Session.name = MFMC_Countable Loading theory "Bourbaki_Witt_Fixpoint" loading_theory = Bourbaki_Witt_Fixpoint Loading theory "Transitive_Closure_Table" loading_theory = Transitive_Closure_Table command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=139name=theoryelapsed=0.084 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=293name=theoryelapsed=0.086 Proofs for inductive predicate(s) "rtrancl_path" command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=535name=byelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=885name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=849name=byelapsed=0.016 Proving monotonicity ... Proving the introduction rules ... command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=981name=byelapsed=0.012 Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=191name=inductiveelapsed=0.088 locale bourbaki_witt_fixpoint = fixes lub :: "'a set \ 'a" and leq :: "('a \ 'a) set" and f :: "'a \ 'a" assumes "bourbaki_witt_fixpoint lub leq f" command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1028name=localeelapsed=0.045 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1301name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=483name=showelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=922name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=613name=haveelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1661name=lemmaelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1723name=lemmaelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=679name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1503name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2778name=lemmaelapsed=0.019 Proofs for inductive predicate(s) "iterates_abovep" command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=762name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1555name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=762name=obtainelapsed=0.018 Proofs for inductive predicate(s) "rtrancl_tab" command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1618name=haveelapsed=0.020 Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=822name=haveelapsed=0.020 Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1699name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=900name=showelapsed=0.019 Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=995name=obtainelapsed=0.021 Proving the simplification rules ... ML_statistics = :now=1464809168.16tasks_ready=25tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=456130560size_allocation_free=455806888size_heap=456130560size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=0threads_total=11threads_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=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=995name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1930name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1047name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4479name=inductiveelapsed=0.110 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1980name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3024name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4697name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1980name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5311name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2059name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2153name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1103name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1158name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2205name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6452name=code_predelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1221name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2271name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2332name=obtainelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4939name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2332name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5016name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2414name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5058name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3118name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5116name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3153name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5172name=ultimatelyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3182name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5183name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3281name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1771name=inductive_setelapsed=0.409 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5264name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3281name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5490name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2016name=definitionelapsed=0.029 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3367name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5539name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6110name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2459name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6520name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2317name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2772name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5038name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2549name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5087name=byelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2986name=lemmaelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2635name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5162name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3601name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2701name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3431name=haveelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5747name=obtainelapsed=0.021 ML_statistics = :now=1464809168.67tasks_ready=26tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1089470464size_allocation_free=104848304size_heap=1089470464size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=8.032time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4934name=lemmaelapsed=0.040 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5747name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3530name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5847name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3640name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5847name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3688name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3782name=nextelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5971name=haveelapsed=0.021 ### theory "Bourbaki_Witt_Fixpoint" ### 0.914s elapsed time, 3.128s cpu time, 0.000s GC time command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3825name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6044name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6177name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6177name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2545name=byelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6271name=showelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3917name=obtainelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3222name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3917name=obtainelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3281name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2889name=byelapsed=0.068 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4070name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3340name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4150name=haveelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3399name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3773name=thuselapsed=0.026 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3573name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4249name=haveelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3581name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3813name=thuselapsed=0.026 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4314name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3854name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4377name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5259name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3589name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6543name=proofelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5259name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7733name=henceelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6590name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5326name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5393name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7853name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6630name=thuselapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5992name=thuselapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7931name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6746name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6028name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7984name=ultimatelyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6823name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6334name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7995name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3709name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9006name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=8533name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4019name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=8653name=showelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4358name=byelapsed=0.010 ML_statistics = :now=1464809169.17tasks_ready=26tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1585446912size_allocation_free=200382392size_heap=1585446912size_heap_free_last_full_GC=0size_heap_free_last_GC=0threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=9.384time_GC=0user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3926name=obtainelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5477name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3926name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5525name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3966name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6653name=byelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6093name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4166name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6149name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4189name=nextelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6215name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4227name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6263name=ultimatelyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4902name=thuselapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3438name=byelapsed=0.187 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6274name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6867name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9112name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6898name=nextelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9152name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5689name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5715name=nextelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9194name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6921name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6452name=code_predelapsed=1.090 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5767name=henceelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7016name=nextelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3989name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5862name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7046name=henceelapsed=0.021 ### theory "Transitive_Closure_Table" ### 1.604s elapsed time, 5.716s cpu time, 0.000s GC time command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4304name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5938name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7099name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9254name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5946name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4361name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6613name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7241name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6946name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6739name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6976name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7374name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=7094name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=7264name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7497name=ultimatelyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4470name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6987name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7508name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4470name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4513name=byelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4601name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7519name=byelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4614name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4662name=nextelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4748name=haveelapsed=0.138 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4839name=ultimatelyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4850name=showelapsed=0.013 ML_statistics = :now=1464809169.75tasks_ready=0tasks_pending=0tasks_running=0tasks_passive=0tasks_urgent=0workers_total=8workers_active=0workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=2097152000size_heap=2117074944size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=1threads_total=11threads_wait_condvar=8threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=11.764time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 Loading theory "Lattice_Syntax" (required by "Rel_PMF_Characterisation" via "Max_Flow_Min_Cut_Countable" via "MFMC_Misc" via "Complete_Partial_Order2") loading_theory = Lattice_Syntax ### theory "Lattice_Syntax" ### 0.011s elapsed time, 0.020s cpu time, 0.000s GC time Loading theory "Complete_Partial_Order2" (required by "Rel_PMF_Characterisation" via "Max_Flow_Min_Cut_Countable" via "MFMC_Misc") loading_theory = Complete_Partial_Order2 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=196name=theoryelapsed=0.248 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1017name=byelapsed=0.014 ML_statistics = :now=1464809170.26tasks_ready=0tasks_pending=7tasks_running=3tasks_passive=0tasks_urgent=0workers_total=8workers_active=3workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=1600542096size_heap=2117074944size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=2threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=12.416time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1345name=byelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1507name=byelapsed=0.018 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1542name=contextelapsed=0.055 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2304name=lemmaelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1647name=byelapsed=0.056 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2557name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3136name=contextelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3530name=showelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2695name=showelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5781name=lemmaelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3669name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4210name=haveelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4342name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6420name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2793name=fixelapsed=0.035 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4501name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3707name=obtainelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5378name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3707name=obtainelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10664name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6171name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2841name=obtainelapsed=0.054 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11853name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6205name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12205name=definitionelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2841name=obtainelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12435name=definitionelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3802name=haveelapsed=0.052 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6205name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6271name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3846name=haveelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6341name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2934name=haveelapsed=0.051 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6392name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3939name=finallyelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2991name=haveelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3947name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6400name=showelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12687name=named_theoremselapsed=0.114 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9890name=thuselapsed=0.017 val cont_intro_tac = fn: Proof.context -> int -> tactic val cont_intro_simproc = fn: Proof.context -> cterm -> thm option command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12756name=MLelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3086name=finallyelapsed=0.039 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6745name=showelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4566name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=13653name=simproc_setupelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4621name=obtainelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3094name=showelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14177name=lemmaelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4621name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5443name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6843name=haveelapsed=0.049 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4696name=haveelapsed=0.021 ML_statistics = :now=1464809170.76tasks_ready=23tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=868671240size_heap=2117074944size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=13.628time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14602name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5491name=obtainelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5342name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5491name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6971name=haveelapsed=0.035 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5350name=showelapsed=0.018 class preorder = ord + assumes "less_le_not_le": "\x y. (x < y) = (x \ y \ \ y \ x)" and "order_refl": "\x. x \ x" and "order_trans": "\x y z. \x \ y; y \ z\ \ x \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14752name=contextelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5585name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7569name=haveelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11078name=letelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5665name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14862name=lemmaelapsed=0.019 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11139name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5739name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11305name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5747name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7697name=haveelapsed=0.052 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11332name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=15592name=lemmaelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8301name=haveelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9979name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14395name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8929name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10047name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9583name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10129name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4775name=fixelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9594name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10208name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4820name=obtainelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7080name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10216name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17526name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4820name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7172name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4964name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7818name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11470name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5009name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7851name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11522name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5160name=haveelapsed=0.019 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8353name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18128name=contextelapsed=0.058 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11522name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5215name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11591name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8404name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5290name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8404name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5298name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11705name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18394name=lemmaelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8473name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11808name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8994name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8884name=finallyelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11816name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19229name=lemmaelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8892name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9053name=obtainelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19503name=lemmaelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9053name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19682name=contextelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9130name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19789name=lemmaelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9549name=finallyelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20280name=lemmaelapsed=0.013 ML_statistics = :now=1464809171.26tasks_ready=31tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2283798528size_allocation_free=449173992size_heap=2303721472size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=15.22time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9557name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20490name=lemmaelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=16889name=byelapsed=0.124 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17065name=byelapsed=0.132 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20822name=lemmaelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17857name=byelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7236name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22669name=contextelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22944name=lemmaelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7278name=obtainelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22944name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7278name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23159name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7344name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23159name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23402name=lemmaselapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7421name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23490name=lemmaselapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7523name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23626name=lemmaselapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7531name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23794name=lemmaselapsed=0.028 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23983name=lemmaselapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17473name=byelapsed=0.261 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24073name=lemmaselapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24211name=lemmaselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7960name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24381name=lemmaselapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8012name=obtainelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24577name=lemmaelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8012name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8079name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8157name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8245name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8253name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24878name=lemmaelapsed=0.090 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18056name=byelapsed=0.249 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18860name=haveelapsed=0.020 ML_statistics = :now=1464809171.76tasks_ready=25tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2933915648size_allocation_free=84032688size_heap=2953838592size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=18.272time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8551name=fixelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=28175name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18970name=ultimatelyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8595name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18981name=showelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8595name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=28931name=lemmaselapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8662name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9196name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8767name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29425name=lemmaselapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8845name=finallyelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9248name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29550name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8853name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9248name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20147name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9315name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29880name=lemmaelapsed=0.031 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9424name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=30459name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17701name=byelapsed=0.613 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9510name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=30890name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9518name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31103name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21286name=letelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21347name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31708name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24817name=byelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21519name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31971name=corollaryelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32195name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25339name=interpretelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21550name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22077name=nextelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22086name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22176name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22213name=henceelapsed=0.023 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32420name=contextelapsed=0.104 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22322name=haveelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32440name=lemmaelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22523name=ultimatelyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20439name=byelapsed=0.288 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22534name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25339name=interpretelapsed=0.164 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33506name=lemmaelapsed=0.040 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25387name=showelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19041name=byelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20200name=byelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25468name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=30697name=applyelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31482name=byelapsed=0.015 ML_statistics = :now=1464809172.26tasks_ready=9tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3536846848size_allocation_free=185552544size_heap=3556769792size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=19.74time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25546name=showelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21696name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32757name=haveelapsed=0.022 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33854name=contextelapsed=0.095 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32837name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21752name=obtainelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34008name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33387name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21752name=obtainelapsed=0.019 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33455name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21838name=haveelapsed=0.021 Proofs for inductive predicate(s) "compact" Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33463name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21936name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34440name=inductiveelapsed=0.043 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22043name=finallyelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22610name=byelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34653name=hide_factelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22051name=showelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25627name=henceelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32901name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25702name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33011name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25758name=ultimatelyelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25769name=showelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33049name=obtainelapsed=0.026 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34679name=contextelapsed=0.113 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25871name=nextelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33049name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34699name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33113name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25895name=letelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33164name=haveelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25931name=haveelapsed=0.023 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33281name=henceelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26044name=obtainelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33351name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26044name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26109name=henceelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33359name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26178name=henceelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26220name=haveelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25801name=byelapsed=0.025 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=35815name=contextelapsed=0.126 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26646name=henceelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=35835name=lemmaelapsed=0.020 ML_statistics = :now=1464809172.76tasks_ready=20tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3985637376size_allocation_free=225199168size_heap=4005560320size_heap_free_last_full_GC=0size_heap_free_last_GC=2098633000threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=21.22time_GC=0.124user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26749name=henceelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34897name=showelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26791name=haveelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36604name=lemmaelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26130name=byelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26877name=haveelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37312name=definitionelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26285name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37410name=definitionelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27815name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27823name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26321name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34886name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36061name=proofelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37599name=lemmaelapsed=0.045 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26831name=byelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36183name=showelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37998name=lemmaelapsed=0.304 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37119name=applyelapsed=0.319 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36420name=thuselapsed=0.324 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38794name=definitionelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26971name=henceelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26419name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27009name=thuselapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26481name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40235name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27044name=nextelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41436name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27072name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38116name=interpretelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27223name=henceelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27318name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38163name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27431name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38430name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27573name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38430name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32144name=byelapsed=1.137 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38486name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27718name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44125name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27780name=finallyelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38715name=byelapsed=0.052 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44885name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27788name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45666name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39447name=interpretelapsed=0.040 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45921name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39499name=interpretelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39928name=interpretelapsed=0.054 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40566name=interpretelapsed=0.040 ML_statistics = :now=1464809173.52tasks_ready=38tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=4156555264size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4157708864threads_in_ML=2threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=22.732time_GC=0.42user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 class ccpo = Sup + order + assumes "ccpo_Sup_upper": "\A x. \Complete_Partial_Order.chain op \ A; x \ A\ \ x \ \A" assumes "ccpo_Sup_least": "\A z. \Complete_Partial_Order.chain op \ A; \x. x \ A \ x \ z\ \ \A \ z" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46182name=contextelapsed=0.057 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39499name=interpretelapsed=0.038 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40621name=interpretelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39980name=interpretelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46202name=lemmaelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39551name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47523name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40621name=interpretelapsed=0.045 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39980name=interpretelapsed=0.062 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41017name=interpretelapsed=0.040 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40676name=interpretelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47911name=lemmaelapsed=0.021 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40032name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41076name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48404name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40111name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40676name=interpretelapsed=0.046 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48850name=lemmaelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40152name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40731name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41321name=interpretelapsed=0.038 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49282name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41705name=byelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41380name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49722name=lemmaelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44368name=interpretelapsed=0.039 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45128name=interpretelapsed=0.042 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44418name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45178name=fixelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44438name=letelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45245name=letelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44515name=henceelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45266name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44631name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45391name=haveelapsed=0.022 class complete_lattice = Inf + ccpo + bounded_lattice + assumes "Inf_lower": "\x A. x \ A \ \A \ x" and "Inf_greatest": "\A z. (\x. x \ A \ z \ x) \ z \ \A" assumes "Sup_upper": "\x A. x \ A \ x \ \A" and "Sup_least": "\A z. (\x. x \ A \ x \ z) \ \A \ z" assumes "Inf_empty": "\{} = \" assumes "Sup_empty": "\{} = \" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=50369name=contextelapsed=0.134 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44706name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45505name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44751name=ultimatelyelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45576name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44046name=byelapsed=0.186 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44762name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45621name=finallyelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39564name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48281name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45629name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46566name=interpretelapsed=0.046 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48673name=henceelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49648name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52775name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46619name=interpretelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48792name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44591name=byelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=50065name=byelapsed=0.045 ML_statistics = :now=1464809174.02tasks_ready=24tasks_pending=3tasks_running=5tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=2595107376size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4157708864threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=25.928time_GC=0.42user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45465name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46619name=interpretelapsed=0.047 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46674name=fixelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51288name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51642name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46769name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51886name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51886name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46887name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51949name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47060name=haveelapsed=0.023 class complete_distrib_lattice = complete_lattice + distrib_lattice + assumes "sup_Inf": "\a B. a \ \B = (\b\B. a \ b)" assumes "inf_Sup": "\a B. a \ \B = (\b\B. a \ b)" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53136name=contextelapsed=0.149 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51991name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47195name=henceelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52557name=byelapsed=0.088 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52114name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47284name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53723name=interpretationelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47459name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53868name=declarationelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47467name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47269name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54011name=interpretationelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52192name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54161name=declarationelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52241name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52241name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52279name=letelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52326name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53232name=byelapsed=0.166 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52393name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53358name=byelapsed=0.179 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52467name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47431name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54435name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52475name=showelapsed=0.017 class complete_lattice = Inf + ccpo + bounded_lattice + assumes "Inf_lower": "\x A. x \ A \ \A \ x" and "Inf_greatest": "\A z. (\x. x \ A \ z \ x) \ z \ \A" assumes "Sup_upper": "\x A. x \ A \ x \ \A" and "Sup_least": "\A z. (\x. x \ A \ x \ z) \ \A \ z" assumes "Inf_empty": "\{} = \" assumes "Sup_empty": "\{} = \" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55218name=contextelapsed=0.132 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55556name=applyelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55977name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56174name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58483name=lemmaelapsed=0.010 ML_statistics = :now=1464809174.52tasks_ready=1tasks_pending=9tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=1820869952size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4157708864threads_in_ML=2threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=27.388time_GC=0.42user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56435name=showelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56084name=byelapsed=0.058 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58704name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56540name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57756name=nextelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56591name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57765name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56707name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57816name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56707name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59383name=interpretationelapsed=0.061 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56796name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57875name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56782name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57875name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57938name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56860name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58002name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59442name=interpretationelapsed=0.069 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56916name=obtainelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58052name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56916name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59940name=interpretationelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58052name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56998name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58135name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57049name=thuselapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58232name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55887name=byelapsed=0.325 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58308name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57157name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58428name=finallyelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59940name=interpretationelapsed=0.097 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57231name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58436name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60246name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57303name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57370name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60693name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57378name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62547name=lemmaelapsed=0.049 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59773name=qedelapsed=0.134 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60761name=henceelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57401name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=63797name=lemmaselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57484name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60905name=haveelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57542name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62508name=finallyelapsed=0.019 locale partial_function_definitions = fixes leq :: "'a \ 'a \ bool" and lub :: "'a set \ 'a" assumes "partial_function_definitions leq lub" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61099name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57635name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62516name=showelapsed=0.018 ### theory "Complete_Partial_Order2" ### 5.020s elapsed time, 17.656s cpu time, 0.296s GC time Loading theory "MFMC_Misc" (required by "Rel_PMF_Characterisation" via "Max_Flow_Min_Cut_Countable") loading_theory = MFMC_Misc command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61297name=thuselapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57701name=finallyelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=64425name=byelapsed=0.031 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57709name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61538name=nextelapsed=0.019 ML_statistics = :now=1464809175.02tasks_ready=2tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=1057111344size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4157708864threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=28.864time_GC=0.42user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61547name=haveelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61335name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=64936name=byelapsed=0.031 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61696name=henceelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61770name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61986name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61815name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62135name=henceelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62209name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62412name=ultimatelyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62254name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62423name=showelapsed=0.020 ML_statistics = :now=1464809175.52tasks_ready=0tasks_pending=2tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=570582072size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4157708864threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=30.208time_GC=0.42user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ML_statistics = :now=1464809176.31tasks_ready=0tasks_pending=2tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4092592128size_allocation_free=4092592128size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4093854720threads_in_ML=1threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=31.272time_GC=0.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=72name=theoryelapsed=1.701 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=500name=byelapsed=0.015 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=775name=byelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=953name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1306name=byelapsed=0.036 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2425name=lemmaelapsed=0.011 ML_statistics = :now=1464809176.81tasks_ready=20tasks_pending=4tasks_running=5tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4092592128size_allocation_free=3645269816size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4093854720threads_in_ML=2threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=32.076time_GC=0.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1193name=byelapsed=0.105 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1383name=byelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1530name=byelapsed=0.012 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1708name=byelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1808name=byelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1609name=byelapsed=0.065 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1934name=byelapsed=0.028 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7667name=lemmaelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2031name=byelapsed=0.035 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=9325name=inductive_simpselapsed=0.015 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2382name=byelapsed=0.053 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2678name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2155name=byelapsed=0.071 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=9420name=definitionelapsed=0.020 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2739name=showelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3198name=byelapsed=0.029 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10726name=lemmaelapsed=0.041 ### theory "MFMC_Misc" ### 2.131s elapsed time, 5.152s cpu time, 0.304s GC time Loading theory "Max_Flow_Min_Cut_Countable" (required by "Rel_PMF_Characterisation") loading_theory = Max_Flow_Min_Cut_Countable command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3082name=byelapsed=0.210 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3344name=byelapsed=0.217 ML_statistics = :now=1464809177.31tasks_ready=57tasks_pending=1tasks_running=7tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4092592128size_allocation_free=1844459960size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4093854720threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=35.024time_GC=0.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2917name=byelapsed=0.350 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3465name=byelapsed=0.176 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3743name=byelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3867name=byelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4109name=showelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3592name=byelapsed=0.143 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6664name=byelapsed=0.020 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6793name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6352name=haveelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7081name=byelapsed=0.037 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6883name=applyelapsed=0.060 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6939name=applyelapsed=0.015 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6383name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7558name=byelapsed=0.012 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6506name=showelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7853name=obtainelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8606name=showelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7853name=obtainelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7308name=byelapsed=0.172 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7913name=haveelapsed=0.048 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=9986name=byelapsed=0.017 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7982name=obtainelapsed=0.048 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10159name=byelapsed=0.027 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7982name=obtainelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2775name=byelapsed=0.032 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8785name=byelapsed=0.170 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10675name=byelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8042name=haveelapsed=0.046 ML_statistics = :now=1464809177.81tasks_ready=18tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4092592128size_allocation_free=1033946888size_heap=4152360960size_heap_free_last_full_GC=0size_heap_free_last_GC=4093854720threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=36.92time_GC=0.724user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10337name=haveelapsed=0.075 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11301name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8093name=ultimatelyelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=47name=theoryelapsed=0.468 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11356name=fixelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8104name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10426name=showelapsed=0.087 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11439name=henceelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8270name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12978name=byelapsed=0.019 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13221name=byelapsed=0.020 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11473name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8388name=ultimatelyelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13364name=byelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13503name=applyelapsed=0.028 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8399name=showelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11528name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4155name=fixelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13532name=subgoalelapsed=0.069 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6373name=byelapsed=0.013 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4216name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11593name=haveelapsed=0.080 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6474name=showelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4258name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7886name=byelapsed=0.029 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11651name=henceelapsed=0.087 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4319name=obtainelapsed=0.048 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8015name=byelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4319name=obtainelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11708name=showelapsed=0.061 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4408name=henceelapsed=0.049 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11823name=haveelapsed=0.043 ML_statistics = :now=1464809178.68tasks_ready=31tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4050169856size_allocation_free=4050169856size_heap=4136955904size_heap_free_last_full_GC=0size_heap_free_last_GC=4051412784threads_in_ML=2threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=39.832time_GC=1.084user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4501name=henceelapsed=0.422 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11894name=showelapsed=0.427 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4635name=fixelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11949name=fixelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4690name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12036name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6069name=haveelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12148name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6162name=haveelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12220name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6191name=finallyelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6199name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12294name=ultimatelyelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12305name=showelapsed=0.066 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=160name=recordelapsed=1.184 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6230name=thuselapsed=0.088 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6230name=thuselapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=316name=definitionelapsed=0.021 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=435name=definitionelapsed=0.020 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8362name=byelapsed=0.013 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=1050name=definitionelapsed=0.018 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12395name=fixelapsed=0.089 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8416name=byelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4239name=byelapsed=0.023 Proofs for inductive predicate(s) "cycle" command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12449name=henceelapsed=0.055 ML_statistics = :now=1464809179.18tasks_ready=32tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4050169856size_allocation_free=3508498520size_heap=4136955904size_heap_free_last_full_GC=0size_heap_free_last_GC=4051412784threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=41.42time_GC=1.084user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12554name=showelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=1677name=inductiveelapsed=0.086 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4570name=byelapsed=0.058 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12603name=showelapsed=0.049 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2478name=definitionelapsed=0.032 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4827name=thuselapsed=0.051 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2855name=lemmaelapsed=0.022 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6120name=byelapsed=0.073 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4900name=nextelapsed=0.050 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4940name=showelapsed=0.051 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=1460name=byelapsed=0.053 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12697name=byelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2632name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2417name=thuselapsed=0.051 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4838name=byelapsed=0.031 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3110name=haveelapsed=0.054 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4084name=byelapsed=0.037 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3243name=haveelapsed=0.049 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4350name=obtainelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3439name=haveelapsed=0.052 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4350name=obtainelapsed=0.065 ML_statistics = :now=1464809179.68tasks_ready=48tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4050169856size_allocation_free=2715010456size_heap=4136955904size_heap_free_last_full_GC=0size_heap_free_last_GC=4051412784threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=43.236time_GC=1.084user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3795name=haveelapsed=0.051 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4479name=obtainelapsed=0.068 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3916name=finallyelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4479name=obtainelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3924name=showelapsed=0.065 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4959name=proofelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4553name=letelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5018name=thuselapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4585name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5095name=nextelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4672name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5154name=obtainelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5022name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5154name=obtainelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5088name=finallyelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5244name=haveelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5096name=showelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2318name=byelapsed=0.017 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5310name=henceelapsed=0.050 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3174name=byelapsed=0.021 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3299name=byelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5416name=haveelapsed=0.049 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4423name=byelapsed=0.012 ML_statistics = :now=1464809180.19tasks_ready=53tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4050169856size_allocation_free=1981100120size_heap=4136955904size_heap_free_last_full_GC=0size_heap_free_last_GC=4051412784threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=45.116time_GC=1.084user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5553name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3511name=applyelapsed=0.079 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5614name=ultimatelyelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5625name=haveelapsed=0.052 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5163name=recordelapsed=0.984 Proofs for inductive predicate(s) "support_flowp" command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5736name=haveelapsed=0.050 Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5844name=haveelapsed=0.048 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5303name=inductive_setelapsed=0.084 ### theory "Max_Flow_Min_Cut_Countable" ### 3.029s elapsed time, 12.400s cpu time, 0.360s GC time command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5978name=ultimatelyelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5046name=byelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5989name=showelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5713name=byelapsed=0.072 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5803name=byelapsed=0.126 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5288name=byelapsed=0.181 ML_statistics = :now=1464809180.73tasks_ready=0tasks_pending=0tasks_running=3tasks_passive=0tasks_urgent=0workers_total=8workers_active=3workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4050169856size_allocation_free=238966376size_heap=4136955904size_heap_free_last_full_GC=0size_heap_free_last_GC=4051412784threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=48.816time_GC=1.084user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6014name=byelapsed=0.128 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5960name=byelapsed=0.370 ML_statistics = :now=1464809181.31tasks_ready=0tasks_pending=0tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3978297344size_allocation_free=3472880552size_heap=4156878848size_heap_free_last_full_GC=0size_heap_free_last_GC=3979345552threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=50.024time_GC=1.204user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10443name=byelapsed=3.577 ML_statistics = :now=1464809181.82tasks_ready=0tasks_pending=0tasks_running=0tasks_passive=0tasks_urgent=0workers_total=8workers_active=0workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3978297344size_allocation_free=2977848304size_heap=4156878848size_heap_free_last_full_GC=0size_heap_free_last_GC=3979345552threads_in_ML=2threads_total=11threads_wait_condvar=8threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=50.824time_GC=1.204user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ML_statistics = :now=1464809182.32tasks_ready=207tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3978297344size_allocation_free=2670214760size_heap=4156878848size_heap_free_last_full_GC=0size_heap_free_last_GC=3979345552threads_in_ML=1threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=2threads_wait_signal=1time_CPU=51.284time_GC=1.204user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 isabelle document -c -o 'pdf' -n 'document' -t '' /media/data/jenkins/workspace/afp-repo-afp/browser_info/AFP/MFMC_Countable/document 2>&1 isabelle document -c -o 'pdf' -n 'outline' -t '/proof,/ML' /media/data/jenkins/workspace/afp-repo-afp/browser_info/AFP/MFMC_Countable/outline 2>&1 This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages loaded. 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[5] [6] [7] [8] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [9] Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] [10] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (31.55771pt too wide) in paragraph at lines 2290--2292 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono1 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF 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[$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [14] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 2933. 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Overfull \hbox (8.39821pt too wide) in paragraph at lines 2978--2980 [][]\OT1/cmr/bx/n/10 lemma $\OT1/cmr/m/n/10 ($\OT1/cmr/bx/n/10 in \OT1/cmr/m/it /10 partial[]function[]definitions$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lub[]sin gleton $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OML/cmm/m/it/10 ;$ \OT1 /cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 lub[]singleton [15] [16] [17] [18] [19] [20] [21] [22] [23] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord [24] Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex [25] Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [26] [27] [28] [29] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) No file root.bbl. [30] (./root.aux) Package rerunfilecheck Warning: File `root.out' has changed. (rerunfilecheck) Rerun to get outlines right (rerunfilecheck) or use package `bookmark'. LaTeX Warning: There were undefined references. ) (see the transcript file for additional information)< /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb> Output written on root.pdf (30 pages, 208231 bytes). Transcript written on root.log. This is BibTeX, Version 0.99d (TeX Live 2015/dev/Debian) The top-level auxiliary file: root.aux The style file: abbrv.bst Database file #1: root.bib This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages loaded. 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[5] [6] [7] [8] [9] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [10] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (31.55771pt too wide) in paragraph at lines 2290--2292 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono1 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF 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[$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [14] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 2933. 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Overfull \hbox (8.39821pt too wide) in paragraph at lines 2978--2980 [][]\OT1/cmr/bx/n/10 lemma $\OT1/cmr/m/n/10 ($\OT1/cmr/bx/n/10 in \OT1/cmr/m/it /10 partial[]function[]definitions$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lub[]sin gleton $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OML/cmm/m/it/10 ;$ \OT1 /cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 lub[]singleton [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] [25] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [26] [27] [28] [29] [30] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) (./root.bbl) [31] (./root.aux) LaTeX Warning: There were undefined references. LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) (see the transcript file for additional information)< /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb> Output written on root.pdf (31 pages, 213480 bytes). Transcript written on root.log. This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages 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/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. 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[5] [6] [7] [8] [9] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [10] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (31.55771pt too wide) in paragraph at lines 2290--2292 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono1 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF 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[$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [14] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 2933. 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Overfull \hbox (8.39821pt too wide) in paragraph at lines 2978--2980 [][]\OT1/cmr/bx/n/10 lemma $\OT1/cmr/m/n/10 ($\OT1/cmr/bx/n/10 in \OT1/cmr/m/it /10 partial[]function[]definitions$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lub[]sin gleton $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OML/cmm/m/it/10 ;$ \OT1 /cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 lub[]singleton [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] [25] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [26] [27] [28] [29] [30] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) (./root.bbl) [31] (./root.aux) ) (see the transcript file for additional information)< /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb> Output written on root.pdf (31 pages, 213288 bytes). Transcript written on root.log. This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages 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/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. 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(/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/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) (/usr/share/texlive/texmf-dist/tex/latex/stmaryrd/Ustmry.fd) LaTeX Warning: Citation `AharoniBergerGeorgakopoulusPerlsteinSpruessel2011JCT' on page 1 undefined on input line 31. (./session.tex (./Transitive_Closure_Table.tex) (./Bourbaki_Witt_Fixpoint.tex) (./Lattice_Syntax.tex [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]) (./Complete_Partial_Order2.tex Overfull \hbox (32.40999pt too wide) in paragraph at lines 46--47 [][] $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/c mm/m/it/10 >$ \OT1/cmr/m/it/10 A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/cmr/m/it/10 op $\OT1/cmr/m/n/10 =$$)$ $=$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/c mr/m/it/10 rel[]set A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/cmr/m/ it/10 op $\OT1/cmr/m/n/10 =$$)$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [2] Overfull \hbox (17.44052pt too wide) in paragraph at lines 262--269 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 blast in-tro$\OT1/cm r/m/n/10 :$ \OT1/cmr/m/it/10 ccpo[]Sup[]least chain[]empty ccpo[]Sup[]upper$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF chain[]Diff$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/ 10 OF chain$\OT1/cmr/m/n/10 ]$$]$$)$$+$[] [3] [4] [5] [6] [7] [8] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 1024. 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Overfull \hbox (34.60019pt too wide) in paragraph at lines 1038--1039 [][] \OT1/cmr/m/it/10 REPEAT[]ALL[]NEW $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 res olve[]tac ctxt $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rev $\OT1/cmr/m/n/10 ($\OT1/ cmr/m/it/10 Named[]Theorems$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 get ctxt $\OT1/ cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 named[]theorems [9] [10] Overfull \hbox (19.68684pt too wide) in paragraph at lines 1375--1388 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule contI$\OT1/cmr/ m/n/10 )$$($\OT1/cmr/m/it/10 drule chain[]fun[]ordD$\OT1/cmr/m/n/10 [$\OT1/cmr/ bx/n/10 where \OT1/cmr/m/it/10 x$\OT1/cmr/m/n/10 =$\OT1/cmr/m/it/10 x$\OT1/cmr/ m/n/10 ]$$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 fun[]lub[]apply image[]image [11] [12] [13] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [14] [15] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [16] Overfull \hbox (10.79999pt too wide) in paragraph at lines 2194--2197 [][] \OT1/cmr/bx/n/10 hence \OT1/cmr/m/it/10 chain$ [] $$ [] $$ [] $$\OT1/ cmr/m/n/10 :$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1 /cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 v$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 f ` ?Y$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1 0 rule chain[]subset$\OT1/cmr/m/n/10 )$ Overfull \hbox (14.49388pt too wide) in paragraph at lines 2209--2211 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule c$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 antisym$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 bl ast in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/ it/10 ccpo[]Sup[]least$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF chain$ [] $$ [] $$ [] $$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [17] Overfull \hbox (49.17293pt too wide) in paragraph at lines 2244--2257 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 mcont[]const$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 ru le Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [ $\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/10 ]$$ )$[] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (31.55771pt too wide) in paragraph at lines 2290--2292 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono1 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2302--2304 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont3 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2304--2306 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont4 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [18] Overfull \hbox (90.12122pt too wide) in paragraph at lines 2341--2356 [][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 g$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 abs[]def$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 ccpo mono cont bot \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo $\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont[]if[]bot$\OT1/cmr/m/n/10 [$\OT1/cmr/ m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/ m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (0.57605pt too wide) in paragraph at lines 2379--2381 [][]\OT1/cmr/bx/n/10 apply$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto in-tro$\OT1/ cmr/m/n/10 :$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissi bleD$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF adm$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it /10 chain[]imageI dest$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 mcont[]monoD$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF [19] [20] [21] Overfull \hbox (132.36125pt too wide) in paragraph at lines 2829--2831 [][]\OT1/cmr/bx/n/10 lemmas $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [22] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 2933. 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[23] Overfull \hbox (8.39821pt too wide) in paragraph at lines 2978--2980 [][]\OT1/cmr/bx/n/10 lemma $\OT1/cmr/m/n/10 ($\OT1/cmr/bx/n/10 in \OT1/cmr/m/it /10 partial[]function[]definitions$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lub[]sin gleton $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OML/cmm/m/it/10 ;$ \OT1 /cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 lub[]singleton Overfull \hbox (51.54703pt too wide) in paragraph at lines 2980--2993 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 lub[]singleton$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 rule Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/10 ] $$)$[] [24] [25] Overfull \hbox (57.17155pt too wide) in paragraph at lines 3394--3408 [][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 a b c \OT1/cmr/bx/n/10 by$\OT1/cmr/ m/n/10 ($\OT1/cmr/m/it/10 blast in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 mono tone[]rel[]prodI dest$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 monotone[]rel[]prodD1 monotone[]rel[]prodD2$\OT1/cmr/m/n/10 )$[] [26] [27] [28] [29] Overfull \hbox (63.24362pt too wide) in paragraph at lines 3902--3915 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 cont[]case[]prodI$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/ 10 rule Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n /10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/1 0 ]$$)$[] [30] [31] Overfull \hbox (1.34406pt too wide) in paragraph at lines 4246--4259 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 best in-tro$\OT1/cmr /m/n/10 :$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcon t$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF complete[]lattice[]ccpo$\OT1/cmr/ m/n/10 ]$ \OT1/cmr/m/it/10 mcont[]sup1 mcont[]sup2 Overfull \hbox (1.5956pt too wide) in paragraph at lines 4351--4357 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init lfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term lfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term lfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] [32] Overfull \hbox (7.72885pt too wide) in paragraph at lines 4386--4392 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init gfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term gfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term gfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] [33] [34] [35] Overfull \hbox (45.8011pt too wide) in paragraph at lines 4921--4928 [][]\OT1/cmr/bx/n/10 qed$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto 4 4 simp add$\ OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[]lub[]def in-tro$\OT1/cmr/m/n/10 :$ \OT 1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper b$\OML/cmm /m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it /10 ccpo[]Sup[]least Overfull \hbox (14.7741pt too wide) in paragraph at lines 5005--5007 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF ccpo[]rel[]prodI$\OT1/cmr/m/n/10 ] $$)$$($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[ ]lub[]def chain[]empty [36] Overfull \hbox (10.33287pt too wide) in paragraph at lines 5015--5017 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] Overfull \hbox (9.0388pt too wide) in paragraph at lines 5036--5038 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF b$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 b$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord Overfull \hbox (117.64188pt too wide) in paragraph at lines 5099--5101 [][]\OT1/cmr/bx/n/10 apply$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule parallel[]fi xp[]induct$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions $\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 partial[]function[]definitions$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [37] Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex [38] Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [39] [40] [41] Overfull \hbox (4.36942pt too wide) in paragraph at lines 660--665 [][] \OT1/cmr/bx/n/10 case \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 thus \O T1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 x c[]nonneg \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 field[]simps mult[]left[]mono$\OT1/cmr/m/n/10 )$[] [42] [43] [44] Overfull \hbox (2.14471pt too wide) in paragraph at lines 1206--1210 [][] \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 Partial[]order $\OT1/cmr/m/n/10 ($ \OT1/cmr/m/it/10 restrict[]rel A leq$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 leq \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 ru le Partial[]order[]restrict[]rel$\OT1/cmr/m/n/10 )$[] Overfull \hbox (17.8366pt too wide) in paragraph at lines 1243--1247 [][] \OT1/cmr/bx/n/10 with \OT1/cmr/m/it/10 lubA \OT1/cmr/bx/n/10 show \OT1/ cmr/m/it/10 lub M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Field $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 restrict[]rel A leq$\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 Field[]restrict[]rel$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [45] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) No file root.bbl. [46] (./root.aux) Package rerunfilecheck Warning: File `root.out' has changed. (rerunfilecheck) Rerun to get outlines right (rerunfilecheck) or use package `bookmark'. LaTeX Warning: There were undefined references. ) (see the transcript file for additional information) Output written on root.pdf (46 pages, 275802 bytes). Transcript written on root.log. This is BibTeX, Version 0.99d (TeX Live 2015/dev/Debian) The top-level auxiliary file: root.aux The style file: abbrv.bst Database file #1: root.bib This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages 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/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. 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(./root.toc) (./session.tex (./Transitive_Closure_Table.tex) (./Bourbaki_Witt_Fixpoint.tex) (./Lattice_Syntax.tex [1{/var/lib/texmf/fonts/ma p/pdftex/updmap/pdftex.map}]) (./Complete_Partial_Order2.tex Overfull \hbox (32.40999pt too wide) in paragraph at lines 46--47 [][] $\OT1/cmr/m/n/10 ($$($\OT1/cmr/m/it/10 A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/c mm/m/it/10 >$ \OT1/cmr/m/it/10 A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/cmr/m/it/10 op $\OT1/cmr/m/n/10 =$$)$ $=$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/c mr/m/it/10 rel[]set A $\OT1/cmr/m/n/10 =$$=$$=$$\OML/cmm/m/it/10 >$ \OT1/cmr/m/ it/10 op $\OT1/cmr/m/n/10 =$$)$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [2] Overfull \hbox (17.44052pt too wide) in paragraph at lines 262--269 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 blast in-tro$\OT1/cm r/m/n/10 :$ \OT1/cmr/m/it/10 ccpo[]Sup[]least chain[]empty ccpo[]Sup[]upper$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF chain[]Diff$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/ 10 OF chain$\OT1/cmr/m/n/10 ]$$]$$)$$+$[] [3] [4] [5] [6] [7] [8] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 1024. 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Overfull \hbox (34.60019pt too wide) in paragraph at lines 1038--1039 [][] \OT1/cmr/m/it/10 REPEAT[]ALL[]NEW $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 res olve[]tac ctxt $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rev $\OT1/cmr/m/n/10 ($\OT1/ cmr/m/it/10 Named[]Theorems$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 get ctxt $\OT1/ cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 named[]theorems [9] [10] [11] Overfull \hbox (19.68684pt too wide) in paragraph at lines 1375--1388 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule contI$\OT1/cmr/ m/n/10 )$$($\OT1/cmr/m/it/10 drule chain[]fun[]ordD$\OT1/cmr/m/n/10 [$\OT1/cmr/ bx/n/10 where \OT1/cmr/m/it/10 x$\OT1/cmr/m/n/10 =$\OT1/cmr/m/it/10 x$\OT1/cmr/ m/n/10 ]$$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 fun[]lub[]apply image[]image [12] [13] [14] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [15] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [16] [17] Overfull \hbox (10.79999pt too wide) in paragraph at lines 2194--2197 [][] \OT1/cmr/bx/n/10 hence \OT1/cmr/m/it/10 chain$ [] $$ [] $$ [] $$\OT1/ cmr/m/n/10 :$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1 /cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 v$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 f ` ?Y$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1 0 rule chain[]subset$\OT1/cmr/m/n/10 )$ Overfull \hbox (14.49388pt too wide) in paragraph at lines 2209--2211 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule c$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 antisym$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 bl ast in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/ it/10 ccpo[]Sup[]least$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF chain$ [] $$ [] $$ [] $$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (49.17293pt too wide) in paragraph at lines 2244--2257 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 mcont[]const$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 ru le Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [ $\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/10 ]$$ )$[] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (31.55771pt too wide) in paragraph at lines 2290--2292 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono1 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [18] Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2302--2304 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont3 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2304--2306 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont4 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (90.12122pt too wide) in paragraph at lines 2341--2356 [][]\OT1/cmr/bx/n/10 unfolding \OT1/cmr/m/it/10 g$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 abs[]def$\OT1/cmr/m/n/10 ]$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 ccpo mono cont bot \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo $\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont[]if[]bot$\OT1/cmr/m/n/10 [$\OT1/cmr/ m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/ m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (0.57605pt too wide) in paragraph at lines 2379--2381 [][]\OT1/cmr/bx/n/10 apply$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto in-tro$\OT1/ cmr/m/n/10 :$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissi bleD$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF adm$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it /10 chain[]imageI dest$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 mcont[]monoD$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF [19] [20] [21] [22] Overfull \hbox (132.36125pt too wide) in paragraph at lines 2829--2831 [][]\OT1/cmr/bx/n/10 lemmas $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [23] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 2933. 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Overfull \hbox (8.39821pt too wide) in paragraph at lines 2978--2980 [][]\OT1/cmr/bx/n/10 lemma $\OT1/cmr/m/n/10 ($\OT1/cmr/bx/n/10 in \OT1/cmr/m/it /10 partial[]function[]definitions$\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 lub[]sin gleton $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OML/cmm/m/it/10 ;$ \OT1 /cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$$:$ \OT1/cmr/m/it/10 lub[]singleton Overfull \hbox (51.54703pt too wide) in paragraph at lines 2980--2993 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 lub[]singleton$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 rule Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/10 ] $$)$[] [24] [25] [26] Overfull \hbox (57.17155pt too wide) in paragraph at lines 3394--3408 [][]\OT1/cmr/bx/n/10 using \OT1/cmr/m/it/10 a b c \OT1/cmr/bx/n/10 by$\OT1/cmr/ m/n/10 ($\OT1/cmr/m/it/10 blast in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 mono tone[]rel[]prodI dest$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 monotone[]rel[]prodD1 monotone[]rel[]prodD2$\OT1/cmr/m/n/10 )$[] [27] [28] [29] Overfull \hbox (63.24362pt too wide) in paragraph at lines 3902--3915 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 cont[]case[]prodI$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/ 10 rule Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n /10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/1 0 ]$$)$[] [30] [31] Overfull \hbox (1.34406pt too wide) in paragraph at lines 4246--4259 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 best in-tro$\OT1/cmr /m/n/10 :$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcon t$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF complete[]lattice[]ccpo$\OT1/cmr/ m/n/10 ]$ \OT1/cmr/m/it/10 mcont[]sup1 mcont[]sup2 [32] Overfull \hbox (1.5956pt too wide) in paragraph at lines 4351--4357 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init lfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term lfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term lfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] Overfull \hbox (7.72885pt too wide) in paragraph at lines 4386--4392 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init gfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term gfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term gfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] [33] [34] [35] Overfull \hbox (45.8011pt too wide) in paragraph at lines 4921--4928 [][]\OT1/cmr/bx/n/10 qed$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto 4 4 simp add$\ OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[]lub[]def in-tro$\OT1/cmr/m/n/10 :$ \OT 1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper b$\OML/cmm /m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it /10 ccpo[]Sup[]least [36] Overfull \hbox (14.7741pt too wide) in paragraph at lines 5005--5007 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF ccpo[]rel[]prodI$\OT1/cmr/m/n/10 ] $$)$$($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[ ]lub[]def chain[]empty Overfull \hbox (10.33287pt too wide) in paragraph at lines 5015--5017 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] Overfull \hbox (9.0388pt too wide) in paragraph at lines 5036--5038 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF b$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 b$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] [37] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord Overfull \hbox (117.64188pt too wide) in paragraph at lines 5099--5101 [][]\OT1/cmr/bx/n/10 apply$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule parallel[]fi xp[]induct$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions $\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 partial[]function[]definitions$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [38] Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [39] Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [40] [41] Overfull \hbox (4.36942pt too wide) in paragraph at lines 660--665 [][] \OT1/cmr/bx/n/10 case \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 thus \O T1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 x c[]nonneg \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 field[]simps mult[]left[]mono$\OT1/cmr/m/n/10 )$[] [42] [43] [44] Overfull \hbox (2.14471pt too wide) in paragraph at lines 1206--1210 [][] \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 Partial[]order $\OT1/cmr/m/n/10 ($ \OT1/cmr/m/it/10 restrict[]rel A leq$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 leq \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 ru le Partial[]order[]restrict[]rel$\OT1/cmr/m/n/10 )$[] [45] Overfull \hbox (17.8366pt too wide) in paragraph at lines 1243--1247 [][] \OT1/cmr/bx/n/10 with \OT1/cmr/m/it/10 lubA \OT1/cmr/bx/n/10 show \OT1/ cmr/m/it/10 lub M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Field $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 restrict[]rel A leq$\OT1/cmr/m/n/10 )$ \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 Field[]restrict[]rel$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [46] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) (./root.bbl) [47] (./root.aux) LaTeX Warning: There were undefined references. LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) (see the transcript file for additional information) Output written on root.pdf (47 pages, 279262 bytes). Transcript written on root.log. This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 79 languages loaded. 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Overfull \hbox (34.60019pt too wide) in paragraph at lines 1038--1039 [][] \OT1/cmr/m/it/10 REPEAT[]ALL[]NEW $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 res olve[]tac ctxt $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rev $\OT1/cmr/m/n/10 ($\OT1/ cmr/m/it/10 Named[]Theorems$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 get ctxt $\OT1/ cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 named[]theorems [9] [10] [11] Overfull \hbox (19.68684pt too wide) in paragraph at lines 1375--1388 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule contI$\OT1/cmr/ m/n/10 )$$($\OT1/cmr/m/it/10 drule chain[]fun[]ordD$\OT1/cmr/m/n/10 [$\OT1/cmr/ bx/n/10 where \OT1/cmr/m/it/10 x$\OT1/cmr/m/n/10 =$\OT1/cmr/m/it/10 x$\OT1/cmr/ m/n/10 ]$$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp add$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 fun[]lub[]apply image[]image [12] [13] [14] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [15] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [16] [17] Overfull \hbox (10.79999pt too wide) in paragraph at lines 2194--2197 [][] \OT1/cmr/bx/n/10 hence \OT1/cmr/m/it/10 chain$ [] $$ [] $$ [] $$\OT1/ cmr/m/n/10 :$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1 /cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 v$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 f ` ?Y$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/1 0 rule chain[]subset$\OT1/cmr/m/n/10 )$ Overfull \hbox (14.49388pt too wide) in paragraph at lines 2209--2211 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule c$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 antisym$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 bl ast in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/ it/10 ccpo[]Sup[]least$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF chain$ [] $$ [] $$ [] $$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 c$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (49.17293pt too wide) in paragraph at lines 2244--2257 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 mcont[]const$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/10 ru le Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [ $\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/10 ]$$ )$[] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT 1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]def initions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax 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fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2296--2298 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono4 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2298--2300 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont1 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [18] Overfull \hbox (36.1576pt too wide) in paragraph at lines 2300--2302 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont2 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2302--2304 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont3 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (36.1576pt too wide) in paragraph at lines 2304--2306 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mcont4 $\OT1/cmr/ m/n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]prese rves[]mcont4$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m 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\OT1/cmr/m/it/10 mono tone[]rel[]prodI dest$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 monotone[]rel[]prodD1 monotone[]rel[]prodD2$\OT1/cmr/m/n/10 )$[] [27] [28] [29] Overfull \hbox (63.24362pt too wide) in paragraph at lines 3902--3915 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule ccpo$\OML/cmm/m /it/10 :$\OT1/cmr/m/it/10 cont[]case[]prodI$\OT1/cmr/m/n/10 )$$($\OT1/cmr/m/it/ 10 rule Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n /10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/m/n/1 0 ]$$)$[] [30] [31] Overfull \hbox (1.34406pt too wide) in paragraph at lines 4246--4259 [][]\OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 best in-tro$\OT1/cmr /m/n/10 :$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcon t$ [] $$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF complete[]lattice[]ccpo$\OT1/cmr/ m/n/10 ]$ \OT1/cmr/m/it/10 mcont[]sup1 mcont[]sup2 [32] Overfull \hbox (1.5956pt too wide) in paragraph at lines 4351--4357 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init lfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term lfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term lfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] Overfull \hbox (7.72885pt too wide) in paragraph at lines 4386--4392 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 init gfp $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1 /cmr/m/it/10 term gfp$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]fun$\OMS/cmsy/m /n/10 g$ $\OT1/cmr/m/n/10 @$$\OMS/cmsy/m/n/10 f$\OT1/cmr/m/it/10 term gfp$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 mono[]body$\OMS/cmsy/m/n/10 g$[] [33] [34] [35] Overfull \hbox (45.8011pt too wide) in paragraph at lines 4921--4928 [][]\OT1/cmr/bx/n/10 qed$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 auto 4 4 simp add$\ OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[]lub[]def in-tro$\OT1/cmr/m/n/10 :$ \OT 1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper b$\OML/cmm /m/it/10 :$\OT1/cmr/m/it/10 ccpo[]Sup[]upper a$\OML/cmm/m/it/10 :$\OT1/cmr/m/it /10 ccpo[]Sup[]least [36] Overfull \hbox (14.7741pt too wide) in paragraph at lines 5005--5007 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF ccpo[]rel[]prodI$\OT1/cmr/m/n/10 ] $$)$$($\OT1/cmr/m/it/10 auto simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 prod[ ]lub[]def chain[]empty Overfull \hbox (10.33287pt too wide) in paragraph at lines 5015--5017 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 a$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] Overfull \hbox (9.0388pt too wide) in paragraph at lines 5036--5038 [][] \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule admissibl e[]leI$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF b$\OT1/cmr/m/n/10 ]$$)$$($\OT1/cmr /m/it/10 auto in-tro$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 b$\OML/cmm/m/it/10 :$\ OT1/cmr/m/it/10 ccpo[]Sup[]least simp add$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 c hain[]empty$\OT1/cmr/m/n/10 )$[] [37] Overfull \hbox (3.33423pt too wide) in paragraph at lines 5087--5088 [][] \OT1/cmr/bx/n/10 and \OT1/cmr/m/it/10 adm$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/i t/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 admissible $\OT1/cmr/m/n/10 ($\OT 1/cmr/m/it/10 prod[]lub $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]lub luba$\OT1/ cmr/m/n/10 )$ $($\OT1/cmr/m/it/10 fun[]lub lubb$\OT1/cmr/m/n/10 )$$)$ $($\OT1/c mr/m/it/10 rel[]prod $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 fun[]ord Overfull \hbox (117.64188pt too wide) in paragraph at lines 5099--5101 [][]\OT1/cmr/bx/n/10 apply$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 rule parallel[]fi xp[]induct$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions $\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF a$\OT1/cmr/m/n/10 ]$ \OT1/cmr/m/it/10 partial[]function[]definitions$\OML/cmm/ m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [38] Overfull \hbox (9.0053pt too wide) in paragraph at lines 5252--5253 []\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]fst $\OT1/cmr/m/n/10 [$ \OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]cal l$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT1/ cmr/m/it/10 OF mcont[]fst$\OT1/cmr/m/n/10 ]$[] Overfull \hbox (17.86363pt too wide) in paragraph at lines 5253--5255 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont[]call[]snd $\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 cont[]intro$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 mcont[]c all$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 THEN mcont2mcont$\OML/cmm/m/it/10 ;$ \OT 1/cmr/m/it/10 OF mcont[]snd$\OT1/cmr/m/n/10 ]$[] ) (./MFMC_Misc.tex Overfull \hbox (30.39157pt too wide) in paragraph at lines 130--132 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 Chains[]into[]chain$\OT1/cmr/m/n/10 :$ \OT1/cmr/m/it/10 M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Chains $\OMS/cmsy/ m/n/10 f$$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 x$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/i t/10 y$\OT1/cmr/m/n/10 )$$\OML/cmm/m/it/10 :$ \OT1/cmr/m/it/10 R x y$\OMS/cmsy/ m/n/10 g$ $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cmr/m/it/10 Complete[]Pa rtial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [39] Overfull \hbox (25.24837pt too wide) in paragraph at lines 148--150 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 chain[]dual$\OT1/cmr/m/n/10 :$ \OT1 /cmr/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^U$ $\OT1/cmr/m/n/10 =$ \OT1/cmr/m/it/10 Complete[]Parti al[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [40] [41] Overfull \hbox (4.36942pt too wide) in paragraph at lines 660--665 [][] \OT1/cmr/bx/n/10 case \OT1/cmr/m/it/10 0 \OT1/cmr/bx/n/10 thus \O T1/cmr/m/it/10 ?case \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 x c[]nonneg \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 field[]simps mult[]left[]mono$\OT1/cmr/m/n/10 )$[] [42] [43] [44] Overfull \hbox (2.14471pt too wide) in paragraph at lines 1206--1210 [][] \OT1/cmr/bx/n/10 show \OT1/cmr/m/it/10 Partial[]order $\OT1/cmr/m/n/10 ($ \OT1/cmr/m/it/10 restrict[]rel A leq$\OT1/cmr/m/n/10 )$ \OT1/cmr/bx/n/10 us-ing \OT1/cmr/m/it/10 leq \OT1/cmr/bx/n/10 by$\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 ru le Partial[]order[]restrict[]rel$\OT1/cmr/m/n/10 )$[] [45] Overfull \hbox (17.8366pt too wide) in paragraph at lines 1243--1247 [][] \OT1/cmr/bx/n/10 with \OT1/cmr/m/it/10 lubA \OT1/cmr/bx/n/10 show \OT1/ cmr/m/it/10 lub M $\OMS/cmsy/m/n/10 2$ \OT1/cmr/m/it/10 Field $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 restrict[]rel A leq$\OT1/cmr/m/n/10 )$ \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 Field[]restrict[]rel$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF [46] Overfull \hbox (1.70967pt too wide) in paragraph at lines 1416--1418 [][]\OT1/cmr/bx/n/10 lemma \OT1/cmr/m/it/10 incseq[]chain[]range$\OT1/cmr/m/n/1 0 :$ \OT1/cmr/m/it/10 inc-seq f $\OT1/cmr/m/n/10 =[]\OMS/cmsy/m/n/10 )$ \OT1/cm r/m/it/10 Complete[]Partial[]Order$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 chain op $\OMS/cmsy/m/n/10 ^^T$ $\OT1/cmr/m/n/10 ($\OT1/cmr/m/it/10 range ) (./Max_Flow_Min_Cut_Countable.tex)) (./root.bbl) [47] (./root.aux) ) (see the transcript file for additional information) Output written on root.pdf (47 pages, 279156 bytes). Transcript written on root.log. *** Failed to load theory "Rel_PMF_Characterisation" (unresolved "Max_Flow_Min_Cut_Countable") *** Type unification failed: Clash of types "ennreal" and "ereal" *** *** Type error in application: incompatible operand type *** *** Operator: op = (d_OUT g x) :: ereal \ bool *** Operand: \\<^sup>+ y. g (x, y) :: ennreal *** *** Coercion Inference: *** *** Local coercion insertion on the operand failed: *** "ennreal" is not a subtype of "ereal" *** *** Now trying to infer coercions globally. *** *** Coercion inference failed: *** uncomparable types in type list *** *** Cannot fulfil subtype constraints: *** ('v \ 'v \ ereal) \ 'v \ ??'a *** <: *** ('v \ 'v \ ereal) *** \ 'v \ ereal *** from function application *** d_OUT::('v \ 'v \ ereal) *** \ 'v \ ereal *** ennreal <: ennreal from function application *** d_OUT g x = (\\<^sup>+ y. g (x, y)) *** ereal <: ennreal from function application op = (d_OUT g x) *** ('v \ 'v \ ereal) \ 'v \ ereal *** <: *** ('v \ 'v \ ??'a) \ 'v \ ereal *** from function application *** d_OUT::('v \ 'v \ ??'a) *** \ 'v \ ereal *** ('v \ 'v \ ereal) \ 'v \ ??'a *** <: *** ('v \ 'v \ ereal) *** \ 'v \ ereal *** from function application *** d_OUT::('v \ 'v \ ereal) *** \ 'v \ ereal *** ('v \ 'v \ ereal) \ 'v \ ereal *** <: *** ('v \ 'v \ ??'a) \ 'v \ ereal *** from function application *** d_OUT::('v \ 'v \ ??'a) *** \ 'v \ ereal *** 'v \ 'v \ ??'a <: 'v \ 'v \ ??'b *** from function application d_OUT g *** 'v \ 'v \ ??'a <: 'v \ 'v \ ??'b *** from function application g::'v \ 'v \ ??'b *** 'v \ ennreal <: 'v \ ennreal *** from function application \\<^sup>+ y. g (x, y) *** 'v \ ennreal <: 'v \ ennreal *** from function application *** (\y. g (x, y))::'v \ ennreal *** 'v \ 'v \ ??'a <: *** 'v \ 'v \ ennreal from function application *** g::'v \ 'v \ ennreal *** At command "definition" (line 155 of "~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thy")