0.09/0.15 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.16 % Command : /export/starexec/sandbox2/solver/bin/run_iprover 120 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT 0.16/0.38 % Computer : n019.cluster.edu 0.16/0.38 % Model : x86_64 x86_64 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.38 % Memory : 8042.1875MB 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.38 % CPULimit : 960 0.16/0.38 % WCLimit : 120 0.16/0.38 % DateTime : Wed Jul 30 06:14:19 EDT 2025 0.16/0.38 % CPUTime : 0.24/0.53 /export/starexec/sandbox2/solver/bin/SPCForProblem: Command not found. 0.24/0.53 Running model finding 0.24/0.53 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core-casc.sh -l tptp -s fnt_schedule -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.24/0.54 0.24/0.54 % ======== iProver multi-core TPTP/SMT ========= 0.24/0.54 0.24/0.54 % Detected problem language: tptp 0.24/0.55 % Checking... 0.65/1.28 % Proving... 4.25/1.98 % SZS status Started for theBenchmark.p 4.25/1.98 % SZS status Satisfiable for theBenchmark.p 4.25/1.98 4.25/1.98 %---------------- iProver v3.9.3 (pre CASC 2025/SMT-COMP 2025) ----------------% 4.25/1.98 4.25/1.98 ------ iProver source info 4.25/1.98 4.25/1.98 git: date: 2025-07-21 10:15:00 +0000 4.25/1.98 git: sha1: d7ebeb21b290b8724a1e08b4c4a533d26e8c009f 4.25/1.98 git: non_committed_changes: true 4.25/1.98 4.25/1.98 ------ Parsing... 4.25/1.98 ------ Clausification by vclausify_rel & Parsing by iProver... 4.25/1.98 ------ Proving... 4.25/1.98 ------ Problem Properties 4.25/1.98 4.25/1.98 4.25/1.98 clauses 1048 4.25/1.98 conjectures 0 4.25/1.98 EPR 100 4.25/1.98 Horn 885 4.25/1.98 unary 104 4.25/1.98 binary 526 4.25/1.98 lits 3016 4.25/1.98 lits eq 776 4.25/1.98 fd_pure 0 4.25/1.98 fd_pseudo 0 4.25/1.98 fd_cond 0 4.25/1.98 fd_pseudo_cond 71 4.25/1.98 AC symbols 0 4.25/1.98 4.25/1.98 ------ Input Options Time Limit: Unbounded 4.25/1.98 4.25/1.98 4.25/1.98 ------ Finite Models: 4.25/1.98 4.25/1.98 ------ lit_activity_flag true 4.25/1.98 4.25/1.98 4.25/1.98 ------ Trying domains of size >= : 1 4.25/1.98 ------ 4.25/1.98 Current options: 4.25/1.98 ------ 4.25/1.98 4.25/1.98 ------ Input Options 4.25/1.98 4.25/1.98 --out_options all 4.25/1.98 --tptp_safe_out true 4.25/1.98 --problem_path "" 4.25/1.98 --include_path "" 4.25/1.98 --clausifier res/vclausify_rel 4.25/1.98 --clausifier_options --mode tclausify -t 41.66 --show_fool true -updr off 4.25/1.98 --stdin false 4.25/1.98 --proof_out true 4.25/1.98 --proof_dot_file "" 4.25/1.98 --proof_reduce_dot [] 4.25/1.98 --suppress_sat_res false 4.25/1.98 --suppress_unsat_res true 4.25/1.98 --stats_out none 4.25/1.98 --stats_mem false 4.25/1.98 --theory_stats_out false 4.25/1.98 4.25/1.98 ------ General Options 4.25/1.98 4.25/1.98 --fof false 4.25/1.98 --time_out_real 124.99 4.25/1.98 --time_out_virtual -1. 4.25/1.98 --rnd_seed 13 4.25/1.98 --symbol_type_check false 4.25/1.98 --clausify_out false 4.25/1.98 --sig_cnt_out false 4.25/1.98 --trig_cnt_out false 4.25/1.98 --trig_cnt_out_tolerance 1. 4.25/1.98 --trig_cnt_out_sk_spl false 4.25/1.98 --abstr_cl_out false 4.25/1.98 4.25/1.98 ------ Interactive Mode 4.25/1.98 4.25/1.98 --interactive_mode false 4.25/1.98 --external_ip_address "" 4.25/1.98 --external_port 0 4.25/1.98 4.25/1.98 ------ Global Options 4.25/1.98 4.25/1.98 --schedule none 4.25/1.98 --add_important_lit false 4.25/1.98 --prop_solver_per_cl 500 4.25/1.98 --subs_bck_mult 8 4.25/1.98 --min_unsat_core false 4.25/1.98 --soft_assumptions false 4.25/1.98 --soft_lemma_size 3 4.25/1.98 --prop_impl_unit_size 0 4.25/1.98 --prop_impl_unit [] 4.25/1.98 --share_sel_clauses true 4.25/1.98 --reset_solvers false 4.25/1.98 --bc_imp_inh [conj_cone] 4.25/1.98 --conj_cone_tolerance 3. 4.25/1.98 --extra_neg_conj none 4.25/1.98 --large_theory_mode true 4.25/1.98 --prolific_symb_bound 200 4.25/1.98 --lt_threshold 2000 4.25/1.98 --clause_weak_htbl true 4.25/1.98 --gc_record_bc_elim false 4.25/1.98 4.25/1.98 ------ Preprocessing Options 4.25/1.98 4.25/1.98 --preprocessing_flag false 4.25/1.98 --time_out_prep_mult 0.1 4.25/1.98 --splitting_mode input 4.25/1.98 --splitting_grd true 4.25/1.98 --splitting_cvd false 4.25/1.98 --splitting_cvd_svl false 4.25/1.98 --splitting_nvd 32 4.25/1.98 --sub_typing false 4.25/1.98 --prep_eq_flat_conj false 4.25/1.98 --prep_eq_flat_all_gr false 4.25/1.98 --prep_gs_sim true 4.25/1.98 --prep_unflatten true 4.25/1.98 --prep_res_sim true 4.25/1.98 --prep_sup_sim_all true 4.25/1.98 --prep_sup_sim_sup false 4.25/1.98 --prep_upred true 4.25/1.98 --prep_well_definedness true 4.25/1.98 --prep_sem_filter exhaustive 4.25/1.98 --prep_sem_filter_out false 4.25/1.98 --pred_elim true 4.25/1.98 --res_sim_input true 4.25/1.98 --eq_ax_congr_red true 4.25/1.98 --pure_diseq_elim true 4.25/1.98 --brand_transform false 4.25/1.98 --non_eq_to_eq false 4.25/1.98 --prep_def_merge true 4.25/1.98 --prep_def_merge_prop_impl false 4.25/1.98 --prep_def_merge_mbd true 4.25/1.98 --prep_def_merge_tr_red false 4.25/1.98 --prep_def_merge_tr_cl false 4.25/1.98 --smt_preprocessing false 4.25/1.98 --smt_ac_axioms fast 4.25/1.98 --preprocessed_out false 4.25/1.98 --preprocessed_stats false 4.25/1.98 4.25/1.98 ------ Abstraction refinement Options 4.25/1.98 4.25/1.98 --abstr_ref [] 4.25/1.98 --abstr_ref_prep false 4.25/1.98 --abstr_ref_until_sat false 4.25/1.98 --abstr_ref_sig_restrict funpre 4.25/1.98 --abstr_ref_af_restrict_to_split_sk false 4.25/1.98 --abstr_ref_under [] 4.25/1.98 4.25/1.98 ------ SAT Options 4.25/1.98 4.25/1.98 --sat_mode true 4.25/1.98 --sat_fm_restart_options "" 4.25/1.98 --sat_gr_def false 4.25/1.98 --sat_epr_types true 4.25/1.98 --sat_non_cyclic_types false 4.25/1.98 --sat_finite_models true 4.25/1.98 --sat_fm_lemmas false 4.25/1.98 --sat_fm_prep false 4.25/1.98 --sat_fm_uc_incr true 4.25/1.98 --sat_out_model pos 4.25/1.98 --sat_out_clauses false 4.25/1.98 4.25/1.98 ------ QBF Options 4.25/1.98 4.25/1.98 --qbf_mode false 4.25/1.98 --qbf_elim_univ false 4.25/1.98 --qbf_dom_inst none 4.25/1.98 --qbf_dom_pre_inst false 4.25/1.98 --qbf_sk_in false 4.25/1.98 --qbf_pred_elim true 4.25/1.98 --qbf_split 512 4.25/1.98 4.25/1.98 ------ BMC1 Options 4.25/1.98 4.25/1.98 --bmc1_incremental false 4.25/1.98 --bmc1_axioms reachable_all 4.25/1.98 --bmc1_min_bound 0 4.25/1.98 --bmc1_max_bound -1 4.25/1.98 --bmc1_max_bound_default -1 4.25/1.98 --bmc1_symbol_reachability true 4.25/1.98 --bmc1_property_lemmas false 4.25/1.98 --bmc1_k_induction false 4.25/1.98 --bmc1_non_equiv_states false 4.25/1.98 --bmc1_deadlock false 4.25/1.98 --bmc1_ucm false 4.25/1.98 --bmc1_add_unsat_core none 4.25/1.98 --bmc1_unsat_core_children false 4.25/1.98 --bmc1_unsat_core_extrapolate_axioms false 4.25/1.98 --bmc1_out_stat full 4.25/1.98 --bmc1_ground_init false 4.25/1.98 --bmc1_pre_inst_next_state false 4.25/1.98 --bmc1_pre_inst_state false 4.25/1.98 --bmc1_pre_inst_reach_state false 4.25/1.98 --bmc1_out_unsat_core false 4.25/1.98 --bmc1_aig_witness_out false 4.25/1.98 --bmc1_verbose false 4.25/1.98 --bmc1_dump_clauses_tptp false 4.25/1.98 --bmc1_dump_unsat_core_tptp false 4.25/1.98 --bmc1_dump_file - 4.25/1.98 --bmc1_ucm_expand_uc_limit 128 4.25/1.98 --bmc1_ucm_n_expand_iterations 6 4.25/1.98 --bmc1_ucm_extend_mode 1 4.25/1.98 --bmc1_ucm_init_mode 2 4.25/1.98 --bmc1_ucm_cone_mode none 4.25/1.98 --bmc1_ucm_reduced_relation_type 0 4.25/1.98 --bmc1_ucm_relax_model 4 4.25/1.98 --bmc1_ucm_full_tr_after_sat true 4.25/1.98 --bmc1_ucm_expand_neg_assumptions false 4.25/1.98 --bmc1_ucm_layered_model none 4.25/1.98 --bmc1_ucm_max_lemma_size 10 4.25/1.98 4.25/1.98 ------ AIG Options 4.25/1.98 4.25/1.98 --aig_mode false 4.25/1.98 4.25/1.98 ------ Instantiation Options 4.25/1.98 4.25/1.98 --instantiation_flag true 4.25/1.98 --inst_sos_flag false 4.25/1.98 --inst_sos_phase true 4.25/1.98 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb] 4.25/1.98 --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb] 4.25/1.98 --inst_lit_sel_side num_symb 4.25/1.98 --inst_solver_per_active 1400 4.25/1.98 --inst_solver_calls_frac 1. 4.25/1.98 --inst_to_smt_solver true 4.25/1.98 --inst_passive_queue_type priority_queues 4.25/1.98 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]] 4.25/1.98 --inst_passive_queues_freq [25;2] 4.25/1.98 --inst_dismatching true 4.25/1.98 --inst_eager_unprocessed_to_passive true 4.25/1.98 --inst_unprocessed_bound 1000 4.25/1.98 --inst_prop_sim_given true 4.25/1.98 --inst_prop_sim_new false 4.25/1.98 --inst_subs_new false 4.25/1.98 --inst_eq_res_simp false 4.25/1.98 --inst_subs_given false 4.25/1.98 --inst_orphan_elimination true 4.25/1.98 --inst_learning_loop_flag true 4.25/1.98 --inst_learning_start 3000 4.25/1.98 --inst_learning_factor 2 4.25/1.98 --inst_start_prop_sim_after_learn 3 4.25/1.98 --inst_sel_renew solver 4.25/1.98 --inst_lit_activity_flag true 4.25/1.98 --inst_restr_to_given false 4.25/1.98 --inst_activity_threshold 500 4.25/1.98 4.25/1.98 ------ Resolution Options 4.25/1.98 4.25/1.98 --resolution_flag false 4.25/1.98 --res_lit_sel adaptive 4.25/1.98 --res_lit_sel_side none 4.25/1.98 --res_ordering kbo 4.25/1.98 --res_to_prop_solver active 4.25/1.98 --res_prop_simpl_new false 4.25/1.98 --res_prop_simpl_given true 4.25/1.98 --res_to_smt_solver true 4.25/1.98 --res_passive_queue_type priority_queues 4.25/1.98 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]] 4.25/1.98 --res_passive_queues_freq [15;5] 4.25/1.98 --res_forward_subs full 4.25/1.98 --res_backward_subs full 4.25/1.98 --res_forward_subs_resolution true 4.25/1.98 --res_backward_subs_resolution true 4.25/1.98 --res_orphan_elimination true 4.25/1.98 --res_time_limit 300. 4.25/1.98 4.25/1.98 ------ Superposition Options 4.25/1.98 4.25/1.98 --superposition_flag false 4.25/1.98 --sup_passive_queue_type priority_queues 4.25/1.98 --sup_passive_queues [[-conj_dist;-num_symb];[+score;+min_def_symb;-max_atom_input_occur;+conj_non_prolific_symb];[+age;-num_symb];[+score;-num_symb]] 4.25/1.98 --sup_passive_queues_freq [8;1;4;4] 4.25/1.98 --demod_completeness_check fast 4.25/1.98 --demod_use_ground true 4.25/1.98 --sup_unprocessed_bound 0 4.25/1.98 --sup_to_prop_solver passive 4.25/1.98 --sup_prop_simpl_new true 4.25/1.98 --sup_prop_simpl_given true 4.25/1.98 --sup_fun_splitting false 4.25/1.98 --sup_iter_deepening 2 4.25/1.98 --sup_restarts_mult 12 4.25/1.98 --sup_score sim_d_gen 4.25/1.98 --sup_share_score_frac 0.2 4.25/1.98 --sup_share_max_num_cl 500 4.25/1.98 --sup_ordering kbo 4.25/1.98 --sup_symb_ordering invfreq 4.25/1.98 --sup_term_weight default 4.25/1.98 4.25/1.98 ------ Superposition Simplification Setup 4.25/1.98 4.25/1.98 --sup_indices_passive [LightNormIndex;FwDemodIndex] 4.25/1.98 --sup_full_triv [SMTSimplify;PropSubs] 4.25/1.98 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] 4.25/1.98 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.25/1.98 --sup_immed_triv [] 4.25/1.98 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes] 4.25/1.98 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes] 4.25/1.98 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod] 4.25/1.98 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.25/1.98 --sup_input_triv [Unflattening;SMTSimplify] 4.25/1.98 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] 4.25/1.98 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.25/1.98 --sup_full_fixpoint true 4.25/1.98 --sup_main_fixpoint true 4.25/1.98 --sup_immed_fixpoint false 4.25/1.98 --sup_input_fixpoint true 4.25/1.98 --sup_cache_sim none 4.25/1.98 --sup_smt_interval 500 4.25/1.98 --sup_bw_gjoin_interval 0 4.25/1.98 4.25/1.98 ------ Combination Options 4.25/1.98 4.25/1.98 --comb_mode clause_based 4.25/1.98 --comb_inst_mult 5 4.25/1.98 --comb_res_mult 1 4.25/1.98 --comb_sup_mult 8 4.25/1.98 --comb_sup_deep_mult 2 4.25/1.98 4.25/1.98 ------ Debug Options 4.25/1.98 4.25/1.98 --dbg_backtrace false 4.25/1.98 --dbg_dump_prop_clauses false 4.25/1.98 --dbg_dump_prop_clauses_file - 4.25/1.98 --dbg_out_stat false 4.25/1.98 --dbg_just_parse false 4.25/1.98 4.25/1.98 4.25/1.98 4.25/1.98 4.25/1.98 ------ Proving... 4.25/1.98 4.25/1.98 4.25/1.98 % SZS status Satisfiable for theBenchmark.p 4.25/1.98 4.25/1.98 ------ Building Model...Done 4.25/1.98 4.25/1.98 %------ The model is defined over ground terms (initial term algebra). 4.25/1.98 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 4.25/1.98 %------ where \phi is a formula over the term algebra. 4.25/1.98 %------ If we have equality in the problem then it is also defined as a predicate above, 4.25/1.98 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type 4.25/1.98 %------ See help for --sat_out_model for different model outputs. 4.25/1.98 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" 4.25/1.98 %------ where the first argument stands for the sort ($i in the unsorted case) 4.25/1.98 % SZS output start Model for theBenchmark.p 4.25/1.98 4.25/1.98 %------ Positive definition of equality_sorted 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_tType,X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set'] : 4.25/1.98 ( equality_sorted(X0_tType,X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_ZF_fun_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_b_b_c_LSCategory_ext_Category_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_fun$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_unit_Category_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_a_fun_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_prod_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='Unit$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_ZF_fun_fun$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_b_prod_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_b_prod$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_fun$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='Unit_unit_unit_Category_ext$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='B_ZF_fun$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_b_fun_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='ZF_ZF_prod$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_fun_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 | 4.25/1.98 ( 4.25/1.98 ( X0_tType='A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$j' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_fun_set'] : 4.25/1.98 ( 'member$j'(X0_'ZF_ZF_fun',X0_'ZF_ZF_fun_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_ZF_fun_bool_fun',X0_'B_ZF_fun'] : 4.25/1.98 ( 'fun_app$e'(X0_'B_ZF_fun_bool_fun',X0_'B_ZF_fun') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'extCategory$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( 'extCategory$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_comp_def$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor_comp_def$c'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'lSCategory$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( 'lSCategory$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( 'fun_app$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_fun',X0_'A_ZF_fun_set'] : 4.25/1.98 ( 'member$f'(X0_'A_ZF_fun',X0_'A_ZF_fun_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_comp_def$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor_comp_def$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$f'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$q' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'fun_app$q'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_prod'] : 4.25/1.98 ( 'fun_app$b'(X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_prod') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( 'category$a'(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_comp_def$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor_comp_def$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.98 ( 'category$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functorM_axioms$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functorM_axioms$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functorExt$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functorExt$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( 'category$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'nTCompDefined$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'nTCompDefined$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$m' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_prod_ZF_fun_set'] : 4.25/1.98 ( 'member$m'(X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_prod_ZF_fun_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTrans$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTrans$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_bool_fun',X0_'ZF'] : 4.25/1.98 ( 'fun_app$d'(X0_'ZF_bool_fun',X0_'ZF') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$e'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF',X0_'ZF_set'] : 4.25/1.98 ( 'member$c'(X0_'ZF',X0_'ZF_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$g' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_fun',X0_'A_b_fun_set'] : 4.25/1.98 ( 'member$g'(X0_'A_b_fun',X0_'A_b_fun_set') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'compDefined$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit_unit_unit_Category_ext',X0_'Unit',X1_'Unit'] : 4.25/1.98 ( 'compDefined$c'(X0_'Unit_unit_unit_Category_ext',X0_'Unit',X1_'Unit') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$b'(X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_comp_def$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor_comp_def$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.98 ( 'functor$d'(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor$f'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category_axioms$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.98 ( 'category_axioms$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'lSCategory_axioms$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( 'lSCategory_axioms$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_a_fun',X0_'B_a_fun_set'] : 4.25/1.98 ( 'member$e'(X0_'B_a_fun',X0_'B_a_fun_set') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'nTCompDefined$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'nTCompDefined$e'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_b_prod_bool_fun',X0_'B_b_prod'] : 4.25/1.98 ( 'fun_app$c'(X0_'B_b_prod_bool_fun',X0_'B_b_prod') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTrans$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTrans$e'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_abbrev$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( 'functor_abbrev$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$g' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_fun_bool_fun',X0_'A_ZF_fun'] : 4.25/1.98 ( 'fun_app$g'(X0_'A_ZF_fun_bool_fun',X0_'A_ZF_fun') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'extCategory$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( 'extCategory$a'(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category_axioms$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( 'category_axioms$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_abbrev$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( 'functor_abbrev$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransExt$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransExt$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functorM$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functorM$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$d'(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTrans$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTrans$b'(X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'mapsTo$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit_unit_unit_Category_ext',X0_'Unit',X1_'Unit',X2_'Unit'] : 4.25/1.98 ( 'mapsTo$c'(X0_'Unit_unit_unit_Category_ext',X0_'Unit',X1_'Unit',X2_'Unit') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$j' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_bool_fun',X0_'A'] : 4.25/1.98 ( 'fun_app$j'(X0_'A_bool_fun',X0_'A') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'compDefined$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'compDefined$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor_abbrev$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X0_'Unit_unit_unit_Category_ext'] : 4.25/1.98 ( 'functor_abbrev$a'(X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X0_'Unit_unit_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor$e'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$h' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'B_set'] : 4.25/1.98 ( 'member$h'(X0_'B',X0_'B_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod',X0_'ZF_ZF_prod_set'] : 4.25/1.98 ( 'member$a'(X0_'ZF_ZF_prod',X0_'ZF_ZF_prod_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$i' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A',X0_'A_set'] : 4.25/1.98 ( 'member$i'(X0_'A',X0_'A_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTrans$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTrans$f'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'nTCompDefined$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'nTCompDefined$c'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$c'(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_a_fun_bool_fun',X0_'B_a_fun'] : 4.25/1.98 ( 'fun_app$f'(X0_'B_a_fun_bool_fun',X0_'B_a_fun') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'category_axioms$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( 'category_axioms$a'(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'preFunctor$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'preFunctor$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_b_prod',X0_'B_b_prod_set'] : 4.25/1.98 ( 'member$b'(X0_'B_b_prod',X0_'B_b_prod_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$i' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_bool_fun',X0_'B'] : 4.25/1.98 ( 'fun_app$i'(X0_'B_bool_fun',X0_'B') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set'] : 4.25/1.98 ( 'member$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'mapsTo$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'mapsTo$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'fun_app$h' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_fun_bool_fun',X0_'A_b_fun'] : 4.25/1.98 ( 'fun_app$h'(X0_'A_b_fun_bool_fun',X0_'A_b_fun') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$k' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit',X0_'Unit_set'] : 4.25/1.98 ( 'member$k'(X0_'Unit',X0_'Unit_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'natTransP$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( 'natTransP$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'nt_abbrev$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'nt_abbrev$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_ZF_fun',X0_'B_ZF_fun_set'] : 4.25/1.98 ( 'member$d'(X0_'B_ZF_fun',X0_'B_ZF_fun_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( 'functor$a'(X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'functor$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.98 ( 'functor$c'(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of 'member$o' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_set',X0_'ZF_set_set'] : 4.25/1.98 ( 'member$o'(X0_'ZF_set',X0_'ZF_set_set') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP0 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( sP0(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP1 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( sP1(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP2 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( sP2(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP3 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( sP3(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP4 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP4(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP5 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP5(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP6 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP6(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP7 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP7(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP8 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP8(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP9 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( sP9(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP10 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP10(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP11 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP11(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP12 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( sP12(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP13 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP13(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP14 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP14(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP15 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP15(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP16 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP16(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP17 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP17(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP18 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP18(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP19 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP19(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP20 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( sP20(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP21 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( sP21(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP22 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( sP22(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP23 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( sP23(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP24 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( sP24(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 $false 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP25 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP25(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP26 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP26(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP27 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP27(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP28 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP28(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP29 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( sP29(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of sP30 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( sP30(X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 $true 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'functorComp$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'functorComp$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'collect$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_ZF_fun_set',X0_'B_ZF_fun_bool_fun'] : 4.25/1.98 ( iProver_Flat_'collect$e'(X0_'B_ZF_fun_set',X0_'B_ZF_fun_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_ZF_fun_set'=iProver_Domain_'B_ZF_fun_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'more_update$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'Unit_unit_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'more_update$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'Unit_unit_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'id$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'id$'(X0_'A_b_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_fun'=iProver_Domain_'A_b_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'makeCat$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'] : 4.25/1.98 ( iProver_Flat_'makeCat$a'(X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'restrict$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_fun',X1_'A_ZF_fun',X0_'A_set'] : 4.25/1.98 ( iProver_Flat_'restrict$c'(X0_'A_ZF_fun',X1_'A_ZF_fun',X0_'A_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'functorComp$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'functorComp$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catDom$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'catDom$a'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'extensional$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_a_fun_set',X0_'B_set'] : 4.25/1.98 ( iProver_Flat_'extensional$c'(X0_'B_a_fun_set',X0_'B_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_a_fun_set'=iProver_Domain_'B_a_fun_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uun$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'uun$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'c$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'c$'(X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'collect$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_set',X0_'ZF_ZF_prod_bool_fun'] : 4.25/1.98 ( iProver_Flat_'collect$'(X0_'ZF_ZF_prod_set',X0_'ZF_ZF_prod_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_prod_set'=iProver_Domain_'ZF_ZF_prod_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mor_update$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X0_'B_set_b_set_fun'] : 4.25/1.98 ( iProver_Flat_'mor_update$a'(X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X0_'B_set_b_set_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uum$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B'] : 4.25/1.98 ( iProver_Flat_'uum$'(X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCod$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCod$c'(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'=iProver_Domain_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uuq$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A'] : 4.25/1.98 ( iProver_Flat_'uuq$'(X0_'ZF_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nt_abbrev$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'nt_abbrev$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$s' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'fun_app$s'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'more$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'more$b'(X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'unitFunctor$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'unitFunctor$'(X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransMap$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_fun',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'natTransMap$d'(X0_'A_b_fun',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_fun'=iProver_Domain_'A_b_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTrans_ext$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_fun',X0_'Unit'] : 4.25/1.98 ( iProver_Flat_'natTrans_ext$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_fun',X0_'Unit') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'the$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'B_bool_fun'] : 4.25/1.98 ( iProver_Flat_'the$a'(X0_'B',X0_'B_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapsTo$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B',X0_'A'] : 4.25/1.98 ( iProver_Flat_'mapsTo$'(X0_'A_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B',X0_'A') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_bool_fun'=iProver_Domain_'A_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'obj$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_set',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'obj$a'(X0_'A_set',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_set'=iProver_Domain_'A_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uuz$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'uuz$'(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'case_prod$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_ZF_fun_fun'] : 4.25/1.98 ( iProver_Flat_'case_prod$'(X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_ZF_fun_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_prod_ZF_fun'=iProver_Domain_'ZF_ZF_prod_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catCod$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'catCod$d'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catDom$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'catDom$c'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTrans$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'] : 4.25/1.98 ( iProver_Flat_'natTrans$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$n' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF',X0_'A_ZF_fun',X0_'A'] : 4.25/1.98 ( iProver_Flat_'fun_app$n'(X0_'ZF',X0_'A_ZF_fun',X0_'A') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uua$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_bool_fun',X0_'ZF_set'] : 4.25/1.98 ( iProver_Flat_'uua$'(X0_'ZF_bool_fun',X0_'ZF_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uup$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'uup$'(X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'extensional$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_ZF_fun_set',X0_'ZF_ZF_prod_set'] : 4.25/1.98 ( iProver_Flat_'extensional$d'(X0_'ZF_ZF_prod_ZF_fun_set',X0_'ZF_ZF_prod_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_prod_ZF_fun_set'=iProver_Domain_'ZF_ZF_prod_ZF_fun_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'obj_update$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_set_ZF_set_fun'] : 4.25/1.98 ( iProver_Flat_'obj_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_set_ZF_set_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catDom_update$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'] : 4.25/1.98 ( iProver_Flat_'catDom_update$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catCod$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'catCod$'(X0_'ZF_ZF_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCatDom$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCatDom$f'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'top$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_set'] : 4.25/1.98 ( iProver_Flat_'top$'(X0_'ZF_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'restrict$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'B_b_prod_b_fun',X0_'B_b_prod_set',X0_'B_b_prod'] : 4.25/1.98 ( iProver_Flat_'restrict$a'(X0_'B',X0_'B_b_prod_b_fun',X0_'B_b_prod_set',X0_'B_b_prod') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapM$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'mapM$a'(X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catExp$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'catExp$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'more$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'C',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'more$c'(X0_'C',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'C'=iProver_Domain_'C'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'oppositeCategory$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'] : 4.25/1.98 ( iProver_Flat_'oppositeCategory$'(X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$r' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'fun_app$r'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTDom$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTDom$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapO$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'mapO$b'(X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'f$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B'] : 4.25/1.98 ( iProver_Flat_'f$'(X0_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransComp$g' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X2_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'natTransComp$g'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X2_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCompDefined$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCompDefined$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uus$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'uus$'(X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_bool_fun'=iProver_Domain_'B_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uud$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_a_fun_bool_fun',X0_'B_a_fun_set'] : 4.25/1.98 ( iProver_Flat_'uud$'(X0_'B_a_fun_bool_fun',X0_'B_a_fun_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_a_fun_bool_fun'=iProver_Domain_'B_a_fun_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransComp$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X1_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X2_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'natTransComp$d'(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X1_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X2_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'=iProver_Domain_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$ab' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A',X0_'B_a_fun',X0_'B'] : 4.25/1.98 ( iProver_Flat_'fun_app$ab'(X0_'A',X0_'B_a_fun',X0_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCatDom$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCatDom$d'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapO$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A'] : 4.25/1.98 ( iProver_Flat_'mapO$f'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'collect$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_b_prod_set',X0_'B_b_prod_bool_fun'] : 4.25/1.98 ( iProver_Flat_'collect$a'(X0_'B_b_prod_set',X0_'B_b_prod_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_b_prod_set'=iProver_Domain_'B_b_prod_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCod$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCod$e'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mor$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit_set',X0_'Unit_unit_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'mor$c'(X0_'Unit_set',X0_'Unit_unit_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit_set'=iProver_Domain_'Unit_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'pair$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_b_prod',X0_'B',X1_'B'] : 4.25/1.98 ( iProver_Flat_'pair$a'(X0_'B_b_prod',X0_'B',X1_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_b_prod'=iProver_Domain_'B_b_prod'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'equivalence_axioms$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.98 ( iProver_Flat_'equivalence_axioms$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'dom_update$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.98 ( iProver_Flat_'dom_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$u' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'fun_app$u'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uuk$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'uuk$'(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uut$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_bool_fun'] : 4.25/1.98 ( iProver_Flat_'uut$'(X0_'ZF_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'comp_update$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun'] : 4.25/1.98 ( iProver_Flat_'comp_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'case_prod$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_b_prod_b_fun',X0_'B_b_b_fun_fun'] : 4.25/1.98 ( iProver_Flat_'case_prod$a'(X0_'B_b_prod_b_fun',X0_'B_b_b_fun_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_b_prod_b_fun'=iProver_Domain_'B_b_prod_b_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'functorM$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.98 ( iProver_Flat_'functorM$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCatDom$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCatDom$b'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransComp$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'natTransComp$f'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uu$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_bool_fun',X0_'B_set'] : 4.25/1.98 ( iProver_Flat_'uu$'(X0_'B_bool_fun',X0_'B_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_bool_fun'=iProver_Domain_'B_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'set$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'set$'(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCatCod$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCatCod$d'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapM$d' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X1_'B'] : 4.25/1.98 ( iProver_Flat_'mapM$d'(X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X1_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'unity$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit'] : 4.25/1.98 ( iProver_Flat_'unity$'(X0_'Unit') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uuo$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'uuo$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uur$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'uur$'(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$z' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'fun_app$z'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'oppositeCategory$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'] : 4.25/1.98 ( iProver_Flat_'oppositeCategory$b'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTDom$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTDom$f'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'uuy$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.98 ( iProver_Flat_'uuy$'(X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_prod_bool_fun'=iProver_Domain_'ZF_ZF_prod_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransComp$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'natTransComp$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$l' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'B_b_fun',X1_'B'] : 4.25/1.98 ( iProver_Flat_'fun_app$l'(X0_'B',X0_'B_b_fun',X1_'B') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mor2ZF$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.98 ( iProver_Flat_'mor2ZF$'(X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_ZF_fun'=iProver_Domain_'B_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'idNatTrans$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'idNatTrans$b'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransMap$c' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'natTransMap$c'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catDom$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'catDom$'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'zFfun$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF',X1_'ZF',X2_'ZF',X0_'ZF_ZF_fun'] : 4.25/1.98 ( iProver_Flat_'zFfun$'(X0_'ZF',X1_'ZF',X2_'ZF',X0_'ZF_ZF_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'catDom_update$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'] : 4.25/1.98 ( iProver_Flat_'catDom_update$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'inverse_rel$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'inverse_rel$'(X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'extensional$b' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B_ZF_fun_set',X0_'B_set'] : 4.25/1.98 ( iProver_Flat_'extensional$b'(X0_'B_ZF_fun_set',X0_'B_set') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B_ZF_fun_set'=iProver_Domain_'B_ZF_fun_set'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$p' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'B',X0_'A_b_fun',X0_'A'] : 4.25/1.98 ( iProver_Flat_'fun_app$p'(X0_'B',X0_'A_b_fun',X0_'A') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'idNatTrans$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.98 ( iProver_Flat_'idNatTrans$'(X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'more$a' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'more$a'(X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'more$' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'Unit',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'more$'(X0_'Unit',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'nTCod$f' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.98 ( iProver_Flat_'nTCod$f'(X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'mapM$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.98 ( iProver_Flat_'mapM$e'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'fun_app$ac' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun'] : 4.25/1.98 ( iProver_Flat_'fun_app$ac'(X0_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun') <=> 4.25/1.98 ( 4.25/1.98 ( 4.25/1.98 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.98 ) 4.25/1.98 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ) 4.25/1.98 ). 4.25/1.98 4.25/1.98 %------ Positive definition of iProver_Flat_'natTransMap$e' 4.25/1.98 fof(lit_def,axiom, 4.25/1.98 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A'] : 4.25/1.98 ( iProver_Flat_'natTransMap$e'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'zFfunCod$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_'zFfunCod$'(X0_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransMap$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'natTransMap$b'(X0_'B',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$k' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_fun_fun',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'fun_app$k'(X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_fun_fun',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'homFtor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_'homFtor$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'category_ext$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_set',X0_'B_set',X0_'B_a_fun',X1_'B_a_fun',X0_'A_b_fun',X0_'B_b_b_fun_fun',X0_'B_c_LSCategory_ext'] : 4.25/1.99 ( iProver_Flat_'category_ext$'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_set',X0_'B_set',X0_'B_a_fun',X1_'B_a_fun',X0_'A_b_fun',X0_'B_b_b_fun_fun',X0_'B_c_LSCategory_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catDom$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catDom$b'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTDom$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTDom$e'(X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'more$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'more$e'(X0_'Unit',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catDom$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catDom$f'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'set$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'set$a'(X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'idNatTrans$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'idNatTrans$e'(X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTDom$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTDom$c'(X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'=iProver_Domain_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'compDefined$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'compDefined$'(X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'makeCat$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'makeCat$c'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'extensional$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_prod_b_fun_set',X0_'B_b_prod_set'] : 4.25/1.99 ( iProver_Flat_'extensional$f'(X0_'B_b_prod_b_fun_set',X0_'B_b_prod_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_prod_b_fun_set'=iProver_Domain_'B_b_prod_b_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'restrict$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_a_fun',X1_'B_a_fun',X0_'B_set'] : 4.25/1.99 ( iProver_Flat_'restrict$d'(X0_'B_a_fun',X1_'B_a_fun',X0_'B_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_a_fun'=iProver_Domain_'B_a_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapM$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'mapM$'(X0_'B_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_ZF_fun'=iProver_Domain_'B_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_set',X0_'A_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$d'(X0_'A_set',X0_'A_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_set'=iProver_Domain_'A_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'equivalence$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'equivalence$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTrans_ext$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_fun',X0_'Unit'] : 4.25/1.99 ( iProver_Flat_'natTrans_ext$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_fun',X0_'Unit') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catExp$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'catExp$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'dom$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'dom$b'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$m' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_fun',X0_'B_b_b_fun_fun',X0_'B'] : 4.25/1.99 ( iProver_Flat_'fun_app$m'(X0_'B_b_fun',X0_'B_b_b_fun_fun',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_fun'=iProver_Domain_'B_b_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCod_update$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCod_update$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catCod$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catCod$c'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'restrict$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_set'] : 4.25/1.99 ( iProver_Flat_'restrict$f'(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransMap$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'natTransMap$'(X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransMap$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'natTransMap$f'(X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'oppositeCategory$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'oppositeCategory$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'functor_ext$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext',X0_'B_ZF_fun',X0_'Unit'] : 4.25/1.99 ( iProver_Flat_'functor_ext$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext',X0_'B_ZF_fun',X0_'Unit') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCod$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCod$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'extensional$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_fun_set',X0_'A_set'] : 4.25/1.99 ( iProver_Flat_'extensional$e'(X0_'A_b_fun_set',X0_'A_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_fun_set'=iProver_Domain_'A_b_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_set',X0_'B_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$b'(X0_'B_set',X0_'B_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_set'=iProver_Domain_'B_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'cod$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'cod$b'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'zFfunComp$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_'zFfunComp$'(X0_'ZF_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'compDefined$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B'] : 4.25/1.99 ( iProver_Flat_'compDefined$a'(X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_bool_fun'=iProver_Domain_'B_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'inverse_rel$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B'] : 4.25/1.99 ( iProver_Flat_'inverse_rel$a'(X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_bool_fun'=iProver_Domain_'B_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'the$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_bool_fun'] : 4.25/1.99 ( iProver_Flat_'the$'(X0_'ZF',X0_'ZF_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatDom$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatDom$c'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catCod$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catCod$e'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catCod$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catCod$b'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'constFunctor$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'constFunctor$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuf$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_fun_bool_fun',X0_'A_b_fun_set'] : 4.25/1.99 ( iProver_Flat_'uuf$'(X0_'A_b_fun_bool_fun',X0_'A_b_fun_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_fun_bool_fun'=iProver_Domain_'A_b_fun_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTDom_update$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTDom_update$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catCod$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catCod$f'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'objIso$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'objIso$'(X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'oppositeCategory$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'oppositeCategory$c'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'cod_update$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_'cod_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'lSCategory_ext$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_c_LSCategory_ext',X0_'B_ZF_fun',X0_'C'] : 4.25/1.99 ( iProver_Flat_'lSCategory_ext$'(X0_'B_c_LSCategory_ext',X0_'B_ZF_fun',X0_'C') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_c_LSCategory_ext'=iProver_Domain_'B_c_LSCategory_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'identityFunctor$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'identityFunctor$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$h' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_fun_set',X0_'A_b_fun_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$h'(X0_'A_b_fun_set',X0_'A_b_fun_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_fun_set'=iProver_Domain_'A_b_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'comp$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'comp$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X2_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'functor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'functor$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mor_update$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_set_ZF_set_fun'] : 4.25/1.99 ( iProver_Flat_'mor_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_set_ZF_set_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catCod$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit_unit_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catCod$a'(X0_'Unit_unit_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit_unit_unit_Category_ext'=iProver_Domain_'Unit_unit_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransMap$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'natTransMap$a'(X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'cod$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_a_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'cod$a'(X0_'B_a_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_a_fun'=iProver_Domain_'B_a_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'makeFtor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'] : 4.25/1.99 ( iProver_Flat_'makeFtor$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransExt$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'natTransExt$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatCod$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatCod$e'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$w' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'fun_app$w'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapO$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'mapO$'(X0_'A',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTDom$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTDom$b'(X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uul$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_'uul$'(X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_ZF_fun'=iProver_Domain_'B_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'identityFunctor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'identityFunctor$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'restrict$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_fun',X1_'A_b_fun',X0_'A_set'] : 4.25/1.99 ( iProver_Flat_'restrict$e'(X0_'A_b_fun',X1_'A_b_fun',X0_'A_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_fun'=iProver_Domain_'A_b_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'category_ext$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_set',X1_'ZF_set',X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X2_'ZF_ZF_fun',X0_'ZF_ZF_ZF_fun_fun',X0_'Unit'] : 4.25/1.99 ( iProver_Flat_'category_ext$a'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_set',X1_'ZF_set',X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X2_'ZF_ZF_fun',X0_'ZF_ZF_ZF_fun_fun',X0_'Unit') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'constFunctor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'constFunctor$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'homFtorMap$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_'homFtorMap$'(X0_'B_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_ZF_fun'=iProver_Domain_'B_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_a_fun_set',X0_'B_a_fun_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$f'(X0_'B_a_fun_set',X0_'B_a_fun_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_a_fun_set'=iProver_Domain_'B_a_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'makeNT$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'makeNT$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'inverse$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'inverse$'(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuv$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_'uuv$'(X0_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'restrict$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_prod_set',X0_'ZF_ZF_prod'] : 4.25/1.99 ( iProver_Flat_'restrict$'(X0_'ZF',X0_'ZF_ZF_prod_ZF_fun',X0_'ZF_ZF_prod_set',X0_'ZF_ZF_prod') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$t' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'B'] : 4.25/1.99 ( iProver_Flat_'fun_app$t'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'extensional$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun_set',X0_'A_set'] : 4.25/1.99 ( iProver_Flat_'extensional$a'(X0_'A_ZF_fun_set',X0_'A_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun_set'=iProver_Domain_'A_ZF_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'functorExt$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'functorExt$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$x' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'fun_app$x'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$j' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$j'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uub$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_bool_fun',X0_'A_set'] : 4.25/1.99 ( iProver_Flat_'uub$'(X0_'A_bool_fun',X0_'A_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_bool_fun'=iProver_Domain_'A_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$af' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_'fun_app$af'(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uux$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'uux$'(X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_b_fun_fun'=iProver_Domain_'B_b_b_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uui$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set'] : 4.25/1.99 ( iProver_Flat_'uui$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'dom$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_a_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'dom$'(X0_'B_a_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_a_fun'=iProver_Domain_'B_a_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'more$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_c_LSCategory_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'more$d'(X0_'B_c_LSCategory_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_c_LSCategory_ext'=iProver_Domain_'B_c_LSCategory_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'zFfunDom$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_'zFfunDom$'(X0_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransP$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'natTransP$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'zFfunApp$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_'zFfunApp$'(X0_'ZF_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$c'(X0_'ZF_set',X0_'ZF_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$ae' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_set',X0_'B_set_b_set_fun',X1_'B_set'] : 4.25/1.99 ( iProver_Flat_'fun_app$ae'(X0_'B_set',X0_'B_set_b_set_fun',X1_'B_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_set'=iProver_Domain_'B_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapM$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'B'] : 4.25/1.99 ( iProver_Flat_'mapM$f'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'isomorphism$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'isomorphism$a'(X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCod_update$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCod_update$'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'hOMCollection$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A',X1_'A'] : 4.25/1.99 ( iProver_Flat_'hOMCollection$'(X0_'ZF_set',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A',X1_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuw$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_prod_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'uuw$'(X0_'B_b_prod_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_prod_bool_fun'=iProver_Domain_'B_b_prod_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuh$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_prod_bool_fun',X0_'B_b_prod_set'] : 4.25/1.99 ( iProver_Flat_'uuh$'(X0_'B_b_prod_bool_fun',X0_'B_b_prod_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_prod_bool_fun'=iProver_Domain_'B_b_prod_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'functorM_axioms$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'functorM_axioms$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'comp$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'comp$'(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'isomorphism$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'isomorphism$'(X0_'B_bool_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_bool_fun'=iProver_Domain_'B_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$o' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'B_ZF_fun',X0_'B'] : 4.25/1.99 ( iProver_Flat_'fun_app$o'(X0_'ZF',X0_'B_ZF_fun',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catDom$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catDom$e'(X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'inverse$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'B'] : 4.25/1.99 ( iProver_Flat_'inverse$a'(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapM$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'mapM$b'(X0_'ZF_ZF_fun',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$ad' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set'] : 4.25/1.99 ( iProver_Flat_'fun_app$ad'(X0_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$aa' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'Unit_unit_fun',X1_'Unit'] : 4.25/1.99 ( iProver_Flat_'fun_app$aa'(X0_'Unit',X0_'Unit_unit_fun',X1_'Unit') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'obj$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'obj$'(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'homFtorMapContra$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B'] : 4.25/1.99 ( iProver_Flat_'homFtorMapContra$'(X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'elem$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'elem$'(X0_'ZF_bool_fun',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'comp$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'comp$a'(X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_b_fun_fun'=iProver_Domain_'B_b_b_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatCod$f' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit_unit_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatCod$f'(X0_'Unit_unit_unit_Category_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit_unit_unit_Category_ext'=iProver_Domain_'Unit_unit_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$v' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'fun_app$v'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTDom$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTDom$d'(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'=iProver_Domain_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catExp$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'catExp$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'more_update$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'Unit_unit_fun'] : 4.25/1.99 ( iProver_Flat_'more_update$a'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'Unit_unit_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'catDom$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'catDom$d'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_fun',X1_'ZF'] : 4.25/1.99 ( iProver_Flat_'fun_app$'(X0_'ZF',X0_'ZF_ZF_fun',X1_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'comp$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X0_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_'comp$d'(X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X0_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_fun_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapO$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'mapO$c'(X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'constFunctor$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'constFunctor$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$i' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$i'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'yFtorNT$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'yFtorNT$a'(X0_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun'=iProver_Domain_'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapsTo$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF',X1_'ZF'] : 4.25/1.99 ( iProver_Flat_'mapsTo$a'(X0_'ZF_bool_fun',X0_'ZF_ZF_unit_Category_ext',X0_'ZF',X1_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'makeCat$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'] : 4.25/1.99 ( iProver_Flat_'makeCat$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapM$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'mapM$c'(X0_'B',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mor$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'mor$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'extensional$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun_set',X0_'ZF_set'] : 4.25/1.99 ( iProver_Flat_'extensional$'(X0_'ZF_ZF_fun_set',X0_'ZF_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun_set'=iProver_Domain_'ZF_ZF_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuu$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_'uuu$'(X0_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uug$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_prod_set'] : 4.25/1.99 ( iProver_Flat_'uug$'(X0_'ZF_ZF_prod_bool_fun',X0_'ZF_ZF_prod_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_prod_bool_fun'=iProver_Domain_'ZF_ZF_prod_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'id$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'id$a'(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'image$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set_set',X0_'ZF_ZF_set_fun',X0_'ZF_set'] : 4.25/1.99 ( iProver_Flat_'image$'(X0_'ZF_set_set',X0_'ZF_ZF_set_fun',X0_'ZF_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set_set'=iProver_Domain_'ZF_set_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'restrict$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_ZF_fun',X1_'B_ZF_fun',X0_'B_set'] : 4.25/1.99 ( iProver_Flat_'restrict$b'(X0_'B_ZF_fun',X1_'B_ZF_fun',X0_'B_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_ZF_fun'=iProver_Domain_'B_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuj$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'uuj$'(X0_'B_b_b_fun_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_b_b_fun_fun'=iProver_Domain_'B_b_b_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'id_update$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_'id_update$'(X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'=iProver_Domain_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'homFtor$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_'homFtor$a'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'preFunctor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_'preFunctor$'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'idNatTrans$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_'idNatTrans$a'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'cod$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'cod$'(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'pair$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_prod',X0_'ZF',X1_'ZF'] : 4.25/1.99 ( iProver_Flat_'pair$'(X0_'ZF_ZF_prod',X0_'ZF',X1_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_prod'=iProver_Domain_'ZF_ZF_prod'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCod$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCod$d'(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'=iProver_Domain_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'makeCat$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'makeCat$b'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCod$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCod$b'(X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'homSet$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_'homSet$'(X0_'A_ZF_fun',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uue$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun_bool_fun',X0_'A_ZF_fun_set'] : 4.25/1.99 ( iProver_Flat_'uue$'(X0_'A_ZF_fun_bool_fun',X0_'A_ZF_fun_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun_bool_fun'=iProver_Domain_'A_ZF_fun_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'collect$g' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun_set',X0_'A_ZF_fun_bool_fun'] : 4.25/1.99 ( iProver_Flat_'collect$g'(X0_'A_ZF_fun_set',X0_'A_ZF_fun_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun_set'=iProver_Domain_'A_ZF_fun_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'isZFfun$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_bool_fun'] : 4.25/1.99 ( iProver_Flat_'isZFfun$'(X0_'ZF_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_bool_fun'=iProver_Domain_'ZF_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'fun_app$y' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'fun_app$y'(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapO$d' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'mapO$d'(X0_'Unit',X0_'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mor$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'mor$b'(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatCod$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatCod$c'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'natTransComp$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext',X1_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext',X2_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'natTransComp$e'(X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext',X1_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext',X2_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'=iProver_Domain_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'uuc$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_ZF_fun_bool_fun',X0_'B_ZF_fun_set'] : 4.25/1.99 ( iProver_Flat_'uuc$'(X0_'B_ZF_fun_bool_fun',X0_'B_ZF_fun_set') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_ZF_fun_bool_fun'=iProver_Domain_'B_ZF_fun_bool_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatCod$b' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatCod$b'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'dom$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_'dom$a'(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'nTCatDom$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_'nTCatDom$e'(X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'comp$c' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit_unit_fun',X0_'Unit_unit_unit_Category_ext',X0_'Unit'] : 4.25/1.99 ( iProver_Flat_'comp$c'(X0_'Unit_unit_fun',X0_'Unit_unit_unit_Category_ext',X0_'Unit') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit_unit_fun'=iProver_Domain_'Unit_unit_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapO$a' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X1_'A'] : 4.25/1.99 ( iProver_Flat_'mapO$a'(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext',X1_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mapO$e' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_'mapO$e'(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_'mor$' 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_set',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_'mor$'(X0_'B_set',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_set'=iProver_Domain_'B_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK31 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK31(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK32 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK32(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK33 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK33(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK34 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK34(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK35 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A',X1_'A',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_sK35(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A',X1_'A',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK36 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_sK36(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK37 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK37(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK38 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK38(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK39 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK39(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK40 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK40(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK41 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK41(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK42 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK42(X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK43 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK43(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK44 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK44(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK45 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun',X1_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK45(X0_'ZF_ZF_ZF_fun_fun',X1_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK46 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_prod',X0_'ZF_ZF_prod_bool_fun',X1_'ZF_ZF_prod_bool_fun'] : 4.25/1.99 ( iProver_Flat_sK46(X0_'ZF_ZF_prod',X0_'ZF_ZF_prod_bool_fun',X1_'ZF_ZF_prod_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_prod'=iProver_Domain_'ZF_ZF_prod'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK47 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK47(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK48 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK48(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK49 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK49(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK50 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X1_'ZF',X2_'ZF'] : 4.25/1.99 ( iProver_Flat_sK50(X0_'ZF',X1_'ZF',X2_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK51 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK51(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK52 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK52(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK53 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK53(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK54 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK54(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK55 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_sK55(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK56 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B_b_prod'] : 4.25/1.99 ( iProver_Flat_sK56(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B_b_prod') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK57 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B_b_prod'] : 4.25/1.99 ( iProver_Flat_sK57(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext',X0_'B_b_prod') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK58 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X1_'ZF_ZF_fun'] : 4.25/1.99 ( iProver_Flat_sK58(X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X1_'ZF_ZF_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK59 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK59(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK60 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK60(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK61 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK61(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK62 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK62(X0_'A_ZF_fun',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_fun'=iProver_Domain_'A_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK63 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK63(X0_'Unit',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK64 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_sK64(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK65 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun'] : 4.25/1.99 ( iProver_Flat_sK65(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK66 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK66(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK67 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK67(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK68 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK68(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK69 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK69(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK70 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'] : 4.25/1.99 ( iProver_Flat_sK70(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK71 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'] : 4.25/1.99 ( iProver_Flat_sK71(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK72 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun'] : 4.25/1.99 ( iProver_Flat_sK72(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK73 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK73(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK74 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK74(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK75 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK75(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK76 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK76(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK77 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK77(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK78 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK78(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK79 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK79(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK80 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK80(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK81 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK81(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK82 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK82(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK83 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK83(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK84 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK84(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK85 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK85(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK86 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK86(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK87 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK87(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK88 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK88(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK89 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK89(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK90 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK90(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK91 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X1_'ZF',X2_'ZF'] : 4.25/1.99 ( iProver_Flat_sK91(X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X1_'ZF',X2_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK92 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun'] : 4.25/1.99 ( iProver_Flat_sK92(X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK93 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK93(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK94 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK94(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK95 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK95(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK96 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK96(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK97 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_bool_fun',X1_'ZF_bool_fun'] : 4.25/1.99 ( iProver_Flat_sK97(X0_'ZF',X0_'ZF_bool_fun',X1_'ZF_bool_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK98 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK98(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK99 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun',X1_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK99(X0_'ZF_ZF_ZF_fun_fun',X1_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun',X1_'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK100 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK100(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK101 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK101(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK102 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK102(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK103 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK103(X0_'ZF',X0_'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK104 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A',X1_'A',X0_'ZF'] : 4.25/1.99 ( iProver_Flat_sK104(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A',X1_'A',X0_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK105 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK105(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK106 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK106(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK107 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK107(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK108 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK108(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK109 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK109(X0_'B',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK110 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK110(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK111 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK111(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK112 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun'] : 4.25/1.99 ( iProver_Flat_sK112(X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK113 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK113(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK114 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK114(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK115 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK115(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK116 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK116(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK117 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK117(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK118 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK118(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK119 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK119(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK120 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK120(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK121 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_sK121(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK122 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK122(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK123 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK123(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK124 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK124(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK125 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK125(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK126 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK126(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK127 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK127(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK128 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK128(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK129 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK129(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK130 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK130(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK131 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK131(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK132 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK132(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK133 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK133(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK134 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK134(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK135 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK135(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK136 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK136(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK137 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK137(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK138 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK138(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK139 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK139(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK140 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK140(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK141 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK141(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK142 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK142(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK143 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK143(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK144 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK144(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK145 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK145(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK146 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK146(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK147 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK147(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK148 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK148(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK149 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK149(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK150 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK150(X0_'B',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK151 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK151(X0_'A',X0_'A_b_b_c_LSCategory_ext_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK152 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X1_'ZF'] : 4.25/1.99 ( iProver_Flat_sK152(X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X1_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK153 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK153(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK154 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun'] : 4.25/1.99 ( iProver_Flat_sK154(X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK155 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK155(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK156 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK156(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK157 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK157(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK158 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK158(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK159 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK159(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK160 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK160(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK161 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK161(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK162 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK162(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK163 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK163(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK164 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK164(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK165 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK165(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK166 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK166(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK167 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK167(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK168 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK168(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK169 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X0_'ZF_ZF_unit_Category_ext'] : 4.25/1.99 ( iProver_Flat_sK169(X0_'Unit',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK170 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'] : 4.25/1.99 ( iProver_Flat_sK170(X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK171 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK171(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK172 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK172(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK173 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK173(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK174 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK174(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK175 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A'] : 4.25/1.99 ( iProver_Flat_sK175(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK176 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK176(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK177 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK177(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK178 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK178(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK179 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK179(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK180 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK180(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK181 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK181(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK182 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK182(X0_'ZF',X0_'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK183 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK183(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK184 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK184(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK185 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK185(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK186 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'Unit',X1_'Unit',X0_'Unit_unit_fun',X1_'Unit_unit_fun'] : 4.25/1.99 ( iProver_Flat_sK186(X0_'Unit',X1_'Unit',X0_'Unit_unit_fun',X1_'Unit_unit_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK187 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'] : 4.25/1.99 ( iProver_Flat_sK187(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK188 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_prod'] : 4.25/1.99 ( iProver_Flat_sK188(X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_prod') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK189 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_prod'] : 4.25/1.99 ( iProver_Flat_sK189(X0_'ZF',X0_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_prod') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK190 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/1.99 ( iProver_Flat_sK190(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK191 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X2_'ZF'] : 4.25/1.99 ( iProver_Flat_sK191(X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X2_'ZF') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK192 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B_set',X1_'B_set',X0_'B_set_b_set_fun',X1_'B_set_b_set_fun'] : 4.25/1.99 ( iProver_Flat_sK192(X0_'B_set',X1_'B_set',X0_'B_set_b_set_fun',X1_'B_set_b_set_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B_set'=iProver_Domain_'B_set'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK193 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/1.99 ( iProver_Flat_sK193(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK194 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK194(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK195 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK195(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK196 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK196(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK197 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK197(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK198 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK198(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK199 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK199(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK200 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK200(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/1.99 ( 4.25/1.99 ( 4.25/1.99 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/1.99 ) 4.25/1.99 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ) 4.25/1.99 ). 4.25/1.99 4.25/1.99 %------ Positive definition of iProver_Flat_sK201 4.25/1.99 fof(lit_def,axiom, 4.25/1.99 (! [X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'] : 4.25/1.99 ( iProver_Flat_sK201(X0_'ZF',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK202 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X2_'ZF'] : 4.25/2.00 ( iProver_Flat_sK202(X0_'ZF',X1_'ZF',X0_'ZF_ZF_fun',X2_'ZF') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK203 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B',X0_'B_bool_fun',X1_'B_bool_fun'] : 4.25/2.00 ( iProver_Flat_sK203(X0_'B',X0_'B_bool_fun',X1_'B_bool_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK204 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun'] : 4.25/2.00 ( iProver_Flat_sK204(X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'=iProver_Domain_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK205 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK205(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK206 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK206(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK207 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK207(X0_'B',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK208 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK208(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK209 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK209(X0_'A',X0_'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK210 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun'] : 4.25/2.00 ( iProver_Flat_sK210(X0_'A_b_b_c_LSCategory_ext_Category_ext',X1_'A_b_b_c_LSCategory_ext_Category_ext',X0_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun',X1_'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A_b_b_c_LSCategory_ext_Category_ext'=iProver_Domain_'A_b_b_c_LSCategory_ext_Category_ext'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK211 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK211(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK212 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK212(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK213 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK213(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK214 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK214(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK215 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK215(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK216 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK216(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK217 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK217(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK218 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK218(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK219 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK219(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK220 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK220(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK221 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK221(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK222 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK222(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK223 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK223(X0_'ZF',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK224 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun'] : 4.25/2.00 ( iProver_Flat_sK224(X0_'ZF_set',X1_'ZF_set',X0_'ZF_set_ZF_set_fun',X1_'ZF_set_ZF_set_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK225 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF',X2_'ZF',X3_'ZF'] : 4.25/2.00 ( iProver_Flat_sK225(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext',X1_'ZF',X2_'ZF',X3_'ZF') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK226 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'] : 4.25/2.00 ( iProver_Flat_sK226(X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK227 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun'] : 4.25/2.00 ( iProver_Flat_sK227(X0_'ZF_ZF_unit_Category_ext',X1_'ZF_ZF_unit_Category_ext',X0_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun',X1_'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_unit_Category_ext'=iProver_Domain_'ZF_ZF_unit_Category_ext'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK228 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B_set',X1_'B_set',X0_'B_set_b_set_fun',X1_'B_set_b_set_fun'] : 4.25/2.00 ( iProver_Flat_sK228(X0_'B_set',X1_'B_set',X0_'B_set_b_set_fun',X1_'B_set_b_set_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B_set'=iProver_Domain_'B_set'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK229 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun'] : 4.25/2.00 ( iProver_Flat_sK229(X0_'ZF_ZF_fun',X1_'ZF_ZF_fun',X0_'ZF_ZF_fun_ZF_ZF_fun_fun',X1_'ZF_ZF_fun_ZF_ZF_fun_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK230 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK230(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK231 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK231(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK232 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK232(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK233 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK233(X0_'ZF',X0_'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK234 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'Unit',X1_'Unit',X0_'Unit_unit_fun',X1_'Unit_unit_fun'] : 4.25/2.00 ( iProver_Flat_sK234(X0_'Unit',X1_'Unit',X0_'Unit_unit_fun',X1_'Unit_unit_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'Unit'=iProver_Domain_'Unit'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK235 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK235(X0_'B',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK236 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK236(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK237 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK237(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK238 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK238(X0_'A',X0_'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK239 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B_b_prod',X0_'B_b_prod_bool_fun',X1_'B_b_prod_bool_fun'] : 4.25/2.00 ( iProver_Flat_sK239(X0_'B_b_prod',X0_'B_b_prod_bool_fun',X1_'B_b_prod_bool_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B_b_prod'=iProver_Domain_'B_b_prod'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK240 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK240(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK241 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK241(X0_'B',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'B'=iProver_Domain_'B'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK242 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK242(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK243 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK243(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK244 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun'] : 4.25/2.00 ( iProver_Flat_sK244(X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'=iProver_Domain_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK245 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK245(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK246 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK246(X0_'ZF_set',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_set'=iProver_Domain_'ZF_set'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK247 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK247(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK248 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK248(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK249 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK249(X0_'ZF_ZF_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_fun'=iProver_Domain_'ZF_ZF_fun'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK250 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext'] : 4.25/2.00 ( iProver_Flat_sK250(X0_'ZF_ZF_ZF_fun_fun',X0_'ZF_ZF_unit_Category_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF_ZF_ZF_fun_fun'=iProver_Domain_'ZF_ZF_ZF_fun_fun'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK251 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK251(X0_'ZF',X0_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext',X1_'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'ZF'=iProver_Domain_'ZF'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 4.25/2.00 %------ Positive definition of iProver_Flat_sK252 4.25/2.00 fof(lit_def,axiom, 4.25/2.00 (! [X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext'] : 4.25/2.00 ( iProver_Flat_sK252(X0_'A',X0_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext',X1_'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext') <=> 4.25/2.00 ( 4.25/2.00 ( 4.25/2.00 ( X0_'A'=iProver_Domain_'A'_1 ) 4.25/2.00 ) 4.25/2.00 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ) 4.25/2.00 ). 4.25/2.00 % SZS output end Model for theBenchmark.p 4.25/2.00 4.28/2.06 EOF