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=0.082 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=293name=theoryelapsed=0.083 Proofs for inductive predicate(s) "rtrancl_path" Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=700name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=535name=byelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=191name=inductiveelapsed=0.058 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=849name=byelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=922name=showelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=613name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1723name=lemmaelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=679name=showelapsed=0.016 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=0.080 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1503name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2778name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1459name=lemmaelapsed=0.010 Proofs for inductive predicate(s) "rtrancl_tab" command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=762name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1555name=haveelapsed=0.017 Proving monotonicity ... command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1661name=lemmaelapsed=0.010 Proving the introduction rules ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=762name=obtainelapsed=0.015 Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1618name=haveelapsed=0.019 Proofs for inductive predicate(s) "iterates_abovep" command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=822name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4479name=inductiveelapsed=0.056 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1699name=showelapsed=0.016 Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=900name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4697name=lemmaelapsed=0.010 ML_statistics = :now=1464825524.81tasks_ready=29tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=444596224size_allocation_free=444272552size_heap=444596224size_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=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=995name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1930name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6452name=code_predelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1047name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1980name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1980name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3024name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2059name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2153name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2205name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4939name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2271name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5016name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=1771name=inductive_setelapsed=0.200 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2332name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5058name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2016name=definitionelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2332name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5116name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2414name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5172name=ultimatelyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5490name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5183name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2986name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5539name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5264name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6110name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4934name=lemmaelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6520name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1103name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3118name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1158name=nextelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3153name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=1221name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=8739name=lemmaelapsed=0.011 ### theory "Bourbaki_Witt_Fixpoint" ### 0.622s elapsed time, 2.456s cpu time, 0.000s GC time command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3182name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2317name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3281name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5038name=byelapsed=0.031 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5087name=byelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3281name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3367name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2549name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5162name=byelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2545name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2635name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=2889name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3222name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=2701name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3281name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3773name=thuselapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5747name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3340name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3399name=haveelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3813name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5747name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3573name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3854name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5847name=obtainelapsed=0.018 ML_statistics = :now=1464825525.32tasks_ready=39tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1290797056size_allocation_free=53501480size_heap=1290797056size_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=8.608time_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=3581name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5847name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6177name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=5971name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6177name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5259name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6044name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6271name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5259name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6543name=proofelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7733name=henceelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5326name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6590name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7853name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5393name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6630name=thuselapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5992name=thuselapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7931name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6452name=code_predelapsed=0.582 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7984name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6028name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6746name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7995name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6334name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6823name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=7166name=lemmaelapsed=0.011 ### theory "Transitive_Closure_Table" ### 0.951s elapsed time, 3.972s cpu time, 0.000s GC time command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=8533name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9006name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3431name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=8653name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3530name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3926name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5477name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3926name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3640name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3966name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3688name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5525name=showelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4166name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3782name=nextelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4189name=nextelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6653name=byelapsed=0.028 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3825name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6613name=byelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4227name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6093name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3917name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4902name=thuselapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=3917name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6149name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6739name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4070name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3438name=byelapsed=0.177 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6215name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4150name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6976name=thuselapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6263name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=7094name=byelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4249name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6274name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=7264name=byelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6867name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4314name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9112name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6898name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=4377name=showelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9152name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6921name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=3989name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9194name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5689name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7016name=nextelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4304name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5715name=nextelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7046name=henceelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4361name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5767name=henceelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7099name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Transitive_Closure_Table.thyoffset=6987name=byelapsed=0.025 ML_statistics = :now=1464825525.82tasks_ready=21tasks_pending=0tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=0size_allocation=1973420032size_allocation_free=194951752size_heap=1973420032size_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=10.488time_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=4358name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5862name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7241name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=9254name=byelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=6946name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5938name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7374name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4470name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=5946name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7497name=ultimatelyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4470name=obtainelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4513name=byelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=7508name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4601name=showelapsed=0.011 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=7519name=byelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4748name=haveelapsed=0.142 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4839name=ultimatelyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Bourbaki_Witt_Fixpoint.thyoffset=4850name=showelapsed=0.017 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" ### 0.009s elapsed time, 0.024s 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 ML_statistics = :now=1464825526.43tasks_ready=0tasks_pending=3tasks_running=1tasks_passive=1tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=1575473920size_heap=2117074944size_heap_free_last_full_GC=0size_heap_free_last_GC=2098611632threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=12.196time_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=196name=theoryelapsed=0.235 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1017name=byelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1345name=byelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=1507name=byelapsed=0.017 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=0.054 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2557name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3136name=contextelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2695name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3530name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2793name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4210name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3669name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5781name=lemmaelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2841name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4342name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3707name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2841name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6420name=lemmaelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4501name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3707name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2934name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5378name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3802name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=2991name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3846name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3086name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10357name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6171name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3939name=finallyelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3094name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10664name=lemmaelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=3947name=showelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6205name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6205name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6745name=showelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4566name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11853name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6843name=haveelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6271name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12205name=definitionelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4621name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6971name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6341name=henceelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12435name=definitionelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4621name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7569name=haveelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6392name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4696name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=6400name=showelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7697name=haveelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5342name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8301name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9890name=thuselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5443name=fixelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8929name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5350name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9583name=ultimatelyelapsed=0.014 ML_statistics = :now=1464825526.93tasks_ready=18tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2097152000size_allocation_free=796251672size_heap=2117074944size_heap_free_last_full_GC=0size_heap_free_last_GC=2098611632threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=13.608time_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=5491name=obtainelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9594name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5491name=obtainelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11078name=letelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5585name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=12687name=named_theoremselapsed=0.111 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7080name=fixelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11139name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5665name=haveelapsed=0.013 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=11305name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7172name=showelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5739name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5747name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4775name=fixelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11332name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14177name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7818name=fixelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4820name=obtainelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8353name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7851name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4820name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8404name=obtainelapsed=0.021 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=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=4964name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9979name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8404name=obtainelapsed=0.018 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=5009name=henceelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10047name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5160name=haveelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10129name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8473name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5215name=haveelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10208name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8884name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=10216name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5290name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8892name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=5298name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8994name=fixelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7236name=fixelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9053name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11470name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7278name=obtainelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9053name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9130name=haveelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7278name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11522name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7344name=haveelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9549name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17526name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11522name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9557name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7421name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11591name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=14395name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7523name=finallyelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=7531name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11705name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11808name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8012name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=11816name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8012name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8551name=fixelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8079name=haveelapsed=0.012 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=18128name=contextelapsed=0.078 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8157name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8595name=obtainelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8245name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8595name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8662name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8253name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8767name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18394name=lemmaelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8845name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=8853name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19229name=lemmaelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9196name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19503name=lemmaelapsed=0.016 ML_statistics = :now=1464825527.43tasks_ready=25tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=2335178752size_allocation_free=261501848size_heap=2355101696size_heap_free_last_full_GC=0size_heap_free_last_GC=2098611632threads_in_ML=5threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=15.608time_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=9248name=obtainelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=16889name=byelapsed=0.114 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19682name=contextelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9248name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19789name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17065name=byelapsed=0.125 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9315name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20280name=lemmaelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9424name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20490name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9510name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=9518name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20822name=lemmaelapsed=0.027 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17857name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22669name=contextelapsed=0.027 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22944name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23159name=lemmaelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23159name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23402name=lemmaselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23490name=lemmaselapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17473name=byelapsed=0.219 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23626name=lemmaselapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23794name=lemmaselapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=23983name=lemmaselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24073name=lemmaselapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18860name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24211name=lemmaselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18970name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24381name=lemmaselapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18981name=showelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24577name=lemmaelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=18056name=byelapsed=0.252 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20147name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21286name=letelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21347name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21519name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24878name=lemmaelapsed=0.099 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21550name=showelapsed=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=22077name=nextelapsed=0.015 ML_statistics = :now=1464825527.93tasks_ready=11tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3054501888size_allocation_free=430953608size_heap=3074424832size_heap_free_last_full_GC=0size_heap_free_last_GC=2098611632threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=17.052time_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=22086name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=28175name=lemmaelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22176name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22213name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=28931name=lemmaselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22322name=haveelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29425name=lemmaselapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22523name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29550name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22534name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=29880name=lemmaelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=17701name=byelapsed=0.617 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20439name=byelapsed=0.285 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=24817name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=19041name=byelapsed=0.033 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=30459name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=20200name=byelapsed=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=21696name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25339name=interpretelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31103name=lemmaelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22610name=byelapsed=0.026 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21752name=obtainelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=30697name=applyelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21752name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31482name=byelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31708name=lemmaelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21838name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=31971name=corollaryelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=21936name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32195name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22043name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=22051name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25339name=interpretelapsed=0.153 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25387name=showelapsed=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=32420name=contextelapsed=0.087 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25468name=fixelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32440name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32649name=assumeelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25546name=showelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32757name=haveelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33506name=lemmaelapsed=0.031 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25627name=henceelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32837name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25702name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33387name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25758name=ultimatelyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33455name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25769name=showelapsed=0.019 ML_statistics = :now=1464825528.44tasks_ready=7tasks_pending=7tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=1size_allocation=3679453184size_allocation_free=10677824size_heap=3699376128size_heap_free_last_full_GC=0size_heap_free_last_GC=2098611632threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=19.952time_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=33463name=showelapsed=0.020 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=0.086 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25871name=nextelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25895name=letelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=32901name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34008name=lemmaelapsed=0.018 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=33011name=fixelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25931name=haveelapsed=0.017 Proofs for inductive predicate(s) "compact" command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26044name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33049name=obtainelapsed=0.020 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=33049name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26044name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34440name=inductiveelapsed=0.039 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34653name=hide_factelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33113name=haveelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26109name=henceelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33164name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26178name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33281name=henceelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26220name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26646name=henceelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33351name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=33359name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26749name=henceelapsed=0.017 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=0.090 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26791name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=25801name=byelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26877name=haveelapsed=0.022 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=27815name=finallyelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26130name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27823name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26285name=fixelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26321name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=34897name=showelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26831name=byelapsed=0.016 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=0.087 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26971name=henceelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26419name=haveelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=35835name=lemmaelapsed=0.014 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=27009name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=26481name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27044name=nextelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36604name=lemmaelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27072name=haveelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36183name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37312name=definitionelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36264name=showelapsed=0.273 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=37410name=definitionelapsed=0.281 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27223name=henceelapsed=0.294 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=36420name=thuselapsed=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=37599name=lemmaelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27431name=henceelapsed=0.020 ML_statistics = :now=1464825529.18tasks_ready=14tasks_pending=5tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=4156555264size_heap=4154458112size_heap_free_last_full_GC=0size_heap_free_last_GC=4157964984threads_in_ML=2threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=21.596time_GC=0.392user_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=27573name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38794name=definitionelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27718name=haveelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27780name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40235name=lemmaelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38116name=interpretelapsed=0.034 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=27788name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38163name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41436name=lemmaelapsed=0.012 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=1.083 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38430name=obtainelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38715name=byelapsed=0.053 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=38486name=thuselapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39447name=interpretelapsed=0.037 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39499name=interpretelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40566name=interpretelapsed=0.037 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39928name=interpretelapsed=0.052 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40621name=interpretelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39499name=interpretelapsed=0.038 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39980name=interpretelapsed=0.022 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39551name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40621name=interpretelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41017name=interpretelapsed=0.032 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40676name=interpretelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39980name=interpretelapsed=0.051 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41076name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40032name=showelapsed=0.013 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=0.053 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40111name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40676name=interpretelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46202name=lemmaelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40152name=thuselapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=40731name=showelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41321name=interpretelapsed=0.030 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41380name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47523name=lemmaelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=41705name=byelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47911name=lemmaelapsed=0.020 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=48404name=lemmaelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44368name=interpretelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45128name=interpretelapsed=0.036 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44418name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48850name=lemmaelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45178name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45245name=letelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44438name=letelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49282name=lemmaelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44515name=henceelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45266name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49722name=lemmaelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45391name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44631name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45505name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44706name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45576name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44751name=ultimatelyelapsed=0.015 ML_statistics = :now=1464825529.69tasks_ready=34tasks_pending=3tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=3268400664size_heap=4154458112size_heap_free_last_full_GC=0size_heap_free_last_GC=4157964984threads_in_ML=4threads_total=11threads_wait_condvar=5threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=23.2time_GC=0.392user_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=44762name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45621name=finallyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=39564name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44046name=byelapsed=0.181 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45629name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48281name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48673name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=49648name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46566name=interpretelapsed=0.041 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=44591name=byelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=48792name=showelapsed=0.018 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=0.128 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46619name=interpretelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=45465name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=50065name=byelapsed=0.044 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46619name=interpretelapsed=0.043 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51288name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46674name=fixelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51642name=byelapsed=0.010 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46769name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51886name=obtainelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51886name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=46887name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51949name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47060name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=51991name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47195name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52114name=showelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52557name=byelapsed=0.087 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47284name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47269name=byelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47459name=finallyelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52192name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47467name=showelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=47431name=byelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52241name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52241name=obtainelapsed=0.017 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=0.141 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52279name=letelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52326name=haveelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52393name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52467name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53723name=interpretationelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=52475name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53868name=declarationelapsed=0.023 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54011name=interpretationelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54161name=declarationelapsed=0.024 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=54435name=byelapsed=0.012 ML_statistics = :now=1464825530.19tasks_ready=0tasks_pending=7tasks_running=3tasks_passive=0tasks_urgent=0workers_total=8workers_active=3workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=2462844968size_heap=4154458112size_heap_free_last_full_GC=0size_heap_free_last_GC=4157964984threads_in_ML=4threads_total=11threads_wait_condvar=6threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=24.772time_GC=0.392user_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=53232name=byelapsed=0.171 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=53358name=byelapsed=0.182 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=0.127 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55556name=applyelapsed=0.041 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 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56435name=showelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56084name=byelapsed=0.057 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=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57756name=nextelapsed=0.013 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=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57816name=fixelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56707name=obtainelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57875name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56707name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59383name=interpretationelapsed=0.062 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57875name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56796name=showelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57938name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56782name=byelapsed=0.011 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56860name=fixelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58002name=fixelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58052name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56916name=obtainelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58052name=obtainelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56916name=obtainelapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59442name=interpretationelapsed=0.071 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58135name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=56998name=haveelapsed=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=58232name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57049name=thuselapsed=0.017 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58308name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58428name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=58436name=showelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=55887name=byelapsed=0.320 ML_statistics = :now=1464825530.69tasks_ready=0tasks_pending=3tasks_running=3tasks_passive=0tasks_urgent=0workers_total=8workers_active=3workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=1796732120size_heap=4154458112size_heap_free_last_full_GC=0size_heap_free_last_GC=4157964984threads_in_ML=2threads_total=11threads_wait_condvar=6threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=25.856time_GC=0.392user_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=57157name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57231name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59940name=interpretationelapsed=0.098 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57303name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60246name=lemmaelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57370name=finallyelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=59773name=qedelapsed=0.116 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57378name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60693name=haveelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57401name=nextelapsed=0.013 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60761name=henceelapsed=0.020 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62547name=lemmaelapsed=0.042 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57484name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57542name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=60905name=haveelapsed=0.025 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57635name=haveelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62508name=finallyelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61099name=haveelapsed=0.019 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=57701name=finallyelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62516name=showelapsed=0.017 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=57709name=showelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61297name=thuselapsed=0.017 ### theory "Complete_Partial_Order2" ### 4.595s elapsed time, 16.208s cpu time, 0.268s 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=61538name=nextelapsed=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=61547name=haveelapsed=0.021 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=64936name=byelapsed=0.029 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61335name=byelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61696name=henceelapsed=0.018 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61770name=fixelapsed=0.014 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61986name=haveelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=61815name=thuselapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62135name=henceelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62209name=fixelapsed=0.012 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62412name=ultimatelyelapsed=0.015 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62423name=showelapsed=0.016 command_timing = :file=~~/src/HOL/Library/Complete_Partial_Order2.thyoffset=62254name=thuselapsed=0.014 ML_statistics = :now=1464825531.19tasks_ready=0tasks_pending=2tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=2size_allocation=4156555264size_allocation_free=489507592size_heap=4154458112size_heap_free_last_full_GC=0size_heap_free_last_GC=4157964984threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=28.536time_GC=0.392user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ML_statistics = :now=1464825531.94tasks_ready=0tasks_pending=2tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4096786432size_allocation_free=4096786432size_heap=4151312384size_heap_free_last_full_GC=0size_heap_free_last_GC=4097882256threads_in_ML=1threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=29.376time_GC=0.668user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ML_statistics = :now=1464825532.44tasks_ready=0tasks_pending=2tasks_running=1tasks_passive=1tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4096786432size_allocation_free=3646318440size_heap=4151312384size_heap_free_last_full_GC=0size_heap_free_last_GC=4097882256threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=30.18time_GC=0.668user_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=1.635 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=953name=byelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1120name=lemmaelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1652name=lemmaelapsed=0.013 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1193name=byelapsed=0.068 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1530name=byelapsed=0.012 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2425name=lemmaelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1708name=byelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1609name=byelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1808name=byelapsed=0.038 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=1934name=byelapsed=0.027 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2031name=byelapsed=0.034 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2155name=byelapsed=0.057 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2382name=byelapsed=0.052 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2678name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7667name=lemmaelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2739name=showelapsed=0.044 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=9420name=definitionelapsed=0.020 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3198name=byelapsed=0.029 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3082name=byelapsed=0.126 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10726name=lemmaelapsed=0.042 ML_statistics = :now=1464825532.94tasks_ready=64tasks_pending=2tasks_running=7tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4096786432size_allocation_free=3010157640size_heap=4151312384size_heap_free_last_full_GC=0size_heap_free_last_GC=4097882256threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=31.228time_GC=0.668user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ### theory "MFMC_Misc" ### 2.108s elapsed time, 5.316s cpu time, 0.276s 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=3465name=byelapsed=0.125 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3344name=byelapsed=0.205 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2917name=byelapsed=0.337 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3743name=byelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3867name=byelapsed=0.036 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6664name=byelapsed=0.019 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4109name=showelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=3592name=byelapsed=0.138 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=6883name=applyelapsed=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=6939name=applyelapsed=0.015 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7558name=byelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6383name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6506name=showelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7853name=obtainelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7853name=obtainelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8606name=showelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7913name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7308name=byelapsed=0.171 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=2775name=byelapsed=0.015 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7982name=obtainelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=9986name=byelapsed=0.016 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7982name=obtainelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10159name=byelapsed=0.025 ML_statistics = :now=1464825533.44tasks_ready=18tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4096786432size_allocation_free=868023616size_heap=4151312384size_heap_free_last_full_GC=0size_heap_free_last_GC=4097882256threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=35.232time_GC=0.668user_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=8785name=byelapsed=0.166 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10337name=haveelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8042name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10675name=byelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=10426name=showelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8093name=ultimatelyelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11301name=haveelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13364name=byelapsed=0.011 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8104name=haveelapsed=0.053 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11356name=fixelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=13532name=subgoalelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11439name=henceelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8270name=haveelapsed=0.053 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4155name=fixelapsed=0.039 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11473name=haveelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8388name=ultimatelyelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4216name=haveelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11528name=haveelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8399name=showelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4258name=haveelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6373name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=47name=theoryelapsed=0.477 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11593name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4319name=obtainelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6474name=showelapsed=0.049 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11651name=henceelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4319name=obtainelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=7886name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8591name=byelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11708name=showelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4408name=henceelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11823name=haveelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=8015name=byelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4501name=henceelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4501name=henceelapsed=0.016 ML_statistics = :now=1464825533.95tasks_ready=21tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=3size_allocation=4114132992size_allocation_free=285677288size_heap=4151881728size_heap_free_last_full_GC=0size_heap_free_last_GC=4097882256threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=37.192time_GC=0.668user_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=11894name=showelapsed=0.066 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4635name=fixelapsed=0.063 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=11949name=fixelapsed=0.084 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4690name=haveelapsed=0.425 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12036name=haveelapsed=0.398 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6069name=haveelapsed=0.042 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12148name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6162name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12220name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6191name=finallyelapsed=0.040 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12294name=ultimatelyelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6199name=haveelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12305name=showelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6230name=thuselapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4239name=byelapsed=0.014 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12395name=fixelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12449name=henceelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4570name=byelapsed=0.034 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=160name=recordelapsed=1.000 ML_statistics = :now=1464825534.76tasks_ready=25tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4052267008size_allocation_free=4052267008size_heap=4139053056size_heap_free_last_full_GC=0size_heap_free_last_GC=4054014184threads_in_ML=1threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=38.024time_GC=1user_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=316name=definitionelapsed=0.019 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=12554name=showelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4827name=thuselapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=435name=definitionelapsed=0.020 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=12603name=showelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4900name=nextelapsed=0.042 Proofs for inductive predicate(s) "cycle" 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=4940name=showelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=1677name=inductiveelapsed=0.041 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6120name=byelapsed=0.072 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2478name=definitionelapsed=0.015 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=2855name=lemmaelapsed=0.010 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=4838name=byelapsed=0.030 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=1460name=byelapsed=0.054 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5018name=thuselapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2417name=thuselapsed=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=2632name=byelapsed=0.023 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5154name=obtainelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3110name=haveelapsed=0.047 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=3243name=haveelapsed=0.046 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=3439name=haveelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5310name=henceelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3795name=haveelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5416name=haveelapsed=0.046 ML_statistics = :now=1464825535.26tasks_ready=54tasks_pending=1tasks_running=4tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4052267008size_allocation_free=2301633904size_heap=4139053056size_heap_free_last_full_GC=0size_heap_free_last_GC=4054014184threads_in_ML=5threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=42time_GC=1user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 command_timing = 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:file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5844name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4479name=obtainelapsed=0.047 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5978name=ultimatelyelapsed=0.043 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4479name=obtainelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5989name=showelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4553name=letelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=2318name=byelapsed=0.017 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=4585name=haveelapsed=0.045 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5046name=byelapsed=0.047 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=4672name=haveelapsed=0.046 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=3299name=byelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5163name=recordelapsed=0.792 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5022name=haveelapsed=0.046 Proofs for inductive predicate(s) "support_flowp" Proving monotonicity ... Proving the introduction rules ... Proving the elimination rules ... Proving the induction rule ... Proving the simplification rules ... ML_statistics = :now=1464825535.77tasks_ready=65tasks_pending=1tasks_running=5tasks_passive=0tasks_urgent=0workers_total=8workers_active=4workers_waiting=0full_GCs=0partial_GCs=4size_allocation=4052267008size_allocation_free=1445276320size_heap=4139053056size_heap_free_last_full_GC=0size_heap_free_last_GC=4054014184threads_in_ML=4threads_total=11threads_wait_condvar=4threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=44.004time_GC=1user_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=5088name=finallyelapsed=0.044 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5303name=inductive_setelapsed=0.082 command_timing = :file=~~/afp/thys/MFMC_Countable/Max_Flow_Min_Cut_Countable.thyoffset=5096name=showelapsed=0.046 ### theory "Max_Flow_Min_Cut_Countable" ### 2.566s elapsed time, 11.072s cpu time, 0.332s GC time command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5288name=byelapsed=0.182 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=0.123 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=6014name=byelapsed=0.107 command_timing = :file=~~/afp/thys/MFMC_Countable/MFMC_Misc.thyoffset=5960name=byelapsed=0.243 ML_statistics = :now=1464825536.39tasks_ready=0tasks_pending=0tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3983540224size_allocation_free=3983540224size_heap=4158976000size_heap_free_last_full_GC=0size_heap_free_last_GC=3984528160threads_in_ML=1threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=46.6time_GC=1.116user_counter0=0user_counter1=0user_counter2=0user_counter3=0user_counter4=0user_counter5=0user_counter6=0user_counter7=0 ML_statistics = :now=1464825536.89tasks_ready=0tasks_pending=0tasks_running=1tasks_passive=0tasks_urgent=0workers_total=8workers_active=1workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3983540224size_allocation_free=3447089144size_heap=4158976000size_heap_free_last_full_GC=0size_heap_free_last_GC=3984528160threads_in_ML=2threads_total=11threads_wait_condvar=7threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=47.392time_GC=1.116user_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=3.241 ML_statistics = :now=1464825537.4tasks_ready=0tasks_pending=0tasks_running=0tasks_passive=0tasks_urgent=0workers_total=8workers_active=0workers_waiting=0full_GCs=0partial_GCs=5size_allocation=3983540224size_allocation_free=2968245680size_heap=4158976000size_heap_free_last_full_GC=0size_heap_free_last_GC=3984528160threads_in_ML=1threads_total=11threads_wait_condvar=8threads_wait_IO=0threads_wait_mutex=0threads_wait_signal=1time_CPU=48.152time_GC=1.116user_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 ]$$]$[] [10] Overfull \hbox (128.17523pt too wide) in paragraph at lines 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:$\OT1/cmr/m/it/10 fixp[]preser ves[]mono1$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2292--2294 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono2 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono2$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 2294--2296 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 fixp[]preserves[]mono3 $\OT1/cmr/m /n/10 =$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 fixp[]preser ves[]mono3$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/i t/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Overfull \hbox (31.55771pt too wide) in paragraph at lines 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[$\OT1/cmr/m/it/10 cont[]intro$\OM L/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 simp$\OT1/cmr/m/n/10 ]$ $=$ \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 compact[]bot$\OT1/cmr/m/n/10 [$\OT1/cm r/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 ccpo$\OT1/cm r/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]axioms$\OT1/cmr/ m/n/10 ]$$]$[] [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. (./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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(./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 =$$)$ \OT1/cmr/m/it/10 Complete[]Partial[]Order$\OML/ cmm/m/it/10 :$\OT1/cmr/m/it/10 chain [2] [3] [4] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 1024. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 1024. 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[5] [6] [7] [8] [9] Overfull \hbox (15.65846pt too wide) in paragraph at lines 2018--2019 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mono[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/i t/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded case []prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ Overfull \hbox (17.9584pt too wide) in paragraph at lines 2030--2031 [][] \OT1/cmr/m/it/10 fixp[]preserves[]mcont[]uc$\OT1/cmr/m/n/10 [$\OT1/cmr/m/ it/10 of case[]prod [] curry$\OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 un-folded cas e[]prod[]curry curry[]case[]prod$\OML/cmm/m/it/10 ;$ [10] Overfull \hbox (1.96896pt too wide) in paragraph at lines 2262--2263 [][] \OT1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 cont[]const$\OT 1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cm r/m/it/10 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definit ions[]axioms$\OT1/cmr/m/n/10 ]$$]$[] Overfull \hbox (128.17523pt too wide) in paragraph at lines 2285--2287 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont$ [] $ $\OT1/cmr/m/n/10 =$ \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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(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty)) (./root.aux) (/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] ) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty)) (./root.out) (./root.out) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) (/usr/share/texlive/texmf-dist/tex/latex/stmaryrd/Ustmry.fd) (./root.toc) (./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] [3] [4] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\sfcode' on input line 1024. 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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. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) (/usr/share/texlive/texmf-dist/tex/latex/stmaryrd/stmaryrd.sty) (./pdfsetup.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg) (/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty) (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty)))) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty (/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty)) (/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty) (/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def) (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg) Package hyperref Warning: Option `pagecolor' is not available anymore. (/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 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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. 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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 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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$\OML/cmm/m 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4351--4357 [][]\OT1/cmr/bx/n/10 declaration []\OT1/cmr/m/it/10 Partial[]Function$\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 ]$$]$[] Overfull \hbox (122.56412pt too wide) in paragraph at lines 2287--2289 [][]\OT1/cmr/bx/n/10 lemmas \OT1/cmr/m/it/10 mcont2mcont $\OT1/cmr/m/n/10 =$ \O T1/cmr/m/it/10 ccpo$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/10 mcont2mcont$\OT1/cmr/m/ n/10 [$\OT1/cmr/m/it/10 OF Partial[]Function$\OML/cmm/m/it/10 :$\OT1/cmr/m/it/1 0 ccpo$\OT1/cmr/m/n/10 [$\OT1/cmr/m/it/10 OF partial[]function[]definitions[]ax ioms$\OT1/cmr/m/n/10 ]$$]$[] 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) ) (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")