<longlongrightarrow> - ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?c\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?x \<noteq> 0; (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?y \<noteq> - \<infinity>; ?x \<noteq> - \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?y\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=11415name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=11334name=byelapsed=0.013
Loading theory "Fekete"
loading_theory = Fekete
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=89name=theoryelapsed=0.242
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=658name=definitionelapsed=0.019
ML_statistics = :now=1489705506.03tasks_ready=57tasks_pending=6tasks_running=2tasks_passive=0tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1232076800size_allocation_free=121092640size_heap=1232076800size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=9.508time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=11278name=definitionelapsed=0.019
### theory "Banach_Density"
### 0.414s elapsed time, 0.828s cpu time, 0.000s GC time
Loading theory "Measure_Preserving_Transformations"
loading_theory = Measure_Preserving_Transformations
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=89name=theoryelapsed=0.242
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=659name=definitionelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=757name=definitionelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=8487name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12411name=definitionelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12540name=lemmaelapsed=0.011
### theory "Fekete"
### 0.407s elapsed time, 0.816s cpu time, 0.000s GC time
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=89name=theoryelapsed=0.261
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=477name=definitionelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=691name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=948name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=18578name=byelapsed=0.146
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=19997name=proofelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=20466name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4316name=definitionelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=20256name=byelapsed=0.015
ML_statistics = :now=1489705506.54tasks_ready=80tasks_pending=6tasks_running=2tasks_passive=0tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1768947712size_allocation_free=326776904size_heap=1768947712size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=10.312time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=26502name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=6362name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=7166name=lemmaelapsed=0.013
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10634name=localeelapsed=0.025
locale mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10732name=localeelapsed=0.028
locale fmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "fmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10796name=localeelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=5873name=byelapsed=0.016
locale pmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "pmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10832name=localeelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10865name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=11137name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=12735name=subsectionelapsed=0.127
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=14022name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=5733name=byelapsed=0.235
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=5284name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18028name=definitionelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=22396name=lemmaelapsed=0.010
ML_statistics = :now=1489705507.14tasks_ready=123tasks_pending=6tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=2097152000size_heap=2132803584size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=11.316time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=2741name=byelapsed=0.147
locale mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=2276name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=26329name=lemmaelapsed=0.011
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=26647name=definitionelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=1940name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=30766name=lemmaelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=31855name=lemmaelapsed=0.015
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=32763name=definitionelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=32830name=definitionelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=34276name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=34861name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=1479name=byelapsed=0.157
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=1239name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=35037name=lemmaelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=1818name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=1693name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=35196name=lemmaelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=35997name=definitionelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=36211name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=36437name=lemmaelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=37060name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=37290name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=41356name=definitionelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=41785name=definitionelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=41882name=definitionelapsed=0.011
ML_statistics = :now=1489705507.64tasks_ready=163tasks_pending=6tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=1382440272size_heap=2132803584size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=12.108time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=43188name=lemmaelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=3291name=byelapsed=0.144
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=44133name=definitionelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=44337name=lemmaelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=44574name=lemmaelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=5006name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=44789name=lemmaelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45008name=lemmaelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47488name=lemmaelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47828name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=4860name=byelapsed=0.085
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=48056name=lemmaelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=4452name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49568name=lemmaelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=12790name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=50452name=lemmaelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=12573name=byelapsed=0.014
locale polish_pmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "polish_pmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=53309name=localeelapsed=0.097
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=53430name=definitionelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=53542name=definitionelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=53751name=definitionelapsed=0.017
### theory "Measure_Preserving_Transformations"
### 1.882s elapsed time, 3.620s cpu time, 0.164s GC time
Loading theory "Recurrence"
loading_theory = Recurrence
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=12222name=byelapsed=0.154
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=11859name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=12451name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=12326name=byelapsed=0.010
ML_statistics = :now=1489705508.14tasks_ready=170tasks_pending=5tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=57190288size_heap=2132803584size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=13.692time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=6103name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=5912name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=5567name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=5478name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=89name=theoryelapsed=0.299
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=1979name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4173name=byelapsed=0.019
locale conservative =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "conservative M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=836name=localeelapsed=0.096
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4461name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=964name=lemmaelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4544name=haveelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1183name=lemmaelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4673name=showelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=3221name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4654name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4606name=byelapsed=0.011
locale conservative_mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "conservative_mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=4441name=localeelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=2386name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=4487name=lemmaelapsed=0.016
ML_statistics = :now=1489705508.64tasks_ready=177tasks_pending=5tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2427453440size_allocation_free=90409920size_heap=2463105024size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=14.296time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=4942name=sublocaleelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=7467name=propositionelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=2840name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12004name=propositionelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12167name=lemmaelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3102name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12416name=lemmaelapsed=0.048
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12607name=contextelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3324name=haveelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3505name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3636name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12627name=definitionelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3711name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12740name=definitionelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3790name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3912name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=18530name=theoremelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=18530name=theoremelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=21181name=definitionelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=21311name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=22816name=definitionelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=24564name=lemmaelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3830name=byelapsed=0.218
ML_statistics = :now=1489705509.15tasks_ready=204tasks_pending=5tasks_running=13tasks_passive=11tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2848980992size_allocation_free=165528176size_heap=2884632576size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=14.872time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3752name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=25576name=lemmaelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=25576name=lemmaelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3694name=byelapsed=0.057
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=35577name=lemmaelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=35577name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3615name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=38281name=lemmaelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3557name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=38281name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=43921name=definitionelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3163name=byelapsed=0.064
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=3252name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47979name=definitionelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=2522name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49895name=definitionelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=2444name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=57316name=lemmaelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=57316name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=2173name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4495name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=4272name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=66700name=lemmaelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=66700name=lemmaelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=5302name=byelapsed=0.059
ML_statistics = :now=1489705509.65tasks_ready=205tasks_pending=5tasks_running=4tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3392143360size_allocation_free=343424408size_heap=3427794944size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=15.484time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=73077name=lemmaelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=73077name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=7034name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=7578name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=76380name=theoremelapsed=0.070
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=76380name=theoremelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78876name=theoremelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78876name=theoremelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=79459name=lemmaelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=79459name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82053name=definitionelapsed=0.098
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82221name=lemmaelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82460name=lemmaelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82700name=lemmaelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=83337name=lemmaelapsed=0.037
ML_statistics = :now=1489705510.15tasks_ready=211tasks_pending=5tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3682598912size_allocation_free=11952832size_heap=3718250496size_heap_free_last_full_GC=0size_heap_free_last_GC=2100519048threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=16.488time_GC=0.164user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
locale conservative_mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "conservative_mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=87417name=contextelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=7827name=byelapsed=0.411
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12951name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=87449name=lemmaelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=99045name=theoremelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=13081name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104458name=lemmaelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104458name=lemmaelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12917name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104738name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=107005name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=8931name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=108851name=lemmaelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=110393name=lemmaelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9425name=haveelapsed=0.011
### theory "Recurrence"
### 2.327s elapsed time, 3.344s cpu time, 0.000s GC time
Loading theory "Invariants"
loading_theory = Invariants
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9665name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=10455name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=10606name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12367name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=12051name=byelapsed=0.267
ML_statistics = :now=1489705510.91tasks_ready=227tasks_pending=4tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=4127195136size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=17.26time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=11795name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=11217name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=10709name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=11632name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=11430name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=89name=theoryelapsed=0.534
locale qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=627name=definitionelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=10939name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=10794name=byelapsed=0.070
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=9007name=lemmaelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=9007name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=8835name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=10127name=lemmaelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9593name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=10127name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=19925name=propositionelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=19925name=propositionelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=22992name=propositionelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=22992name=propositionelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=27134name=sublocaleelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9273name=byelapsed=0.135
locale fmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "fmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=27330name=contextelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9107name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=9359name=byelapsed=0.015
locale fmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "fmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=31873name=contextelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=47086name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=2561name=byelapsed=0.039
ML_statistics = :now=1489705511.41tasks_ready=244tasks_pending=4tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=3443969720size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=18.056time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=2414name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=59263name=theoremelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=59263name=theoremelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=82358name=theoremelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=84309name=theoremelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=86505name=propositionelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=92071name=corollaryelapsed=0.011
### theory "Invariants"
### 1.134s elapsed time, 2.008s cpu time, 0.400s GC time
Loading theory "Ergodicity"
loading_theory = Ergodicity
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=1186name=byelapsed=0.205
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=2286name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=1948name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=2070name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=1809name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=939name=byelapsed=0.095
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=89name=theoryelapsed=0.243
ML_statistics = :now=1489705511.92tasks_ready=245tasks_pending=3tasks_running=5tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=2806388832size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=18.748time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
locale ergodic_qmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_qmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=677name=localeelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=5498name=byelapsed=0.030
locale ergodic_mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=800name=localeelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=5458name=byelapsed=0.049
locale ergodic_fmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_fmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=841name=localeelapsed=0.070
locale ergodic_pmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_pmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=884name=localeelapsed=0.099
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4726name=byelapsed=0.150
locale ergodic_conservative =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_conservative M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=927name=localeelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9409name=showelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9470name=byelapsed=0.058
locale ergodic_conservative_mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_conservative_mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=986name=localeelapsed=0.088
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1053name=sublocaleelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9337name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1111name=sublocaleelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9218name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=8904name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1170name=sublocaleelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1241name=sublocaleelapsed=0.019
ML_statistics = :now=1489705512.42tasks_ready=246tasks_pending=3tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=2330749240size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=19.548time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9014name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1380name=lemmaelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=2589name=lemmaelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3138name=lemmaelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3489name=lemmaelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3840name=lemmaelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4955name=byelapsed=0.103
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=5051name=lemmaelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7533name=lemmaelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=8079name=lemmaelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=8509name=lemmaelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=8939name=lemmaelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=10227name=lemmaelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=10825name=lemmaelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=11106name=lemmaelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=11748name=theoremelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=12413name=lemmaelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=13322name=lemmaelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=14691name=theoremelapsed=0.052
ML_statistics = :now=1489705512.92tasks_ready=259tasks_pending=3tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=1123997104size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=21.088time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=15178name=theoremelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16104name=theoremelapsed=0.062
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16720name=theoremelapsed=0.062
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17336name=lemmaelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19059name=lemmaelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=20780name=lemmaelapsed=0.057
### theory "Ergodicity"
### 1.654s elapsed time, 3.244s cpu time, 0.000s GC time
Loading theory "Kingman"
loading_theory = Kingman
ML_statistics = :now=1489705513.43tasks_ready=265tasks_pending=2tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4127195136size_allocation_free=472442464size_heap=4128243712size_heap_free_last_full_GC=0size_heap_free_last_GC=4129971968threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=21.888time_GC=0.564user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=8242name=applyelapsed=1.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=8253name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=12890name=applyelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=89name=theoryelapsed=0.706
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=12935name=applyelapsed=0.365
locale mpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "mpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=1538name=contextelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=1605name=definitionelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=4642name=lemmaelapsed=0.014
ML_statistics = :now=1489705514.23tasks_ready=272tasks_pending=2tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=4028628992size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=22.756time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18432name=byelapsed=0.223
Found termination order: "(\<lambda>p. size (fst p)) <*mlex*> {}"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=12474name=funelapsed=0.324
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=17327name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=17869name=definitionelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18338name=byelapsed=0.325
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=20948name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=21872name=lemmaelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=23824name=definitionelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=24412name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=25162name=lemmaelapsed=0.012
ML_statistics = :now=1489705514.73tasks_ready=300tasks_pending=2tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=3365802344size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=23.536time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
locale fmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "fmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=27298name=contextelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=27318name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=47505name=theoremelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=20692name=byelapsed=0.164
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=49870name=definitionelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=50230name=definitionelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=21667name=byelapsed=0.117
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=62148name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68995name=theoremelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=1312name=byelapsed=0.071
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=76777name=lemmaelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=78497name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=79660name=lemmaelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=81487name=lemmaelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=83504name=theoremelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=91069name=theoremelapsed=0.014
ML_statistics = :now=1489705515.24tasks_ready=315tasks_pending=2tasks_running=4tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=2177133384size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=24.92time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
locale ergodic_pmpt =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
  assumes "ergodic_pmpt M T"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=98204name=contextelapsed=0.106
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=101844name=propositionelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=103196name=propositionelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=23409name=byelapsed=0.354
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=104756name=propositionelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=107027name=propositionelapsed=0.045
### theory "Kingman"
### 2.094s elapsed time, 3.696s cpu time, 0.392s GC time
Loading theory "Gouezel_Karlsson"
loading_theory = Gouezel_Karlsson
ML_statistics = :now=1489705515.74tasks_ready=322tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=1602922360size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=25.72time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89name=theoryelapsed=0.400
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=2363name=lemmaelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=3501name=byelapsed=0.578
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=3378name=byelapsed=0.024
locale Gouezel_Karlsson_Kingman =
  fixes M :: "'a measure" 
    and T :: "'a \<Rightarrow> 'a" 
    and u :: "nat \<Rightarrow> 'a \<Rightarrow> real" 
  assumes "Gouezel_Karlsson_Kingman M T u"
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=4006name=localeelapsed=0.194
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=3220name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=4350name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=12682name=lemmaelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=24679name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=44483name=lemmaelapsed=0.039
ML_statistics = :now=1489705516.24tasks_ready=320tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=1198057032size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=26.408time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=8023name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=67177name=lemmaelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=6227name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=80068name=lemmaelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93718name=lemmaelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96599name=theoremelapsed=0.093
### theory "Gouezel_Karlsson"
### 0.978s elapsed time, 1.792s cpu time, 0.000s GC time
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=34737name=byelapsed=0.152
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=34663name=byelapsed=0.038
ML_statistics = :now=1489705516.74tasks_ready=305tasks_pending=1tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4028628992size_allocation_free=564599488size_heap=4136632320size_heap_free_last_full_GC=0size_heap_free_last_GC=4030800424threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=27.164time_GC=0.956user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33232name=proofelapsed=0.541
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33941name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33870name=byelapsed=0.041
ML_statistics = :now=1489705517.38tasks_ready=307tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=1workers_waiting=1full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=3605860216size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=1threads_total=7threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=28.348time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
ML_statistics = :now=1489705517.88tasks_ready=307tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=1workers_waiting=1full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=3311096192size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=1threads_total=7threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=28.748time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33050name=applyelapsed=1.339
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33111name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=23114name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=23030name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33578name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=33422name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=20368name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10339name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47444name=applyelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9964name=byelapsed=0.070
ML_statistics = :now=1489705518.38tasks_ready=299tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=3008326432size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=29.152time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=10582name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47326name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47246name=byelapsed=0.092
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46019name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45756name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11970name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11808name=byelapsed=0.077
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45426name=byelapsed=0.111
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47134name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=9729name=byelapsed=0.088
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46330name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=47041name=byelapsed=0.062
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=9154name=byelapsed=0.053
ML_statistics = :now=1489705518.88tasks_ready=302tasks_pending=1tasks_running=18tasks_passive=16tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=2427620152size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=29.92time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=8919name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45956name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46914name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46240name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46828name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=8857name=byelapsed=0.225
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=8198name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=21946name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45887name=byelapsed=0.105
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46698name=byelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=20547name=byelapsed=0.109
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46143name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19413name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=46489name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45819name=byelapsed=0.021
ML_statistics = :now=1489705519.38tasks_ready=286tasks_pending=1tasks_running=14tasks_passive=11tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=1866516056size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=30.72time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=8402name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=12315name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=9568name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=10774name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=10621name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=10514name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47916name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47883name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=10063name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47800name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11621name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47682name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=47607name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11525name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=4462name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11454name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11318name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=11024name=byelapsed=0.011
ML_statistics = :now=1489705519.89tasks_ready=272tasks_pending=1tasks_running=14tasks_passive=12tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=4size_allocation=3980394496size_allocation_free=689893904size_heap=4156555264size_heap_free_last_full_GC=0size_heap_free_last_GC=3983069232threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=32.224time_GC=1.2user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78857name=byelapsed=0.103
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=46749name=byelapsed=0.269
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78703name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78458name=byelapsed=0.062
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=78072name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=77892name=byelapsed=0.131
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=77549name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=77301name=byelapsed=0.020
ML_statistics = :now=1489705520.42tasks_ready=273tasks_pending=1tasks_running=19tasks_passive=17tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3962568704size_allocation_free=3962568704size_heap=4164943872size_heap_free_last_full_GC=0size_heap_free_last_GC=3964787272threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=33.052time_GC=1.288user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=77021name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=46640name=byelapsed=0.459
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=22153name=byelapsed=0.013
*** Failed to finish proof (line 490 of "~~/afp/thys/Ergodic_Theory/Recurrence.thy"):
*** goal (1 subgoal):
***  1. \<lbrakk>recurrent_subset A =
***              A \<inter> (\<Union>x\<in>{0<..}. (T ^^ x) --` A);
***      \<And>k. {Suc k..} = {k<..}\<rbrakk>
***     \<Longrightarrow> A \<inter> (\<Union>x\<in>{0<..}. (T ^^ x) --` A) =
***                       A \<inter> (\<Union>x. (T \<circ> T ^^ x) --` A)
*** At command "by" (line 490 of "~~/afp/thys/Ergodic_Theory/Recurrence.thy")
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=66522name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=2576name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=66394name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=58035name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=2478name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=60288name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=2442name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=60074name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=2071name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=59317name=byelapsed=0.122
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=59016name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=3828name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=3582name=byelapsed=0.033
ML_statistics = :now=1489705520.92tasks_ready=284tasks_pending=1tasks_running=11tasks_passive=9tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3962568704size_allocation_free=3334381472size_heap=4164943872size_heap_free_last_full_GC=0size_heap_free_last_GC=3964787272threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=33.852time_GC=1.288user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1857name=byelapsed=0.154
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1732name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=3314name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1623name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1563name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1355name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=1194name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=22283name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=28963name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=28645name=qedelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=28421name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=2710name=byelapsed=0.235
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=27791name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=5426name=byelapsed=0.010
ML_statistics = :now=1489705521.42tasks_ready=275tasks_pending=1tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3962568704size_allocation_free=2647298112size_heap=4164943872size_heap_free_last_full_GC=0size_heap_free_last_GC=3964787272threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=34.56time_GC=1.288user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7989name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=6577name=byelapsed=0.101
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=5921name=byelapsed=0.070
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=5784name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=5318name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=5713name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=22751name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7320name=byelapsed=0.180
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=20223name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=6191name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7250name=byelapsed=0.069
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7102name=applyelapsed=0.018
ML_statistics = :now=1489705521.92tasks_ready=271tasks_pending=1tasks_running=19tasks_passive=17tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3962568704size_allocation_free=1432891632size_heap=4164943872size_heap_free_last_full_GC=0size_heap_free_last_GC=3964787272threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=36.032time_GC=1.288user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19938name=byelapsed=0.119
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7129name=byelapsed=0.108
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19904name=byelapsed=0.113
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7001name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19797name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=6933name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=6859name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18246name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19032name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=6612name=byelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=6285name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=5945name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=6107name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=7899name=byelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=4729name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=11948name=byelapsed=0.011
ML_statistics = :now=1489705522.42tasks_ready=258tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3962568704size_allocation_free=825652984size_heap=4164943872size_heap_free_last_full_GC=0size_heap_free_last_GC=3964787272threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=36.836time_GC=1.288user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=12937name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=13242name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1371name=proofelapsed=0.194
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1433name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1722name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=13747name=byelapsed=0.098
*** Failed to finish proof (line 278 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. \<And>x xa.
***        \<lbrakk>\<And>m. T --` (T ^^ m) --` B = (T \<circ> T ^^ m) --` B;
***         \<And>k. {Suc k..} = {k<..}; x \<in> (T ^^ xa) --` B;
***         0 < xa\<rbrakk>
***        \<Longrightarrow> \<exists>xa. x \<in> (T \<circ> T ^^ xa) --` B
*** At command "by" (line 278 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=2355name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=2861name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=10091name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=9564name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=2685name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1983name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=3024name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1876name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=9472name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=558name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=17167name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16352name=haveelapsed=0.010
ML_statistics = :now=1489705522.95tasks_ready=251tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=3984588800size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=38.072time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16411name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=29575name=byelapsed=0.101
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=29536name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16572name=haveelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=29359name=byelapsed=0.156
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16975name=byelapsed=0.158
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=29238name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=29123name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=18515name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=24159name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=18142name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=25592name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16845name=byelapsed=0.251
ML_statistics = :now=1489705523.46tasks_ready=237tasks_pending=1tasks_running=10tasks_passive=9tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=3399632832size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=38.776time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16746name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=22773name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=22169name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16662name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=22386name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16288name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=3322name=proofelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13144name=haveelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=3765name=showelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=3854name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13992name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=3641name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13719name=applyelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13806name=applyelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13884name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=23398name=byelapsed=0.075
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=51223name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=50593name=proofelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=50733name=haveelapsed=0.011
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=51119name=byelapsed=0.011
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13479name=byelapsed=0.121
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=13364name=byelapsed=0.018
ML_statistics = :now=1489705523.96tasks_ready=233tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=2826713440size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=39.548time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=51089name=byelapsed=0.151
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=15835name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=50975name=byelapsed=0.137
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=50921name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=100732name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=100051name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=99216name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=98503name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=2257name=byelapsed=0.018
ML_statistics = :now=1489705524.47tasks_ready=235tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=2291853816size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=40.352time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=59331name=assumeelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=59552name=letelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=59824name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61773name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61735name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61564name=byelapsed=0.064
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61469name=byelapsed=0.174
ML_statistics = :now=1489705524.97tasks_ready=242tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=1288104872size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=41.956time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61319name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=61058name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7538name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7710name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7808name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16154name=byelapsed=1.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=8407name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=8271name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=8126name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7789name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7609name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60665name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60594name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60342name=byelapsed=0.069
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16112name=byelapsed=0.215
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=16066name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60292name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60204name=byelapsed=0.067
ML_statistics = :now=1489705525.47tasks_ready=233tasks_pending=1tasks_running=18tasks_passive=15tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=6size_allocation=3984588800size_allocation_free=765701192size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3987657552threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=42.76time_GC=1.356user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=60100name=byelapsed=0.156
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10305name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10736name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11181name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11268name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11394name=haveelapsed=0.015
ML_statistics = :now=1489705526.01tasks_ready=257tasks_pending=1tasks_running=20tasks_passive=17tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=3974103040size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=43.856time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11660name=byelapsed=0.134
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11608name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11461name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11355name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11253name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10809name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10695name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7017name=byelapsed=0.095
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=6959name=byelapsed=0.073
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=6812name=byelapsed=0.019
ML_statistics = :now=1489705526.51tasks_ready=247tasks_pending=1tasks_running=27tasks_passive=25tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=3409746760size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=44.636time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=6462name=byelapsed=0.180
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=6292name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10623name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10506name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=15946name=byelapsed=1.524
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=15721name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10256name=byelapsed=0.273
ML_statistics = :now=1489705527.01tasks_ready=242tasks_pending=1tasks_running=27tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=2746776656size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=45.436time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=15656name=byelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=15344name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10078name=byelapsed=0.086
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=9867name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=4256name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=14901name=byelapsed=0.097
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=4154name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=3477name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=11166name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=14760name=byelapsed=0.114
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2968name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=14664name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2719name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=14436name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2891name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=14287name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=10961name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=9398name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=54325name=interpretelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=9289name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=9246name=byelapsed=0.014
ML_statistics = :now=1489705527.51tasks_ready=226tasks_pending=1tasks_running=19tasks_passive=17tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=2167068320size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=46.204time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=9128name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=5491name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=63279name=interpretelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=8605name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=63604name=proofelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7145name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=66314name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65894name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65300name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65806name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65473name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65383name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=8018name=byelapsed=0.326
ML_statistics = :now=1489705528.01tasks_ready=227tasks_pending=1tasks_running=23tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=956894784size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=47.808time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=24084name=byelapsed=0.175
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=54314name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65653name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=54418name=proofelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=54643name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55412name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55574name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55836name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55972name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=56275name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=56089name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55955name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7840name=byelapsed=0.327
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55561name=byelapsed=0.094
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7703name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7534name=byelapsed=0.057
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7304name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55352name=byelapsed=0.075
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=7243name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=6357name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=52639name=haveelapsed=0.011
ML_statistics = :now=1489705528.52tasks_ready=220tasks_pending=1tasks_running=18tasks_passive=16tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=7size_allocation=3974103040size_allocation_free=425053704size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3976199992threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=48.608time_GC=1.424user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=52872name=byelapsed=0.134
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55283name=byelapsed=0.183
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=55754name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=54514name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=63749name=unfoldingelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=52823name=byelapsed=0.114
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=52624name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64112name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64453name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=47909name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64723name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=48676name=assumeelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=65056name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64959name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=49488name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=49029name=applyelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=45011name=assumeelapsed=0.015
ML_statistics = :now=1489705529.04tasks_ready=221tasks_pending=1tasks_running=20tasks_passive=18tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=8size_allocation=3965714432size_allocation_free=3965714432size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3968332128threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=49.252time_GC=1.516user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=46726name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=42572name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=42695name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=44612name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=42934name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=42453name=byelapsed=0.047
ML_statistics = :now=1489705529.55tasks_ready=227tasks_pending=1tasks_running=23tasks_passive=21tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=8size_allocation=3965714432size_allocation_free=2674277272size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3968332128threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=50.864time_GC=1.516user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41724name=byelapsed=0.604
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41635name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41454name=byelapsed=0.012
ML_statistics = :now=1489705530.05tasks_ready=224tasks_pending=1tasks_running=26tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=8size_allocation=3965714432size_allocation_free=1845791632size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3968332128threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=51.664time_GC=1.516user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=40298name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=32830name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=37064name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=39615name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=39459name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=39544name=byelapsed=0.033
ML_statistics = :now=1489705530.55tasks_ready=235tasks_pending=1tasks_running=32tasks_passive=29tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=8size_allocation=3965714432size_allocation_free=1240127312size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3968332128threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=52.456time_GC=1.516user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=39337name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=39096name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=32177name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27413name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64247name=byelapsed=1.777
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27385name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27278name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27215name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=38670name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64898name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=38342name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=37880name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64638name=applyelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64704name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=37543name=qedelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64566name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=37533name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64414name=byelapsed=0.069
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=64051name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=35740name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=35636name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=63258name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=35566name=byelapsed=0.030
ML_statistics = :now=1489705531.05tasks_ready=223tasks_pending=1tasks_running=36tasks_passive=33tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=8size_allocation=3965714432size_allocation_free=648616504size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3968332128threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=53.26time_GC=1.516user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62797name=applyelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62863name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62469name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=42437name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=34709name=alsoelapsed=0.090
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62719name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=34992name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=34449name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=34052name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=33955name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=33688name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=35213name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62159name=applyelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=62212name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=33376name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=59570name=applyelapsed=0.096
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=33229name=byelapsed=0.114
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41378name=byelapsed=0.023
ML_statistics = :now=1489705531.58tasks_ready=220tasks_pending=1tasks_running=29tasks_passive=27tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=9size_allocation=3949985792size_allocation_free=3949985792size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3953052608threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=54.132time_GC=1.58user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=40812name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=40588name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41313name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=41045name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=40895name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=59609name=byelapsed=0.219
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=48395name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61647name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=27963name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=28451name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32319name=defineelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32868name=haveelapsed=0.082
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42247name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61953name=byelapsed=0.214
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45812name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=46161name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=46308name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61844name=byelapsed=0.062
ML_statistics = :now=1489705532.08tasks_ready=240tasks_pending=1tasks_running=23tasks_passive=21tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=9size_allocation=3949985792size_allocation_free=2764451096size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3953052608threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=55.736time_GC=1.58user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=47492name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=47274name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=46661name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=46775name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45927name=haveelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=46077name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60716name=byelapsed=0.238
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61490name=byelapsed=0.094
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44514name=haveelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61303name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=61133name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44747name=assumeelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44950name=haveelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45219name=haveelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45466name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45577name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45591name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60907name=applyelapsed=0.129
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45745name=showelapsed=0.010
ML_statistics = :now=1489705532.58tasks_ready=243tasks_pending=1tasks_running=28tasks_passive=26tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=9size_allocation=3949985792size_allocation_free=2197058632size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3953052608threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=56.54time_GC=1.58user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45796name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45682name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=45361name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44708name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=33120name=defineelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34998name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36835name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39722name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=41277name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=41701name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42059name=haveelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60948name=byelapsed=0.310
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60421name=applyelapsed=0.068
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42230name=byelapsed=0.110
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42192name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=41643name=byelapsed=0.017
ML_statistics = :now=1489705533.08tasks_ready=247tasks_pending=1tasks_running=34tasks_passive=32tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=9size_allocation=3949985792size_allocation_free=1703589616size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3953052608threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=57.344time_GC=1.58user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32712name=applyelapsed=0.069
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32806name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32467name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32309name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60481name=byelapsed=0.250
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=27742name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=27660name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=31542name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60327name=byelapsed=0.091
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60165name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=60002name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=58354name=obtainelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=31256name=byelapsed=0.177
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=59080name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=28724name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=59010name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=58915name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=28434name=byelapsed=0.073
ML_statistics = :now=1489705533.59tasks_ready=233tasks_pending=1tasks_running=34tasks_passive=32tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=9size_allocation=3949985792size_allocation_free=1003026920size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3953052608threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=58.148time_GC=1.58user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=58150name=byelapsed=0.118
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=28084name=byelapsed=0.118
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=57762name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=41417name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=57376name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39909name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=63491name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40073name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40241name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40438name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40576name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40816name=haveelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40965name=haveelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=41217name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=35002name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40946name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40770name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=35193name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40549name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=34910name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=29518name=haveelapsed=0.103
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=40379name=byelapsed=0.172
ML_statistics = :now=1489705534.14tasks_ready=245tasks_pending=1tasks_running=33tasks_passive=31tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=3943694336size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=59.564time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=33933name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=31455name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39701name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=31256name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39643name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=37878name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=31126name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=33714name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39483name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49442name=byelapsed=0.161
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39303name=byelapsed=0.109
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=37432name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=39186name=byelapsed=0.018
ML_statistics = :now=1489705534.64tasks_ready=249tasks_pending=1tasks_running=33tasks_passive=31tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=3356524488size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=60.372time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=38148name=byelapsed=0.143
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=38710name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=38006name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=37944name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49329name=byelapsed=0.310
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=35751name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36000name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36214name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36450name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36383name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=36195name=byelapsed=0.015
ML_statistics = :now=1489705535.14tasks_ready=245tasks_pending=1tasks_running=35tasks_passive=33tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=2631171256size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=61.172time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34911name=byelapsed=0.401
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32067name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=35981name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34544name=byelapsed=0.014
ML_statistics = :now=1489705535.64tasks_ready=246tasks_pending=1tasks_running=37tasks_passive=35tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=1477095128size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=62.776time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34440name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34361name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34265name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34209name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=34106name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=35215name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=31642name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44378name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44201name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44096name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44017name=applyelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=44061name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43499name=applyelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=32635name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43686name=applyelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43791name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42451name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43627name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43216name=applyelapsed=0.014
ML_statistics = :now=1489705536.14tasks_ready=234tasks_pending=1tasks_running=23tasks_passive=21tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=971566816size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=63.576time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43303name=byelapsed=0.136
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=43013name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42778name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=42571name=byelapsed=0.147
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=31046name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=30893name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=30575name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=30179name=byelapsed=0.014
ML_statistics = :now=1489705536.64tasks_ready=229tasks_pending=1tasks_running=20tasks_passive=18tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=10size_allocation=3943694336size_allocation_free=431438904size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3947017320threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=64.38time_GC=1.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=29546name=proofelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=29305name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24135name=haveelapsed=0.078
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26046name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=25912name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=25836name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=25469name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24358name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24089name=byelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=23476name=byelapsed=0.021
ML_statistics = :now=1489705537.19tasks_ready=234tasks_pending=1tasks_running=26tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=11size_allocation=3927965696size_allocation_free=3927965696size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3930365912threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=65.036time_GC=1.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18827name=byelapsed=0.284
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=23594name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=22387name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24884name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24797name=applyelapsed=0.115
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24829name=byelapsed=0.015
ML_statistics = :now=1489705537.7tasks_ready=229tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=11size_allocation=3927965696size_allocation_free=2841000496size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3930365912threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=66.644time_GC=1.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24720name=byelapsed=0.090
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=24654name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=11037name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=10900name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=10361name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18514name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=23919name=byelapsed=0.102
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=23764name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=23666name=byelapsed=0.035
ML_statistics = :now=1489705538.2tasks_ready=219tasks_pending=1tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=11size_allocation=3927965696size_allocation_free=2308213000size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3930365912threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=67.448time_GC=1.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=15495name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=17469name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=17736name=defineelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=21659name=defineelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34814name=haveelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=44025name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=44331name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=44149name=byelapsed=0.027
ML_statistics = :now=1489705538.7tasks_ready=251tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=11size_allocation=3927965696size_allocation_free=1671092376size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3930365912threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=68.248time_GC=1.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=43089name=byelapsed=0.210
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38693name=defineelapsed=0.085
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38890name=haveelapsed=0.028
ML_statistics = :now=1489705539.2tasks_ready=257tasks_pending=1tasks_running=11tasks_passive=9tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=11size_allocation=3927965696size_allocation_free=1123623976size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3930365912threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=69.052time_GC=1.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=40974name=byelapsed=0.415
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=39821name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=39743name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=39239name=applyelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=39326name=applyelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38499name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=6824name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=6997name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7095name=haveelapsed=0.013
ML_statistics = :now=1489705539.79tasks_ready=253tasks_pending=1tasks_running=16tasks_passive=14tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=3916431360size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=70.752time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7398name=byelapsed=0.118
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=7076name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=6896name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=40808name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=39909name=haveelapsed=0.071
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=40326name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=40230name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35288name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37040name=haveelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37244name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37397name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37495name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37691name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37880name=haveelapsed=0.070
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38064name=haveelapsed=0.076
ML_statistics = :now=1489705540.3tasks_ready=263tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=3401991736size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=71.556time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38312name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38222name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=38047name=byelapsed=0.094
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37189name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37020name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35211name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36779name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36599name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36536name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35095name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36329name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37839name=byelapsed=0.037
ML_statistics = :now=1489705540.8tasks_ready=251tasks_pending=1tasks_running=16tasks_passive=14tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=2893320024size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=72.356time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37674name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36065name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36234name=byelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36199name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35646name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=16627name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=36046name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23332name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24099name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24335name=haveelapsed=0.011
ML_statistics = :now=1489705541.3tasks_ready=266tasks_pending=1tasks_running=21tasks_passive=19tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=2357385480size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=73.16time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29524name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29698name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29874name=haveelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30116name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30288name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30633name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31111name=haveelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31453name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31545name=haveelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33230name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33408name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33782name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33937name=haveelapsed=0.011
ML_statistics = :now=1489705541.8tasks_ready=307tasks_pending=1tasks_running=21tasks_passive=19tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=1266744640size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=74.764time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34077name=haveelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34359name=haveelapsed=0.033
ML_statistics = :now=1489705542.3tasks_ready=309tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=12size_allocation=3916431360size_allocation_free=828059616size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3918611352threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=75.568time_GC=1.988user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34697name=byelapsed=0.698
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32975name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25798name=byelapsed=0.016
ML_statistics = :now=1489705542.91tasks_ready=306tasks_pending=1tasks_running=25tasks_passive=23tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=3896508416size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=76.768time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25637name=byelapsed=0.349
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25198name=byelapsed=0.198
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24995name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24953name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=17459name=byelapsed=0.030
ML_statistics = :now=1489705543.41tasks_ready=301tasks_pending=1tasks_running=23tasks_passive=21tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=3354802096size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=77.576time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32566name=byelapsed=0.076
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32407name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32302name=byelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32183name=byelapsed=0.103
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25871name=byelapsed=0.170
ML_statistics = :now=1489705543.91tasks_ready=296tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=2875486904size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=78.38time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34621name=byelapsed=0.348
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49189name=byelapsed=9.315
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32719name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1854name=qedelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1786name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34340name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=1733name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=34058name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=32047name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31910name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31756name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31676name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31526name=byelapsed=0.013
ML_statistics = :now=1489705544.41tasks_ready=287tasks_pending=1tasks_running=27tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=2375308928size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=79.18time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31431name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=17610name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=17530name=byelapsed=0.068
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=31250name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30996name=byelapsed=0.098
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=16073name=byelapsed=0.096
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25990name=byelapsed=0.023
ML_statistics = :now=1489705544.92tasks_ready=279tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=1182823336size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=80.784time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2222name=qedelapsed=0.693
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2200name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2144name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49002name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18606name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=45078name=haveelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=45289name=obtainelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=45450name=defineelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=45706name=haveelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47463name=defineelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47621name=haveelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33918name=byelapsed=0.581
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=48961name=defineelapsed=0.024
ML_statistics = :now=1489705545.42tasks_ready=285tasks_pending=1tasks_running=20tasks_passive=18tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=13size_allocation=3896508416size_allocation_free=595500664size_heap=4170186752size_heap_free_last_full_GC=0size_heap_free_last_GC=3899468384threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=81.584time_GC=2.172user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30814name=byelapsed=0.077
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=51939name=haveelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=53420name=haveelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=54691name=haveelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30562name=applyelapsed=0.166
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=54904name=obtainelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=56579name=defineelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30407name=applyelapsed=0.084
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65512name=haveelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66335name=haveelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30472name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66509name=haveelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66730name=byelapsed=0.115
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66666name=byelapsed=0.044
ML_statistics = :now=1489705545.94tasks_ready=294tasks_pending=1tasks_running=24tasks_passive=22tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=14size_allocation=3865051136size_allocation_free=3865051136size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3867161752threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=82.38time_GC=2.248user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66472name=byelapsed=0.057
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30234name=byelapsed=0.274
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24733name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65625name=proofelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66215name=showelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66314name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=66063name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=30097name=byelapsed=0.186
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29849name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=16762name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29675name=byelapsed=0.010
ML_statistics = :now=1489705546.44tasks_ready=288tasks_pending=1tasks_running=26tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=14size_allocation=3865051136size_allocation_free=3321523336size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3867161752threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=83.184time_GC=2.248user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65892name=byelapsed=0.306
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33623name=applyelapsed=0.293
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65368name=byelapsed=0.119
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33668name=byelapsed=0.129
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25535name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65259name=byelapsed=0.115
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25479name=byelapsed=0.088
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=48869name=qedelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25415name=byelapsed=0.041
linarith_split_limit exceeded (current value is 9)
ML_statistics = :now=1489705546.94tasks_ready=293tasks_pending=1tasks_running=37tasks_passive=35tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=14size_allocation=3865051136size_allocation_free=2692567568size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3867161752threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=83.984time_GC=2.248user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=25365name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=48857name=byelapsed=0.143
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=48791name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=64723name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33389name=byelapsed=0.145
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=64578name=byelapsed=0.086
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=64492name=byelapsed=0.102
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29499name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28033name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29251name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=64192name=byelapsed=0.120
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=64080name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63875name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28110name=byelapsed=0.068
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63302name=applyelapsed=0.019
ML_statistics = :now=1489705547.44tasks_ready=291tasks_pending=1tasks_running=35tasks_passive=33tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=14size_allocation=3865051136size_allocation_free=1386327272size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3867161752threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=85.588time_GC=2.248user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=29088name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63360name=applyelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28928name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63754name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63645name=applyelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28793name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28640name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63681name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=63180name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28468name=byelapsed=0.143
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28368name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=28279name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60670name=haveelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27947name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61117name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27883name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61362name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61619name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33211name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61843name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62106name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=33087name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62385name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62611name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62934name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57973name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57803name=applyelapsed=0.034
ML_statistics = :now=1489705547.95tasks_ready=303tasks_pending=1tasks_running=30tasks_passive=28tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=14size_allocation=3865051136size_allocation_free=698400824size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3867161752threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=86.392time_GC=2.248user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57820name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27638name=byelapsed=0.081
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27423name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=26393name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57545name=byelapsed=0.141
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27291name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27154name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57382name=byelapsed=0.071
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57312name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=27022name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=57207name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=26873name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62831name=applyelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62868name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=26710name=byelapsed=0.086
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59417name=haveelapsed=0.099
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=26289name=byelapsed=0.123
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=26225name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60025name=byelapsed=0.011
ML_statistics = :now=1489705548.5tasks_ready=293tasks_pending=1tasks_running=29tasks_passive=27tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=3875536896size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=87.332time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60195name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60079name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24906name=byelapsed=0.095
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59901name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59753name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24555name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59716name=byelapsed=0.141
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59286name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59599name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62755name=byelapsed=0.104
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58262name=haveelapsed=0.012
ML_statistics = :now=1489705549tasks_ready=289tasks_pending=1tasks_running=28tasks_passive=26tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=3324291928size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=88.136time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=59049name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58916name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58865name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58753name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24499name=byelapsed=0.486
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23818name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58569name=byelapsed=0.081
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23676name=byelapsed=0.086
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23482name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23317name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58534name=byelapsed=0.169
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58044name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=58422name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23123name=byelapsed=0.098
ML_statistics = :now=1489705549.5tasks_ready=274tasks_pending=1tasks_running=28tasks_passive=26tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=2812828520size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=88.94time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62594name=byelapsed=0.126
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=23006name=byelapsed=0.177
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=24316name=byelapsed=0.113
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=22640name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=22262name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62345name=byelapsed=0.294
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=22097name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35857name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=62040name=byelapsed=0.120
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=35762name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61576name=byelapsed=0.062
ML_statistics = :now=1489705550tasks_ready=261tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=1836267856size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=90.54time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=37478name=byelapsed=0.053
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=40581name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61350name=byelapsed=0.073
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9171name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9416name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=61097name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60609name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9979name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60478name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10483name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=60964name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10617name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10735name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10846name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=65709name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=55341name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=11005name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=56070name=byelapsed=0.071
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=55103name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10941name=byelapsed=0.115
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10831name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=54856name=byelapsed=0.104
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10583name=byelapsed=0.041
ML_statistics = :now=1489705550.5tasks_ready=260tasks_pending=1tasks_running=17tasks_passive=15tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=1302389576size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=91.352time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10464name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10374name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10255name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=54680name=byelapsed=0.189
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=54368name=byelapsed=0.075
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
ML_statistics = :now=1489705551.01tasks_ready=255tasks_pending=1tasks_running=20tasks_passive=18tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=15size_allocation=3875536896size_allocation_free=768524832size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3877173584threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=92.152time_GC=2.376user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
linarith_split_limit exceeded (current value is 9)
linarith_split_limit exceeded (current value is 9)
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52069name=applyelapsed=0.353
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=10160name=byelapsed=0.504
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52464name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=53404name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=53289name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=53172name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=53011name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9728name=byelapsed=0.266
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52939name=byelapsed=0.091
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52737name=byelapsed=0.041
ML_statistics = :now=1489705551.51tasks_ready=254tasks_pending=1tasks_running=27tasks_passive=25tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=16size_allocation=3850371072size_allocation_free=3850371072size_heap=4185915392size_heap_free_last_full_GC=0size_heap_free_last_GC=3852298176threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=93.084time_GC=2.428user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52628name=byelapsed=0.094
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=52385name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9944name=byelapsed=0.241
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=51233name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9515name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=49199name=byelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9271name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=9152name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=45625name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=51865name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=8951name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=49698name=haveelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=8856name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=49889name=haveelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=51002name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=8664name=byelapsed=0.109
ML_statistics = :now=1489705552.01tasks_ready=244tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=16size_allocation=3850371072size_allocation_free=3230602080size_heap=4185915392size_heap_free_last_full_GC=0size_heap_free_last_GC=3852298176threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=93.888time_GC=2.428user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=21155name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50029name=proofelapsed=0.177
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20938name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50078name=assumeelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50279name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50512name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50905name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20522name=byelapsed=0.091
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50769name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20304name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=49637name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=19875name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50681name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20175name=applyelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20188name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=20023name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=19932name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=50491name=byelapsed=0.109
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46073name=obtainelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=19793name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=42176name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46306name=haveelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47283name=haveelapsed=0.016
ML_statistics = :now=1489705552.51tasks_ready=240tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=16size_allocation=3850371072size_allocation_free=2004122512size_heap=4185915392size_heap_free_last_full_GC=0size_heap_free_last_GC=3852298176threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=95.492time_GC=2.428user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=18193name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47446name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47416name=byelapsed=0.093
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=16327name=byelapsed=0.117
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=11229name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=42718name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=42546name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=42432name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=41604name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=16981name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=19013name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46538name=proofelapsed=0.168
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46585name=assumeelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46915name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47258name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=18974name=byelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47144name=byelapsed=0.064
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=47073name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=72003name=assumeelapsed=0.014
ML_statistics = :now=1489705553.01tasks_ready=232tasks_pending=1tasks_running=22tasks_passive=20tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=16size_allocation=3850371072size_allocation_free=1401227176size_heap=4185915392size_heap_free_last_full_GC=0size_heap_free_last_GC=3852298176threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=96.292time_GC=2.428user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=72920name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=73188name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46878name=byelapsed=0.091
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=73859name=proofelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=74879name=showelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=46260name=byelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=71974name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=71840name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=3946name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=57519name=assumeelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=3729name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=57963name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=3543name=byelapsed=0.011
### Rule already declared as introduction (intro)
### ((\<lambda>x. x) \<longlongrightarrow> ?a) (at ?a within ?s)
### Rule already declared as introduction (intro)
### ((\<lambda>x. ?k) \<longlongrightarrow> ?k) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. ereal (?f x)) \<longlongrightarrow> ereal ?x) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. - ?f x) \<longlongrightarrow> - ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?c\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?x \<noteq> 0; (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?y \<noteq> - \<infinity>; ?x \<noteq> - \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?y\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=21351name=byelapsed=0.011
### Rule already declared as introduction (intro)
### ((\<lambda>x. x) \<longlongrightarrow> ?a) (at ?a within ?s)
### Rule already declared as introduction (intro)
### ((\<lambda>x. ?k) \<longlongrightarrow> ?k) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. ereal (?f x)) \<longlongrightarrow> ereal ?x) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. - ?f x) \<longlongrightarrow> - ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?c\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?x \<noteq> 0; (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?y \<noteq> - \<infinity>; ?x \<noteq> - \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?y\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=21104name=applyelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=3263name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=2886name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=27395name=byelapsed=0.014
ML_statistics = :now=1489705553.51tasks_ready=240tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=16size_allocation=3850371072size_allocation_free=749800664size_heap=4185915392size_heap_free_last_full_GC=0size_heap_free_last_GC=3852298176threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=97.096time_GC=2.428user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=27305name=byelapsed=0.506
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=27163name=byelapsed=0.012
ML_statistics = :now=1489705554.05tasks_ready=238tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=17size_allocation=3850371072size_allocation_free=3850371072size_heap=4183818240size_heap_free_last_full_GC=0size_heap_free_last_GC=3853169704threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=98.032time_GC=2.536user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=21160name=byelapsed=0.795
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=17292name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=17077name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=27070name=byelapsed=0.403
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=16928name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39835name=applyelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39715name=byelapsed=0.030
ML_statistics = :now=1489705554.55tasks_ready=259tasks_pending=1tasks_running=9tasks_passive=7tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=17size_allocation=3850371072size_allocation_free=3205910968size_heap=4183818240size_heap_free_last_full_GC=0size_heap_free_last_GC=3853169704threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=98.832time_GC=2.536user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39631name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38324name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=37723name=byelapsed=0.083
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39512name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=16721name=byelapsed=0.374
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=15536name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38635name=byelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=14981name=byelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=15945name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=15786name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39418name=byelapsed=0.159
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38261name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=4141name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38005name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39266name=byelapsed=0.052
ML_statistics = :now=1489705555.05tasks_ready=244tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=17size_allocation=3850371072size_allocation_free=1853130472size_heap=4183818240size_heap_free_last_full_GC=0size_heap_free_last_GC=3853169704threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=100.436time_GC=2.536user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38545name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39179name=byelapsed=0.159
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38192name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=39024name=byelapsed=0.062
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38448name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38804name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=38124name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=11110name=byelapsed=0.052
ML_statistics = :now=1489705555.55tasks_ready=243tasks_pending=1tasks_running=5tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=17size_allocation=3850371072size_allocation_free=1134746216size_heap=4183818240size_heap_free_last_full_GC=0size_heap_free_last_GC=3853169704threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=101.24time_GC=2.536user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=43586name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=43256name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=41405name=byelapsed=0.073
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=38903name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=40144name=byelapsed=0.084
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=39928name=byelapsed=0.064
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=24901name=byelapsed=0.046
ML_statistics = :now=1489705556.05tasks_ready=252tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=17size_allocation=3850371072size_allocation_free=419506000size_heap=4183818240size_heap_free_last_full_GC=0size_heap_free_last_GC=3853169704threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=102.04time_GC=2.536user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=24535name=byelapsed=0.114
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=24508name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=24355name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=23989name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=23551name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=23462name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=23332name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=28453name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=28206name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42995name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42863name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=40948name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=39450name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42756name=byelapsed=0.057
ML_statistics = :now=1489705556.62tasks_ready=245tasks_pending=1tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=18size_allocation=3837788160size_allocation_free=3180654424size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3839764472threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=103.296time_GC=2.672user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42669name=byelapsed=0.251
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42428name=byelapsed=0.032
ML_statistics = :now=1489705557.12tasks_ready=243tasks_pending=1tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=18size_allocation=3837788160size_allocation_free=2526233344size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3839764472threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=104.096time_GC=2.672user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42343name=byelapsed=0.480
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=42076name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=41980name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=41841name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=41563name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=39000name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=37696name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=37346name=byelapsed=0.022
ML_statistics = :now=1489705557.62tasks_ready=238tasks_pending=1tasks_running=11tasks_passive=9tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=18size_allocation=3837788160size_allocation_free=1921095864size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3839764472threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=104.9time_GC=2.672user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=37256name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=36929name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=36998name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=36634name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=36485name=byelapsed=0.077
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=36154name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=25050name=byelapsed=0.051
ML_statistics = :now=1489705558.12tasks_ready=243tasks_pending=1tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=18size_allocation=3837788160size_allocation_free=1294980488size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3839764472threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=105.7time_GC=2.672user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=3995name=byelapsed=3.255
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=72517name=byelapsed=0.075
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=72396name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=72288name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=81619name=byelapsed=0.162
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=81534name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=72030name=byelapsed=0.169
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=87910name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=81351name=byelapsed=0.141
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=80907name=byelapsed=0.027
ML_statistics = :now=1489705558.66tasks_ready=255tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=19size_allocation=3824156672size_allocation_free=3824156672size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3825869616threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=107.136time_GC=2.8user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=80777name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=14195name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=14127name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=13892name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=13820name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=13718name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=99032name=byelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=98971name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=21124name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=98670name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=20453name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=94448name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=20190name=byelapsed=0.080
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=94418name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19939name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=94271name=qedelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=89828name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19601name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=89518name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19563name=byelapsed=0.036
ML_statistics = :now=1489705559.17tasks_ready=277tasks_pending=1tasks_running=21tasks_passive=19tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=19size_allocation=3824156672size_allocation_free=3145088896size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3825869616threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=107.94time_GC=2.8user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19497name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19305name=applyelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=19059name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=20769name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=49717name=byelapsed=0.153
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=80599name=byelapsed=0.170
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=80518name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=80341name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=79915name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=103801name=byelapsed=0.096
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=79791name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=103580name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=103489name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=110190name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=101859name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=109837name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=101666name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=109604name=byelapsed=0.015
ML_statistics = :now=1489705559.67tasks_ready=279tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=19size_allocation=3824156672size_allocation_free=2413015384size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3825869616threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=108.74time_GC=2.8user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=44182name=proofelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=100894name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=100721name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=102984name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=99676name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82691name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=44556name=byelapsed=0.105
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=44471name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=108838name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=7619name=byelapsed=0.090
*** Failed to finish proof (line 175 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. \<And>x xa.
***        \<lbrakk>\<And>m. T --` (T ^^ m) --` A = (T \<circ> T ^^ m) --` A;
***         \<And>k. {Suc k..} = {k<..};
***         \<forall>xa. x \<in> (T \<circ> T ^^ xa) --` A; 0 < xa\<rbrakk>
***        \<Longrightarrow> x \<in> (T ^^ xa) --` A
*** At command "by" (line 175 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=108747name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=22979name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=108496name=byelapsed=0.185
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=107676name=byelapsed=0.010
ML_statistics = :now=1489705560.17tasks_ready=296tasks_pending=1tasks_running=10tasks_passive=8tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=19size_allocation=3824156672size_allocation_free=1018540024size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3825869616threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=110.352time_GC=2.8user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=22769name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=105830name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=22402name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21291name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=106260name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=106380name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21022name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=20409name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=106992name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=20527name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=106866name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21817name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26166name=interpretelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21730name=applyelapsed=0.093
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21762name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=27116name=byelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21653name=byelapsed=0.092
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=21587name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=20852name=byelapsed=0.100
ML_statistics = :now=1489705560.67tasks_ready=293tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=19size_allocation=3824156672size_allocation_free=389603664size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3825869616threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=111.152time_GC=2.8user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=27045name=byelapsed=0.216
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=20697name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=20599name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=48222name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=50334name=byelapsed=0.143
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=48597name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=48734name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=49679name=applyelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=49790name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=49597name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=48688name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=48565name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=16075name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=15975name=byelapsed=0.014
ML_statistics = :now=1489705561.24tasks_ready=299tasks_pending=1tasks_running=12tasks_passive=10tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=20size_allocation=3812622336size_allocation_free=3812622336size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3814558024threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=111.616time_GC=2.928user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=15803name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=15751name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=15671name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=15338name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=47948name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=47809name=byelapsed=0.199
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=47485name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=47541name=byelapsed=0.109
ML_statistics = :now=1489705561.74tasks_ready=290tasks_pending=1tasks_running=9tasks_passive=7tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=20size_allocation=3812622336size_allocation_free=2460364008size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3814558024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=1threads_wait_signal=1time_CPU=113.224time_GC=2.928user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=59792name=interpretelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=64415name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65439name=obtainelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65684name=haveelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74807name=byelapsed=0.034
ML_statistics = :now=1489705562.24tasks_ready=326tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=20size_allocation=3812622336size_allocation_free=1734633384size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3814558024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=114.024time_GC=2.928user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74592name=byelapsed=0.111
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74503name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74387name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74026name=haveelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74150name=haveelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74289name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=74243name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73841name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73673name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73545name=byelapsed=0.089
ML_statistics = :now=1489705562.74tasks_ready=328tasks_pending=1tasks_running=14tasks_passive=12tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=20size_allocation=3812622336size_allocation_free=1057660336size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3814558024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=114.828time_GC=2.928user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=72544name=byelapsed=0.091
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26772name=applyelapsed=2.117
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=72437name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26789name=applyelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=62713name=applyelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=62747name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26838name=applyelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73338name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=19245name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73245name=byelapsed=0.125
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65354name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=73070name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=66038name=byelapsed=0.191
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=61973name=byelapsed=0.030
ML_statistics = :now=1489705563.32tasks_ready=317tasks_pending=1tasks_running=16tasks_passive=14tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=21size_allocation=3800039424size_allocation_free=3800039424size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3802654008threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=116.112time_GC=3.06user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=61175name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60847name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60750name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60561name=byelapsed=0.071
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60476name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60404name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=17480name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=13295name=proofelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=13650name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=22112name=applyelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=22183name=applyelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=72675name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67636name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=68516name=byelapsed=0.010
ML_statistics = :now=1489705563.82tasks_ready=318tasks_pending=1tasks_running=13tasks_passive=11tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=21size_allocation=3800039424size_allocation_free=3193909040size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3802654008threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=116.916time_GC=3.06user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=72064name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71814name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71744name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71614name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71413name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=23951name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=23846name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=23655name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71278name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=71126name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65428name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=70843name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=70768name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=70563name=byelapsed=0.016
ML_statistics = :now=1489705564.32tasks_ready=315tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=21size_allocation=3800039424size_allocation_free=2542037872size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3802654008threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=117.72time_GC=3.06user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69980name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=66576name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69572name=byelapsed=0.094
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69474name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69018name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69404name=byelapsed=0.077
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=69268name=byelapsed=0.038
ML_statistics = :now=1489705564.82tasks_ready=313tasks_pending=1tasks_running=17tasks_passive=15tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=21size_allocation=3800039424size_allocation_free=1182252240size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3802654008threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=119.324time_GC=3.06user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26457name=applyelapsed=1.956
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26474name=applyelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=26537name=applyelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=66991name=byelapsed=0.165
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=68385name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=77207name=interpretelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67077name=byelapsed=0.124
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=78173name=interpretelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=66865name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=66457name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=78417name=interpretelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=68253name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=68151name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=78591name=interpretelapsed=0.047
ML_statistics = :now=1489705565.32tasks_ready=316tasks_pending=1tasks_running=13tasks_passive=11tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=21size_allocation=3800039424size_allocation_free=496552752size_heap=4181721088size_heap_free_last_full_GC=0size_heap_free_last_GC=3802654008threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=120.124time_GC=3.06user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=82345name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67985name=byelapsed=0.276
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=82274name=byelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=82140name=byelapsed=0.124
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=81839name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=81998name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=81909name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67831name=byelapsed=0.348
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=81563name=byelapsed=0.180
*** Failed to finish proof (line 1480 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. (\<And>N.
***         0 < N \<Longrightarrow>
***         {x \<in> space M.
***          \<forall>n\<in>{N..}.
***             0 \<le> birkhoff_sum f n x \<longrightarrow>
***             \<not> birkhoff_sum f n x \<le> e}
***         \<in> null_sets M) \<Longrightarrow>
***     (\<Union>x\<in>{0<..}.
***         {xa \<in> space M.
***          \<forall>n\<in>{x..}.
***             0 \<le> birkhoff_sum f n xa \<longrightarrow>
***             \<not> birkhoff_sum f n xa \<le> e})
***     \<in> null_sets M
*** At command "by" (line 1480 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
ML_statistics = :now=1489705565.88tasks_ready=324tasks_pending=1tasks_running=15tasks_passive=13tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=22size_allocation=3787456512size_allocation_free=3787456512size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3788891232threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=120.768time_GC=3.208user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=86907name=interpretelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=88960name=assumeelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67588name=byelapsed=0.180
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=67395name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=30639name=applyelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=90673name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=91021name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=92058name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=91431name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=91254name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=90454name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=30652name=applyelapsed=0.179
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65799name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=89872name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=62844name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65561name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=63240name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=63539name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65202name=byelapsed=0.028
ML_statistics = :now=1489705566.39tasks_ready=328tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=22size_allocation=3787456512size_allocation_free=3137499240size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3788891232threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=121.572time_GC=3.208user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=65035name=byelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=64848name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=66099name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68982name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68884name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=67001name=proofelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=64381name=byelapsed=0.183
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68754name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=64251name=byelapsed=0.105
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68624name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=63983name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68439name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=63913name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=68347name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=63709name=byelapsed=0.085
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=63110name=byelapsed=0.011
ML_statistics = :now=1489705566.89tasks_ready=329tasks_pending=1tasks_running=13tasks_passive=10tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=22size_allocation=3787456512size_allocation_free=1759666024size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3788891232threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=123.176time_GC=3.208user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=64628name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=61627name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=61396name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=66424name=byelapsed=0.201
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=29335name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=66080name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=65560name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=65221name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60962name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=64115name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=60091name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=62872name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=63815name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=91398name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=95781name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=59972name=byelapsed=0.111
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=97276name=assumeelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=25095name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=25008name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=98136name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=98098name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=5295name=defineelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=96697name=assumeelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=97030name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=11010name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=97236name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=91387name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=67493name=interpretelapsed=0.014
ML_statistics = :now=1489705567.39tasks_ready=326tasks_pending=1tasks_running=3tasks_passive=0tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=22size_allocation=3787456512size_allocation_free=1193770912size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3788891232threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=123.98time_GC=3.208user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=12627name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=12474name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=12280name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=67493name=interpretelapsed=0.095
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8625name=haveelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=68516name=obtainelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8817name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=68861name=defineelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8945name=haveelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=69155name=defineelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9253name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=69531name=defineelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9568name=haveelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9717name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=10079name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=10062name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9965name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9815name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9681name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9526name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=78474name=haveelapsed=0.014
ML_statistics = :now=1489705567.89tasks_ready=368tasks_pending=1tasks_running=11tasks_passive=9tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=22size_allocation=3787456512size_allocation_free=583160024size_heap=4177526784size_heap_free_last_full_GC=0size_heap_free_last_GC=3788891232threads_in_ML=2threads_total=7threads_wait_condvar=2threads_wait_IO=0threads_wait_mutex=1threads_wait_signal=1time_CPU=124.784time_GC=3.208user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=78726name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=78996name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=79411name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=79230name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8594name=byelapsed=0.135
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=78458name=byelapsed=0.146
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=78280name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=77481name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=77414name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=77294name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8541name=byelapsed=0.128
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=77188name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8169name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=77074name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=76897name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=69695name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7805name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=69520name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=76740name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7691name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7604name=byelapsed=0.057
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=76383name=applyelapsed=0.081
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=76458name=applyelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7425name=byelapsed=0.038
ML_statistics = :now=1489705568.48tasks_ready=360tasks_pending=1tasks_running=24tasks_passive=21tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=23size_allocation=3768582144size_allocation_free=3160910920size_heap=4173332480size_heap_free_last_full_GC=0size_heap_free_last_GC=3771007024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=126.264time_GC=3.388user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7265name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=76195name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=75726name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8426name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=22094name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=7171name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=75406name=applyelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=8227name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6954name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=75483name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=75275name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=75196name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=74974name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=69345name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=68256name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=107232name=interpretelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6900name=byelapsed=0.230
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=105153name=interpretelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6367name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=106078name=assumeelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6280name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6743name=byelapsed=0.050
ML_statistics = :now=1489705568.99tasks_ready=342tasks_pending=1tasks_running=26tasks_passive=24tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=23size_allocation=3768582144size_allocation_free=2501253048size_heap=4173332480size_heap_free_last_full_GC=0size_heap_free_last_GC=3771007024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=127.068time_GC=3.388user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=107014name=byelapsed=0.060
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=105143name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=6598name=byelapsed=0.074
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=5960name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=102181name=interpretelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9359name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=9236name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=11921name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=11235name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=102701name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=10994name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=102079name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=4858name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=4656name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=5260name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=5160name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=98581name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=98788name=assumeelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99539name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99841name=haveelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=80773name=interpretelapsed=0.175
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=100062name=byelapsed=0.107
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=100024name=byelapsed=0.024
ML_statistics = :now=1489705569.49tasks_ready=343tasks_pending=1tasks_running=5tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=23size_allocation=3768582144size_allocation_free=1803828928size_heap=4173332480size_heap_free_last_full_GC=0size_heap_free_last_GC=3771007024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=127.868time_GC=3.388user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99707name=applyelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99750name=byelapsed=0.061
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=83834name=interpretelapsed=0.189
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99337name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=99088name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=98755name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=98571name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=97913name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=97786name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=87006name=obtainelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93574name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=91508name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92196name=haveelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92486name=haveelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92842name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=3679name=byelapsed=0.238
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93516name=byelapsed=0.057
ML_statistics = :now=1489705569.99tasks_ready=335tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=23size_allocation=3768582144size_allocation_free=1118853384size_heap=4173332480size_heap_free_last_full_GC=0size_heap_free_last_GC=3771007024threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=128.672time_GC=3.388user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=87919name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=88151name=obtainelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93415name=byelapsed=0.050
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=88650name=haveelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89028name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89193name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89353name=haveelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89650name=haveelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90010name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90273name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93256name=byelapsed=0.120
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90452name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90748name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90715name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92473name=byelapsed=0.119
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90599name=byelapsed=0.078
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92176name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=86192name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=80716name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92024name=byelapsed=0.068
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=50862name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=91487name=byelapsed=0.181
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=50179name=haveelapsed=0.135
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=50421name=qedelapsed=0.013
ML_statistics = :now=1489705570.58tasks_ready=332tasks_pending=1tasks_running=17tasks_passive=15tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=24size_allocation=3743416320size_allocation_free=3743416320size_heap=4168089600size_heap_free_last_full_GC=0size_heap_free_last_GC=3744952712threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=130.104time_GC=3.6user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=50023name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=91805name=byelapsed=0.069
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=5873name=byelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93013name=byelapsed=0.120
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90435name=byelapsed=0.133
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=92783name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89637name=byelapsed=0.130
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89333name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89176name=byelapsed=0.087
ML_statistics = :now=1489705571.08tasks_ready=322tasks_pending=1tasks_running=13tasks_passive=10tasks_urgent=0workers_total=4workers_active=2workers_waiting=1full_GCs=0partial_GCs=24size_allocation=3743416320size_allocation_free=3305279224size_heap=4168089600size_heap_free_last_full_GC=0size_heap_free_last_GC=3744952712threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=130.772time_GC=3.6user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=88629name=byelapsed=0.065
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=4783name=byelapsed=0.153
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=88951name=byelapsed=0.083
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=90184name=byelapsed=0.102
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=4953name=byelapsed=0.121
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=89951name=byelapsed=0.066
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=88134name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=87686name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=86954name=applyelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=9682name=byelapsed=0.044
### Ignoring duplicate introduction (intro)
### open {}
### Ignoring duplicate introduction (intro)
### \<lbrakk>open ?S; open ?T\<rbrakk> \<Longrightarrow> open (?S \<union> ?T)
### Ignoring duplicate introduction (intro)
### \<forall>x\<in>?A. open (?B x) \<Longrightarrow>
### open (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. open T\<rbrakk>
### \<Longrightarrow> open (\<Inter>?S)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. open (?B x)\<rbrakk>
### \<Longrightarrow> open (\<Inter>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### closed {}
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<union> ?T)
### Ignoring duplicate introduction (intro)
### closed UNIV
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<inter> ?T)
### Ignoring duplicate introduction (intro)
### \<forall>x\<in>?A. closed (?B x) \<Longrightarrow>
### closed (\<Inter>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<forall>S\<in>?K. closed S \<Longrightarrow> closed (\<Inter>?K)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. closed T\<rbrakk>
### \<Longrightarrow> closed (\<Union>?S)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. closed (?B x)\<rbrakk>
### \<Longrightarrow> closed (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<lbrakk>open ?S; closed ?T\<rbrakk> \<Longrightarrow> open (?S - ?T)
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; open ?T\<rbrakk> \<Longrightarrow> closed (?S - ?T)
### Ignoring duplicate introduction (intro)
### closed ?S \<Longrightarrow> open (- ?S)
### Ignoring duplicate introduction (intro)
### open ?S \<Longrightarrow> closed (- ?S)
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=9572name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=86996name=byelapsed=0.044
### Ignoring duplicate introduction (intro)
### continuous_on ?s (linepath ?a ?b)
### Ignoring duplicate introduction (intro)
### (\<And>i. continuous_on UNIV (\<lambda>x. ?f x i)) \<Longrightarrow>
### continuous_on UNIV ?f
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=9445name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=86890name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=12508name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=86661name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=9077name=byelapsed=0.050
### Ignoring duplicate introduction (intro)
### open {}
### Ignoring duplicate introduction (intro)
### \<lbrakk>open ?S; open ?T\<rbrakk> \<Longrightarrow> open (?S \<union> ?T)
### Ignoring duplicate introduction (intro)
### \<forall>x\<in>?A. open (?B x) \<Longrightarrow>
### open (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. open T\<rbrakk>
### \<Longrightarrow> open (\<Inter>?S)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. open (?B x)\<rbrakk>
### \<Longrightarrow> open (\<Inter>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### closed {}
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<union> ?T)
### Ignoring duplicate introduction (intro)
### closed UNIV
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<inter> ?T)
### Ignoring duplicate introduction (intro)
### \<forall>x\<in>?A. closed (?B x) \<Longrightarrow>
### closed (\<Inter>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<forall>S\<in>?K. closed S \<Longrightarrow> closed (\<Inter>?K)
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. closed T\<rbrakk>
### \<Longrightarrow> closed (\<Union>?S)
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=83571name=byelapsed=0.038
### Ignoring duplicate introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. closed (?B x)\<rbrakk>
### \<Longrightarrow> closed (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate introduction (intro)
### \<lbrakk>open ?S; closed ?T\<rbrakk> \<Longrightarrow> open (?S - ?T)
### Ignoring duplicate introduction (intro)
### \<lbrakk>closed ?S; open ?T\<rbrakk> \<Longrightarrow> closed (?S - ?T)
### Ignoring duplicate introduction (intro)
### closed ?S \<Longrightarrow> open (- ?S)
### Ignoring duplicate introduction (intro)
### open ?S \<Longrightarrow> closed (- ?S)
### Ignoring duplicate introduction (intro)
### continuous_on ?s (linepath ?a ?b)
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=83397name=byelapsed=0.013
### Ignoring duplicate introduction (intro)
### (\<And>i. continuous_on UNIV (\<lambda>x. ?f x i)) \<Longrightarrow>
### continuous_on UNIV ?f
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=13230name=applyelapsed=0.073
ML_statistics = :now=1489705571.58tasks_ready=313tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=24size_allocation=3743416320size_allocation_free=2876539672size_heap=4168089600size_heap_free_last_full_GC=0size_heap_free_last_GC=3744952712threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=131.48time_GC=3.6user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=13299name=byelapsed=0.051
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=12972name=applyelapsed=0.013
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. x) has_derivative (\<lambda>x. x)) ?F1 \<equiv> True
### Rule already declared as introduction (intro)
### open {}
### Ignoring duplicate rewrite rule:
### (id has_derivative id) (at ?a1) \<equiv> True
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; open ?T\<rbrakk> \<Longrightarrow> open (?S \<union> ?T)
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. ?c1) has_derivative (\<lambda>x. 0::?'b1)) ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### \<lbrakk>(?f1 has_derivative ?f'1) ?F1;
###  (?g1 has_derivative ?g'1) ?F1\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f1 x + ?g1 x) has_derivative
###                    (\<lambda>x. ?f'1 x + ?g'1 x))
###                    ?F1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### (\<And>i.
###     i \<in> ?I1 \<Longrightarrow>
###     (?f1 i has_derivative ?f'1 i) ?F1) \<Longrightarrow>
### ((\<lambda>x. \<Sum>i\<in>?I1. ?f1 i x) has_derivative
###  (\<lambda>x. \<Sum>i\<in>?I1. ?f'1 i x))
###  ?F1 \<equiv>
### True
### Ignoring duplicate rewrite rule:
### (?f1 has_derivative ?f'1) ?F1 \<Longrightarrow>
### ((\<lambda>x. - ?f1 x) has_derivative (\<lambda>x. - ?f'1 x)) ?F1 \<equiv>
### True
### Ignoring duplicate rewrite rule:
### \<lbrakk>(?f1 has_derivative ?f'1) ?F1;
###  (?g1 has_derivative ?g'1) ?F1\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f1 x - ?g1 x) has_derivative
###                    (\<lambda>x. ?f'1 x - ?g'1 x))
###                    ?F1 \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. open (?B x) \<Longrightarrow>
### open (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate rewrite rule:
### \<lbrakk>(?f1 has_derivative ?f'1) (at ?x1 within ?s1);
###  (?g1 has_derivative ?g'1) (at ?x1 within ?s1)\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f1 x * ?g1 x) has_derivative
###                    (\<lambda>h. ?f1 ?x1 * ?g'1 h + ?f'1 h * ?g1 ?x1))
###                    (at ?x1 within ?s1) \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>(?f1 has_derivative ?f'1) (at ?x1 within ?s1);
###  (?g1 has_derivative ?g'1) (at ?x1 within ?s1)\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f1 x *\<^sub>R ?g1 x) has_derivative
###                    (\<lambda>h.
###                        ?f1 ?x1 *\<^sub>R ?g'1 h + ?f'1 h *\<^sub>R ?g1 ?x1))
###                    (at ?x1 within ?s1) \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. open T\<rbrakk>
### \<Longrightarrow> open (\<Inter>?S)
### Ignoring duplicate rewrite rule:
### (\<And>i.
###     i \<in> ?I1 \<Longrightarrow>
###     (?f1 i has_derivative ?f'1 i) (at ?x1 within ?s1)) \<Longrightarrow>
### ((\<lambda>x. \<Prod>i\<in>?I1. ?f1 i x) has_derivative
###  (\<lambda>y.
###      \<Sum>i\<in>?I1. ?f'1 i y * (\<Prod>j\<in>?I1 - {i}. ?f1 j ?x1)))
###  (at ?x1 within ?s1) \<equiv>
### True
### Ignoring duplicate rewrite rule:
### (?f1 has_derivative ?f'1) (at ?x1 within ?s1) \<Longrightarrow>
### ((\<lambda>x. ?f1 x ^ ?n1) has_derivative
###  (\<lambda>y. of_nat ?n1 * ?f'1 y * ?f1 ?x1 ^ (?n1 - 1)))
###  (at ?x1 within ?s1) \<equiv>
### True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 ?x1 \<noteq> (0::?'a1);
###  (?f1 has_derivative ?f'1) (at ?x1 within ?s1)\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. inverse (?f1 x)) has_derivative
###                    (\<lambda>h.
###                        - (inverse (?f1 ?x1) * ?f'1 h * inverse (?f1 ?x1))))
###                    (at ?x1 within ?s1) \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. open (?B x)\<rbrakk>
### \<Longrightarrow> open (\<Inter>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### closed {}
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<union> ?T)
### Rule already declared as introduction (intro)
### closed UNIV
### Ignoring duplicate rewrite rule:
### \<lbrakk>(?f1 has_derivative ?f'1) (at ?x1 within ?s1);
###  (?g1 has_derivative ?g'1) (at ?x1 within ?s1);
###  ?g1 ?x1 \<noteq> (0::?'a1)\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f1 x / ?g1 x) has_derivative
###                    (\<lambda>h.
###                        - ?f1 ?x1 *
###                        (inverse (?g1 ?x1) * ?g'1 h * inverse (?g1 ?x1)) +
###                        ?f'1 h / ?g1 ?x1))
###                    (at ?x1 within ?s1) \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<inter> ?T)
### Ignoring duplicate rewrite rule:
### (\<lambda>x. x) differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (\<lambda>z. ?a1) differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable ?F1; ?g1 differentiable ?F1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x + ?g1 x) differentiable ?F1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### ?f1 differentiable ?F1 \<Longrightarrow>
### (\<lambda>x. - ?f1 x) differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable ?F1; ?g1 differentiable ?F1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x - ?g1 x) differentiable ?F1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable at ?x1 within ?s1;
###  ?g1 differentiable at ?x1 within ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x * ?g1 x) differentiable at ?x1
###                   within ?s1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable at ?x1 within ?s1;
###  ?f1 ?x1 \<noteq> (0::?'b1)\<rbrakk>
### \<Longrightarrow> (\<lambda>x. inverse (?f1 x)) differentiable at ?x1
###                   within ?s1 \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. closed (?B x) \<Longrightarrow>
### closed (\<Inter>x\<in>?A. ?B x)
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable at ?x1 within ?s1;
###  ?g1 differentiable at ?x1 within ?s1; ?g1 ?x1 \<noteq> (0::?'b1)\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x / ?g1 x) differentiable at ?x1
###                   within ?s1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### ?f1 differentiable at ?x1 within ?s1 \<Longrightarrow>
### (\<lambda>x. ?f1 x ^ ?n1) differentiable at ?x1 within ?s1 \<equiv> True
### Rule already declared as introduction (intro)
### \<forall>S\<in>?K. closed S \<Longrightarrow> closed (\<Inter>?K)
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable at ?x1 within ?s1;
###  ?g1 differentiable at ?x1 within ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x *\<^sub>R ?g1 x) differentiable at ?x1
###                   within ?s1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. ?c1) has_vector_derivative (0::?'a1)) ?net1 \<equiv> True
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. x) has_vector_derivative 1) ?net1 \<equiv> True
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. ?k1) has_field_derivative (0::?'a1)) ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. x) has_field_derivative (1::?'a1)) ?F1 \<equiv> True
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. closed T\<rbrakk>
### \<Longrightarrow> closed (\<Union>?S)
### Ignoring duplicate rewrite rule:
### (?g1 has_derivative ?g'1) ?F1 \<Longrightarrow>
### ((\<lambda>x. cnj (?g1 x)) has_derivative (\<lambda>x. cnj (?g'1 x)))
###  ?F1 \<equiv>
### True
### Ignoring duplicate rewrite rule:
### (\<lambda>x. x) differentiable_on ?S1 \<equiv> True
### Ignoring duplicate rewrite rule:
### id differentiable_on ?S1 \<equiv> True
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. closed (?B x)\<rbrakk>
### \<Longrightarrow> closed (\<Union>x\<in>?A. ?B x)
### Ignoring duplicate rewrite rule:
### (\<lambda>z. ?c1) differentiable_on ?S1 \<equiv> True
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; closed ?T\<rbrakk> \<Longrightarrow> open (?S - ?T)
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable_on ?S1; ?g1 differentiable_on ?S1\<rbrakk>
### \<Longrightarrow> (\<lambda>z. ?f1 z * ?g1 z) differentiable_on ?S1 \<equiv>
###                   True
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; open ?T\<rbrakk> \<Longrightarrow> closed (?S - ?T)
### Ignoring duplicate rewrite rule:
### ?f1 differentiable_on ?S1 \<Longrightarrow>
### (\<lambda>z. - ?f1 z) differentiable_on ?S1 \<equiv> True
### Rule already declared as introduction (intro)
### closed ?S \<Longrightarrow> open (- ?S)
### Rule already declared as introduction (intro)
### open ?S \<Longrightarrow> closed (- ?S)
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable_on ?S1; ?g1 differentiable_on ?S1\<rbrakk>
### \<Longrightarrow> (\<lambda>z. ?f1 z + ?g1 z) differentiable_on ?S1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable_on ?S1; ?g1 differentiable_on ?S1\<rbrakk>
### \<Longrightarrow> (\<lambda>z. ?f1 z - ?g1 z) differentiable_on ?S1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable_on ?S1;
###  \<And>x. x \<in> ?S1 \<Longrightarrow> ?f1 x \<noteq> (0::?'b1)\<rbrakk>
### \<Longrightarrow> (\<lambda>x. inverse (?f1 x)) differentiable_on
###                   ?S1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 differentiable_on ?S1; ?g1 differentiable_on ?S1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x *\<^sub>R ?g1 x) differentiable_on
###                   ?S1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### ((\<lambda>x. (norm x)\<^sup>2) has_derivative
###  (\<lambda>x. 2 *\<^sub>R (?a1 \<bullet> x)))
###  (at ?a1) \<equiv>
### True
### Ignoring duplicate rewrite rule:
### (\<lambda>x. (norm x)\<^sup>2) differentiable at ?a1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (\<lambda>x. (norm x)\<^sup>2) differentiable_on ?S1 \<equiv> True
### Ignoring duplicate rewrite rule:
### ?a1 \<noteq> (0::?'a1) \<Longrightarrow>
### norm differentiable at ?a1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (0::?'a1) \<notin> ?S1 \<Longrightarrow>
### norm differentiable_on ?S1 \<equiv> True
### Ignoring duplicate rewrite rule:
### op * ?c1 field_differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (\<lambda>z. ?c1) field_differentiable ?F1 \<equiv> True
### Rule already declared as introduction (intro)
### continuous_on ?s (linepath ?a ?b)
### Ignoring duplicate rewrite rule:
### (\<lambda>z. z) field_differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### id field_differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### op + ?c1 field_differentiable ?F1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (?f1 has_derivative ?f'1) ?F1 \<Longrightarrow>
### ((\<lambda>x. of_real (?f1 x)) has_derivative
###  (\<lambda>x. of_real (?f'1 x)))
###  ?F1 \<equiv>
### True
### Ignoring duplicate rewrite rule:
### (\<lambda>x. x) C1_differentiable_on ?s1 \<equiv> True
### Ignoring duplicate rewrite rule:
### (\<lambda>z. ?a1) C1_differentiable_on ?s1 \<equiv> True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 C1_differentiable_on ?s1; ?g1 C1_differentiable_on ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x + ?g1 x) C1_differentiable_on
###                   ?s1 \<equiv>
###                   True
### Rule already declared as introduction (intro)
### (\<And>i. continuous_on UNIV (\<lambda>x. ?f x i)) \<Longrightarrow>
### continuous_on UNIV ?f
### Ignoring duplicate rewrite rule:
### ?f1 C1_differentiable_on ?s1 \<Longrightarrow>
### (\<lambda>x. - ?f1 x) C1_differentiable_on ?s1 \<equiv> True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 C1_differentiable_on ?s1; ?g1 C1_differentiable_on ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x - ?g1 x) C1_differentiable_on
###                   ?s1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 C1_differentiable_on ?s1; ?g1 C1_differentiable_on ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x * ?g1 x) C1_differentiable_on
###                   ?s1 \<equiv>
###                   True
### Ignoring duplicate rewrite rule:
### \<lbrakk>?f1 C1_differentiable_on ?s1; ?g1 C1_differentiable_on ?s1\<rbrakk>
### \<Longrightarrow> (\<lambda>x. ?f1 x *\<^sub>R ?g1 x) C1_differentiable_on
###                   ?s1 \<equiv>
###                   True
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=15075name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=13080name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=14273name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=12768name=applyelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=14208name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16290name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=14081name=applyelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16167name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=14102name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16048name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=13934name=byelapsed=0.041
### Rule already declared as introduction (intro)
### open {}
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; open ?T\<rbrakk> \<Longrightarrow> open (?S \<union> ?T)
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. open (?B x) \<Longrightarrow>
### open (\<Union>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. open T\<rbrakk>
### \<Longrightarrow> open (\<Inter>?S)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. open (?B x)\<rbrakk>
### \<Longrightarrow> open (\<Inter>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### closed {}
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<union> ?T)
### Rule already declared as introduction (intro)
### closed UNIV
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; closed ?T\<rbrakk>
### \<Longrightarrow> closed (?S \<inter> ?T)
### Rule already declared as introduction (intro)
### \<forall>x\<in>?A. closed (?B x) \<Longrightarrow>
### closed (\<Inter>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### \<forall>S\<in>?K. closed S \<Longrightarrow> closed (\<Inter>?K)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?S; \<forall>T\<in>?S. closed T\<rbrakk>
### \<Longrightarrow> closed (\<Union>?S)
### Rule already declared as introduction (intro)
### \<lbrakk>finite ?A; \<forall>x\<in>?A. closed (?B x)\<rbrakk>
### \<Longrightarrow> closed (\<Union>x\<in>?A. ?B x)
### Rule already declared as introduction (intro)
### \<lbrakk>open ?S; closed ?T\<rbrakk> \<Longrightarrow> open (?S - ?T)
### Rule already declared as introduction (intro)
### \<lbrakk>closed ?S; open ?T\<rbrakk> \<Longrightarrow> closed (?S - ?T)
### Rule already declared as introduction (intro)
### closed ?S \<Longrightarrow> open (- ?S)
### Rule already declared as introduction (intro)
### open ?S \<Longrightarrow> closed (- ?S)
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=15922name=byelapsed=0.038
### Rule already declared as introduction (intro)
### continuous_on ?s (linepath ?a ?b)
### Rule already declared as introduction (intro)
### (\<And>i. continuous_on UNIV (\<lambda>x. ?f x i)) \<Longrightarrow>
### continuous_on UNIV ?f
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=13623name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=15784name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=15618name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=15406name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=19232name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=16612name=byelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=19495name=applyelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=23087name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=19599name=applyelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=22878name=byelapsed=0.047
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=24738name=byelapsed=0.010
ML_statistics = :now=1489705572.08tasks_ready=306tasks_pending=1tasks_running=6tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=24size_allocation=3743416320size_allocation_free=2269064040size_heap=4168089600size_heap_free_last_full_GC=0size_heap_free_last_GC=3744952712threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=132.364time_GC=3.6user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=30153name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=29965name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=29881name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=24232name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=29755name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=7374name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=7165name=byelapsed=0.046
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=14391name=byelapsed=0.058
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=14059name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=13914name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=13748name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=15315name=byelapsed=0.148
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=13555name=byelapsed=0.097
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=15223name=byelapsed=0.108
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=15911name=byelapsed=0.146
ML_statistics = :now=1489705572.58tasks_ready=298tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=24size_allocation=3743416320size_allocation_free=835413368size_heap=4168089600size_heap_free_last_full_GC=0size_heap_free_last_GC=3744952712threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=133.968time_GC=3.6user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=16865name=byelapsed=0.076
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4240name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Banach_Density.thyoffset=16416name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4134name=byelapsed=0.034
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18704name=byelapsed=0.063
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=4015name=byelapsed=0.036
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=3908name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27857name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27750name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=27687name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=40839name=interpretelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=40888name=interpretelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=41104name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=18957name=byelapsed=0.246
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49259name=interpretelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=40822name=byelapsed=0.077
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49307name=interpretelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=16261name=showelapsed=0.082
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49376name=showelapsed=0.082
ML_statistics = :now=1489705573.12tasks_ready=294tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=25size_allocation=3713007616size_allocation_free=3713007616size_heap=4180672512size_heap_free_last_full_GC=0size_heap_free_last_GC=3714624216threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=134.9time_GC=3.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49517name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=48921name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=16624name=byelapsed=0.120
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=49242name=byelapsed=0.086
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=18473name=byelapsed=0.075
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=17787name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=25198name=byelapsed=0.146
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=17724name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=25311name=byelapsed=0.076
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=73457name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=74815name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=56655name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=76266name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=76089name=byelapsed=0.018
ML_statistics = :now=1489705573.62tasks_ready=293tasks_pending=1tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=25size_allocation=3713007616size_allocation_free=2923839840size_heap=4180672512size_heap_free_last_full_GC=0size_heap_free_last_GC=3714624216threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=135.7time_GC=3.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=73387name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=56492name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=56448name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=54176name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=54116name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=56238name=byelapsed=0.073
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=55935name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=87399name=byelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=55672name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=55517name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=87347name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=55403name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=86668name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=86409name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=86169name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=54960name=byelapsed=0.067
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85960name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85869name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85671name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85560name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85457name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=85366name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=3194name=byelapsed=0.100
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=83922name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=4814name=byelapsed=0.010
ML_statistics = :now=1489705574.13tasks_ready=284tasks_pending=1tasks_running=8tasks_passive=6tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=25size_allocation=3713007616size_allocation_free=2223274864size_heap=4180672512size_heap_free_last_full_GC=0size_heap_free_last_GC=3714624216threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=136.504time_GC=3.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=83809name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=4739name=byelapsed=0.044
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=9918name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=9781name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=9241name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=30199name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=30165name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=4471name=applyelapsed=0.374
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=4371name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=54582name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=54422name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=55870name=haveelapsed=0.010
ML_statistics = :now=1489705574.63tasks_ready=297tasks_pending=1tasks_running=6tasks_passive=3tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=25size_allocation=3713007616size_allocation_free=1562992120size_heap=4180672512size_heap_free_last_full_GC=0size_heap_free_last_GC=3714624216threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=137.304time_GC=3.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56105name=haveelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=54260name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=53367name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56743name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=53243name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=57007name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=52659name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=52041name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=51887name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=58098name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=51780name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=58034name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=53115name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=32475name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=53034name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=83758name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=52913name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=83896name=haveelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=84066name=haveelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=52782name=byelapsed=0.072
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=84296name=byelapsed=0.052
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=54098name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=84049name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=51677name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=51490name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=83873name=byelapsed=0.038
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=57319name=byelapsed=0.033
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56988name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=85847name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=83736name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=86017name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=83148name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=82912name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56652name=applyelapsed=0.053
ML_statistics = :now=1489705575.13tasks_ready=287tasks_pending=1tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=25size_allocation=3713007616size_allocation_free=311036656size_heap=4180672512size_heap_free_last_full_GC=0size_heap_free_last_GC=3714624216threads_in_ML=3threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=138.964time_GC=3.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=86247name=byelapsed=0.059
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56717name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=86000name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56388name=byelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=85824name=byelapsed=0.041
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=85687name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=85099name=byelapsed=0.097
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=84863name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=56093name=byelapsed=0.272
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=2540name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=55853name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=55622name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=1640name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3119name=byelapsed=0.029
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3037name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=4605name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=4514name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=4139name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=4390name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=4228name=byelapsed=0.023
ML_statistics = :now=1489705575.66tasks_ready=274tasks_pending=1tasks_running=6tasks_passive=4tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=26size_allocation=3716153344size_allocation_free=3716153344size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3717896408threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=139.404time_GC=3.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=12172name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=11987name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3476name=byelapsed=0.030
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=13156name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=14159name=byelapsed=0.079
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16343name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16707name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16091name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16535name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=16959name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=15895name=byelapsed=0.021
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=15682name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17323name=byelapsed=0.035
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=10998name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17151name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17627name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17829name=obtainelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19351name=haveelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19554name=obtainelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=18278name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19998name=haveelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=18842name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=18619name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=20563name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=18383name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=20340name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=20103name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19979name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17993name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=17814name=byelapsed=0.032
ML_statistics = :now=1489705576.16tasks_ready=267tasks_pending=1tasks_running=3tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=26size_allocation=3716153344size_allocation_free=2396039536size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3717896408threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=141.004time_GC=3.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19719name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=19539name=byelapsed=0.027
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=21954name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=21375name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=21775name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=21804name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=21539name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=21387name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=20895name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=3140name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=21236name=byelapsed=0.064
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=24811name=byelapsed=0.055
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=2586name=proofelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=52052name=byelapsed=0.127
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=2994name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=77665name=assumeelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=78484name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=51944name=byelapsed=0.103
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=77202name=byelapsed=0.022
ML_statistics = :now=1489705576.66tasks_ready=259tasks_pending=1tasks_running=4tasks_passive=2tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=26size_allocation=3716153344size_allocation_free=1696887640size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3717896408threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=141.804time_GC=3.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=51892name=byelapsed=0.045
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=79647name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=80584name=assumeelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=78866name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=25153name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=81474name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=80112name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=101471name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=101344name=byelapsed=0.022
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=103571name=interpretelapsed=0.042
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=87670name=assumeelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=93902name=haveelapsed=0.049
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=94236name=obtainelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=91056name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96248name=haveelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96455name=byelapsed=0.039
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=90557name=byelapsed=0.054
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96417name=byelapsed=0.032
ML_statistics = :now=1489705577.16tasks_ready=271tasks_pending=1tasks_running=7tasks_passive=5tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=26size_allocation=3716153344size_allocation_free=995277488size_heap=4184866816size_heap_free_last_full_GC=0size_heap_free_last_GC=3717896408threads_in_ML=2threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=142.608time_GC=3.836user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=88725name=byelapsed=0.056
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96230name=byelapsed=0.037
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=96088name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=85628name=byelapsed=0.032
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=85473name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=83883name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=95630name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=95519name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=95232name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=2371name=byelapsed=0.048
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=94694name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=95126name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=6016name=byelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=94794name=byelapsed=0.024
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=94901name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=6401name=applyelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Gouezel_Karlsson.thyoffset=94221name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=10656name=byelapsed=0.018
### Rule already declared as introduction (intro)
### ((\<lambda>x. x) \<longlongrightarrow> ?a) (at ?a within ?s)
### Rule already declared as introduction (intro)
### ((\<lambda>x. ?k) \<longlongrightarrow> ?k) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. ereal (?f x)) \<longlongrightarrow> ereal ?x) ?F
### Rule already declared as introduction (intro)
### (?f \<longlongrightarrow> ?x) ?F \<Longrightarrow>
### ((\<lambda>x. - ?f x) \<longlongrightarrow> - ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?c\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?x \<noteq> 0; (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?c * ?f x) \<longlongrightarrow> ?c * ?x) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>?y \<noteq> - \<infinity>; ?x \<noteq> - \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
### Rule already declared as introduction (intro)
### \<lbrakk>\<bar>?y\<bar> \<noteq> \<infinity>;
###  (?f \<longlongrightarrow> ?x) ?F\<rbrakk>
### \<Longrightarrow> ((\<lambda>x. ?f x + ?y) \<longlongrightarrow> ?x + ?y) ?F
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=19050name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=21543name=byelapsed=0.023
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=13513name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Fekete.thyoffset=13485name=byelapsed=0.028
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=26106name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=26001name=byelapsed=0.017
command_timing = :file=~~/afp/thys/Ergodic_Theory/SG_Library_Complement.thyoffset=25560name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=23671name=byelapsed=0.043
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=1174name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=44101name=qedelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=48275name=byelapsed=0.025
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=43646name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=52712name=defineelapsed=0.089
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=48436name=byelapsed=0.137
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=53242name=byelapsed=0.012
ML_statistics = :now=1489705577.71tasks_ready=166tasks_pending=1tasks_running=2tasks_passive=0tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=27size_allocation=3708813312size_allocation_free=3708813312size_heap=4182769664size_heap_free_last_full_GC=0size_heap_free_last_GC=3710631392threads_in_ML=1threads_total=7threads_wait_condvar=3threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=143.852time_GC=3.964user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82389name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=82925name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104592name=byelapsed=0.015
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104414name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=104292name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=2167name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Recurrence.thyoffset=110669name=interpretelapsed=0.040
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=50484name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=92669name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=92546name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=9111name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=3827name=byelapsed=0.031
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=11602name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Ergodicity.thyoffset=11410name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=54905name=assumeelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=53550name=assumeelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=55332name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=55579name=haveelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=54394name=byelapsed=0.014
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=56054name=assumeelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=75890name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=75729name=byelapsed=0.018
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=56987name=byelapsed=0.013
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=45700name=byelapsed=0.011
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=59462name=byelapsed=0.019
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=82529name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=15306name=byelapsed=0.020
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=28275name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=15406name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=62990name=byelapsed=0.016
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=63176name=byelapsed=0.026
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=29289name=byelapsed=0.012
command_timing = :file=~~/afp/thys/Ergodic_Theory/Measure_Preserving_Transformations.thyoffset=32130name=byelapsed=0.010
ML_statistics = :now=1489705578.22tasks_ready=1tasks_pending=0tasks_running=2tasks_passive=1tasks_urgent=0workers_total=4workers_active=2workers_waiting=0full_GCs=0partial_GCs=27size_allocation=3708813312size_allocation_free=3090472704size_heap=4182769664size_heap_free_last_full_GC=0size_heap_free_last_GC=3710631392threads_in_ML=2threads_total=7threads_wait_condvar=2threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=144.636time_GC=3.964user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0
command_timing = :file=~~/afp/thys/Ergodic_Theory/Kingman.thyoffset=103469name=byelapsed=0.010
command_timing = :file=~~/afp/thys/Ergodic_Theory/Invariants.thyoffset=51585name=byelapsed=0.044
isabelle document -c -o 'pdf' -n 'outline' -t '/proof,/ML' /media/data/jenkins/workspace/afp-repo-afp/browser_info/AFP/Ergodic_Theory/outline 2>&1
isabelle document -c -o 'pdf' -n 'document' -t '' /media/data/jenkins/workspace/afp-repo-afp/browser_info/AFP/Ergodic_Theory/document 2>&1
This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty
Including comment 'isadelimproof' Excluding comment 'isatagproof'
Including comment 'isadelimML' Excluding comment 'isatagML') (./isabellesym.sty
) (/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
No file root.aux.
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./session.tex
(./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.m
ap}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .
[2] [3] [4] [5] [6] [7] [8]) (./Fekete.tex [9] [10]) (./Banach_Density.tex
[11]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density
[12] [13]) (./Measure_Preserving_Transformations.tex [14] [15] [16] [17]
[18]

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[19] [20] [21] [22] [23] [24] [25] [26] [27]
Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$
[28] [29] [30]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [31] (./root.aux)

Package rerunfilecheck Warning: File `root.out' has changed.
(rerunfilecheck)                Rerun to get outlines right
(rerunfilecheck)                or use package `bookmark'.

 )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fo
nts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/ty
pe1/public/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/pu
blic/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/a
msfonts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
s/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
mi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/t
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/t
exmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dis
t/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/font
s/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1
/public/amsfonts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/publi
c/amsfonts/cm/cmtt10.pfb>
Output written on root.pdf (31 pages, 239909 bytes).
Transcript written on root.log.
This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty
Including comment 'isadelimproof' Excluding comment 'isatagproof'
Including comment 'isadelimML' Excluding comment 'isatagML') (./isabellesym.sty
) (/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
(./root.aux) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(./root.out) (./root.out)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./root.toc)
(./session.tex (./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/
updmap/pdftex.map}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .
[2] [3] [4] [5] [6] [7] [8] [9]) (./Fekete.tex [10] [11]) (./Banach_Density.tex
[12]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density
[13] [14]) (./Measure_Preserving_Transformations.tex [15] [16] [17] [18]

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$
[29] [30]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
[31]) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [32] (./root.aux) )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fo
nts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/ty
pe1/public/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/pu
blic/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/a
msfonts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
s/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
mi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/t
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/t
exmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dis
t/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/font
s/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1
/public/amsfonts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/publi
c/amsfonts/cm/cmtt10.pfb>
Output written on root.pdf (32 pages, 248919 bytes).
Transcript written on root.log.
This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty
Including comment 'isadelimproof' Excluding comment 'isatagproof'
Including comment 'isadelimML' Excluding comment 'isatagML') (./isabellesym.sty
) (/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
(./root.aux) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(./root.out) (./root.out)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./root.toc)
(./session.tex (./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/
updmap/pdftex.map}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .
[2] [3] [4] [5] [6] [7] [8] [9]) (./Fekete.tex [10] [11]) (./Banach_Density.tex
[12]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density
[13] [14]) (./Measure_Preserving_Transformations.tex [15] [16] [17] [18]

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$
[29] [30]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
[31]) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [32] (./root.aux) )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fo
nts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/ty
pe1/public/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/pu
blic/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/a
msfonts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfont
s/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cm
mi8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/
share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/t
exlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/t
exmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dis
t/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/font
s/type1/public/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1
/public/amsfonts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/publi
c/amsfonts/cm/cmtt10.pfb>
Output written on root.pdf (32 pages, 249086 bytes).
Transcript written on root.log.

This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty) (./isabellesym.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
No file root.aux.
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./session.tex
(./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.m
ap}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .

Overfull \hbox (78.72745pt too wide) in paragraph at lines 239--255
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis UN[]insert Un
[]insert[]left sup[]bot$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]neutral One[]
nat[]def atLeast[]0 atLeast[]Suc[]greaterThan
[2] [3]
Overfull \hbox (32.32002pt too wide) in paragraph at lines 440--445
[][]  \OT1/cmr/bx/n/10 more-over ob-tain \OT1/cmr/m/it/10 b1 \OT1/cmr/bx/n/10 w
here \OT1/cmr/m/it/10 b $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 b1$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 n $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10 ?k \OT1/cmr/bx/n/
10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/
m/n/10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis div[]mu
lt[]mod[]eq$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (7.14348pt too wide) in paragraph at lines 534--539
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ $\OMS/cmsy/m/n/10 8 $\OT1/cmr/m/it/10 n$\OM
S/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 N$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 P n \
OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 eventually
[]sequentially

Overfull \hbox (9.54086pt too wide) in paragraph at lines 539--543
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 M \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 8 $\OT1/cmr/m/it/10 m$\OMS/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 M$\OML/
cmm/m/it/10 :$ \OT1/cmr/m/it/10 ereal$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u m$\O
T1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 us-
ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n/10
 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Lim[]PInfty$\
OT1/cmr/m/n/10 )$[] 
[4]
Overfull \hbox (2.75903pt too wide) in paragraph at lines 629--631
[][]  \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ \OT1/cmr/m/it/10 powr[]def exp[]minus $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 exp[]add $\OT1/cmr/m/n/
10 [$\OT1/cmr/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 ln[]inverse
$\OT1/cmr/m/n/10 )$[] 
[5]
Overfull \hbox (66.97374pt too wide) in paragraph at lines 743--745
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule tendst
o[]diff$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m/it/10 ;$ \OT1/cmr/
m/it/10 rule tendsto[]mult$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m
/it/10 ;$ \OT1/cmr/m/it/10 rule LIMSEQ[]ignore[]initial[]segment$\OT1/cmr/m/n/1
0 [$\OT1/cmr/m/it/10 OF
[6]
Overfull \hbox (48.35219pt too wide) in paragraph at lines 906--909
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 continuous[]on $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 closure C$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 f[] \OT1/c
mr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 comp[]def continuous[]on[]closure[]sequ
entially[] 
[7]
Overfull \hbox (33.36096pt too wide) in paragraph at lines 1089--1091
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous
[]on[]subset$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of UNIV$\OT1/cmr/m/n/10 ]$$\OML
/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it
/10 assms in-tro$\OT1/cmr/m/n/10 !$$:$ \OT1/cmr/m/it/10 continuous[]intros$\OT1
/cmr/m/n/10 )$[] 
[8]
Overfull \hbox (3.7949pt too wide) in paragraph at lines 1093--1096
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 continuous[]on[]closed[]Un$\OT
1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [] [] $\OMS/cmsy/m/n/10 ^^C$ $^^C$$^^C$$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto
 in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 continuous[]intros$\OT1/cmr/m/n/10 
)$[] 
[9] [10]
Overfull \hbox (9.86078pt too wide) in paragraph at lines 1389--1392
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 p $\OML/cmm/m/it/10 >$ \OT1/
cmr/m/it/10 0[] []p $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 1[] \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/
cmr/m/it/10 algebra[]simps divide[]simps powr[]mono2$ [] $$\OT1/cmr/m/n/10 )$[]
 
[11]
Overfull \hbox (49.25273pt too wide) in paragraph at lines 1507--1520
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms e2ennre
al[]neg eq[]onp[]same[]args ereal[]mult[]le[]0[]iff lin-ear times[]ennreal$\OML
/cmm/m/it/10 :$\OT1/cmr/m/it/10 abs[]eq$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (24.13213pt too wide) in paragraph at lines 1587--1589
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 ennreal[]lessI ennreal[]neq[]top mult$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 comm
ute mult[]divide[]eq[]ennreal

Overfull \hbox (13.61127pt too wide) in paragraph at lines 1589--1591
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 divide[]ennreal[]def ennreal[]less[]zero[]iff ennreal[]neq[]top less[]irrefl
[12]
Overfull \hbox (82.8285pt too wide) in paragraph at lines 1675--1681
[][]   $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp$\OT1/cmr/m/n/10 :$ \OT1/cm
r/m/it/10 antimono[]def ennreal[]mono[]minus continuous[]on[]id continuous[]on[
]const[]minus[]ennreal$\OT1/cmr/m/n/10 )$[] 
[13] [14] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [15]
Overfull \hbox (23.86977pt too wide) in paragraph at lines 2195--2200
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 a$\OT1/cmr/m/n/10 :$ 
\OT1/cmr/m/it/10 emea-sure M A $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M
 $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$
\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[
]set

Overfull \hbox (13.28947pt too wide) in paragraph at lines 2209--2214
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 emea-sure M B $\OT1/c
mr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A
 $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us
-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[]set
[16] [17]
Overfull \hbox (32.39624pt too wide) in paragraph at lines 2411--2414
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 g[]def \OT1/cmr/bx/n/10 b
y $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule nn[]integral[]diff$\OML/cmm/m/it/10 
;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms enn
real[]mult[]eq[]top[]iff$\OT1/cmr/m/n/10 )$[] 
) (./Fekete.tex [18]
Overfull \hbox (23.22952pt too wide) in paragraph at lines 92--95
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($$($\OT1/cmr/
m/it/10 Suc a$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/c
mr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 u$\OT1/c
mr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/cmr
/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 commute add
$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]commute$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (53.2516pt too wide) in paragraph at lines 95--100
[][]    \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OMS/cmsy/m/n/10
 ^^T$ \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 
^^C$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$$
+$\OT1/cmr/m/it/10 u n \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms []n$\OML/
cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] []a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n
$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OML/cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] 
eventually[]subadditive[]def
[19]
Overfull \hbox (102.03658pt too wide) in paragraph at lines 221--225
[][]    \OT1/cmr/bx/n/10 more-over have \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^C
$\OT1/cmr/m/it/10 u r $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u r$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 ordered[]comm[]semiring[]class$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 comm[]mult[]left[]mono$\OT1/cmr/m/n/10 )$[] 
[20]
Overfull \hbox (53.52942pt too wide) in paragraph at lines 300--303
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 3$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/
m/it/10 C $\OML/cmm/m/it/10 <$ $"$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 N \OT1
/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis []0 $\OML/cmm/m/it/10
 <$ $"$[] []\OT1/cmr/m/it/10 3 $\OMS/cmsy/m/n/10 ^^C$ \OT1/cmr/m/it/10 C $\OML/
cmm/m/it/10 =$ $"$ $<$ \OT1/cmr/m/it/10 real N[] linordered[]field[]class$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 sign[]simps$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2
4$\OT1/cmr/m/n/10 )$
[21]
Overfull \hbox (0.74756pt too wide) in paragraph at lines 441--454
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]ereal$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[]e
ventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (15.18639pt too wide) in paragraph at lines 516--529
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]bounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[
]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[22]
Overfull \hbox (26.17522pt too wide) in paragraph at lines 590--607
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]unbounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]im
p[]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[23] [24]
Overfull \hbox (6.76318pt too wide) in paragraph at lines 904--910
[][]  \OT1/cmr/bx/n/10 show $\OMS/cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ \OT1/cmr/
m/it/10 t $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 if \OT1/cm
r/m/it/10 t $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 V \OT1/cmr/bx/n/10 for \OT1/c
mr/m/it/10 t \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 V[]def \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 real[
]root[]pos[]pos[]le
[25]
Overfull \hbox (8.28645pt too wide) in paragraph at lines 995--1001
[][]  \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?the-sis \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 spectral[]radius[]def \OT1/cmr/bx/n/10 us-ing \OT1/cm
r/m/it/10 submultiplicative[]converges
) (./Banach_Density.tex [26] [27]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density

Overfull \hbox (6.92912pt too wide) in paragraph at lines 312--317
[][]    \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 upper[]Banach[]density $\OT
1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/
cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 l \OT1/cmr/bx/n/10 us-ing
 \OT1/cmr/m/it/10 upper[]Banach[]density[]event2

Overfull \hbox (14.50876pt too wide) in paragraph at lines 352--355
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset
[28]
Overfull \hbox (17.2666pt too wide) in paragraph at lines 444--447
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 upper[]Banach[]density[]union$
\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of A B$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10
 A$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 s
imp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 sup$\OML/cmm/m/it/10 :$\OT1/cmr/m/i
t/10 absorb2$\OT1/cmr/m/n/10 )$[] 
[29] [30]
Overfull \hbox (6.15201pt too wide) in paragraph at lines 662--664
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 card$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/cmr/m/it/10 n$
\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 
card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/i
t/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/1
0 g$ $[$ $\OT1/cmr/m/n/10 ($$\OMS/cmsy/m/n/10 f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/
cmr/m/it/10 k$\OMS/cmsy/m/n/10 g$ $[$ $f$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^
@$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 (
$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$)$$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 n

Overfull \hbox (31.44565pt too wide) in paragraph at lines 695--698
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr
/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\O
ML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $
\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l
$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\
OT1/cmr/m/it/10 n

Overfull \hbox (36.10168pt too wide) in paragraph at lines 711--714
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-sup $\
OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \
OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$
 $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/
10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$
$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\OT1/cmr/m/it/10 n$\
OT1/cmr/m/n/10 )$[] 
[31] [32]
Overfull \hbox (21.14922pt too wide) in paragraph at lines 909--912
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-inf $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/
10 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m
/it/10 =$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-inf $\O
T1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \O
T1/cmr/m/it/10 ereal 1 $\OMS/cmsy/m/n/10 ^^@$ \OT1/cmr/m/it/10 card$\OT1/cmr/m/
n/10 ($$($\OT1/cmr/m/it/10 UNIV$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10 A$\OT1/cm
r/m/n/10 )$
[33]
Overfull \hbox (0.37827pt too wide) in paragraph at lines 1012--1015
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 by $\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson ereal[]less[]eq$\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 not[]less of[]nat[]0[]less[]iff 
pos[]divide[]less[]eq$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (14.50876pt too wide) in paragraph at lines 1064--1067
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset

Overfull \hbox (110.4387pt too wide) in paragraph at lines 1146--1154
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 lower[]Banach[]density[]in[]01$\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 upper[]Ban
ach[]density[]finite$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/1
0 ]$ \OT1/cmr/m/it/10 lower[]Banach[]density[]le[]upper[] 
) (./Measure_Preserving_Transformations.tex [34]
Overfull \hbox (36.93236pt too wide) in paragraph at lines 119--122
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 f[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able M N \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF

Overfull \hbox (35.96774pt too wide) in paragraph at lines 122--125
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 g[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 g $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able N P \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF
[35] [36]
Overfull \hbox (5.10562pt too wide) in paragraph at lines 282--286
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 U[]def \OT1/cmr/bx/n/10 u
s-ing []\OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able M
 N[] \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto$\OML/cmm/m/it
/10 ;$ \OT1/cmr/m/it/10 me-son measurable[]space$\OT1/cmr/m/n/10 )$[] 
[37] [38] [39]
Overfull \hbox (27.25337pt too wide) in paragraph at lines 747--751
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 f$\OMS/cmsy/m/n/10 ^^@$\OT1/c
mr/m/it/10 `$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 space N$\OT1/cmr/m/n/10 )$ $\OM
S/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 space M $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 
space M \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Int[]abso
rb1 measurable[]space

Overfull \hbox (32.61676pt too wide) in paragraph at lines 792--806
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]total[]measure
$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis prob[]space$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 emeasure[]space[]1
[40]
Overfull \hbox (10.39244pt too wide) in paragraph at lines 874--878
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 mpt[]def qmpt[]def qmpt[]
axioms[]def mpt[]axioms[]def \OT1/cmr/bx/n/10 us-ing $\OMS/cmsy/m/n/10 ^^C$ $^^
C$$^^C$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/
n/10 )$
[41]
Overfull \hbox (40.67062pt too wide) in paragraph at lines 1043--1047
[][]  \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OT1/cmr/m/n/10 =$
 \OT1/cmr/m/it/10 emea-sure $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 distr lborel bo
rel $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 op $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10
 c$\OT1/cmr/m/n/10 )$$)$ \OT1/cmr/m/it/10 A \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/1
0 ($\OT1/cmr/m/it/10 rule emeasure[]distr$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 sy
mmetric$\OT1/cmr/m/n/10 ]$$\OML/cmm/m/it/10 ;$
[42]
Overfull \hbox (51.46826pt too wide) in paragraph at lines 1126--1130
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10
 mpt[]def qmpt[]def qmpt[]axioms[]def quasi[]measure[]preserving[]def

Overfull \hbox (5.11209pt too wide) in paragraph at lines 1141--1145
[][]    \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 measurab
le$\OT1/cmr/m/n/10 ]$$:$ $($$\OML/cmm/m/it/10 ^^U$ $\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/i
t/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 indicator A $\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$)$$:$$:
$\OT1/cmr/m/it/10 ennreal$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it
/10 borel[]measurable

Overfull \hbox (88.22876pt too wide) in paragraph at lines 1202--1205
[][]      \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 B $\OMS/cmsy/m/n/10 2$ \OT
1/cmr/m/it/10 sets $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 M $[] $$[][]$ N$\OT1/cmr
/m/n/10 )$[] []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]measu
re$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure
[43]
Overfull \hbox (25.27127pt too wide) in paragraph at lines 1218--1220
[][]      \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]mea
sure$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure$\OT1/cmr/m/n/1
0 )$[] 

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[44] [45]
Overfull \hbox (47.91531pt too wide) in paragraph at lines 1650--1663
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-ing
$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms measure[]preserving[]def mem[]Collec
t[]eq sets$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 Int[]space[]eq2
[46]
Overfull \hbox (40.97867pt too wide) in paragraph at lines 1747--1752
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tqm quasi[]measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[]
 
[47] [48]
Overfull \hbox (10.56776pt too wide) in paragraph at lines 2074--2079
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tm measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (6.58662pt too wide) in paragraph at lines 2138--2152
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tm assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/bx/n/10 by \OT1/cmr/m/it/10 auto[
] 

Overfull \hbox (8.42105pt too wide) in paragraph at lines 2160--2174
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tn[]measure[]preserving assms$\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[49]
Overfull \hbox (14.91591pt too wide) in paragraph at lines 2302--2307
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def

Overfull \hbox (14.91591pt too wide) in paragraph at lines 2344--2349
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def
[50]
Overfull \hbox (33.24617pt too wide) in paragraph at lines 2459--2462
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def \OT1/c
mr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis add$\OML/cmm/m/it/10 :$
\OT1/cmr/m/it/10 commute add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 right[]neutral
 atLeast0LessThan
[51]
Overfull \hbox (28.89758pt too wide) in paragraph at lines 2602--2604
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 no[]types$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-i
ng$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 Suc[]eq[]plus1 birkhoff[]sum[]cocycle qm
pt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 birkhoff[]sum[]1$\OT1/cmr/m/n/10 ($\OT1/
cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[52] [53]
Overfull \hbox (16.78928pt too wide) in paragraph at lines 2854--2863
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 qmpt[]def qmpt[]axioms[]def \OT
1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]quasi[]measure[]preserving$\OT1/cmr
/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$[] 

Overfull \hbox (47.48772pt too wide) in paragraph at lines 2921--2936
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 mpt[]def mpt[]axioms[]def \OT1/
cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]qmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/
10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 Tinv[]measure[]preserving$\OT1/
cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (14.72844pt too wide) in paragraph at lines 2943--2958
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 fmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]mpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/
cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$
\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 finite[]measure[]axioms$\OT1/cmr/m/n/10 )$[
] 
[54]
Overfull \hbox (3.48405pt too wide) in paragraph at lines 2965--2984
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 pmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]fmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add
$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$ 
[55]
Overfull \hbox (2.76042pt too wide) in paragraph at lines 3192--3196
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m2$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def

Overfull \hbox (2.76042pt too wide) in paragraph at lines 3205--3209
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m3$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def
[56] [57]
Overfull \hbox (11.281pt too wide) in paragraph at lines 3336--3349
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[]on
[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp 
add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 nat[]left[]shift[]def$\OT1/cmr/m/n/10 )
$[] 

Overfull \hbox (24.72952pt too wide) in paragraph at lines 3383--3391
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]left[]shift[]def$\OT1/cmr/m/n/1
0 )$[] 

Overfull \hbox (31.5017pt too wide) in paragraph at lines 3391--3393
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]right[]shift[]def$\OT1/cmr/m/n/
10 )$[] 
[58]
Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$

Overfull \hbox (41.81247pt too wide) in paragraph at lines 3492--3494
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule measure[]p
reserving[]is[]quasi[]measure[]preserving$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
 measure[]preserving[]distr$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[59] [60]
Overfull \hbox (57.08336pt too wide) in paragraph at lines 3748--3756
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]finite[]measur
e$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/m/it/10 finite[]measure[]axioms finite[]meas
ure[]def

Overfull \hbox (24.31699pt too wide) in paragraph at lines 3772--3779
[][]\OT1/cmr/m/it/10 measure[]preserving[]finite[]measure$\OT1/cmr/m/n/10 [$\OT
1/cmr/m/it/10 OF mpt[]factorE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n
/10 )$$[$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$$]$ \OT1/cmr/m/it/10 finit
e[]measure[]axioms

Overfull \hbox (19.21115pt too wide) in paragraph at lines 3830--3833
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 quasi[]measure[]preserving[]
AE measure[]preserving[]is[]quasi[]measure[]preserving
[61] [62] [63]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
[64]
Overfull \hbox (39.9908pt too wide) in paragraph at lines 4116--4119
[][]      \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 P[]def \OT1/cmr/bx/n/10
 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule distr[]distr$\OML/cmm/m/it/10 ;$ \
OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 J $\OMS/cms
y/m/n/10 ^^R$ \OT1/cmr/m/it/10 H[] measurable[]restrict[]subset$\OT1/cmr/m/n/10
 )$[] 

Overfull \hbox (12.6075pt too wide) in paragraph at lines 4181--4184
[][]      \OT1/cmr/bx/n/10 un-fold-ing []\OT1/cmr/m/it/10 natural[]extension[]m
easure $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 lim[] \OT1/cmr/bx/n/10 by $\OT1/cmr
/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 P$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (66.90619pt too wide) in paragraph at lines 4184--4186
[][]    \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 natural[]extension[]map $\OMS/cm
sy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able natural[]extension[]measure natural[
]extension[]measure[] 
[65] [66]
Overfull \hbox (1.82825pt too wide) in paragraph at lines 4366--4368
[][]          \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\O
T1/cmr/m/n/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/1
0 lift-ing$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 PiE UNIV[]I mem[]Collect[]eq res
trict[]Pi[]cancel$\OT1/cmr/m/n/10 )$[] 
[67]
Overfull \hbox (78.3306pt too wide) in paragraph at lines 4472--4475
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$\OT1
/cmr/m/it/10 invertible[]qmpt[]def \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/1
0 natural[]extension[]map[]def []natural[]extension[]measure
[68]
Overfull \hbox (41.89711pt too wide) in paragraph at lines 4611--4614
[][]      \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 natural[]extension[]proj 
$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension[]map x$\OT1/cmr/m/n/10 )
$ $=$ \OT1/cmr/m/it/10 T $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension
[]proj

Overfull \hbox (8.13927pt too wide) in paragraph at lines 4614--4617
[][]        \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 natural[]extension[]p
roj[]def natural[]extension[]map[]def int[]left[]shift[]def
[69]) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [70] (./root.aux)

Package rerunfilecheck Warning: File `root.out' has changed.
(rerunfilecheck)                Rerun to get outlines right
(rerunfilecheck)                or use package `bookmark'.

 )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbsy10.pfb></usr/share/texlive/texmf-dist/f
onts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/t
ype1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/p
ublic/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfon
ts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/
cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.p
fb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></us
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share
/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texliv
e/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-
dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dist/fon
ts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/typ
e1/public/amsfonts/cm/cmsy5.pfb></usr/share/texlive/texmf-dist/fonts/type1/publ
ic/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsf
onts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/c
m/cmtt10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols
/msbm10.pfb>
Output written on root.pdf (70 pages, 375388 bytes).
Transcript written on root.log.
This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty) (./isabellesym.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
(./root.aux) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(./root.out) (./root.out)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./root.toc)
(./session.tex (./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/
updmap/pdftex.map}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .
[2]
Overfull \hbox (78.72745pt too wide) in paragraph at lines 239--255
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis UN[]insert Un
[]insert[]left sup[]bot$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]neutral One[]
nat[]def atLeast[]0 atLeast[]Suc[]greaterThan
[3] [4]
Overfull \hbox (32.32002pt too wide) in paragraph at lines 440--445
[][]  \OT1/cmr/bx/n/10 more-over ob-tain \OT1/cmr/m/it/10 b1 \OT1/cmr/bx/n/10 w
here \OT1/cmr/m/it/10 b $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 b1$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 n $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10 ?k \OT1/cmr/bx/n/
10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/
m/n/10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis div[]mu
lt[]mod[]eq$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (7.14348pt too wide) in paragraph at lines 534--539
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ $\OMS/cmsy/m/n/10 8 $\OT1/cmr/m/it/10 n$\OM
S/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 N$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 P n \
OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 eventually
[]sequentially

Overfull \hbox (9.54086pt too wide) in paragraph at lines 539--543
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 M \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 8 $\OT1/cmr/m/it/10 m$\OMS/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 M$\OML/
cmm/m/it/10 :$ \OT1/cmr/m/it/10 ereal$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u m$\O
T1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 us-
ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n/10
 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Lim[]PInfty$\
OT1/cmr/m/n/10 )$[] 
[5]
Overfull \hbox (2.75903pt too wide) in paragraph at lines 629--631
[][]  \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ \OT1/cmr/m/it/10 powr[]def exp[]minus $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 exp[]add $\OT1/cmr/m/n/
10 [$\OT1/cmr/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 ln[]inverse
$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (66.97374pt too wide) in paragraph at lines 743--745
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule tendst
o[]diff$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m/it/10 ;$ \OT1/cmr/
m/it/10 rule tendsto[]mult$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m
/it/10 ;$ \OT1/cmr/m/it/10 rule LIMSEQ[]ignore[]initial[]segment$\OT1/cmr/m/n/1
0 [$\OT1/cmr/m/it/10 OF
[6] [7]
Overfull \hbox (48.35219pt too wide) in paragraph at lines 906--909
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 continuous[]on $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 closure C$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 f[] \OT1/c
mr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 comp[]def continuous[]on[]closure[]sequ
entially[] 
[8]
Overfull \hbox (33.36096pt too wide) in paragraph at lines 1089--1091
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous
[]on[]subset$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of UNIV$\OT1/cmr/m/n/10 ]$$\OML
/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it
/10 assms in-tro$\OT1/cmr/m/n/10 !$$:$ \OT1/cmr/m/it/10 continuous[]intros$\OT1
/cmr/m/n/10 )$[] 

Overfull \hbox (3.7949pt too wide) in paragraph at lines 1093--1096
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 continuous[]on[]closed[]Un$\OT
1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [] [] $\OMS/cmsy/m/n/10 ^^C$ $^^C$$^^C$$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto
 in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 continuous[]intros$\OT1/cmr/m/n/10 
)$[] 
[9] [10]
Overfull \hbox (9.86078pt too wide) in paragraph at lines 1389--1392
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 p $\OML/cmm/m/it/10 >$ \OT1/
cmr/m/it/10 0[] []p $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 1[] \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/
cmr/m/it/10 algebra[]simps divide[]simps powr[]mono2$ [] $$\OT1/cmr/m/n/10 )$[]
 
[11]
Overfull \hbox (49.25273pt too wide) in paragraph at lines 1507--1520
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms e2ennre
al[]neg eq[]onp[]same[]args ereal[]mult[]le[]0[]iff lin-ear times[]ennreal$\OML
/cmm/m/it/10 :$\OT1/cmr/m/it/10 abs[]eq$\OT1/cmr/m/n/10 )$[] 
[12]
Overfull \hbox (24.13213pt too wide) in paragraph at lines 1587--1589
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 ennreal[]lessI ennreal[]neq[]top mult$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 comm
ute mult[]divide[]eq[]ennreal

Overfull \hbox (13.61127pt too wide) in paragraph at lines 1589--1591
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 divide[]ennreal[]def ennreal[]less[]zero[]iff ennreal[]neq[]top less[]irrefl

Overfull \hbox (82.8285pt too wide) in paragraph at lines 1675--1681
[][]   $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp$\OT1/cmr/m/n/10 :$ \OT1/cm
r/m/it/10 antimono[]def ennreal[]mono[]minus continuous[]on[]id continuous[]on[
]const[]minus[]ennreal$\OT1/cmr/m/n/10 )$[] 
[13] [14] [15] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd)
[16]
Overfull \hbox (23.86977pt too wide) in paragraph at lines 2195--2200
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 a$\OT1/cmr/m/n/10 :$ 
\OT1/cmr/m/it/10 emea-sure M A $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M
 $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$
\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[
]set

Overfull \hbox (13.28947pt too wide) in paragraph at lines 2209--2214
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 emea-sure M B $\OT1/c
mr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A
 $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us
-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[]set
[17] [18]
Overfull \hbox (32.39624pt too wide) in paragraph at lines 2411--2414
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 g[]def \OT1/cmr/bx/n/10 b
y $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule nn[]integral[]diff$\OML/cmm/m/it/10 
;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms enn
real[]mult[]eq[]top[]iff$\OT1/cmr/m/n/10 )$[] 
) (./Fekete.tex [19]
Overfull \hbox (23.22952pt too wide) in paragraph at lines 92--95
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($$($\OT1/cmr/
m/it/10 Suc a$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/c
mr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 u$\OT1/c
mr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/cmr
/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 commute add
$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]commute$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (53.2516pt too wide) in paragraph at lines 95--100
[][]    \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OMS/cmsy/m/n/10
 ^^T$ \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 
^^C$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$$
+$\OT1/cmr/m/it/10 u n \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms []n$\OML/
cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] []a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n
$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OML/cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] 
eventually[]subadditive[]def
[20]
Overfull \hbox (102.03658pt too wide) in paragraph at lines 221--225
[][]    \OT1/cmr/bx/n/10 more-over have \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^C
$\OT1/cmr/m/it/10 u r $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u r$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 ordered[]comm[]semiring[]class$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 comm[]mult[]left[]mono$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (53.52942pt too wide) in paragraph at lines 300--303
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 3$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/
m/it/10 C $\OML/cmm/m/it/10 <$ $"$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 N \OT1
/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis []0 $\OML/cmm/m/it/10
 <$ $"$[] []\OT1/cmr/m/it/10 3 $\OMS/cmsy/m/n/10 ^^C$ \OT1/cmr/m/it/10 C $\OML/
cmm/m/it/10 =$ $"$ $<$ \OT1/cmr/m/it/10 real N[] linordered[]field[]class$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 sign[]simps$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2
4$\OT1/cmr/m/n/10 )$
[21]
Overfull \hbox (0.74756pt too wide) in paragraph at lines 441--454
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]ereal$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[]e
ventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[22]
Overfull \hbox (15.18639pt too wide) in paragraph at lines 516--529
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]bounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[
]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (26.17522pt too wide) in paragraph at lines 590--607
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]unbounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]im
p[]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[23] [24] [25]
Overfull \hbox (6.76318pt too wide) in paragraph at lines 904--910
[][]  \OT1/cmr/bx/n/10 show $\OMS/cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ \OT1/cmr/
m/it/10 t $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 if \OT1/cm
r/m/it/10 t $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 V \OT1/cmr/bx/n/10 for \OT1/c
mr/m/it/10 t \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 V[]def \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 real[
]root[]pos[]pos[]le

Overfull \hbox (8.28645pt too wide) in paragraph at lines 995--1001
[][]  \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?the-sis \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 spectral[]radius[]def \OT1/cmr/bx/n/10 us-ing \OT1/cm
r/m/it/10 submultiplicative[]converges
) (./Banach_Density.tex [26] [27]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density
[28]
Overfull \hbox (6.92912pt too wide) in paragraph at lines 312--317
[][]    \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 upper[]Banach[]density $\OT
1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/
cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 l \OT1/cmr/bx/n/10 us-ing
 \OT1/cmr/m/it/10 upper[]Banach[]density[]event2

Overfull \hbox (14.50876pt too wide) in paragraph at lines 352--355
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset
[29]
Overfull \hbox (17.2666pt too wide) in paragraph at lines 444--447
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 upper[]Banach[]density[]union$
\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of A B$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10
 A$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 s
imp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 sup$\OML/cmm/m/it/10 :$\OT1/cmr/m/i
t/10 absorb2$\OT1/cmr/m/n/10 )$[] 
[30]
Overfull \hbox (6.15201pt too wide) in paragraph at lines 662--664
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 card$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/cmr/m/it/10 n$
\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 
card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/i
t/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/1
0 g$ $[$ $\OT1/cmr/m/n/10 ($$\OMS/cmsy/m/n/10 f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/
cmr/m/it/10 k$\OMS/cmsy/m/n/10 g$ $[$ $f$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^
@$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 (
$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$)$$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 n
[31]
Overfull \hbox (31.44565pt too wide) in paragraph at lines 695--698
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr
/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\O
ML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $
\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l
$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\
OT1/cmr/m/it/10 n

Overfull \hbox (36.10168pt too wide) in paragraph at lines 711--714
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-sup $\
OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \
OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$
 $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/
10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$
$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\OT1/cmr/m/it/10 n$\
OT1/cmr/m/n/10 )$[] 
[32]
Overfull \hbox (21.14922pt too wide) in paragraph at lines 909--912
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-inf $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/
10 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m
/it/10 =$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-inf $\O
T1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \O
T1/cmr/m/it/10 ereal 1 $\OMS/cmsy/m/n/10 ^^@$ \OT1/cmr/m/it/10 card$\OT1/cmr/m/
n/10 ($$($\OT1/cmr/m/it/10 UNIV$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10 A$\OT1/cm
r/m/n/10 )$
[33]
Overfull \hbox (0.37827pt too wide) in paragraph at lines 1012--1015
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 by $\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson ereal[]less[]eq$\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 not[]less of[]nat[]0[]less[]iff 
pos[]divide[]less[]eq$\OT1/cmr/m/n/10 )$[] 
[34]
Overfull \hbox (14.50876pt too wide) in paragraph at lines 1064--1067
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset

Overfull \hbox (110.4387pt too wide) in paragraph at lines 1146--1154
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 lower[]Banach[]density[]in[]01$\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 upper[]Ban
ach[]density[]finite$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/1
0 ]$ \OT1/cmr/m/it/10 lower[]Banach[]density[]le[]upper[] 
) (./Measure_Preserving_Transformations.tex [35]
Overfull \hbox (36.93236pt too wide) in paragraph at lines 119--122
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 f[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able M N \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF

Overfull \hbox (35.96774pt too wide) in paragraph at lines 122--125
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 g[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 g $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able N P \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF
[36]
Overfull \hbox (5.10562pt too wide) in paragraph at lines 282--286
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 U[]def \OT1/cmr/bx/n/10 u
s-ing []\OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able M
 N[] \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto$\OML/cmm/m/it
/10 ;$ \OT1/cmr/m/it/10 me-son measurable[]space$\OT1/cmr/m/n/10 )$[] 
[37] [38] [39]
Overfull \hbox (27.25337pt too wide) in paragraph at lines 747--751
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 f$\OMS/cmsy/m/n/10 ^^@$\OT1/c
mr/m/it/10 `$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 space N$\OT1/cmr/m/n/10 )$ $\OM
S/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 space M $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 
space M \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Int[]abso
rb1 measurable[]space
[40]
Overfull \hbox (32.61676pt too wide) in paragraph at lines 792--806
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]total[]measure
$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis prob[]space$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 emeasure[]space[]1

Overfull \hbox (10.39244pt too wide) in paragraph at lines 874--878
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 mpt[]def qmpt[]def qmpt[]
axioms[]def mpt[]axioms[]def \OT1/cmr/bx/n/10 us-ing $\OMS/cmsy/m/n/10 ^^C$ $^^
C$$^^C$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/
n/10 )$
[41] [42]
Overfull \hbox (40.67062pt too wide) in paragraph at lines 1043--1047
[][]  \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OT1/cmr/m/n/10 =$
 \OT1/cmr/m/it/10 emea-sure $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 distr lborel bo
rel $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 op $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10
 c$\OT1/cmr/m/n/10 )$$)$ \OT1/cmr/m/it/10 A \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/1
0 ($\OT1/cmr/m/it/10 rule emeasure[]distr$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 sy
mmetric$\OT1/cmr/m/n/10 ]$$\OML/cmm/m/it/10 ;$

Overfull \hbox (51.46826pt too wide) in paragraph at lines 1126--1130
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10
 mpt[]def qmpt[]def qmpt[]axioms[]def quasi[]measure[]preserving[]def

Overfull \hbox (5.11209pt too wide) in paragraph at lines 1141--1145
[][]    \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 measurab
le$\OT1/cmr/m/n/10 ]$$:$ $($$\OML/cmm/m/it/10 ^^U$ $\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/i
t/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 indicator A $\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$)$$:$$:
$\OT1/cmr/m/it/10 ennreal$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it
/10 borel[]measurable
[43]
Overfull \hbox (88.22876pt too wide) in paragraph at lines 1202--1205
[][]      \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 B $\OMS/cmsy/m/n/10 2$ \OT
1/cmr/m/it/10 sets $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 M $[] $$[][]$ N$\OT1/cmr
/m/n/10 )$[] []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]measu
re$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure

Overfull \hbox (25.27127pt too wide) in paragraph at lines 1218--1220
[][]      \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]mea
sure$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure$\OT1/cmr/m/n/1
0 )$[] 
[44]

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[45] [46]
Overfull \hbox (47.91531pt too wide) in paragraph at lines 1650--1663
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-ing
$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms measure[]preserving[]def mem[]Collec
t[]eq sets$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 Int[]space[]eq2

Overfull \hbox (40.97867pt too wide) in paragraph at lines 1747--1752
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tqm quasi[]measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[]
 
[47] [48]
Overfull \hbox (10.56776pt too wide) in paragraph at lines 2074--2079
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tm measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[] 
[49]
Overfull \hbox (6.58662pt too wide) in paragraph at lines 2138--2152
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tm assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/bx/n/10 by \OT1/cmr/m/it/10 auto[
] 

Overfull \hbox (8.42105pt too wide) in paragraph at lines 2160--2174
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tn[]measure[]preserving assms$\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[50]
Overfull \hbox (14.91591pt too wide) in paragraph at lines 2302--2307
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def

Overfull \hbox (14.91591pt too wide) in paragraph at lines 2344--2349
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def
[51]
Overfull \hbox (33.24617pt too wide) in paragraph at lines 2459--2462
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def \OT1/c
mr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis add$\OML/cmm/m/it/10 :$
\OT1/cmr/m/it/10 commute add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 right[]neutral
 atLeast0LessThan
[52]
Overfull \hbox (28.89758pt too wide) in paragraph at lines 2602--2604
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 no[]types$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-i
ng$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 Suc[]eq[]plus1 birkhoff[]sum[]cocycle qm
pt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 birkhoff[]sum[]1$\OT1/cmr/m/n/10 ($\OT1/
cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[53] [54]
Overfull \hbox (16.78928pt too wide) in paragraph at lines 2854--2863
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 qmpt[]def qmpt[]axioms[]def \OT
1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]quasi[]measure[]preserving$\OT1/cmr
/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$[] 

Overfull \hbox (47.48772pt too wide) in paragraph at lines 2921--2936
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 mpt[]def mpt[]axioms[]def \OT1/
cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]qmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/
10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 Tinv[]measure[]preserving$\OT1/
cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (14.72844pt too wide) in paragraph at lines 2943--2958
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 fmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]mpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/
cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$
\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 finite[]measure[]axioms$\OT1/cmr/m/n/10 )$[
] 

Overfull \hbox (3.48405pt too wide) in paragraph at lines 2965--2984
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 pmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]fmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add
$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$ 
[55] [56]
Overfull \hbox (2.76042pt too wide) in paragraph at lines 3192--3196
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m2$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def

Overfull \hbox (2.76042pt too wide) in paragraph at lines 3205--3209
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m3$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def
[57]
Overfull \hbox (11.281pt too wide) in paragraph at lines 3336--3349
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[]on
[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp 
add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 nat[]left[]shift[]def$\OT1/cmr/m/n/10 )
$[] 
[58]
Overfull \hbox (24.72952pt too wide) in paragraph at lines 3383--3391
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]left[]shift[]def$\OT1/cmr/m/n/1
0 )$[] 

Overfull \hbox (31.5017pt too wide) in paragraph at lines 3391--3393
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]right[]shift[]def$\OT1/cmr/m/n/
10 )$[] 

Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$

Overfull \hbox (41.81247pt too wide) in paragraph at lines 3492--3494
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule measure[]p
reserving[]is[]quasi[]measure[]preserving$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
 measure[]preserving[]distr$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[59] [60] [61]
Overfull \hbox (57.08336pt too wide) in paragraph at lines 3748--3756
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]finite[]measur
e$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/m/it/10 finite[]measure[]axioms finite[]meas
ure[]def

Overfull \hbox (24.31699pt too wide) in paragraph at lines 3772--3779
[][]\OT1/cmr/m/it/10 measure[]preserving[]finite[]measure$\OT1/cmr/m/n/10 [$\OT
1/cmr/m/it/10 OF mpt[]factorE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n
/10 )$$[$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$$]$ \OT1/cmr/m/it/10 finit
e[]measure[]axioms

Overfull \hbox (19.21115pt too wide) in paragraph at lines 3830--3833
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 quasi[]measure[]preserving[]
AE measure[]preserving[]is[]quasi[]measure[]preserving
[62] [63]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
[64]
Overfull \hbox (39.9908pt too wide) in paragraph at lines 4116--4119
[][]      \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 P[]def \OT1/cmr/bx/n/10
 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule distr[]distr$\OML/cmm/m/it/10 ;$ \
OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 J $\OMS/cms
y/m/n/10 ^^R$ \OT1/cmr/m/it/10 H[] measurable[]restrict[]subset$\OT1/cmr/m/n/10
 )$[] 
[65]
Overfull \hbox (12.6075pt too wide) in paragraph at lines 4181--4184
[][]      \OT1/cmr/bx/n/10 un-fold-ing []\OT1/cmr/m/it/10 natural[]extension[]m
easure $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 lim[] \OT1/cmr/bx/n/10 by $\OT1/cmr
/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 P$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (66.90619pt too wide) in paragraph at lines 4184--4186
[][]    \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 natural[]extension[]map $\OMS/cm
sy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able natural[]extension[]measure natural[
]extension[]measure[] 
[66] [67]
Overfull \hbox (1.82825pt too wide) in paragraph at lines 4366--4368
[][]          \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\O
T1/cmr/m/n/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/1
0 lift-ing$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 PiE UNIV[]I mem[]Collect[]eq res
trict[]Pi[]cancel$\OT1/cmr/m/n/10 )$[] 
[68]
Overfull \hbox (78.3306pt too wide) in paragraph at lines 4472--4475
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$\OT1
/cmr/m/it/10 invertible[]qmpt[]def \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/1
0 natural[]extension[]map[]def []natural[]extension[]measure
[69]
Overfull \hbox (41.89711pt too wide) in paragraph at lines 4611--4614
[][]      \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 natural[]extension[]proj 
$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension[]map x$\OT1/cmr/m/n/10 )
$ $=$ \OT1/cmr/m/it/10 T $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension
[]proj

Overfull \hbox (8.13927pt too wide) in paragraph at lines 4614--4617
[][]        \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 natural[]extension[]p
roj[]def natural[]extension[]map[]def int[]left[]shift[]def
) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [70] (./root.aux) )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbsy10.pfb></usr/share/texlive/texmf-dist/f
onts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/t
ype1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/p
ublic/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfon
ts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/
cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.p
fb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></us
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share
/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texliv
e/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-
dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dist/fon
ts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/typ
e1/public/amsfonts/cm/cmsy5.pfb></usr/share/texlive/texmf-dist/fonts/type1/publ
ic/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsf
onts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/c
m/cmtt10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols
/msbm10.pfb>
Output written on root.pdf (70 pages, 383492 bytes).
Transcript written on root.log.
This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
LaTeX2e <2016/02/01>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.

(./root.tex (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo)) (./isabelle.sty
(./comment.sty Excluding comment 'comment') Including comment 'isadelimtheory'
Including comment 'isatagtheory' Including comment 'isadelimproof'
Including comment 'isatagproof' Including comment 'isadelimML'
Including comment 'isatagML' Including comment 'isadelimvisible'
Including comment 'isatagvisible' Excluding comment 'isadeliminvisible'
Excluding comment 'isataginvisible') (./isabelletags.sty) (./isabellesym.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty)
(/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty))
(./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty))))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty))

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty))
(./root.aux) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)))
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
(./root.out) (./root.out)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd)
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (./root.toc)
(./session.tex (./SG_Library_Complement.tex [1{/var/lib/texmf/fonts/map/pdftex/
updmap/pdftex.map}]
Overfull \hbox (56.76758pt too wide) in paragraph at lines 136--139
\OT1/cmr/m/n/10.95 The next two lem-mas be-long nat-u-rally to []\OT1/cmtt/m/n/
10.95 Set_Interval.thy\OT1/cmr/m/n/10.95 , next to []\OT1/cmtt/m/n/10.95 UN_le_
add_shift\OT1/cmr/m/n/10.95 .
[2]
Overfull \hbox (78.72745pt too wide) in paragraph at lines 239--255
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis UN[]insert Un
[]insert[]left sup[]bot$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]neutral One[]
nat[]def atLeast[]0 atLeast[]Suc[]greaterThan
[3] [4]
Overfull \hbox (32.32002pt too wide) in paragraph at lines 440--445
[][]  \OT1/cmr/bx/n/10 more-over ob-tain \OT1/cmr/m/it/10 b1 \OT1/cmr/bx/n/10 w
here \OT1/cmr/m/it/10 b $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 b1$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 n $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10 ?k \OT1/cmr/bx/n/
10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/
m/n/10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis div[]mu
lt[]mod[]eq$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (7.14348pt too wide) in paragraph at lines 534--539
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ $\OMS/cmsy/m/n/10 8 $\OT1/cmr/m/it/10 n$\OM
S/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 N$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 P n \
OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 eventually
[]sequentially

Overfull \hbox (9.54086pt too wide) in paragraph at lines 539--543
[][]  \OT1/cmr/bx/n/10 ob-tain \OT1/cmr/m/it/10 M \OT1/cmr/bx/n/10 where $\OMS/
cmsy/m/n/10 8 $\OT1/cmr/m/it/10 m$\OMS/cmsy/m/n/10 ^^U$\OT1/cmr/m/it/10 M$\OML/
cmm/m/it/10 :$ \OT1/cmr/m/it/10 ereal$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u m$\O
T1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 N \OT1/cmr/bx/n/10 us-
ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n/10
 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Lim[]PInfty$\
OT1/cmr/m/n/10 )$[] 
[5]
Overfull \hbox (2.75903pt too wide) in paragraph at lines 629--631
[][]  \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ \OT1/cmr/m/it/10 powr[]def exp[]minus $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 exp[]add $\OT1/cmr/m/n/
10 [$\OT1/cmr/m/it/10 symmetric$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 ln[]inverse
$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (66.97374pt too wide) in paragraph at lines 743--745
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule tendst
o[]diff$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m/it/10 ;$ \OT1/cmr/
m/it/10 rule tendsto[]mult$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OML/cmm/m
/it/10 ;$ \OT1/cmr/m/it/10 rule LIMSEQ[]ignore[]initial[]segment$\OT1/cmr/m/n/1
0 [$\OT1/cmr/m/it/10 OF
[6] [7]
Overfull \hbox (48.35219pt too wide) in paragraph at lines 906--909
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 continuous[]on $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 closure C$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 f[] \OT1/c
mr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 comp[]def continuous[]on[]closure[]sequ
entially[] 
[8]
Overfull \hbox (33.36096pt too wide) in paragraph at lines 1089--1091
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous
[]on[]subset$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of UNIV$\OT1/cmr/m/n/10 ]$$\OML
/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it
/10 assms in-tro$\OT1/cmr/m/n/10 !$$:$ \OT1/cmr/m/it/10 continuous[]intros$\OT1
/cmr/m/n/10 )$[] 

Overfull \hbox (3.7949pt too wide) in paragraph at lines 1093--1096
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 continuous[]on[]closed[]Un$\OT
1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [] [] $\OMS/cmsy/m/n/10 ^^C$ $^^C$$^^C$$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto
 in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 continuous[]intros$\OT1/cmr/m/n/10 
)$[] 
[9] [10]
Overfull \hbox (9.86078pt too wide) in paragraph at lines 1389--1392
[][]    \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 p $\OML/cmm/m/it/10 >$ \OT1/
cmr/m/it/10 0[] []p $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 1[] \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/
cmr/m/it/10 algebra[]simps divide[]simps powr[]mono2$ [] $$\OT1/cmr/m/n/10 )$[]
 
[11]
Overfull \hbox (49.25273pt too wide) in paragraph at lines 1507--1520
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms e2ennre
al[]neg eq[]onp[]same[]args ereal[]mult[]le[]0[]iff lin-ear times[]ennreal$\OML
/cmm/m/it/10 :$\OT1/cmr/m/it/10 abs[]eq$\OT1/cmr/m/n/10 )$[] 
[12]
Overfull \hbox (24.13213pt too wide) in paragraph at lines 1587--1589
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 ennreal[]lessI ennreal[]neq[]top mult$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 comm
ute mult[]divide[]eq[]ennreal

Overfull \hbox (13.61127pt too wide) in paragraph at lines 1589--1591
[][]    \OT1/cmr/bx/n/10 ap-ply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis assms
 divide[]ennreal[]def ennreal[]less[]zero[]iff ennreal[]neq[]top less[]irrefl

Overfull \hbox (82.8285pt too wide) in paragraph at lines 1675--1681
[][]   $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto simp$\OT1/cmr/m/n/10 :$ \OT1/cm
r/m/it/10 antimono[]def ennreal[]mono[]minus continuous[]on[]id continuous[]on[
]const[]minus[]ennreal$\OT1/cmr/m/n/10 )$[] 
[13] [14] [15] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd)
[16]
Overfull \hbox (23.86977pt too wide) in paragraph at lines 2195--2200
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 a$\OT1/cmr/m/n/10 :$ 
\OT1/cmr/m/it/10 emea-sure M A $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M
 $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$
\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[
]set

Overfull \hbox (13.28947pt too wide) in paragraph at lines 2209--2214
[][]  \OT1/cmr/bx/n/10 ul-ti-mately have \OT1/cmr/m/it/10 emea-sure M B $\OT1/c
mr/m/n/10 =$ \OT1/cmr/m/it/10 emea-sure M $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A
 $\OMS/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us
-ing \OT1/cmr/m/it/10 emeasure[]Un[]null[]set
[17] [18]
Overfull \hbox (32.39624pt too wide) in paragraph at lines 2411--2414
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 g[]def \OT1/cmr/bx/n/10 b
y $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule nn[]integral[]diff$\OML/cmm/m/it/10 
;$ \OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms enn
real[]mult[]eq[]top[]iff$\OT1/cmr/m/n/10 )$[] 
) (./Fekete.tex [19]
Overfull \hbox (23.22952pt too wide) in paragraph at lines 92--95
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($$($\OT1/cmr/
m/it/10 Suc a$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/c
mr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 u$\OT1/c
mr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n$\OT1/cmr
/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 commute add
$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 left[]commute$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (53.2516pt too wide) in paragraph at lines 95--100
[][]    \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OMS/cmsy/m/n/10
 ^^T$ \OT1/cmr/m/it/10 u$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 a$\OMS/cmsy/m/n/10 
^^C$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OT1/cmr/m/n/10 )$$
+$\OT1/cmr/m/it/10 u n \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms []n$\OML/
cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] []a$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 n
$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 r$\OML/cmm/m/it/10 >$\OT1/cmr/m/it/10 N0[] 
eventually[]subadditive[]def
[20]
Overfull \hbox (102.03658pt too wide) in paragraph at lines 221--225
[][]    \OT1/cmr/bx/n/10 more-over have \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^C
$\OT1/cmr/m/it/10 u r $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/1
0 ^^C$\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 u r$\OT1/cmr/m/n/
10 )$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr
/m/n/10 :$ \OT1/cmr/m/it/10 ordered[]comm[]semiring[]class$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 comm[]mult[]left[]mono$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (53.52942pt too wide) in paragraph at lines 300--303
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 3$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/
m/it/10 C $\OML/cmm/m/it/10 <$ $"$$\OMS/cmsy/m/n/10 ^^C$\OT1/cmr/m/it/10 N \OT1
/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis []0 $\OML/cmm/m/it/10
 <$ $"$[] []\OT1/cmr/m/it/10 3 $\OMS/cmsy/m/n/10 ^^C$ \OT1/cmr/m/it/10 C $\OML/
cmm/m/it/10 =$ $"$ $<$ \OT1/cmr/m/it/10 real N[] linordered[]field[]class$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 sign[]simps$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2
4$\OT1/cmr/m/n/10 )$
[21]
Overfull \hbox (0.74756pt too wide) in paragraph at lines 441--454
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]ereal$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[]e
ventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[22]
Overfull \hbox (15.18639pt too wide) in paragraph at lines 516--529
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]bounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]imp[
]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (26.17522pt too wide) in paragraph at lines 590--607
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule subadditive[]c
onverges[]unbounded$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF subadditive[]im
p[]eventually[]subadditive$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[23] [24] [25]
Overfull \hbox (6.76318pt too wide) in paragraph at lines 904--910
[][]  \OT1/cmr/bx/n/10 show $\OMS/cmsy/m/n/10 ^^C$$\OT1/cmr/m/n/10 :$ \OT1/cmr/
m/it/10 t $\OMS/cmsy/m/n/10 ^^U$ \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 if \OT1/cm
r/m/it/10 t $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 V \OT1/cmr/bx/n/10 for \OT1/c
mr/m/it/10 t \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 V[]def \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 real[
]root[]pos[]pos[]le

Overfull \hbox (8.28645pt too wide) in paragraph at lines 995--1001
[][]  \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?the-sis \OT1/cmr/bx/n/10 un-
fold-ing \OT1/cmr/m/it/10 spectral[]radius[]def \OT1/cmr/bx/n/10 us-ing \OT1/cm
r/m/it/10 submultiplicative[]converges
) (./Banach_Density.tex [26] [27]
Overfull \hbox (34.05534pt too wide) in paragraph at lines 261--262
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 upper[]Banach[]density $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/cmr/m/
n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 upper[]Banach[]density A $\OT1/
cmr/m/n/10 +$ \OT1/cmr/m/it/10 upper[]Banach[]density
[28]
Overfull \hbox (6.92912pt too wide) in paragraph at lines 312--317
[][]    \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 upper[]Banach[]density $\OT
1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 [$ \OT1/cmr/m/it/10 B$\OT1/
cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 l \OT1/cmr/bx/n/10 us-ing
 \OT1/cmr/m/it/10 upper[]Banach[]density[]event2

Overfull \hbox (14.50876pt too wide) in paragraph at lines 352--355
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset
[29]
Overfull \hbox (17.2666pt too wide) in paragraph at lines 444--447
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 upper[]Banach[]density[]union$
\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 of A B$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10
 A$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 s
imp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 sup$\OML/cmm/m/it/10 :$\OT1/cmr/m/i
t/10 absorb2$\OT1/cmr/m/n/10 )$[] 
[30]
Overfull \hbox (6.15201pt too wide) in paragraph at lines 662--664
[][]    \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 card$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/cmr/m/it/10 n$
\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr/m/it/10 
card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/i
t/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/
it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/1
0 g$ $[$ $\OT1/cmr/m/n/10 ($$\OMS/cmsy/m/n/10 f$$\OML/cmm/m/it/10 :$$:$$<$\OT1/
cmr/m/it/10 k$\OMS/cmsy/m/n/10 g$ $[$ $f$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 ^^
@$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 abs$\OT1/cmr/m/n/10 (
$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$$)$$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 n
[31]
Overfull \hbox (31.44565pt too wide) in paragraph at lines 695--698
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 ^^T$ \OT1/cmr
/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\O
ML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $
\OMS/cmsy/m/n/10 \$ $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/1
0 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l
$\OT1/cmr/m/n/10 )$$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\
OT1/cmr/m/it/10 n

Overfull \hbox (36.10168pt too wide) in paragraph at lines 711--714
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-sup $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/1
0 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$ $\OML/cmm/m
/it/10 =$ \OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-sup $\
OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \
OT1/cmr/m/it/10 card $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$
 $f$\OT1/cmr/m/it/10 k$\OML/cmm/m/it/10 :$$:$\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/
10 ($\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 +$\OT1/cmr/m/it/10 l$\OT1/cmr/m/n/10 )$
$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 =$\OT1/cmr/m/it/10 n$\
OT1/cmr/m/n/10 )$[] 
[32]
Overfull \hbox (21.14922pt too wide) in paragraph at lines 909--912
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 lim-inf $\OT1/cmr/m/n/10 ($$\
OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 car
d $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 A $\OMS/cmsy/m/n/10 \$ $f$$\OML/cmm/m/it/
10 :$$:$$<$\OT1/cmr/m/it/10 n$\OMS/cmsy/m/n/10 g$$\OT1/cmr/m/n/10 )$$\OML/cmm/m
/it/10 =$\OT1/cmr/m/it/10 n$\OT1/cmr/m/n/10 )$ $=$ \OT1/cmr/m/it/10 lim-inf $\O
T1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \O
T1/cmr/m/it/10 ereal 1 $\OMS/cmsy/m/n/10 ^^@$ \OT1/cmr/m/it/10 card$\OT1/cmr/m/
n/10 ($$($\OT1/cmr/m/it/10 UNIV$\OMS/cmsy/m/n/10 ^^@$\OT1/cmr/m/it/10 A$\OT1/cm
r/m/n/10 )$
[33]
Overfull \hbox (0.37827pt too wide) in paragraph at lines 1012--1015
[][]    \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 that \OT1/cmr/bx/n/10 by $\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson ereal[]less[]eq$\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 not[]less of[]nat[]0[]less[]iff 
pos[]divide[]less[]eq$\OT1/cmr/m/n/10 )$[] 
[34]
Overfull \hbox (14.50876pt too wide) in paragraph at lines 1064--1067
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis Int[]lower2 Int[]mono card[]mono finite
[]lessThan finite[]subset

Overfull \hbox (110.4387pt too wide) in paragraph at lines 1146--1154
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 lower[]Banach[]density[]in[]01$\OT1
/cmr/m/n/10 ($\OT1/cmr/m/it/10 3$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 upper[]Ban
ach[]density[]finite$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/1
0 ]$ \OT1/cmr/m/it/10 lower[]Banach[]density[]le[]upper[] 
) (./Measure_Preserving_Transformations.tex [35]
Overfull \hbox (36.93236pt too wide) in paragraph at lines 119--122
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 f[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able M N \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF

Overfull \hbox (35.96774pt too wide) in paragraph at lines 122--125
[][]  \OT1/cmr/bx/n/10 have \OT1/cmr/m/it/10 g[]meas $\OT1/cmr/m/n/10 [$\OT1/cm
r/m/it/10 measurable$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 g $\OMS/cmsy/m/n/10
 2$ \OT1/cmr/m/it/10 mea-sur-able N P \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\O
T1/cmr/m/it/10 rule quasi[]measure[]preservingE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it
/10 1$\OT1/cmr/m/n/10 )$$[$\OT1/cmr/m/it/10 OF
[36]
Overfull \hbox (5.10562pt too wide) in paragraph at lines 282--286
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 U[]def \OT1/cmr/bx/n/10 u
s-ing []\OT1/cmr/m/it/10 f $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able M
 N[] \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto$\OML/cmm/m/it
/10 ;$ \OT1/cmr/m/it/10 me-son measurable[]space$\OT1/cmr/m/n/10 )$[] 
[37] [38] [39]
Overfull \hbox (27.25337pt too wide) in paragraph at lines 747--751
[][]  \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 f$\OMS/cmsy/m/n/10 ^^@$\OT1/c
mr/m/it/10 `$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 space N$\OT1/cmr/m/n/10 )$ $\OM
S/cmsy/m/n/10 \$ \OT1/cmr/m/it/10 space M $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 
space M \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 meson Int[]abso
rb1 measurable[]space
[40]
Overfull \hbox (32.61676pt too wide) in paragraph at lines 792--806
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]total[]measure
$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/1
0 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis prob[]space$\OML/cmm/m/it/10 :$\
OT1/cmr/m/it/10 emeasure[]space[]1

Overfull \hbox (10.39244pt too wide) in paragraph at lines 874--878
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 mpt[]def qmpt[]def qmpt[]
axioms[]def mpt[]axioms[]def \OT1/cmr/bx/n/10 us-ing $\OMS/cmsy/m/n/10 ^^C$ $^^
C$$^^C$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/
n/10 )$
[41] [42]
Overfull \hbox (40.67062pt too wide) in paragraph at lines 1043--1047
[][]  \OT1/cmr/bx/n/10 also have $\OML/cmm/m/it/10 :$$:$$:$ $\OT1/cmr/m/n/10 =$
 \OT1/cmr/m/it/10 emea-sure $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 distr lborel bo
rel $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 op $\OT1/cmr/m/n/10 +$ \OT1/cmr/m/it/10
 c$\OT1/cmr/m/n/10 )$$)$ \OT1/cmr/m/it/10 A \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/1
0 ($\OT1/cmr/m/it/10 rule emeasure[]distr$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 sy
mmetric$\OT1/cmr/m/n/10 ]$$\OML/cmm/m/it/10 ;$

Overfull \hbox (51.46826pt too wide) in paragraph at lines 1126--1130
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10
 mpt[]def qmpt[]def qmpt[]axioms[]def quasi[]measure[]preserving[]def

Overfull \hbox (5.11209pt too wide) in paragraph at lines 1141--1145
[][]    \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 measurab
le$\OT1/cmr/m/n/10 ]$$:$ $($$\OML/cmm/m/it/10 ^^U$ $\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/i
t/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 indicator A $\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$\OT1/cmr/m/it/10 y$\OT1/cmr/m/n/10 )$$)$$:$$:
$\OT1/cmr/m/it/10 ennreal$\OT1/cmr/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it
/10 borel[]measurable
[43]
Overfull \hbox (88.22876pt too wide) in paragraph at lines 1202--1205
[][]      \OT1/cmr/bx/n/10 us-ing []\OT1/cmr/m/it/10 B $\OMS/cmsy/m/n/10 2$ \OT
1/cmr/m/it/10 sets $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 M $[] $$[][]$ N$\OT1/cmr
/m/n/10 )$[] []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]measu
re$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure

Overfull \hbox (25.27127pt too wide) in paragraph at lines 1218--1220
[][]      \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1
/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 sigma[]finite[]measure N[] sigma[]finite[]mea
sure$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 emeasure[]pair[]measure$\OT1/cmr/m/n/1
0 )$[] 
[44]

Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.


Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding):
(hyperref)                removing `math shift' on input line 1260.

[45] [46]
Overfull \hbox (47.91531pt too wide) in paragraph at lines 1650--1663
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/m/n
/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-ing
$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms measure[]preserving[]def mem[]Collec
t[]eq sets$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 Int[]space[]eq2

Overfull \hbox (40.97867pt too wide) in paragraph at lines 1747--1752
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tqm quasi[]measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[]
 
[47] [48]
Overfull \hbox (10.56776pt too wide) in paragraph at lines 2074--2079
[][]    \OT1/cmr/bx/n/10 then show \OT1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tm measure[]preserving[]comp \OT1/cmr/bx/n/10 by $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 metis funpow[]Suc[]right$\OT1/cmr/m/n/10 )$[] 
[49]
Overfull \hbox (6.58662pt too wide) in paragraph at lines 2138--2152
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tm assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 assms$\OT1/cmr/m/n/10 ($\OT1
/cmr/m/it/10 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/bx/n/10 by \OT1/cmr/m/it/10 auto[
] 

Overfull \hbox (8.42105pt too wide) in paragraph at lines 2160--2174
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]preserves[]nn[
]integral$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Tn[]measure[]preserving assms$\
OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[50]
Overfull \hbox (14.91591pt too wide) in paragraph at lines 2302--2307
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def

Overfull \hbox (14.91591pt too wide) in paragraph at lines 2344--2349
[][]  \OT1/cmr/bx/n/10 then have $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/
cmr/m/it/10 x$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 birkhoff[]sum f n x$\OT1/cmr
/m/n/10 )$ $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 borel[]measurable M \OT1/cmr/b
x/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def
[51]
Overfull \hbox (33.24617pt too wide) in paragraph at lines 2459--2462
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 birkhoff[]sum[]def \OT1/c
mr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis add$\OML/cmm/m/it/10 :$
\OT1/cmr/m/it/10 commute add$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 right[]neutral
 atLeast0LessThan
[52]
Overfull \hbox (28.89758pt too wide) in paragraph at lines 2602--2604
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\OT1/cmr/
m/n/10 ($\OT1/cmr/m/it/10 no[]types$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 lift-i
ng$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 Suc[]eq[]plus1 birkhoff[]sum[]cocycle qm
pt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 birkhoff[]sum[]1$\OT1/cmr/m/n/10 ($\OT1/
cmr/m/it/10 2$\OT1/cmr/m/n/10 )$
[53] [54]
Overfull \hbox (16.78928pt too wide) in paragraph at lines 2854--2863
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 qmpt[]def qmpt[]axioms[]def \OT
1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]quasi[]measure[]preserving$\OT1/cmr
/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$[] 

Overfull \hbox (47.48772pt too wide) in paragraph at lines 2921--2936
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 mpt[]def mpt[]axioms[]def \OT1/
cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 Tinv[]qmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/
10 OF assms$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 Tinv[]measure[]preserving$\OT1/
cmr/m/n/10 [$\OT1/cmr/m/it/10 OF

Overfull \hbox (14.72844pt too wide) in paragraph at lines 2943--2958
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 fmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]mpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/
cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add$
\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 finite[]measure[]axioms$\OT1/cmr/m/n/10 )$[
] 

Overfull \hbox (3.48405pt too wide) in paragraph at lines 2965--2984
[][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 pmpt[]def \OT1/cmr/bx/n/10 us-i
ng \OT1/cmr/m/it/10 Tinv[]fmpt$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1
/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 simp add
$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$ 
[55] [56]
Overfull \hbox (2.76042pt too wide) in paragraph at lines 3192--3196
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m2$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def

Overfull \hbox (2.76042pt too wide) in paragraph at lines 3205--3209
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 emeasure[]Diff[]null[]set$\O
T1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF []U $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 n
ull[]sets M[] m3$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/
10 null[]sets[]def
[57]
Overfull \hbox (11.281pt too wide) in paragraph at lines 3336--3349
[][]\OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[]on
[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto simp 
add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 nat[]left[]shift[]def$\OT1/cmr/m/n/10 )
$[] 
[58]
Overfull \hbox (24.72952pt too wide) in paragraph at lines 3383--3391
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]left[]shift[]def$\OT1/cmr/m/n/1
0 )$[] 

Overfull \hbox (31.5017pt too wide) in paragraph at lines 3391--3393
[][]\OT1/cmr/bx/n/10 apply $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule continuous[
]on[]coordinatewise[]then[]product$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 auto si
mp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 int[]right[]shift[]def$\OT1/cmr/m/n/
10 )$[] 

Overfull \hbox (4.63538pt too wide) in paragraph at lines 3476--3477
[][]  \OT1/cmr/bx/n/10 shows \OT1/cmr/m/it/10 qmpt[]factor $\OT1/cmr/m/n/10 ($$
\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($
$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 f
 $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it/10
 x$\OT1/cmr/m/n/10 )$$)$$)$ $($\OT1/cmr/m/it/10 distr M borel $\OT1/cmr/m/n/10 
($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10
 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 n$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/1
0 f $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 T^^n$\OT1/cmr/m/n/10 )$\OT1/cmr/m/it
/10 x$\OT1/cmr/m/n/10 )$$)$$)$$)$

Overfull \hbox (41.81247pt too wide) in paragraph at lines 3492--3494
[][]    \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule measure[]p
reserving[]is[]quasi[]measure[]preserving$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
 measure[]preserving[]distr$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF
[59] [60] [61]
Overfull \hbox (57.08336pt too wide) in paragraph at lines 3748--3756
[][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 measure[]preserving[]finite[]measur
e$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1
0 1$\OT1/cmr/m/n/10 )$$]$ \OT1/cmr/m/it/10 finite[]measure[]axioms finite[]meas
ure[]def

Overfull \hbox (24.31699pt too wide) in paragraph at lines 3772--3779
[][]\OT1/cmr/m/it/10 measure[]preserving[]finite[]measure$\OT1/cmr/m/n/10 [$\OT
1/cmr/m/it/10 OF mpt[]factorE$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 1$\OT1/cmr/m/n
/10 )$$[$\OT1/cmr/m/it/10 OF assms$\OT1/cmr/m/n/10 ]$$]$ \OT1/cmr/m/it/10 finit
e[]measure[]axioms

Overfull \hbox (19.21115pt too wide) in paragraph at lines 3830--3833
[][]      \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 quasi[]measure[]preserving[]
AE measure[]preserving[]is[]quasi[]measure[]preserving
[62] [63]
Overfull \hbox (9.08395pt too wide) in paragraph at lines 4008--4009
[][]    \OT1/cmr/m/it/10 projective[]family$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10
 lim UNIV $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 I$\OML/cmm/
m/it/10 :$ \OT1/cmr/m/it/10 distr M $\OT1/cmr/m/n/10 ($$^^E$$[][]$ \OT1/cmr/m/i
t/10 i$\OMS/cmsy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/
10 borel$\OT1/cmr/m/n/10 )$ $($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 x$\OML/cm
m/m/it/10 :$ $\OT1/cmr/m/n/10 ($$\OML/cmm/m/it/10 ^^U$\OT1/cmr/m/it/10 i$\OMS/c
msy/m/n/10 2$\OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$ $\OT1/cmr/m/n/10 ($\OT1/cmr
/m/it/10 T^^$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 nat$\OT1/cmr/m/n/10 ($\OT1/cmr/
m/it/10 i$\OMS/cmsy/m/n/10 ^^@$

Overfull \hbox (25.12938pt too wide) in paragraph at lines 4018--4019
[][]  \OT1/cmr/m/it/10 mpt$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mpt[]factor natu
ral[]extension[]measure natural[]extension[]map natural[]extension[]proj
[64]
Overfull \hbox (39.9908pt too wide) in paragraph at lines 4116--4119
[][]      \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 P[]def \OT1/cmr/bx/n/10
 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule distr[]distr$\OML/cmm/m/it/10 ;$ \
OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ []\OT1/cmr/m/it/10 J $\OMS/cms
y/m/n/10 ^^R$ \OT1/cmr/m/it/10 H[] measurable[]restrict[]subset$\OT1/cmr/m/n/10
 )$[] 
[65]
Overfull \hbox (12.6075pt too wide) in paragraph at lines 4181--4184
[][]      \OT1/cmr/bx/n/10 un-fold-ing []\OT1/cmr/m/it/10 natural[]extension[]m
easure $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 lim[] \OT1/cmr/bx/n/10 by $\OT1/cmr
/m/n/10 ($\OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 P$\OML/
cmm/m/it/10 :$\OT1/cmr/m/it/10 prob[]space[]axioms$\OT1/cmr/m/n/10 )$[] 

Overfull \hbox (66.90619pt too wide) in paragraph at lines 4184--4186
[][]    \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 natural[]extension[]map $\OMS/cm
sy/m/n/10 2$ \OT1/cmr/m/it/10 mea-sur-able natural[]extension[]measure natural[
]extension[]measure[] 
[66] [67]
Overfull \hbox (1.82825pt too wide) in paragraph at lines 4366--4368
[][]          \OT1/cmr/bx/n/10 by $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 metis $\O
T1/cmr/m/n/10 ($\OT1/cmr/m/it/10 mono[]tags$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/1
0 lift-ing$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 PiE UNIV[]I mem[]Collect[]eq res
trict[]Pi[]cancel$\OT1/cmr/m/n/10 )$[] 
[68]
Overfull \hbox (78.3306pt too wide) in paragraph at lines 4472--4475
[][]    \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 I$\OML/cmm/m/it/10 :$\OT1
/cmr/m/it/10 invertible[]qmpt[]def \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/1
0 natural[]extension[]map[]def []natural[]extension[]measure
[69]
Overfull \hbox (41.89711pt too wide) in paragraph at lines 4611--4614
[][]      \OT1/cmr/bx/n/10 then have \OT1/cmr/m/it/10 natural[]extension[]proj 
$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension[]map x$\OT1/cmr/m/n/10 )
$ $=$ \OT1/cmr/m/it/10 T $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 natural[]extension
[]proj

Overfull \hbox (8.13927pt too wide) in paragraph at lines 4614--4617
[][]        \OT1/cmr/bx/n/10 un-fold-ing \OT1/cmr/m/it/10 natural[]extension[]p
roj[]def natural[]extension[]map[]def int[]left[]shift[]def
) (./Recurrence.tex) (./Invariants.tex) (./Ergodicity.tex) (./Kingman.tex)
(./Gouezel_Karlsson.tex)) [70] (./root.aux) )
(see the transcript file for additional information)</usr/share/texlive/texmf-d
ist/fonts/type1/public/amsfonts/cm/cmbsy10.pfb></usr/share/texlive/texmf-dist/f
onts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/t
ype1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/p
ublic/amsfonts/cm/cmex10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/
amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfon
ts/cm/cmmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/
cmmi7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.p
fb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></us
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share
/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texliv
e/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-
dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texlive/texmf-dist/fon
ts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/typ
e1/public/amsfonts/cm/cmsy5.pfb></usr/share/texlive/texmf-dist/fonts/type1/publ
ic/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsf
onts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/c
m/cmtt10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols
/msbm10.pfb>
Output written on root.pdf (70 pages, 383405 bytes).
Transcript written on root.log.

*** Failed to finish proof (line 1480 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. (\<And>N.
***         0 < N \<Longrightarrow>
***         {x \<in> space M.
***          \<forall>n\<in>{N..}.
***             0 \<le> birkhoff_sum f n x \<longrightarrow>
***             \<not> birkhoff_sum f n x \<le> e}
***         \<in> null_sets M) \<Longrightarrow>
***     (\<Union>x\<in>{0<..}.
***         {xa \<in> space M.
***          \<forall>n\<in>{x..}.
***             0 \<le> birkhoff_sum f n xa \<longrightarrow>
***             \<not> birkhoff_sum f n xa \<le> e})
***     \<in> null_sets M
*** At command "by" (line 1480 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
*** Failed to finish proof (line 175 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. \<And>x xa.
***        \<lbrakk>\<And>m. T --` (T ^^ m) --` A = (T \<circ> T ^^ m) --` A;
***         \<And>k. {Suc k..} = {k<..};
***         \<forall>xa. x \<in> (T \<circ> T ^^ xa) --` A; 0 < xa\<rbrakk>
***        \<Longrightarrow> x \<in> (T ^^ xa) --` A
*** At command "by" (line 175 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
*** Failed to finish proof (line 278 of "~~/afp/thys/Ergodic_Theory/Invariants.thy"):
*** goal (1 subgoal):
***  1. \<And>x xa.
***        \<lbrakk>\<And>m. T --` (T ^^ m) --` B = (T \<circ> T ^^ m) --` B;
***         \<And>k. {Suc k..} = {k<..}; x \<in> (T ^^ xa) --` B;
***         0 < xa\<rbrakk>
***        \<Longrightarrow> \<exists>xa. x \<in> (T \<circ> T ^^ xa) --` B
*** At command "by" (line 278 of "~~/afp/thys/Ergodic_Theory/Invariants.thy")
*** Failed to finish proof (line 490 of "~~/afp/thys/Ergodic_Theory/Recurrence.thy"):
*** goal (1 subgoal):
***  1. \<lbrakk>recurrent_subset A =
***              A \<inter> (\<Union>x\<in>{0<..}. (T ^^ x) --` A);
***      \<And>k. {Suc k..} = {k<..}\<rbrakk>
***     \<Longrightarrow> A \<inter> (\<Union>x\<in>{0<..}. (T ^^ x) --` A) =
***                       A \<inter> (\<Union>x. (T \<circ> T ^^ x) --` A)
*** At command "by" (line 490 of "~~/afp/thys/Ergodic_Theory/Recurrence.thy")