0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_iprover 120 /export/starexec/sandbox2/benchmark/theBenchmark.p SAT 0.12/0.34 % Computer : n024.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Wed Jul 30 05:31:34 EDT 2025 0.12/0.34 % CPUTime : 0.19/0.46 /export/starexec/sandbox2/solver/bin/SPCForProblem: Command not found. 0.19/0.46 Running model finding 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core-casc.sh -l tptp -s fnt_schedule -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.47 0.19/0.47 % ======== iProver multi-core TPTP/SMT ========= 0.19/0.47 0.19/0.47 % Detected problem language: tptp 0.19/0.48 % Checking... 0.54/1.14 % Proving... 4.35/1.86 % SZS status Started for theBenchmark.p 4.35/1.86 % SZS status Satisfiable for theBenchmark.p 4.35/1.86 4.35/1.86 %---------------- iProver v3.9.3 (pre CASC 2025/SMT-COMP 2025) ----------------% 4.35/1.86 4.35/1.86 ------ iProver source info 4.35/1.86 4.35/1.86 git: date: 2025-07-21 10:15:00 +0000 4.35/1.86 git: sha1: d7ebeb21b290b8724a1e08b4c4a533d26e8c009f 4.35/1.86 git: non_committed_changes: true 4.35/1.86 4.35/1.86 ------ Parsing... 4.35/1.86 ------ Clausification by vclausify_rel & Parsing by iProver... 4.35/1.86 ------ Proving... 4.35/1.86 ------ Problem Properties 4.35/1.86 4.35/1.86 4.35/1.86 clauses 791 4.35/1.86 conjectures 0 4.35/1.86 EPR 52 4.35/1.86 Horn 745 4.35/1.86 unary 271 4.35/1.86 binary 306 4.35/1.86 lits 1644 4.35/1.86 lits eq 658 4.35/1.86 fd_pure 0 4.35/1.86 fd_pseudo 0 4.35/1.86 fd_cond 0 4.35/1.86 fd_pseudo_cond 49 4.35/1.86 AC symbols 0 4.35/1.86 4.35/1.86 ------ Input Options Time Limit: Unbounded 4.35/1.86 4.35/1.86 4.35/1.86 ------ Finite Models: 4.35/1.86 4.35/1.86 ------ lit_activity_flag true 4.35/1.86 4.35/1.86 4.35/1.86 ------ Trying domains of size >= : 1 4.35/1.86 ------ 4.35/1.86 Current options: 4.35/1.86 ------ 4.35/1.86 4.35/1.86 ------ Input Options 4.35/1.86 4.35/1.86 --out_options all 4.35/1.86 --tptp_safe_out true 4.35/1.86 --problem_path "" 4.35/1.86 --include_path "" 4.35/1.86 --clausifier res/vclausify_rel 4.35/1.86 --clausifier_options --mode tclausify -t 41.66 --show_fool true -updr off 4.35/1.86 --stdin false 4.35/1.86 --proof_out true 4.35/1.86 --proof_dot_file "" 4.35/1.86 --proof_reduce_dot [] 4.35/1.86 --suppress_sat_res false 4.35/1.86 --suppress_unsat_res true 4.35/1.86 --stats_out none 4.35/1.86 --stats_mem false 4.35/1.86 --theory_stats_out false 4.35/1.86 4.35/1.86 ------ General Options 4.35/1.86 4.35/1.86 --fof false 4.35/1.86 --time_out_real 124.99 4.35/1.86 --time_out_virtual -1. 4.35/1.86 --rnd_seed 13 4.35/1.86 --symbol_type_check false 4.35/1.86 --clausify_out false 4.35/1.86 --sig_cnt_out false 4.35/1.86 --trig_cnt_out false 4.35/1.86 --trig_cnt_out_tolerance 1. 4.35/1.86 --trig_cnt_out_sk_spl false 4.35/1.86 --abstr_cl_out false 4.35/1.86 4.35/1.86 ------ Interactive Mode 4.35/1.86 4.35/1.86 --interactive_mode false 4.35/1.86 --external_ip_address "" 4.35/1.86 --external_port 0 4.35/1.86 4.35/1.86 ------ Global Options 4.35/1.86 4.35/1.86 --schedule none 4.35/1.86 --add_important_lit false 4.35/1.86 --prop_solver_per_cl 500 4.35/1.86 --subs_bck_mult 8 4.35/1.86 --min_unsat_core false 4.35/1.86 --soft_assumptions false 4.35/1.86 --soft_lemma_size 3 4.35/1.86 --prop_impl_unit_size 0 4.35/1.86 --prop_impl_unit [] 4.35/1.86 --share_sel_clauses true 4.35/1.86 --reset_solvers false 4.35/1.86 --bc_imp_inh [conj_cone] 4.35/1.86 --conj_cone_tolerance 3. 4.35/1.86 --extra_neg_conj none 4.35/1.86 --large_theory_mode true 4.35/1.86 --prolific_symb_bound 200 4.35/1.86 --lt_threshold 2000 4.35/1.86 --clause_weak_htbl true 4.35/1.86 --gc_record_bc_elim false 4.35/1.86 4.35/1.86 ------ Preprocessing Options 4.35/1.86 4.35/1.86 --preprocessing_flag false 4.35/1.86 --time_out_prep_mult 0.1 4.35/1.86 --splitting_mode input 4.35/1.86 --splitting_grd true 4.35/1.86 --splitting_cvd false 4.35/1.86 --splitting_cvd_svl false 4.35/1.86 --splitting_nvd 32 4.35/1.86 --sub_typing false 4.35/1.86 --prep_eq_flat_conj false 4.35/1.86 --prep_eq_flat_all_gr false 4.35/1.86 --prep_gs_sim true 4.35/1.86 --prep_unflatten true 4.35/1.86 --prep_res_sim true 4.35/1.86 --prep_sup_sim_all true 4.35/1.86 --prep_sup_sim_sup false 4.35/1.86 --prep_upred true 4.35/1.86 --prep_well_definedness true 4.35/1.86 --prep_sem_filter exhaustive 4.35/1.86 --prep_sem_filter_out false 4.35/1.86 --pred_elim true 4.35/1.86 --res_sim_input true 4.35/1.86 --eq_ax_congr_red true 4.35/1.86 --pure_diseq_elim true 4.35/1.86 --brand_transform false 4.35/1.86 --non_eq_to_eq false 4.35/1.86 --prep_def_merge true 4.35/1.86 --prep_def_merge_prop_impl false 4.35/1.86 --prep_def_merge_mbd true 4.35/1.86 --prep_def_merge_tr_red false 4.35/1.86 --prep_def_merge_tr_cl false 4.35/1.86 --smt_preprocessing false 4.35/1.86 --smt_ac_axioms fast 4.35/1.86 --preprocessed_out false 4.35/1.86 --preprocessed_stats false 4.35/1.86 4.35/1.86 ------ Abstraction refinement Options 4.35/1.86 4.35/1.86 --abstr_ref [] 4.35/1.86 --abstr_ref_prep false 4.35/1.86 --abstr_ref_until_sat false 4.35/1.86 --abstr_ref_sig_restrict funpre 4.35/1.86 --abstr_ref_af_restrict_to_split_sk false 4.35/1.86 --abstr_ref_under [] 4.35/1.86 4.35/1.86 ------ SAT Options 4.35/1.86 4.35/1.86 --sat_mode true 4.35/1.86 --sat_fm_restart_options "" 4.35/1.86 --sat_gr_def false 4.35/1.86 --sat_epr_types true 4.35/1.86 --sat_non_cyclic_types false 4.35/1.86 --sat_finite_models true 4.35/1.86 --sat_fm_lemmas false 4.35/1.86 --sat_fm_prep false 4.35/1.86 --sat_fm_uc_incr true 4.35/1.86 --sat_out_model pos 4.35/1.86 --sat_out_clauses false 4.35/1.86 4.35/1.86 ------ QBF Options 4.35/1.86 4.35/1.86 --qbf_mode false 4.35/1.86 --qbf_elim_univ false 4.35/1.86 --qbf_dom_inst none 4.35/1.86 --qbf_dom_pre_inst false 4.35/1.86 --qbf_sk_in false 4.35/1.86 --qbf_pred_elim true 4.35/1.86 --qbf_split 512 4.35/1.86 4.35/1.86 ------ BMC1 Options 4.35/1.86 4.35/1.86 --bmc1_incremental false 4.35/1.86 --bmc1_axioms reachable_all 4.35/1.86 --bmc1_min_bound 0 4.35/1.86 --bmc1_max_bound -1 4.35/1.86 --bmc1_max_bound_default -1 4.35/1.86 --bmc1_symbol_reachability true 4.35/1.86 --bmc1_property_lemmas false 4.35/1.86 --bmc1_k_induction false 4.35/1.86 --bmc1_non_equiv_states false 4.35/1.86 --bmc1_deadlock false 4.35/1.86 --bmc1_ucm false 4.35/1.86 --bmc1_add_unsat_core none 4.35/1.86 --bmc1_unsat_core_children false 4.35/1.86 --bmc1_unsat_core_extrapolate_axioms false 4.35/1.86 --bmc1_out_stat full 4.35/1.86 --bmc1_ground_init false 4.35/1.86 --bmc1_pre_inst_next_state false 4.35/1.86 --bmc1_pre_inst_state false 4.35/1.86 --bmc1_pre_inst_reach_state false 4.35/1.86 --bmc1_out_unsat_core false 4.35/1.86 --bmc1_aig_witness_out false 4.35/1.86 --bmc1_verbose false 4.35/1.86 --bmc1_dump_clauses_tptp false 4.35/1.86 --bmc1_dump_unsat_core_tptp false 4.35/1.86 --bmc1_dump_file - 4.35/1.86 --bmc1_ucm_expand_uc_limit 128 4.35/1.86 --bmc1_ucm_n_expand_iterations 6 4.35/1.86 --bmc1_ucm_extend_mode 1 4.35/1.86 --bmc1_ucm_init_mode 2 4.35/1.86 --bmc1_ucm_cone_mode none 4.35/1.86 --bmc1_ucm_reduced_relation_type 0 4.35/1.86 --bmc1_ucm_relax_model 4 4.35/1.86 --bmc1_ucm_full_tr_after_sat true 4.35/1.86 --bmc1_ucm_expand_neg_assumptions false 4.35/1.86 --bmc1_ucm_layered_model none 4.35/1.86 --bmc1_ucm_max_lemma_size 10 4.35/1.86 4.35/1.86 ------ AIG Options 4.35/1.86 4.35/1.86 --aig_mode false 4.35/1.86 4.35/1.86 ------ Instantiation Options 4.35/1.86 4.35/1.86 --instantiation_flag true 4.35/1.86 --inst_sos_flag false 4.35/1.86 --inst_sos_phase true 4.35/1.86 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb] 4.35/1.86 --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb] 4.35/1.86 --inst_lit_sel_side num_symb 4.35/1.86 --inst_solver_per_active 1400 4.35/1.86 --inst_solver_calls_frac 1. 4.35/1.86 --inst_to_smt_solver true 4.35/1.86 --inst_passive_queue_type priority_queues 4.35/1.86 --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]] 4.35/1.86 --inst_passive_queues_freq [25;2] 4.35/1.86 --inst_dismatching true 4.35/1.86 --inst_eager_unprocessed_to_passive true 4.35/1.86 --inst_unprocessed_bound 1000 4.35/1.86 --inst_prop_sim_given true 4.35/1.86 --inst_prop_sim_new false 4.35/1.86 --inst_subs_new false 4.35/1.86 --inst_eq_res_simp false 4.35/1.86 --inst_subs_given false 4.35/1.86 --inst_orphan_elimination true 4.35/1.86 --inst_learning_loop_flag true 4.35/1.86 --inst_learning_start 3000 4.35/1.86 --inst_learning_factor 2 4.35/1.86 --inst_start_prop_sim_after_learn 3 4.35/1.86 --inst_sel_renew solver 4.35/1.86 --inst_lit_activity_flag true 4.35/1.86 --inst_restr_to_given false 4.35/1.86 --inst_activity_threshold 500 4.35/1.86 4.35/1.86 ------ Resolution Options 4.35/1.86 4.35/1.86 --resolution_flag false 4.35/1.86 --res_lit_sel adaptive 4.35/1.86 --res_lit_sel_side none 4.35/1.86 --res_ordering kbo 4.35/1.86 --res_to_prop_solver active 4.35/1.86 --res_prop_simpl_new false 4.35/1.86 --res_prop_simpl_given true 4.35/1.86 --res_to_smt_solver true 4.35/1.86 --res_passive_queue_type priority_queues 4.35/1.86 --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]] 4.35/1.86 --res_passive_queues_freq [15;5] 4.35/1.86 --res_forward_subs full 4.35/1.86 --res_backward_subs full 4.35/1.86 --res_forward_subs_resolution true 4.35/1.86 --res_backward_subs_resolution true 4.35/1.86 --res_orphan_elimination true 4.35/1.86 --res_time_limit 300. 4.35/1.86 4.35/1.86 ------ Superposition Options 4.35/1.86 4.35/1.86 --superposition_flag false 4.35/1.86 --sup_passive_queue_type priority_queues 4.35/1.86 --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]] 4.35/1.86 --sup_passive_queues_freq [8;1;4;4] 4.35/1.86 --demod_completeness_check fast 4.35/1.86 --demod_use_ground true 4.35/1.86 --sup_unprocessed_bound 0 4.35/1.86 --sup_to_prop_solver passive 4.35/1.86 --sup_prop_simpl_new true 4.35/1.86 --sup_prop_simpl_given true 4.35/1.86 --sup_fun_splitting false 4.35/1.86 --sup_iter_deepening 2 4.35/1.86 --sup_restarts_mult 12 4.35/1.86 --sup_score sim_d_gen 4.35/1.86 --sup_share_score_frac 0.2 4.35/1.86 --sup_share_max_num_cl 500 4.35/1.86 --sup_ordering kbo 4.35/1.86 --sup_symb_ordering invfreq 4.35/1.86 --sup_term_weight default 4.35/1.86 4.35/1.86 ------ Superposition Simplification Setup 4.35/1.86 4.35/1.86 --sup_indices_passive [LightNormIndex;FwDemodIndex] 4.35/1.86 --sup_full_triv [SMTSimplify;PropSubs] 4.35/1.86 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] 4.35/1.86 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.35/1.86 --sup_immed_triv [] 4.35/1.86 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes] 4.35/1.86 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes] 4.35/1.86 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod] 4.35/1.86 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.35/1.86 --sup_input_triv [Unflattening;SMTSimplify] 4.35/1.86 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability] 4.35/1.86 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes] 4.35/1.86 --sup_full_fixpoint true 4.35/1.86 --sup_main_fixpoint true 4.35/1.86 --sup_immed_fixpoint false 4.35/1.86 --sup_input_fixpoint true 4.35/1.86 --sup_cache_sim none 4.35/1.86 --sup_smt_interval 500 4.35/1.86 --sup_bw_gjoin_interval 0 4.35/1.86 4.35/1.86 ------ Combination Options 4.35/1.86 4.35/1.86 --comb_mode clause_based 4.35/1.86 --comb_inst_mult 5 4.35/1.86 --comb_res_mult 1 4.35/1.86 --comb_sup_mult 8 4.35/1.86 --comb_sup_deep_mult 2 4.35/1.86 4.35/1.86 ------ Debug Options 4.35/1.86 4.35/1.86 --dbg_backtrace false 4.35/1.86 --dbg_dump_prop_clauses false 4.35/1.86 --dbg_dump_prop_clauses_file - 4.35/1.86 --dbg_out_stat false 4.35/1.86 --dbg_just_parse false 4.35/1.86 4.35/1.86 4.35/1.86 4.35/1.86 4.35/1.86 ------ Proving... 4.35/1.86 4.35/1.86 4.35/1.86 % SZS status Satisfiable for theBenchmark.p 4.35/1.86 4.35/1.86 ------ Building Model...Done 4.35/1.86 4.35/1.86 %------ The model is defined over ground terms (initial term algebra). 4.35/1.86 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 4.35/1.86 %------ where \phi is a formula over the term algebra. 4.35/1.86 %------ If we have equality in the problem then it is also defined as a predicate above, 4.35/1.86 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type 4.35/1.86 %------ See help for --sat_out_model for different model outputs. 4.35/1.86 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "=" 4.35/1.86 %------ where the first argument stands for the sort ($i in the unsorted case) 4.35/1.86 % SZS output start Model for theBenchmark.p 4.35/1.86 4.35/1.86 %------ Positive definition of equality_sorted 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_tType,X0_'C_d_prod_update_set',X1_'C_d_prod_update_set'] : 4.35/1.86 ( equality_sorted(X0_tType,X0_'C_d_prod_update_set',X1_'C_d_prod_update_set') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_b_update_prod$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_a_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_a_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_d_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_b_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_d_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_update_fun_c_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_d_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_update_fun_d_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_c_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_b_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_update_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_c_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_a_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_c_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_c_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_a_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_update_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_b_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_d_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_a_update_fun_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_d_prod_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_d_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_c_prod_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_d_update_fun_d_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='A_a_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_a_update_fun_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_a_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_c_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_a_update_a_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_a_update_a_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_c_prod_update_b_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_d_update_fun_c_update_b_update_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_b_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_c_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_update_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_c_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='B_update_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_a_prod_update$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_a_update_fun_set$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_d_prod_d_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_c_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_update_d_update_prod_b_update_b_update_prod_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='C_c_d_prod_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 | 4.35/1.86 ( 4.35/1.86 ( X0_tType='D_c_d_prod_prod_update_b_b_prod_update_fun$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$au' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$au'(X0_'D_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'pred_fun$' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_bool_fun',X0_'B_update_bool_fun',X0_'C_update_b_update_fun'] : 4.35/1.86 ( 'pred_fun$'(X0_'C_update_bool_fun',X0_'B_update_bool_fun',X0_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'member$d' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_a_update_fun_set'] : 4.35/1.86 ( 'member$d'(X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_a_update_fun_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ai' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_c_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$ai'(X0_'D_c_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ao' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_b_d_prod_update_fun'] : 4.35/1.86 ( 'register$ao'(X0_'D_update_b_d_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$i' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$i'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' & X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ay' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_d_b_prod_update_fun'] : 4.35/1.86 ( 'register$ay'(X0_'A_update_d_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'separating$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_itself',X0_'B_update_set'] : 4.35/1.86 ( 'separating$c'(X0_'B_itself',X0_'B_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$j' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.86 ( 'compatible$j'(X0_'B_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$an' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_bool_fun',X0_'B_update'] : 4.35/1.86 ( 'fun_app$an'(X0_'B_update_bool_fun',X0_'B_update') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$q' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_c_prod_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$q'(X0_'A_c_prod_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$ai' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_bool_fun',X0_'C_update'] : 4.35/1.86 ( 'fun_app$ai'(X0_'C_update_bool_fun',X0_'C_update') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$m' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_c_prod_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$m'(X0_'C_c_prod_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$as' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$as'(X0_'C_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ak' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_d_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$ak'(X0_'D_d_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$n' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.86 ( 'compatible$n'(X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ax' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_d_b_prod_update_fun'] : 4.35/1.86 ( 'register$ax'(X0_'C_update_d_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$n' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_a_prod_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$n'(X0_'C_a_prod_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$aj' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_bool_fun',X0_'A_update'] : 4.35/1.86 ( 'fun_app$aj'(X0_'A_update_bool_fun',X0_'A_update') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'separating$d' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_itself',X0_'A_update_set'] : 4.35/1.86 ( 'separating$d'(X0_'B_itself',X0_'A_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$aw' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_d_a_prod_update_fun'] : 4.35/1.86 ( 'register$aw'(X0_'C_update_d_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$d' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_b_update_fun'] : 4.35/1.86 ( 'register$d'(X0_'B_update_b_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$as' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_a_prod_update_fun',X0_'C_update_b_a_prod_update_fun'] : 4.35/1.86 ( 'compatible$as'(X0_'A_update_b_a_prod_update_fun',X0_'C_update_b_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'separating$' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_itself',X0_'D_update_set'] : 4.35/1.86 ( 'separating$'(X0_'A_itself',X0_'D_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bi' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_a_prod_update_fun'] : 4.35/1.86 ( 'register$bi'(X0_'A_update_a_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'preregister$' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_b_update_fun'] : 4.35/1.86 ( 'preregister$'(X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$k' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun'] : 4.35/1.86 ( 'fun_app$k'(X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$o' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'register$o'(X0_'C_d_prod_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'quotient$' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_b_update_bool_fun_fun',X0_'B_update_a_update_fun',X0_'A_update_b_update_fun',X0_'B_update_a_update_bool_fun_fun'] : 4.35/1.86 ( 'quotient$'(X0_'B_update_b_update_bool_fun_fun',X0_'B_update_a_update_fun',X0_'A_update_b_update_fun',X0_'B_update_a_update_bool_fun_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ac' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_a_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$ac'(X0_'A_a_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'preregister$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun'] : 4.35/1.86 ( 'preregister$c'(X0_'A_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$o' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.86 ( 'compatible$o'(X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'member$f' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_a_update_fun',X0_'C_update_a_update_fun_set'] : 4.35/1.86 ( 'member$f'(X0_'C_update_a_update_fun',X0_'C_update_a_update_fun_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'preregister$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_update_fun'] : 4.35/1.86 ( 'preregister$b'(X0_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'member$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update',X0_'A_update_set'] : 4.35/1.86 ( 'member$c'(X0_'A_update',X0_'A_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bl' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_c_prod_update_fun'] : 4.35/1.86 ( 'register$bl'(X0_'A_update_a_c_prod_update_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_a_c_prod_update_fun'='uvc$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_update_fun'] : 4.35/1.86 ( 'register$c'(X0_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.86 ( 'compatible$c'(X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$u' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$u'(X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$y' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_d_prod_update_a_update_fun'] : 4.35/1.86 ( 'register$y'(X0_'A_d_prod_update_a_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'quotient$e' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_update_bool_fun_fun',X0_'A_update_d_update_fun',X0_'D_update_a_update_fun',X0_'A_update_d_update_bool_fun_fun'] : 4.35/1.86 ( 'quotient$e'(X0_'A_update_a_update_bool_fun_fun',X0_'A_update_d_update_fun',X0_'D_update_a_update_fun',X0_'A_update_d_update_bool_fun_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$k' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_a_b_prod_update_fun'] : 4.35/1.86 ( 'register$k'(X0_'C_d_prod_update_a_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$be' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_a_prod_update_fun'] : 4.35/1.86 ( 'register$be'(X0_'A_update_b_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'member$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update',X0_'C_update_set'] : 4.35/1.86 ( 'member$b'(X0_'C_update',X0_'C_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$ag' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$ag'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' & X1_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bd' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_d_a_prod_update_fun'] : 4.35/1.86 ( 'register$bd'(X0_'A_update_d_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$v' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_d_update_fun'] : 4.35/1.86 ( 'register$v'(X0_'A_update_d_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'separating$a' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_itself',X0_'C_update_set'] : 4.35/1.86 ( 'separating$a'(X0_'B_itself',X0_'C_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$g' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_b_update_fun'] : 4.35/1.86 ( 'register$g'(X0_'D_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_update_fun'] : 4.35/1.86 ( 'register$b'(X0_'A_update_a_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$y' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$y'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' & X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$ag' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_c_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$ag'(X0_'C_c_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bm' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_b_prod_update_fun'] : 4.35/1.86 ( 'register$bm'(X0_'A_update_a_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$am' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'compatible$am'(X0_'C_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$i' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_c_prod_update_a_b_prod_update_fun'] : 4.35/1.86 ( 'register$i'(X0_'C_c_prod_update_a_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$l' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_a_update_fun',X0_'A_update_a_update_fun'] : 4.35/1.86 ( 'compatible$l'(X0_'B_update_a_update_fun',X0_'A_update_a_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$aa' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_c_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$aa'(X0_'A_c_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' & X1_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$aj' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_a_prod_update_fun',X0_'D_update_b_a_prod_update_fun'] : 4.35/1.86 ( 'compatible$aj'(X0_'C_update_b_a_prod_update_fun',X0_'D_update_b_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bj' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_b_a_prod_update_fun'] : 4.35/1.86 ( 'register$bj'(X0_'B_update_b_a_prod_update_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'B_update_b_a_prod_update_fun'='uva$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$f' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_a_update_fun'] : 4.35/1.86 ( 'register$f'(X0_'B_update_a_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$ag' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_a_a_prod_update_fun',X1_'C_update_a_a_prod_update_fun'] : 4.35/1.86 ( 'compatible$ag'(X0_'C_update_a_a_prod_update_fun',X1_'C_update_a_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'pred_fun$d' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_bool_fun',X0_'B_update_bool_fun',X0_'D_update_b_update_fun'] : 4.35/1.86 ( 'pred_fun$d'(X0_'D_update_bool_fun',X0_'B_update_bool_fun',X0_'D_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'preregister$p' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'B_update_c_update_fun'] : 4.35/1.86 ( 'preregister$p'(X0_'B_update_c_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$j' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_a_prod_update_a_b_prod_update_fun'] : 4.35/1.86 ( 'register$j'(X0_'C_a_prod_update_a_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'quotient$c' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'A_update_c_d_prod_update_bool_fun_fun'] : 4.35/1.86 ( 'quotient$c'(X0_'A_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'A_update_c_d_prod_update_bool_fun_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$aj' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_a_prod_update_b_update_fun'] : 4.35/1.86 ( 'register$aj'(X0_'D_a_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$aq' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_a_b_prod_update_fun',X0_'A_update_a_b_prod_update_fun'] : 4.35/1.86 ( 'compatible$aq'(X0_'C_update_a_b_prod_update_fun',X0_'A_update_a_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$az' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_d_b_prod_update_fun'] : 4.35/1.86 ( 'register$az'(X0_'D_update_d_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$f' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.86 ( 'compatible$f'(X0_'C_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$a' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.86 ( 'compatible$a'(X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$h' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.86 ( 'compatible$h'(X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$an' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_b_b_prod_update_fun',X0_'D_update_b_b_prod_update_fun'] : 4.35/1.86 ( 'compatible$an'(X0_'C_update_b_b_prod_update_fun',X0_'D_update_b_b_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$ag' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update'] : 4.35/1.86 ( 'fun_app$ag'(X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$q' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$q'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X1_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' & X1_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bg' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_update_a_c_prod_update_fun'] : 4.35/1.86 ( 'register$bg'(X0_'C_update_a_c_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$m' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$m'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' & X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$an' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_d_prod_update_fun'] : 4.35/1.86 ( 'register$an'(X0_'A_update_b_d_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$bk' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_a_d_prod_update_fun'] : 4.35/1.86 ( 'register$bk'(X0_'A_update_a_d_prod_update_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_a_d_prod_update_fun'='uvb$' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$ac' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$ac'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' & X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun',X0_'B_update_b_update_fun'] : 4.35/1.86 ( 'compatible$b'(X0_'A_update_b_update_fun',X0_'B_update_b_update_fun') <=> 4.35/1.86 $false 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'rel_fun$u' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'] : 4.35/1.86 ( 'rel_fun$u'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun') <=> 4.35/1.86 ( 4.35/1.86 ( 4.35/1.86 ( X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' & X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun'='comp$j' ) 4.35/1.86 ) 4.35/1.86 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'fun_app$ah' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_bool_fun',X0_'D_update'] : 4.35/1.86 ( 'fun_app$ah'(X0_'D_update_bool_fun',X0_'D_update') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'pred_fun$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_d_prod_update_bool_fun',X0_'B_update_bool_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.86 ( 'pred_fun$b'(X0_'C_d_prod_update_bool_fun',X0_'B_update_bool_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$p' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.86 ( 'compatible$p'(X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'register$h' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'C_c_prod_update_a_a_prod_update_fun'] : 4.35/1.86 ( 'register$h'(X0_'C_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'separating$b' 4.35/1.86 fof(lit_def,axiom, 4.35/1.86 (! [X0_'A_itself',X0_'C_update_set'] : 4.35/1.86 ( 'separating$b'(X0_'A_itself',X0_'C_update_set') <=> 4.35/1.86 $true 4.35/1.86 ) 4.35/1.86 ) 4.35/1.86 ). 4.35/1.86 4.35/1.86 %------ Positive definition of 'compatible$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( 'compatible$i'(X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ak' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_b_prod_update_fun',X1_'C_update_a_b_prod_update_fun'] : 4.35/1.87 ( 'compatible$ak'(X0_'C_update_a_b_prod_update_fun',X1_'C_update_a_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ap' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_b_prod_update_fun',X0_'C_update_b_b_prod_update_fun'] : 4.35/1.87 ( 'compatible$ap'(X0_'A_update_b_b_prod_update_fun',X0_'C_update_b_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$z' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_d_prod_update_b_update_fun'] : 4.35/1.87 ( 'register$z'(X0_'A_d_prod_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_b_a_prod_update_fun'] : 4.35/1.87 ( 'register$l'(X0_'C_c_prod_update_b_a_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ar' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_b_prod_update_fun',X0_'D_update_a_b_prod_update_fun'] : 4.35/1.87 ( 'compatible$ar'(X0_'C_update_a_b_prod_update_fun',X0_'D_update_a_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$p' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_c_prod_update_b_a_prod_update_fun'] : 4.35/1.87 ( 'register$p'(X0_'A_c_prod_update_b_a_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'separating$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_itself',X0_'C_d_prod_update_set'] : 4.35/1.87 ( 'separating$e'(X0_'B_itself',X0_'C_d_prod_update_set') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$q' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.87 ( 'compatible$q'(X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$al' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_b_prod_update_fun',X1_'C_update_b_b_prod_update_fun'] : 4.35/1.87 ( 'compatible$al'(X0_'C_update_b_b_prod_update_fun',X1_'C_update_b_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ai' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun'] : 4.35/1.87 ( 'compatible$ai'(X0_'C_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$am' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_d_prod_update_fun'] : 4.35/1.87 ( 'register$am'(X0_'C_update_b_d_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'member$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update',X0_'D_update_set'] : 4.35/1.87 ( 'member$a'(X0_'D_update',X0_'D_update_set') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'fun_app$aq' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun_bool_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( 'fun_app$aq'(X0_'A_update_b_update_fun_bool_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'preregister$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun'] : 4.35/1.87 ( 'preregister$k'(X0_'B_update_b_update_fun') <=> 4.35/1.87 $false 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$at' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_b_prod_update_fun'] : 4.35/1.87 ( 'register$at'(X0_'A_update_b_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$bh' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_a_b_prod_update_fun'] : 4.35/1.87 ( 'register$bh'(X0_'B_update_a_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'member$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update',X0_'C_d_prod_update_set'] : 4.35/1.87 ( 'member$'(X0_'C_d_prod_update',X0_'C_d_prod_update_set') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun'] : 4.35/1.87 ( 'register$a'(X0_'A_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'rel_fun$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'] : 4.35/1.87 ( 'rel_fun$e'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun'='comp$' & X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun'='comp$a' ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'fun_app$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.87 ( 'fun_app$i'(X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.87 ( 'compatible$e'(X0_'A_update_a_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.87 $false 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'preregister$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun'] : 4.35/1.87 ( 'preregister$d'(X0_'D_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'member$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun',X0_'D_update_a_update_fun_set'] : 4.35/1.87 ( 'member$e'(X0_'D_update_a_update_fun',X0_'D_update_a_update_fun_set') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'preregister$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun'] : 4.35/1.87 ( 'preregister$h'(X0_'A_update_a_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$w' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_c_update_fun'] : 4.35/1.87 ( 'register$w'(X0_'A_update_c_update_fun') <=> 4.35/1.87 $false 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ah' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_a_prod_update_fun',X1_'C_update_b_a_prod_update_fun'] : 4.35/1.87 ( 'compatible$ah'(X0_'C_update_b_a_prod_update_fun',X1_'C_update_b_a_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$ao' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_b_prod_update_fun',X0_'C_update_a_b_prod_update_fun'] : 4.35/1.87 ( 'compatible$ao'(X0_'A_update_a_b_prod_update_fun',X0_'C_update_a_b_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$ah' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update_b_update_fun'] : 4.35/1.87 ( 'register$ah'(X0_'C_a_prod_update_b_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'compatible$u' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun',X1_'B_update_b_update_fun'] : 4.35/1.87 ( 'compatible$u'(X0_'B_update_b_update_fun',X1_'B_update_b_update_fun') <=> 4.35/1.87 $false 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'less_eq$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_set',X1_'A_update_set'] : 4.35/1.87 ( 'less_eq$'(X0_'A_update_set',X1_'A_update_set') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'quotient$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_bool_fun_fun',X0_'A_update_b_update_fun',X0_'B_update_a_update_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.87 ( 'quotient$h'(X0_'A_update_a_update_bool_fun_fun',X0_'A_update_b_update_fun',X0_'B_update_a_update_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.87 $false 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$bf' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_d_prod_update_fun'] : 4.35/1.87 ( 'register$bf'(X0_'D_update_a_d_prod_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'fun_app$j' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( 'fun_app$j'(X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of 'register$af' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_a_update_fun'] : 4.35/1.87 ( 'register$af'(X0_'C_c_prod_update_a_update_fun') <=> 4.35/1.87 $true 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$s' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'C_a_prod_update_a_b_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$s'(X0_'C_a_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'C_a_prod_update_a_b_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update_b_update_fun'=iProver_Domain_'C_a_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uu$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update_set'] : 4.35/1.87 ( iProver_Flat_'uu$'(X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_bool_fun'=iProver_Domain_'C_d_prod_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dk' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_prod',X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$dk'(X0_'B_update_b_update_prod',X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cx' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update',X0_'C_update_d_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cx'(X0_'D_update',X0_'C_update_d_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvl$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_a_prod_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvl$'(X0_'C_update_a_a_prod_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_a_prod_update_fun'=iProver_Domain_'C_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$f'(X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_bool_fun'] : 4.35/1.87 ( iProver_Flat_'register$'(X0_'C_update_a_update_fun_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uun$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_b_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uun$'(X0_'A_update_b_b_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_b_prod_update_fun'=iProver_Domain_'A_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$as' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun',X0_'C_update_a_update_fun',X0_'D_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$as'(X0_'D_update_a_update_fun',X0_'C_update_a_update_fun',X0_'D_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_d_prod_update',X1_'D_d_prod_update',X2_'D_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$i'(X0_'D_d_prod_update',X1_'D_d_prod_update',X2_'D_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_d_prod_update'=iProver_Domain_'D_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$ae' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'D_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$ae'(X0_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'D_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$g' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'B_update_a_b_prod_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$g'(X0_'A_b_prod_update',X0_'B_update_a_b_prod_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dt' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$dt'(X0_'C_d_prod_update_b_update_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'relcompp$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_c_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'relcompp$f'(X0_'A_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_c_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_c_update_bool_fun_fun'=iProver_Domain_'A_update_c_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$cc' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_d_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$cc'(X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_d_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$cf' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_d_update_fun',X0_'A_update_d_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$cf'(X0_'B_update_d_update_fun',X0_'A_update_d_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_d_update_fun'=iProver_Domain_'B_update_d_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$v' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$v'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$s' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$s'(X0_'C_d_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_d_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$'(X0_'A_update_a_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cw' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun',X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$cw'(X0_'C_update_b_update_fun',X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$be' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_b_update_prod_fun',X1_'C_update_b_update_b_update_prod_fun',X0_'C_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$be'(X0_'C_update_b_update_b_update_prod_fun',X1_'C_update_b_update_b_update_prod_fun',X0_'C_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_b_update_prod_fun'=iProver_Domain_'C_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvt$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_bool_fun'] : 4.35/1.87 ( iProver_Flat_'uvt$'(X0_'C_update_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_bool_fun'=iProver_Domain_'C_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'relcompp$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'relcompp$h'(X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'id$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'id$'(X0_'B_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun',X0_'D_update_b_update_fun',X0_'A_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$h'(X0_'A_update_b_update_fun',X0_'D_update_b_update_fun',X0_'A_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$q' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update',X0_'A_update_d_update_fun',X0_'D_update_d_update_fun',X0_'A_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'register_pair$q'(X0_'D_update',X0_'A_update_d_update_fun',X0_'D_update_d_update_fun',X0_'A_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$w' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_c_prod_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun',X0_'C_update_b_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$w'(X0_'A_c_prod_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun',X0_'C_update_b_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_c_prod_update_b_a_prod_update_fun'=iProver_Domain_'A_c_prod_update_b_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$av' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun'] : 4.35/1.87 ( iProver_Flat_'comp$av'(X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$n' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_c_prod_update',X0_'B_update',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$n'(X0_'B_c_prod_update',X0_'B_update',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_c_prod_update'=iProver_Domain_'B_c_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dd' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_prod',X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_update_c_d_prod_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$dd'(X0_'A_update_a_update_prod',X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_update_c_d_prod_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'B_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$e'(X0_'A_b_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'B_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update_b_update_fun'=iProver_Domain_'A_b_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$k'(X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'id_update$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'id_update$c'(X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$k'(X0_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uuw$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_d_d_prod_update_fun',X0_'A_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'uuw$'(X0_'A_update_d_d_prod_update_fun',X0_'A_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_d_d_prod_update_fun'=iProver_Domain_'A_update_d_d_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$o' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_b_prod_update',X0_'C_update',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$o'(X0_'C_b_prod_update',X0_'C_update',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_b_prod_update'=iProver_Domain_'C_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$aq' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_a_update_fun',X0_'A_update_a_update_fun',X1_'B_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$aq'(X0_'B_update_a_update_fun',X0_'A_update_a_update_fun',X1_'B_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_a_update_fun'=iProver_Domain_'B_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update',X0_'C_update',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$h'(X0_'C_d_prod_update',X0_'C_update',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bi' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_b_update_prod_fun',X1_'A_update_b_update_b_update_prod_fun',X0_'A_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bi'(X0_'A_update_b_update_b_update_prod_fun',X1_'A_update_b_update_b_update_prod_fun',X0_'A_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_b_update_prod_fun'=iProver_Domain_'A_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uur$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_d_b_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uur$'(X0_'C_update_d_b_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_d_b_prod_update_fun'=iProver_Domain_'C_update_d_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$w' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_c_d_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$w'(X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_c_d_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'convol$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'convol$'(X0_'C_update_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_b_update_prod_fun'=iProver_Domain_'C_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update',X0_'D_update',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$k'(X0_'D_c_prod_update',X0_'D_update',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update'=iProver_Domain_'D_c_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bn' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'C_a_prod_update_a_b_prod_update_fun',X0_'C_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bn'(X0_'A_b_prod_update',X0_'C_a_prod_update_a_b_prod_update_fun',X0_'C_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$d'(X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_c_prod_update',X0_'C_update_a_c_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$e'(X0_'A_c_prod_update',X0_'C_update_a_c_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_c_prod_update'=iProver_Domain_'A_c_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvj$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_b_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvj$'(X0_'A_update_b_b_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_b_prod_update_fun'=iProver_Domain_'A_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$du' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$du'(X0_'C_d_prod_update_b_update_fun',X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$y' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_c_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$y'(X0_'C_d_prod_c_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_a_prod_update',X0_'A_update_b_a_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$a'(X0_'B_a_prod_update',X0_'A_update_b_a_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ab' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update',X0_'A_update_c_d_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ab'(X0_'C_d_prod_update',X0_'A_update_c_d_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'conversep$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'conversep$'(X0_'A_update_b_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_bool_fun_fun'=iProver_Domain_'A_update_b_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bp' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_a_prod_update',X0_'C_c_prod_update_b_a_prod_update_fun',X0_'C_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bp'(X0_'B_a_prod_update',X0_'C_c_prod_update_b_a_prod_update_fun',X0_'C_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$di' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_prod',X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$di'(X0_'B_update_b_update_prod',X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'pred_fun$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_bool_fun',X0_'C_update_bool_fun',X0_'A_update_bool_fun'] : 4.35/1.87 ( iProver_Flat_'pred_fun$a'(X0_'C_update_a_update_fun_bool_fun',X0_'C_update_bool_fun',X0_'A_update_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'collect$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_set',X0_'A_update_bool_fun'] : 4.35/1.87 ( iProver_Flat_'collect$c'(X0_'A_update_set',X0_'A_update_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_set'=iProver_Domain_'A_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$c'(X0_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'preregister$j' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_bool_fun'] : 4.35/1.87 ( iProver_Flat_'preregister$j'(X0_'C_d_prod_update_a_update_fun_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_bool_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$br' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_b_prod_update',X0_'C_a_prod_update_b_b_prod_update_fun',X0_'C_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$br'(X0_'B_b_prod_update',X0_'C_a_prod_update_b_b_prod_update_fun',X0_'C_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uum$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_b_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uum$'(X0_'C_update_b_b_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_b_prod_update_fun'=iProver_Domain_'C_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$by' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$by'(X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_d_prod_update',X0_'B_update',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$e'(X0_'B_d_prod_update',X0_'B_update',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ad' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_d_prod_update',X0_'A_update_b_d_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ad'(X0_'B_d_prod_update',X0_'A_update_b_d_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$an' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun',X0_'D_update_b_update_fun',X0_'C_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$an'(X0_'C_update_b_update_fun',X0_'D_update_b_update_fun',X0_'C_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$g' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_d_prod_update',X0_'D_update',X1_'D_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$g'(X0_'D_d_prod_update',X0_'D_update',X1_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_d_prod_update'=iProver_Domain_'D_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$db' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_prod',X0_'C_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_update_c_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$db'(X0_'A_update_a_update_prod',X0_'C_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_update_c_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'collect$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_set',X0_'C_d_prod_update_a_update_fun_bool_fun'] : 4.35/1.87 ( iProver_Flat_'collect$e'(X0_'C_d_prod_update_a_update_fun_set',X0_'C_d_prod_update_a_update_fun_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_set'=iProver_Domain_'C_d_prod_update_a_update_fun_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ao' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun',X1_'D_update_b_update_fun',X0_'D_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ao'(X0_'D_update_b_update_fun',X1_'D_update_b_update_fun',X0_'D_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'image$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_set',X0_'C_update_a_update_fun',X0_'C_update_set'] : 4.35/1.87 ( iProver_Flat_'image$b'(X0_'A_update_set',X0_'C_update_a_update_fun',X0_'C_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_set'=iProver_Domain_'A_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cm' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'D_d_prod_update_b_update_fun',X0_'D_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cm'(X0_'B_update',X0_'D_d_prod_update_b_update_fun',X0_'D_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bm' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'C_c_prod_update_a_b_prod_update_fun',X0_'C_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bm'(X0_'A_b_prod_update',X0_'C_c_prod_update_a_b_prod_update_fun',X0_'C_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$g' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$g'(X0_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$a'(X0_'C_c_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_c_prod_update_a_b_prod_update_fun'=iProver_Domain_'C_c_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_d_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'D_d_prod_update_a_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$k'(X0_'D_d_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'D_d_prod_update_a_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_d_prod_update_b_update_fun'=iProver_Domain_'D_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$a'(X0_'B_update_b_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'C_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$l'(X0_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'C_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register$ae' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_bool_fun'] : 4.35/1.87 ( iProver_Flat_'register$ae'(X0_'C_d_prod_update_a_update_fun_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_bool_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bv' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bv'(X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uub$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_bool_fun',X0_'C_update_set'] : 4.35/1.87 ( iProver_Flat_'uub$'(X0_'C_update_bool_fun',X0_'C_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_bool_fun'=iProver_Domain_'C_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_d_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$a'(X0_'D_update_a_d_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_d_prod_update_fun'=iProver_Domain_'D_update_a_d_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cy' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update',X0_'C_d_prod_update_c_update_fun',X0_'C_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cy'(X0_'C_update',X0_'C_d_prod_update_c_update_fun',X0_'C_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$u' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update',X0_'C_update_a_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$u'(X0_'A_update',X0_'C_update_a_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvm$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_a_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvm$'(X0_'C_update_b_a_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_a_prod_update_fun'=iProver_Domain_'C_update_b_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$q' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_d_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$q'(X0_'D_d_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$i'(X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uwa$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_bool_fun',X0_'A_update_set'] : 4.35/1.87 ( iProver_Flat_'uwa$'(X0_'C_update_a_update_fun_bool_fun',X0_'A_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$i'(X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_c_prod_update_a_b_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$m'(X0_'D_c_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_c_prod_update_a_b_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update_b_update_fun'=iProver_Domain_'D_c_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$aj' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$aj'(X0_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'=iProver_Domain_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$n' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$n'(X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_d_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bu' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_b_prod_update',X0_'A_c_prod_update_b_b_prod_update_fun',X0_'A_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bu'(X0_'B_b_prod_update',X0_'A_c_prod_update_b_b_prod_update_fun',X0_'A_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bv' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$bv'(X0_'D_update_b_update_fun',X0_'D_update_a_update_fun_d_update_b_update_fun_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun',X0_'C_update_b_update_fun',X0_'A_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$i'(X0_'A_update_b_update_fun',X0_'C_update_b_update_fun',X0_'A_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dq' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_prod',X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_d_prod_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$dq'(X0_'B_update_b_update_prod',X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_d_prod_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$v' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_a_prod_update',X0_'C_update_a_a_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$v'(X0_'A_a_prod_update',X0_'C_update_a_a_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_a_prod_update'=iProver_Domain_'A_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'grp$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_set',X0_'D_update_a_update_fun_d_update_b_update_fun_fun'] : 4.35/1.87 ( iProver_Flat_'grp$c'(X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_a_update_fun_set',X0_'D_update_a_update_fun_d_update_b_update_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bg' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update',X0_'D_update_d_update_fun',X1_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bg'(X0_'D_update',X0_'D_update_d_update_fun',X1_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$v' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'B_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$v'(X0_'C_d_prod_update_b_update_fun',X0_'B_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_b_prod_update',X0_'B_update',X1_'B_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$f'(X0_'B_b_prod_update',X0_'B_update',X1_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$x' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'D_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$x'(X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'D_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvn$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_a_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvn$'(X0_'D_update_b_a_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_a_prod_update_fun'=iProver_Domain_'D_update_b_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bp' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bp'(X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$m'(X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$'(X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun'=iProver_Domain_'C_d_prod_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ch' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'C_a_prod_update_b_update_fun',X0_'C_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ch'(X0_'B_update',X0_'C_a_prod_update_b_update_fun',X0_'C_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$k'(X0_'D_c_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update_a_a_prod_update_fun'=iProver_Domain_'D_c_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bo' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'C_d_prod_update_a_b_prod_update_fun',X0_'C_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bo'(X0_'A_b_prod_update',X0_'C_d_prod_update_a_b_prod_update_fun',X0_'C_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bf' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$bf'(X0_'C_update_a_update_fun_c_update_b_update_fun_fun',X0_'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cp' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun',X0_'B_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$cp'(X0_'A_update_a_update_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun',X0_'B_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bq' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_b_prod_update',X0_'C_c_prod_update_b_b_prod_update_fun',X0_'C_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bq'(X0_'B_b_prod_update',X0_'C_c_prod_update_b_b_prod_update_fun',X0_'C_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'relcompp$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_d_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'relcompp$l'(X0_'A_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_d_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_d_update_bool_fun_fun'=iProver_Domain_'A_update_d_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$am' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$am'(X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dw' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$dw'(X0_'C_d_prod_update_b_update_fun',X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_b_prod_update',X1_'C_b_prod_update',X2_'C_b_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$k'(X0_'C_b_prod_update',X1_'C_b_prod_update',X2_'C_b_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_b_prod_update'=iProver_Domain_'C_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'g$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'g$'(X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bg' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_a_update_prod_fun',X0_'C_update_a_update_a_update_prod_fun',X0_'D_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bg'(X0_'D_update_a_update_a_update_prod_fun',X0_'C_update_a_update_a_update_prod_fun',X0_'D_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_a_update_prod_fun'=iProver_Domain_'D_update_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ba' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update',X0_'A_update_d_c_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ba'(X0_'D_c_prod_update',X0_'A_update_d_c_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update'=iProver_Domain_'D_c_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uui$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_d_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uui$'(X0_'D_update_b_d_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_d_prod_update_fun'=iProver_Domain_'D_update_b_d_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_d_prod_update',X1_'B_d_prod_update',X2_'B_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$e'(X0_'B_d_prod_update',X1_'B_d_prod_update',X2_'B_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$aa' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update',X0_'A_update_d_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$aa'(X0_'D_update',X0_'A_update_d_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'preregister$i' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_bool_fun'] : 4.35/1.87 ( iProver_Flat_'preregister$i'(X0_'D_update_a_update_fun_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cg' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'C_c_prod_update_b_update_fun',X0_'C_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cg'(X0_'B_update',X0_'C_c_prod_update_b_update_fun',X0_'C_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ck' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'D_c_prod_update_b_update_fun',X0_'D_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ck'(X0_'B_update',X0_'D_c_prod_update_b_update_fun',X0_'D_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_d_prod_update',X0_'D_update_b_d_prod_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$l'(X0_'B_d_prod_update',X0_'D_update_b_d_prod_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'convol$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'convol$f'(X0_'C_d_prod_update_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_a_update_prod_fun'=iProver_Domain_'C_d_prod_update_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$ad' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_a_prod_update_c_c_prod_update_fun',X0_'A_update_c_update_fun',X1_'A_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$ad'(X0_'A_a_prod_update_c_c_prod_update_fun',X0_'A_update_c_update_fun',X1_'A_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_a_prod_update_c_c_prod_update_fun'=iProver_Domain_'A_a_prod_update_c_c_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ca' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'B_a_prod_update_b_update_fun',X0_'B_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ca'(X0_'B_update',X0_'B_a_prod_update_b_update_fun',X0_'B_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$r' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_d_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$r'(X0_'D_update_d_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_d_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'D_update_d_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'convol$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'convol$b'(X0_'C_update_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_a_update_prod_fun'=iProver_Domain_'C_update_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_b_prod_update',X1_'B_b_prod_update',X2_'B_b_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$d'(X0_'B_b_prod_update',X1_'B_b_prod_update',X2_'B_b_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$v' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_d_prod_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$v'(X0_'D_c_d_prod_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_d_prod_prod_update_a_a_prod_update_fun'=iProver_Domain_'D_c_d_prod_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_a_prod_update_b_update_fun',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$f'(X0_'D_a_prod_update_b_update_fun',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_a_prod_update_b_update_fun'=iProver_Domain_'D_a_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$s' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$s'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvh$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_a_prod_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvh$'(X0_'D_update_b_a_prod_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_a_prod_update_fun'=iProver_Domain_'D_update_b_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$l'(X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bz' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bz'(X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$s' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_a_prod_update',X0_'C_update_b_a_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$s'(X0_'B_a_prod_update',X0_'C_update_b_a_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uuk$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_d_d_prod_update_fun',X0_'A_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'uuk$'(X0_'A_update_d_d_prod_update_fun',X0_'A_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_d_d_prod_update_fun'=iProver_Domain_'A_update_d_d_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$a'(X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bh' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update',X0_'D_update_c_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bh'(X0_'C_update',X0_'D_update_c_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$h'(X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$z' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$z'(X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cj' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'A_a_prod_update_b_update_fun',X0_'A_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cj'(X0_'B_update',X0_'A_a_prod_update_b_update_fun',X0_'A_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cn' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun',X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'B_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$cn'(X0_'D_update_b_update_fun',X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'B_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_b_a_prod_update_fun',X0_'C_update_b_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$d'(X0_'C_c_prod_update_b_a_prod_update_fun',X0_'C_update_b_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_c_prod_update_b_a_prod_update_fun'=iProver_Domain_'C_c_prod_update_b_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$g' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$g'(X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dv' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$dv'(X0_'C_d_prod_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$t' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_d_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$t'(X0_'C_d_prod_d_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_d_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_d_prod_d_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bb' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bb'(X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$b'(X0_'C_a_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update_a_b_prod_update_fun'=iProver_Domain_'C_a_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$x' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$x'(X0_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_d_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$h'(X0_'C_a_prod_update_b_update_fun',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update_b_update_fun'=iProver_Domain_'C_a_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$k' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$k'(X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'A_update_a_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$j' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update',X1_'D_c_prod_update',X2_'D_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$j'(X0_'D_c_prod_update',X1_'D_c_prod_update',X2_'D_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update'=iProver_Domain_'D_c_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$cg' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun',X0_'D_update_b_update_fun',X0_'B_update_d_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$cg'(X0_'B_update_b_update_fun',X0_'D_update_b_update_fun',X0_'B_update_d_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$al' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_bool_fun',X0_'D_update_d_update_bool_fun_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$al'(X0_'D_update_bool_fun',X0_'D_update_d_update_bool_fun_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_bool_fun'=iProver_Domain_'D_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bt' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_bool_fun',X0_'B_update_bool_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bt'(X0_'A_update_bool_fun',X0_'B_update_bool_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_bool_fun'=iProver_Domain_'A_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$r' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'C_c_prod_update_a_b_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$r'(X0_'C_c_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'C_c_prod_update_a_b_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_c_prod_update_b_update_fun'=iProver_Domain_'C_c_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$l'(X0_'D_c_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update_a_b_prod_update_fun'=iProver_Domain_'D_c_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'f$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'f$'(X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_a_b_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$c'(X0_'B_update_a_b_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_a_b_prod_update_fun'=iProver_Domain_'B_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cc' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update',X0_'A_d_prod_update_a_update_fun',X0_'A_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cc'(X0_'A_update',X0_'A_d_prod_update_a_update_fun',X0_'A_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cd' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'A_d_prod_update_b_update_fun',X0_'A_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cd'(X0_'B_update',X0_'A_d_prod_update_b_update_fun',X0_'A_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dl' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_prod',X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_d_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$dl'(X0_'A_update_a_update_prod',X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_d_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$w' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_d_prod_update',X0_'B_update_b_d_prod_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$w'(X0_'B_d_prod_update',X0_'B_update_b_d_prod_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'A_update_a_b_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$f'(X0_'A_b_prod_update',X0_'A_update_a_b_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'convol$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'convol$c'(X0_'D_update_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_a_update_prod_fun'=iProver_Domain_'D_update_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_a_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$d'(X0_'A_update_a_a_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_a_prod_update_fun'=iProver_Domain_'A_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bb' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_b_prod_update',X0_'A_update_d_b_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bb'(X0_'D_b_prod_update',X0_'A_update_d_b_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$l' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update',X1_'C_a_prod_update',X2_'C_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$l'(X0_'C_a_prod_update',X1_'C_a_prod_update',X2_'C_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update'=iProver_Domain_'C_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'D_update_b_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$m'(X0_'B_update',X0_'D_update_b_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$n' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update',X0_'B_update_a_update_fun',X0_'A_update_a_update_fun',X0_'B_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'register_pair$n'(X0_'A_update',X0_'B_update_a_update_fun',X0_'A_update_a_update_fun',X0_'B_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cz' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update',X0_'C_update_c_d_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cz'(X0_'C_d_prod_update',X0_'C_update_c_d_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bq' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bq'(X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_b_update_prod_fun'=iProver_Domain_'C_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$v' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_c_prod_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun',X0_'C_update_b_b_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$v'(X0_'A_c_prod_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun',X0_'C_update_b_b_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'A_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$aa' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'D_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$aa'(X0_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'D_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$ai' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$ai'(X0_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'D_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'top$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_set'] : 4.35/1.87 ( iProver_Flat_'top$a'(X0_'D_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_set'=iProver_Domain_'D_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cb' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update',X0_'B_update_c_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cb'(X0_'C_update',X0_'B_update_c_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$af' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'D_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$af'(X0_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'D_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'=iProver_Domain_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'top$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_set'] : 4.35/1.87 ( iProver_Flat_'top$'(X0_'C_d_prod_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_set'=iProver_Domain_'C_d_prod_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$'(X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'A_update_a_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uwd$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'uwd$'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun'=iProver_Domain_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ca' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ca'(X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uus$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_d_b_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uus$'(X0_'A_update_d_b_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_d_b_prod_update_fun'=iProver_Domain_'A_update_d_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvs$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'uvs$'(X0_'A_update_b_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$aa' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_d_prod_update_a_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$aa'(X0_'D_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_d_prod_update_a_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$b'(X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'id_update$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'id_update$a'(X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$e' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'C_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$e'(X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'C_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$au' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update',X0_'D_update_a_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$au'(X0_'A_update',X0_'D_update_a_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bz' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bz'(X0_'B_update',X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bx' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bx'(X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ak' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun',X0_'C_update_a_update_fun',X0_'A_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ak'(X0_'A_update_a_update_fun',X0_'C_update_a_update_fun',X0_'A_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$at' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun',X0_'A_update_a_update_fun',X1_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$at'(X0_'D_update_a_update_fun',X0_'A_update_a_update_fun',X1_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ai' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ai'(X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun',X0_'B_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$d'(X0_'C_update_b_update_fun',X0_'B_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$ak' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$ak'(X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uwb$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'A_update_set'] : 4.35/1.87 ( iProver_Flat_'uwb$'(X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'A_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_bool_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$u' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_d_prod_update_b_update_fun',X0_'B_a_prod_update_b_update_fun',X0_'A_d_prod_update_b_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$u'(X0_'A_d_prod_update_b_update_fun',X0_'B_a_prod_update_b_update_fun',X0_'A_d_prod_update_b_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_d_prod_update_b_update_fun'=iProver_Domain_'A_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$as' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_b_prod_update',X0_'D_update_d_b_prod_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$as'(X0_'D_b_prod_update',X0_'D_update_d_b_prod_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_c_prod_update_b_update_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$d'(X0_'D_c_prod_update_b_update_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_c_prod_update_b_update_fun'=iProver_Domain_'D_c_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$aj' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_a_prod_update_a_a_prod_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun',X0_'A_a_prod_update_c_c_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$aj'(X0_'A_a_prod_update_a_a_prod_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun',X0_'A_a_prod_update_c_c_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_a_prod_update_a_a_prod_update_fun'=iProver_Domain_'A_a_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$aw' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun'] : 4.35/1.87 ( iProver_Flat_'comp$aw'(X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uux$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_d_c_prod_update_fun',X0_'A_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'uux$'(X0_'A_update_d_c_prod_update_fun',X0_'A_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_d_c_prod_update_fun'=iProver_Domain_'A_update_d_c_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$az' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update',X0_'B_update_a_update_fun',X0_'B_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$az'(X0_'A_update',X0_'B_update_a_update_fun',X0_'B_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvq$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_b_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvq$'(X0_'A_update_a_b_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_b_prod_update_fun'=iProver_Domain_'A_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_a_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$m'(X0_'D_a_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_a_prod_update_a_b_prod_update_fun'=iProver_Domain_'D_a_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bl' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bl'(X0_'D_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_update_b_update_prod_fun'=iProver_Domain_'D_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'compatible$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'compatible$'(X0_'D_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ay' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ay'(X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvw$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_bool_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvw$'(X0_'A_update_bool_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_bool_fun'=iProver_Domain_'A_update_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_fun$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_fun$h'(X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'map_prod$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'map_prod$a'(X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_d_prod_update',X0_'D_update_a_d_prod_update_fun',X0_'D_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$c'(X0_'A_d_prod_update',X0_'D_update_a_d_prod_update_fun',X0_'D_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_d_prod_update'=iProver_Domain_'A_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ar' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_b_update_fun_bool_fun',X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$ar'(X0_'A_update_b_update_fun_bool_fun',X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_b_update_fun_bool_fun'=iProver_Domain_'A_update_b_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$de' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_prod',X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_d_prod_update_prod'] : 4.35/1.87 ( iProver_Flat_'fun_app$de'(X0_'B_update_b_update_prod',X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_d_prod_update_prod') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$ce' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update',X0_'C_d_prod_update_c_d_prod_update_fun',X1_'C_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$ce'(X0_'C_d_prod_update',X0_'C_d_prod_update_c_d_prod_update_fun',X1_'C_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'relcompp$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_d_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_d_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'relcompp$d'(X0_'B_update_d_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_d_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_d_update_bool_fun_fun'=iProver_Domain_'B_update_d_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cr' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_update_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun',X0_'B_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$cr'(X0_'A_update_a_update_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun',X0_'B_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_tensor$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_tensor$f'(X0_'C_a_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_a_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$dy' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'B_update_set_b_update_fun',X0_'B_update_set'] : 4.35/1.87 ( iProver_Flat_'fun_app$dy'(X0_'B_update',X0_'B_update_set_b_update_fun',X0_'B_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bk' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bk'(X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$aw' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_a_prod_update',X0_'C_update_d_a_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$aw'(X0_'D_a_prod_update',X0_'C_update_d_a_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_a_prod_update'=iProver_Domain_'D_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uve$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_a_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'uve$'(X0_'A_update_a_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_a_a_prod_update_fun'=iProver_Domain_'A_update_a_a_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'top$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_set'] : 4.35/1.87 ( iProver_Flat_'top$c'(X0_'A_update_set') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_set'=iProver_Domain_'A_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ac' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_a_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ac'(X0_'C_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_a_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_a_prod_update_b_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$b'(X0_'A_a_prod_update_b_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_a_prod_update_b_update_fun'=iProver_Domain_'A_a_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'uvf$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_b_b_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'uvf$'(X0_'D_update_b_b_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_b_b_prod_update_fun'=iProver_Domain_'D_update_b_b_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$cl' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update',X0_'D_a_prod_update_b_update_fun',X0_'D_a_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$cl'(X0_'B_update',X0_'D_a_prod_update_b_update_fun',X0_'D_a_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$t' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_c_prod_update_b_update_fun',X0_'B_a_prod_update_b_update_fun',X0_'C_c_prod_update_b_a_prod_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$t'(X0_'C_c_prod_update_b_update_fun',X0_'B_a_prod_update_b_update_fun',X0_'C_c_prod_update_b_a_prod_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_c_prod_update_b_update_fun'=iProver_Domain_'C_c_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$h' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$h'(X0_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'collect$' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_set',X0_'C_d_prod_update_bool_fun'] : 4.35/1.87 ( iProver_Flat_'collect$'(X0_'C_d_prod_update_set',X0_'C_d_prod_update_bool_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_set'=iProver_Domain_'C_d_prod_update_set'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bl' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_a_prod_update',X0_'C_c_prod_update_a_a_prod_update_fun',X0_'C_c_prod_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$bl'(X0_'A_a_prod_update',X0_'C_c_prod_update_a_a_prod_update_fun',X0_'C_c_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_a_prod_update'=iProver_Domain_'A_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'rel_fun$al' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'rel_fun$al'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$t' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_b_prod_update',X0_'C_update_a_b_prod_update_fun',X0_'C_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$t'(X0_'A_b_prod_update',X0_'C_update_a_b_prod_update_fun',X0_'C_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$b' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_d_prod_update',X0_'A_update_a_d_prod_update_fun',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'fun_app$b'(X0_'A_d_prod_update',X0_'A_update_a_d_prod_update_fun',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_d_prod_update'=iProver_Domain_'A_d_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp_update$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_c_d_prod_update_fun',X0_'C_d_prod_update'] : 4.35/1.87 ( iProver_Flat_'comp_update$m'(X0_'C_d_prod_update_c_d_prod_update_fun',X0_'C_d_prod_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_c_d_prod_update_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$ap' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun',X0_'B_update_a_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$ap'(X0_'D_update_a_update_fun',X0_'B_update_a_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'register_pair$j' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_d_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'register_pair$j'(X0_'A_d_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_d_prod_update_b_update_fun'=iProver_Domain_'A_d_prod_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$z' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_b_update_fun',X0_'C_update_b_update_fun',X0_'B_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$z'(X0_'B_update_b_update_fun',X0_'C_update_b_update_fun',X0_'B_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'convol$d' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'convol$d'(X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_d_prod_update_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bh' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_a_update_prod_fun',X1_'C_update_a_update_a_update_prod_fun',X0_'C_update_c_update_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bh'(X0_'C_update_a_update_a_update_prod_fun',X1_'C_update_a_update_a_update_prod_fun',X0_'C_update_c_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_a_update_a_update_prod_fun'=iProver_Domain_'C_update_a_update_a_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'fun_app$bw' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun'] : 4.35/1.87 ( iProver_Flat_'fun_app$bw'(X0_'D_update_a_update_fun_d_update_b_update_fun_fun',X0_'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'comp$bu' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_update_prod_a_update_a_update_prod_fun'] : 4.35/1.87 ( iProver_Flat_'comp$bu'(X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'compatible$ad' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun'] : 4.35/1.87 ( iProver_Flat_'compatible$ad'(X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'tensor_update$m' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_a_prod_update',X0_'C_update',X0_'A_update'] : 4.35/1.87 ( iProver_Flat_'tensor_update$m'(X0_'C_a_prod_update',X0_'C_update',X0_'A_update') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'C_a_prod_update'=iProver_Domain_'C_a_prod_update'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'conversep$a' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'A_update_c_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'conversep$a'(X0_'A_update_c_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'A_update_c_update_bool_fun_fun'=iProver_Domain_'A_update_c_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'relcompp$c' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'B_update_c_d_prod_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_bool_fun_fun'] : 4.35/1.87 ( iProver_Flat_'relcompp$c'(X0_'B_update_c_d_prod_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_c_d_prod_update_bool_fun_fun') <=> 4.35/1.87 ( 4.35/1.87 ( 4.35/1.87 ( X0_'B_update_c_d_prod_update_bool_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_bool_fun_fun'_1 ) 4.35/1.87 ) 4.35/1.87 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ) 4.35/1.87 ). 4.35/1.87 4.35/1.87 %------ Positive definition of iProver_Flat_'collect$f' 4.35/1.87 fof(lit_def,axiom, 4.35/1.87 (! [X0_'C_update_a_update_fun_set',X0_'C_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_'collect$f'(X0_'C_update_a_update_fun_set',X0_'C_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_set'=iProver_Domain_'C_update_a_update_fun_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$x' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update',X0_'B_update_b_update_fun',X1_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$x'(X0_'B_update',X0_'B_update_b_update_fun',X1_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$br' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_a_update_a_update_prod_fun'] : 4.35/1.88 ( iProver_Flat_'comp$br'(X0_'C_d_prod_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_a_update_a_update_prod_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'id_update$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'id_update$'(X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'convol$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_b_update_prod_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'convol$a'(X0_'A_update_b_update_b_update_prod_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_b_update_prod_fun'=iProver_Domain_'A_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'pred_fun$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun',X0_'D_update_bool_fun',X0_'A_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'pred_fun$e'(X0_'D_update_a_update_fun_bool_fun',X0_'D_update_bool_fun',X0_'A_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$w' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$w'(X0_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_d_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'conversep$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'conversep$b'(X0_'A_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_c_d_prod_update_bool_fun_fun'=iProver_Domain_'A_update_c_d_prod_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp_update$f' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_c_prod_update',X1_'B_c_prod_update',X2_'B_c_prod_update'] : 4.35/1.88 ( iProver_Flat_'comp_update$f'(X0_'B_c_prod_update',X1_'B_c_prod_update',X2_'B_c_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_c_prod_update'=iProver_Domain_'B_c_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun',X0_'A_update_c_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$e'(X0_'C_update_c_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun',X0_'A_update_c_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_update_bool_fun_fun'=iProver_Domain_'C_update_c_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$l' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$l'(X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'collect$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_set',X0_'C_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'collect$b'(X0_'C_update_set',X0_'C_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_set'=iProver_Domain_'C_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_b_update_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$g'(X0_'C_c_prod_update_b_update_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_b_update_fun'=iProver_Domain_'C_c_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_a_prod_update',X0_'B_update_b_a_prod_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$'(X0_'B_a_prod_update',X0_'B_update_b_a_prod_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bf' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_b_update_prod_fun',X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bf'(X0_'A_update_b_update_b_update_prod_fun',X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_b_update_prod_fun'=iProver_Domain_'A_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$a'(X0_'B_update_c_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_update_fun_a_update_a_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_a_update_a_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvx$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'uvx$'(X0_'C_update_c_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_update_bool_fun_fun'=iProver_Domain_'C_update_c_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'compatible$m' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'compatible$m'(X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$ah' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$ah'(X0_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ae' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_d_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ae'(X0_'C_d_prod_d_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_d_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dn' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'D_update_c_update_prod_a_update_a_update_prod_fun',X0_'D_update_c_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dn'(X0_'A_update_a_update_prod',X0_'D_update_c_update_prod_a_update_a_update_prod_fun',X0_'D_update_c_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bc' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_a_prod_update',X0_'A_update_d_a_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bc'(X0_'D_a_prod_update',X0_'A_update_d_a_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_a_prod_update'=iProver_Domain_'D_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$g'(X0_'C_update_b_update_bool_fun_fun',X0_'C_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_bool_fun_fun'=iProver_Domain_'C_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$e'(X0_'B_update_d_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_a_update_a_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_a_update_a_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuf$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun_set'] : 4.35/1.88 ( iProver_Flat_'uuf$'(X0_'C_update_a_update_fun_bool_fun',X0_'C_update_a_update_fun_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$r' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_c_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$r'(X0_'D_c_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$f' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_set',X0_'A_update_b_update_fun',X0_'A_update_set'] : 4.35/1.88 ( iProver_Flat_'image$f'(X0_'B_update_set',X0_'A_update_b_update_fun',X0_'A_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_set'=iProver_Domain_'B_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uud$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun_set'] : 4.35/1.88 ( iProver_Flat_'uud$'(X0_'D_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'conversep$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_d_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'conversep$c'(X0_'A_update_d_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_d_update_bool_fun_fun'=iProver_Domain_'A_update_d_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvd$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_b_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvd$'(X0_'A_update_a_b_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_b_prod_update_fun'=iProver_Domain_'A_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$n' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_b_prod_update',X0_'D_update_b_b_prod_update_fun',X0_'D_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$n'(X0_'B_b_prod_update',X0_'D_update_b_b_prod_update_fun',X0_'D_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$cq' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun',X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$cq'(X0_'D_update_b_update_fun',X0_'B_update_c_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuc$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_bool_fun',X0_'A_update_set'] : 4.35/1.88 ( iProver_Flat_'uuc$'(X0_'A_update_bool_fun',X0_'A_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_bool_fun'=iProver_Domain_'A_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'h$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'h$'(X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$ac' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$ac'(X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$da' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$da'(X0_'B_update_b_update_prod',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$az' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_c_d_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$az'(X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_c_d_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$y' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun',X0_'D_update_a_update_fun',X0_'C_update_d_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$y'(X0_'C_update_a_update_fun',X0_'D_update_a_update_fun',X0_'C_update_d_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dr' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'D_update_d_update_prod_a_update_a_update_prod_fun',X0_'D_update_d_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dr'(X0_'A_update_a_update_prod',X0_'D_update_d_update_prod_a_update_a_update_prod_fun',X0_'D_update_d_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$c'(X0_'C_d_prod_update_a_b_prod_update_fun',X0_'C_update_a_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_b_prod_update_fun'=iProver_Domain_'C_d_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'tensor_update$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_c_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'tensor_update$b'(X0_'C_update_a_c_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_c_prod_update_fun'=iProver_Domain_'C_update_a_c_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bs' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_a_update_a_update_prod_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bs'(X0_'D_update_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_a_update_a_update_prod_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_b_update_prod_fun'=iProver_Domain_'D_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ao' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_bool_fun',X0_'B_update_b_update_bool_fun_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ao'(X0_'B_update_bool_fun',X0_'B_update_b_update_bool_fun_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_bool_fun'=iProver_Domain_'B_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$r' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'A_update_c_update_fun',X0_'D_update_c_update_fun',X0_'A_d_prod_update'] : 4.35/1.88 ( iProver_Flat_'register_pair$r'(X0_'C_update',X0_'A_update_c_update_fun',X0_'D_update_c_update_fun',X0_'A_d_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uwf$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'uwf$'(X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_bool_fun_fun'=iProver_Domain_'B_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bs' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_b_prod_update',X0_'C_d_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bs'(X0_'B_b_prod_update',X0_'C_d_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bo' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bo'(X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$p' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$p'(X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp_update$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_d_update_fun',X0_'D_update'] : 4.35/1.88 ( iProver_Flat_'comp_update$b'(X0_'D_update_d_update_fun',X0_'D_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_d_update_fun'=iProver_Domain_'D_update_d_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp_update$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_b_prod_update',X1_'D_b_prod_update',X2_'D_b_prod_update'] : 4.35/1.88 ( iProver_Flat_'comp_update$g'(X0_'D_b_prod_update',X1_'D_b_prod_update',X2_'D_b_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dg' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_update_d_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dg'(X0_'B_update_b_update_prod',X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_update_d_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ds' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'D_update_d_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$ds'(X0_'B_update_b_update_prod',X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'D_update_d_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_set',X0_'D_update_b_update_fun',X0_'D_update_set'] : 4.35/1.88 ( iProver_Flat_'image$e'(X0_'B_update_set',X0_'D_update_b_update_fun',X0_'D_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_set'=iProver_Domain_'B_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'top$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_set'] : 4.35/1.88 ( iProver_Flat_'top$b'(X0_'C_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_set'=iProver_Domain_'C_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$'(X0_'C_c_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_c_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvu$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'uvu$'(X0_'C_d_prod_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_bool_fun'=iProver_Domain_'C_d_prod_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bc' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bc'(X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun'=iProver_Domain_'C_d_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ae' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update',X0_'A_update_b_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ae'(X0_'B_update',X0_'A_update_b_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_set',X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set'] : 4.35/1.88 ( iProver_Flat_'image$d'(X0_'B_update_set',X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_set'=iProver_Domain_'B_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bj' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bj'(X0_'C_update_b_update_b_update_prod_fun',X0_'A_update_b_update_b_update_prod_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_b_update_prod_fun'=iProver_Domain_'C_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$aa' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_d_prod_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$aa'(X0_'C_c_d_prod_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uua$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_bool_fun',X0_'D_update_set'] : 4.35/1.88 ( iProver_Flat_'uua$'(X0_'D_update_bool_fun',X0_'D_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_bool_fun'=iProver_Domain_'D_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuv$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_a_prod_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuv$'(X0_'B_update_d_a_prod_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_a_prod_update_fun'=iProver_Domain_'B_update_d_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$j'(X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ac' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'A_update_c_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ac'(X0_'C_update',X0_'A_update_c_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$cs' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$cs'(X0_'C_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvy$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'uvy$'(X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun'=iProver_Domain_'C_d_prod_update_c_d_prod_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bd' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun',X0_'A_update_a_update_fun',X1_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bd'(X0_'C_d_prod_update_a_update_fun',X0_'A_update_a_update_fun',X1_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun'=iProver_Domain_'C_d_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$l' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_c_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$l'(X0_'A_c_prod_update_b_update_fun',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_c_prod_update_b_update_fun'=iProver_Domain_'A_c_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$c'(X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun',X0_'A_update_b_update_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$p' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'B_update_c_update_fun',X0_'A_update_c_update_fun',X0_'B_a_prod_update'] : 4.35/1.88 ( iProver_Flat_'register_pair$p'(X0_'C_update',X0_'B_update_c_update_fun',X0_'A_update_c_update_fun',X0_'B_a_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'tensor_update$l' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update',X0_'C_update',X1_'C_update'] : 4.35/1.88 ( iProver_Flat_'tensor_update$l'(X0_'C_c_prod_update',X0_'C_update',X1_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update'=iProver_Domain_'C_c_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'grp$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_bool_fun_fun',X0_'A_update_set',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'grp$'(X0_'A_update_b_update_bool_fun_fun',X0_'A_update_set',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_bool_fun_fun'=iProver_Domain_'A_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$cd' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_update_fun',X0_'A_update_c_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$cd'(X0_'B_update_c_update_fun',X0_'A_update_c_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_update_fun'=iProver_Domain_'B_update_c_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvo$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_b_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvo$'(X0_'C_update_a_b_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_b_prod_update_fun'=iProver_Domain_'C_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dj' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dj'(X0_'A_update_a_update_prod',X0_'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_c_d_prod_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$r' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_b_prod_update',X0_'C_update_b_b_prod_update_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$r'(X0_'B_b_prod_update',X0_'C_update_b_b_prod_update_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ad' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ad'(X0_'C_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$'(X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'A_update_a_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_d_prod_update_b_update_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$c'(X0_'D_d_prod_update_b_update_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_d_prod_update_b_update_fun'=iProver_Domain_'D_d_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_set',X0_'C_update_b_update_fun',X0_'C_update_set'] : 4.35/1.88 ( iProver_Flat_'image$c'(X0_'B_update_set',X0_'C_update_b_update_fun',X0_'C_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_set'=iProver_Domain_'B_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$l' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_c_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'D_c_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$l'(X0_'D_c_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'D_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_c_prod_update_b_update_fun'=iProver_Domain_'D_c_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$q' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update',X0_'C_update_b_update_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$q'(X0_'B_update',X0_'C_update_b_update_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$g'(X0_'C_d_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$n' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_c_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$n'(X0_'D_update_c_update_prod_a_update_a_update_prod_fun',X0_'D_update_a_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_c_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'D_update_c_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuu$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_b_prod_update_fun',X0_'B_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuu$'(X0_'B_update_d_b_prod_update_fun',X0_'B_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_b_prod_update_fun'=iProver_Domain_'B_update_d_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$a'(X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun'=iProver_Domain_'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$j'(X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$s' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_a_update_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$s'(X0_'C_c_prod_update_a_update_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_a_update_fun'=iProver_Domain_'C_c_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'compatible$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun',X0_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'compatible$d'(X0_'D_update_a_update_fun_bool_fun',X0_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$f' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$f'(X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$ae' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_a_prod_update_a_a_prod_update_fun',X0_'A_update_a_update_fun',X1_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$ae'(X0_'A_a_prod_update_a_a_prod_update_fun',X0_'A_update_a_update_fun',X1_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_a_prod_update_a_a_prod_update_fun'=iProver_Domain_'A_a_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$cu' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun',X0_'B_update_c_d_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$cu'(X0_'A_update_a_update_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun',X0_'B_update_c_d_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$h' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_a_prod_update',X0_'A_update_a_a_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$h'(X0_'A_a_prod_update',X0_'A_update_a_a_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_a_prod_update'=iProver_Domain_'A_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$cb' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun'] : 4.35/1.88 ( iProver_Flat_'comp$cb'(X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp_update$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_update_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'comp_update$c'(X0_'C_update_c_update_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_update_fun'=iProver_Domain_'C_update_c_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bm' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bm'(X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$ad' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$ad'(X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$av' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_b_prod_update',X0_'C_update_d_b_prod_update_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$av'(X0_'D_b_prod_update',X0_'C_update_d_b_prod_update_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_d_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$j'(X0_'D_d_prod_update_a_a_prod_update_fun',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_d_prod_update_a_a_prod_update_fun'=iProver_Domain_'D_d_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bd' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_a_update_fun',X1_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bd'(X0_'A_update',X0_'A_update_a_update_fun',X1_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bw' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_d_update_prod_a_update_a_update_prod_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bw'(X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'A_update_a_update_prod_b_update_b_update_prod_fun',X0_'C_update_d_update_prod_a_update_a_update_prod_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ag' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_c_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ag'(X0_'C_d_prod_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_d_prod_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$cv' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'B_update_d_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$cv'(X0_'C_update_b_update_fun',X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'B_update_d_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dh' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_c_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dh'(X0_'A_update_a_update_prod',X0_'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_d_prod_update_c_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_c_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$b'(X0_'B_update_c_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_c_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_update_bool_fun_fun'=iProver_Domain_'B_update_c_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuy$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_d_a_prod_update_fun',X0_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuy$'(X0_'A_update_d_a_prod_update_fun',X0_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_d_a_prod_update_fun'=iProver_Domain_'A_update_d_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$au' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'comp$au'(X0_'B_update_d_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_d_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_d_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$o' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$o'(X0_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$f' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$f'(X0_'C_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_d_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_update_d_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uul$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_c_d_prod_update_fun',X0_'A_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'uul$'(X0_'A_update_c_d_prod_update_fun',X0_'A_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_c_d_prod_update_fun'=iProver_Domain_'A_update_c_d_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$b'(X0_'C_update_c_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_update_c_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ax' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ax'(X0_'B_update_d_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'B_update_d_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_d_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_d_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$d'(X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun'=iProver_Domain_'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$af' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_c_d_prod_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$af'(X0_'D_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_c_d_prod_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uug$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_d_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uug$'(X0_'C_update_b_d_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_d_prod_update_fun'=iProver_Domain_'C_update_b_d_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'compatible$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'compatible$g'(X0_'C_update_a_update_fun_bool_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'tensor_update$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_a_prod_update',X0_'D_update',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'tensor_update$j'(X0_'D_a_prod_update',X0_'D_update',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_a_prod_update'=iProver_Domain_'D_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bj' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$bj'(X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$by' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$by'(X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$x' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_a_prod_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun',X1_'A_update_b_b_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$x'(X0_'A_a_prod_update_b_b_prod_update_fun',X0_'A_update_b_b_prod_update_fun',X1_'A_update_b_b_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_a_prod_update_b_b_prod_update_fun'=iProver_Domain_'A_a_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_fun$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_fun$b'(X0_'B_update_c_update_fun_c_update_b_update_fun_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_update_fun_c_update_b_update_fun_fun'=iProver_Domain_'B_update_c_update_fun_c_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$i' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_a_prod_update_b_update_fun',X0_'B_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$i'(X0_'B_a_prod_update_b_update_fun',X0_'B_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_a_prod_update_b_update_fun'=iProver_Domain_'B_a_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$z' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_d_prod_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$z'(X0_'C_c_d_prod_prod_update_a_a_prod_update_fun',X0_'C_update_a_update_fun',X0_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_d_prod_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_c_d_prod_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ay' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_a_prod_update',X0_'B_update_d_a_prod_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ay'(X0_'D_a_prod_update',X0_'B_update_d_a_prod_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_a_prod_update'=iProver_Domain_'D_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'grp$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_set',X0_'C_update_a_update_fun_c_update_b_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'grp$a'(X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_a_update_fun_set',X0_'C_update_a_update_fun_c_update_b_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$am' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_bool_fun',X0_'C_update_c_update_bool_fun_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$am'(X0_'C_update_bool_fun',X0_'C_update_c_update_bool_fun_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_bool_fun'=iProver_Domain_'C_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'compatible$r' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun',X0_'B_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'compatible$r'(X0_'D_update_a_update_fun_bool_fun',X0_'B_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'convol$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'convol$e'(X0_'D_update_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_b_update_prod_fun'=iProver_Domain_'D_update_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bt' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_a_prod_update',X0_'A_c_prod_update_b_a_prod_update_fun',X0_'A_c_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bt'(X0_'B_a_prod_update',X0_'A_c_prod_update_b_a_prod_update_fun',X0_'A_c_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$f' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X1_'C_update_b_update_fun',X0_'C_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$f'(X0_'C_update_b_update_fun',X1_'C_update_b_update_fun',X0_'C_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$k' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_d_prod_update_a_update_fun',X0_'A_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$k'(X0_'A_d_prod_update_a_update_fun',X0_'A_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_d_prod_update_a_update_fun'=iProver_Domain_'A_d_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$j'(X0_'C_d_prod_update_b_update_bool_fun_fun',X0_'C_d_prod_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_bool_fun_fun'=iProver_Domain_'C_d_prod_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$w' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_c_d_prod_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$w'(X0_'D_c_d_prod_prod_update_b_b_prod_update_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ax' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_b_prod_update',X0_'B_update_d_b_prod_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ax'(X0_'D_b_prod_update',X0_'B_update_d_b_prod_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'tensor_update$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_a_prod_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'tensor_update$'(X0_'A_update_b_a_prod_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_a_prod_update_fun'=iProver_Domain_'A_update_b_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$r' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$r'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uup$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_b_prod_update_fun',X0_'B_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uup$'(X0_'B_update_b_b_prod_update_fun',X0_'B_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_b_prod_update_fun'=iProver_Domain_'B_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$ab' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'D_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$ab'(X0_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'D_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'=iProver_Domain_'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uue$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_a_update_fun_set'] : 4.35/1.88 ( iProver_Flat_'uue$'(X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_a_update_fun_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_bool_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$j' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$j'(X0_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun',X0_'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun',X0_'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$p' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_d_prod_update',X0_'C_update_b_d_prod_update_fun',X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$p'(X0_'B_d_prod_update',X0_'C_update_b_d_prod_update_fun',X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_d_prod_update'=iProver_Domain_'B_d_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$o' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$o'(X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuo$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_b_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuo$'(X0_'D_update_b_b_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_b_prod_update_fun'=iProver_Domain_'D_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuh$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_d_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuh$'(X0_'A_update_b_d_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_d_prod_update_fun'=iProver_Domain_'A_update_b_d_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ce' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_d_prod_update_fun',X0_'A_update_c_d_prod_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ce'(X0_'B_update_c_d_prod_update_fun',X0_'A_update_c_d_prod_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_d_prod_update_fun'=iProver_Domain_'B_update_c_d_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_set',X0_'D_update_a_update_fun',X0_'D_update_set'] : 4.35/1.88 ( iProver_Flat_'image$a'(X0_'A_update_set',X0_'D_update_a_update_fun',X0_'D_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_set'=iProver_Domain_'A_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$m' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_b_prod_update_a_update_fun',X0_'A_update_a_update_fun',X0_'B_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$m'(X0_'A_b_prod_update_a_update_fun',X0_'A_update_a_update_fun',X0_'B_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_b_prod_update_a_update_fun'=iProver_Domain_'A_b_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_c_prod_update',X0_'A_update_a_c_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$d'(X0_'A_c_prod_update',X0_'A_update_a_c_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_c_prod_update'=iProver_Domain_'A_c_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'grp$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_set',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'grp$b'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_set',X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$p' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$p'(X0_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dc' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dc'(X0_'B_update_b_update_prod',X0_'C_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_update_c_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuj$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_d_prod_update_fun',X0_'B_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuj$'(X0_'B_update_b_d_prod_update_fun',X0_'B_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_d_prod_update_fun'=iProver_Domain_'B_update_b_d_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_fun',X0_'B_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$g'(X0_'A_update_b_update_fun',X0_'B_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvv$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'uvv$'(X0_'D_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_bool_fun'=iProver_Domain_'D_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'preregister$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_'preregister$a'(X0_'C_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun_bool_fun'=iProver_Domain_'C_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$'(X0_'B_update_b_update_bool_fun_fun',X0_'B_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_bool_fun_fun'=iProver_Domain_'B_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuz$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_b_prod_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuz$'(X0_'C_update_b_b_prod_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_b_prod_update_fun'=iProver_Domain_'C_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$p' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun',X0_'B_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$p'(X0_'D_update_b_update_fun',X0_'B_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bx' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_c_update_fun',X1_'C_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bx'(X0_'C_update',X0_'C_update_c_update_fun',X1_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uuq$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_d_a_prod_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uuq$'(X0_'C_update_d_a_prod_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_d_a_prod_update_fun'=iProver_Domain_'C_update_d_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvi$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_a_prod_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvi$'(X0_'C_update_b_a_prod_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_a_prod_update_fun'=iProver_Domain_'C_update_b_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$n' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_d_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$n'(X0_'D_d_prod_update_a_b_prod_update_fun',X0_'D_update_a_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_d_prod_update_a_b_prod_update_fun'=iProver_Domain_'D_d_prod_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$m' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$m'(X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'id_update$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update'] : 4.35/1.88 ( iProver_Flat_'id_update$b'(X0_'C_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ba' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_c_d_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ba'(X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_c_d_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$o' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_d_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_d_prod_update_a_b_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$o'(X0_'D_d_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_d_prod_update_a_b_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_d_prod_update_b_update_fun'=iProver_Domain_'D_d_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$m' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$m'(X0_'D_update_b_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun',X0_'A_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_bool_fun_fun'=iProver_Domain_'D_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$q' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$q'(X0_'D_update_d_update_prod_b_update_b_update_prod_fun',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'D_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvp$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_b_prod_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvp$'(X0_'C_update_a_b_prod_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_b_prod_update_fun'=iProver_Domain_'C_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun',X0_'B_update_a_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$c'(X0_'C_update_a_update_fun',X0_'B_update_a_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$al' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun',X0_'C_update_b_update_fun',X0_'D_update_c_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$al'(X0_'D_update_b_update_fun',X0_'C_update_b_update_fun',X0_'D_update_c_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'image$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_set',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_set'] : 4.35/1.88 ( iProver_Flat_'image$'(X0_'A_update_set',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_set'=iProver_Domain_'A_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$am' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_fun',X1_'A_update_b_update_fun',X0_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$am'(X0_'A_update_b_update_fun',X1_'A_update_b_update_fun',X0_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bi' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'B_update_d_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$bi'(X0_'D_update',X0_'B_update_d_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$o' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'B_update_d_update_fun',X0_'A_update_d_update_fun',X0_'B_a_prod_update'] : 4.35/1.88 ( iProver_Flat_'register_pair$o'(X0_'D_update',X0_'B_update_d_update_fun',X0_'A_update_d_update_fun',X0_'B_a_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$c'(X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X0_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uwc$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun',X0_'A_update_set'] : 4.35/1.88 ( iProver_Flat_'uwc$'(X0_'D_update_a_update_fun_bool_fun',X0_'A_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$y' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_b_prod_update',X0_'B_update_b_b_prod_update_fun',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$y'(X0_'B_b_prod_update',X0_'B_update_b_b_prod_update_fun',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvr$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_b_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvr$'(X0_'D_update_a_b_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_b_prod_update_fun'=iProver_Domain_'D_update_a_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$x' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_c_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$x'(X0_'C_d_prod_c_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_c_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_d_prod_c_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dm' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_d_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dm'(X0_'B_update_b_update_prod',X0_'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_d_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_pair$u' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_d_prod_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun',X0_'D_update_b_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_pair$u'(X0_'A_d_prod_update_b_a_prod_update_fun',X0_'A_update_b_a_prod_update_fun',X0_'D_update_b_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_d_prod_update_b_a_prod_update_fun'=iProver_Domain_'A_d_prod_update_b_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$do' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_b_update_prod',X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$do'(X0_'B_update_b_update_prod',X0_'D_update_c_update_prod_b_update_b_update_prod_fun',X0_'D_update_c_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_b_update_prod'=iProver_Domain_'B_update_b_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'pred_fun$c' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_bool_fun',X0_'A_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'pred_fun$c'(X0_'C_d_prod_update_a_update_fun_bool_fun',X0_'C_d_prod_update_bool_fun',X0_'A_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_bool_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dp' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'D_update_c_d_prod_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$dp'(X0_'A_update_a_update_prod',X0_'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun',X0_'D_update_c_d_prod_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$af' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_b_prod_update',X0_'A_update_b_b_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$af'(X0_'B_b_prod_update',X0_'A_update_b_b_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_b_prod_update'=iProver_Domain_'B_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ap' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_bool_fun',X0_'A_update_a_update_bool_fun_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ap'(X0_'A_update_bool_fun',X0_'A_update_a_update_bool_fun_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_bool_fun'=iProver_Domain_'A_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'collect$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_set',X0_'D_update_bool_fun'] : 4.35/1.88 ( iProver_Flat_'collect$a'(X0_'D_update_set',X0_'D_update_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_set'=iProver_Domain_'D_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$bn' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun'] : 4.35/1.88 ( iProver_Flat_'comp$bn'(X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'tensor_update$i' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_b_prod_update',X0_'D_update',X0_'B_update'] : 4.35/1.88 ( iProver_Flat_'tensor_update$i'(X0_'D_b_prod_update',X0_'D_update',X0_'B_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_b_prod_update'=iProver_Domain_'D_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$n' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_a_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_a_prod_update_a_b_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$n'(X0_'D_a_prod_update_b_update_fun',X0_'A_b_prod_update_b_update_fun',X0_'D_a_prod_update_a_b_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_a_prod_update_b_update_fun'=iProver_Domain_'D_a_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$o' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_a_prod_update',X0_'D_update_b_a_prod_update_fun',X0_'D_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$o'(X0_'B_a_prod_update',X0_'D_update_b_a_prod_update_fun',X0_'D_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_a_prod_update'=iProver_Domain_'B_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$a' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$a'(X0_'A_update_b_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_bool_fun_fun'=iProver_Domain_'A_update_b_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ab' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_c_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ab'(X0_'D_c_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'D_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'D_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$d'(X0_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun',X0_'C_update_c_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$i' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_c_d_prod_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$i'(X0_'A_update_c_d_prod_update_bool_fun_fun',X0_'A_update_a_update_bool_fun_fun',X1_'A_update_c_d_prod_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_c_d_prod_update_bool_fun_fun'=iProver_Domain_'A_update_c_d_prod_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ah' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_c_d_prod_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ah'(X0_'C_c_d_prod_prod_update_b_b_prod_update_fun',X0_'A_a_prod_update_b_b_prod_update_fun',X0_'C_c_d_prod_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_d_prod_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_c_d_prod_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$e'(X0_'C_c_prod_update_b_b_prod_update_fun',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_c_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvg$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_a_prod_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvg$'(X0_'A_update_b_a_prod_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_a_prod_update_fun'=iProver_Domain_'A_update_b_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$co' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$co'(X0_'D_update_b_update_fun',X0_'A_update_a_update_fun_d_update_b_update_fun_fun',X0_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$u' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_d_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$u'(X0_'C_d_prod_d_prod_update_b_b_prod_update_fun',X0_'C_d_prod_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_d_prod_update_b_b_prod_update_fun'=iProver_Domain_'C_d_prod_d_prod_update_b_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$n' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$n'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun',X0_'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun',X0_'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvz$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_d_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'uvz$'(X0_'D_update_d_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_d_update_bool_fun_fun'=iProver_Domain_'D_update_d_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_'register$e'(X0_'D_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_bool_fun'=iProver_Domain_'D_update_a_update_fun_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$g' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$g'(X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun',X0_'C_d_prod_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$be' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$be'(X0_'C_update_b_update_fun',X0_'C_update_a_update_fun_c_update_b_update_fun_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'collect$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun_set',X0_'D_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_'collect$d'(X0_'D_update_a_update_fun_set',X0_'D_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun_set'=iProver_Domain_'D_update_a_update_fun_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'register_tensor$ab' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'register_tensor$ab'(X0_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun'=iProver_Domain_'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uut$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_d_b_prod_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'uut$'(X0_'D_update_d_b_prod_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_d_b_prod_update_fun'=iProver_Domain_'D_update_d_b_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$cf' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_c_prod_update_a_update_fun',X0_'C_c_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$cf'(X0_'A_update',X0_'C_c_prod_update_a_update_fun',X0_'C_c_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'relcompp$k' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_d_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun',X0_'A_update_d_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'relcompp$k'(X0_'D_update_d_update_bool_fun_fun',X0_'D_update_a_update_bool_fun_fun',X0_'A_update_d_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_d_update_bool_fun_fun'=iProver_Domain_'D_update_d_update_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$q' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_c_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$q'(X0_'C_c_prod_update_b_update_fun',X0_'A_a_prod_update_b_update_fun',X0_'C_c_prod_update_a_a_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_c_prod_update_b_update_fun'=iProver_Domain_'C_c_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp_update$h' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_a_prod_update',X1_'D_a_prod_update',X2_'D_a_prod_update'] : 4.35/1.88 ( iProver_Flat_'comp_update$h'(X0_'D_a_prod_update',X1_'D_a_prod_update',X2_'D_a_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_a_prod_update'=iProver_Domain_'D_a_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$df' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_prod',X0_'C_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_update_d_update_prod'] : 4.35/1.88 ( iProver_Flat_'fun_app$df'(X0_'A_update_a_update_prod',X0_'C_update_d_update_prod_a_update_a_update_prod_fun',X0_'C_update_d_update_prod') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_prod'=iProver_Domain_'A_update_a_update_prod'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ci' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update',X0_'A_c_prod_update_b_update_fun',X0_'A_c_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ci'(X0_'B_update',X0_'A_c_prod_update_b_update_fun',X0_'A_c_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$z' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_d_prod_update',X0_'A_update_d_d_prod_update_fun',X0_'A_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$z'(X0_'D_d_prod_update',X0_'A_update_d_d_prod_update_fun',X0_'A_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_d_prod_update'=iProver_Domain_'D_d_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$dx' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$dx'(X0_'D_update_b_update_fun',X0_'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun',X0_'B_update_c_d_prod_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_b_update_fun'=iProver_Domain_'D_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$b' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_update_fun',X0_'A_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$b'(X0_'C_update_a_update_fun',X0_'A_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ak' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$ak'(X0_'C_d_prod_update_bool_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'C_d_prod_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_bool_fun'=iProver_Domain_'C_d_prod_update_bool_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'comp$ar' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_a_update_fun',X0_'D_update_a_update_fun',X0_'A_update_d_update_fun'] : 4.35/1.88 ( iProver_Flat_'comp$ar'(X0_'A_update_a_update_fun',X0_'D_update_a_update_fun',X0_'A_update_d_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_a_update_fun'=iProver_Domain_'A_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'top$d' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'B_update_set'] : 4.35/1.88 ( iProver_Flat_'top$d'(X0_'B_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'B_update_set'=iProver_Domain_'B_update_set'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'map_prod$e' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'map_prod$e'(X0_'C_update_d_update_prod_b_update_b_update_prod_fun',X0_'C_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_d_update_prod_b_update_b_update_prod_fun'=iProver_Domain_'C_update_d_update_prod_b_update_b_update_prod_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'rel_fun$t' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun'] : 4.35/1.88 ( iProver_Flat_'rel_fun$t'(X0_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun',X0_'C_d_prod_update_c_d_prod_update_bool_fun_fun',X0_'B_update_b_update_bool_fun_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'=iProver_Domain_'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'uvk$' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_a_a_prod_update_fun',X0_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'uvk$'(X0_'C_update_a_a_prod_update_fun',X0_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_a_a_prod_update_fun'=iProver_Domain_'C_update_a_a_prod_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$bk' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$bk'(X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun',X0_'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun',X0_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun'=iProver_Domain_'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$at' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_b_prod_update',X0_'D_update_a_b_prod_update_fun',X0_'D_update'] : 4.35/1.88 ( iProver_Flat_'fun_app$at'(X0_'A_b_prod_update',X0_'D_update_a_b_prod_update_fun',X0_'D_update') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_b_prod_update'=iProver_Domain_'A_b_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_'fun_app$ct' 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update_b_update_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_'fun_app$ct'(X0_'C_update_b_update_fun',X0_'A_update_a_update_fun_c_update_b_update_fun_fun',X0_'A_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK0 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update_a_update_fun',X0_'D_update_a_update_fun_bool_fun',X1_'D_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_sK0(X0_'D_update_a_update_fun',X0_'D_update_a_update_fun_bool_fun',X1_'D_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK1 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK1(X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK2 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK2(X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK3 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK3(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK4 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK4(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK5 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'D_update_a_update_fun',X0_'D_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK5(X0_'D_update',X0_'D_update_a_update_fun',X0_'D_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK6 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK6(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK7 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK7(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK8 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK8(X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK9 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK9(X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK10 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK10(X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK11 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK11(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK12 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK12(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK13 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK13(X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK14 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK14(X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK15 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK15(X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK16 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK16(X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK17 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK17(X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK18 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK18(X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK19 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK19(X0_'A_update',X0_'A_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK20 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_fun',X0_'A_update_set'] : 4.35/1.88 ( iProver_Flat_sK20(X0_'A_update_b_update_fun',X0_'A_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK21 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update_b_update_fun',X0_'A_update_set'] : 4.35/1.88 ( iProver_Flat_sK21(X0_'A_update_b_update_fun',X0_'A_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update_b_update_fun'=iProver_Domain_'A_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK22 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK22(X0_'A_update',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK23 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK23(X0_'A_update',X0_'C_d_prod_update_a_update_fun',X1_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK24 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK24(X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK25 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK25(X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK26 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK26(X0_'A_update',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK27 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK27(X0_'A_update',X0_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK28 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set'] : 4.35/1.88 ( iProver_Flat_sK28(X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK29 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set'] : 4.35/1.88 ( iProver_Flat_sK29(X0_'C_d_prod_update_b_update_fun',X0_'C_d_prod_update_set') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_b_update_fun'=iProver_Domain_'C_d_prod_update_b_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK30 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update',X0_'C_d_prod_update_set',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK30(X0_'C_d_prod_update',X0_'C_d_prod_update_set',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK31 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK31(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK32 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK32(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK33 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_a_update_fun_bool_fun',X1_'C_d_prod_update_a_update_fun_bool_fun'] : 4.35/1.88 ( iProver_Flat_sK33(X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_a_update_fun_bool_fun',X1_'C_d_prod_update_a_update_fun_bool_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_d_prod_update_a_update_fun'=iProver_Domain_'C_d_prod_update_a_update_fun'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK34 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK34(X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK35 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK35(X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK36 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK36(X0_'A_update',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK37 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'A_update',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.88 ( iProver_Flat_sK37(X0_'A_update',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK38 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK38(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.88 ( 4.35/1.88 ( 4.35/1.88 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.88 ) 4.35/1.88 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ) 4.35/1.88 ). 4.35/1.88 4.35/1.88 %------ Positive definition of iProver_Flat_sK39 4.35/1.88 fof(lit_def,axiom, 4.35/1.88 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.88 ( iProver_Flat_sK39(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK40 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK40(X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK41 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK41(X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK42 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK42(X0_'A_update',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK43 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK43(X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK44 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK44(X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK45 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK45(X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK46 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK46(X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK47 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK47(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK48 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK48(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK49 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK49(X0_'A_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK50 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK50(X0_'A_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK51 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK51(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK52 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK52(X0_'C_update',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK53 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update_a_update_fun',X0_'D_update_set'] : 4.35/1.89 ( iProver_Flat_sK53(X0_'D_update_a_update_fun',X0_'D_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK54 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update_a_update_fun',X0_'D_update_set'] : 4.35/1.89 ( iProver_Flat_sK54(X0_'D_update_a_update_fun',X0_'D_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update_a_update_fun'=iProver_Domain_'D_update_a_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK55 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_set',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK55(X0_'D_update',X0_'D_update_set',X0_'D_update_a_update_fun',X1_'D_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK56 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK56(X0_'A_update',X0_'D_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK57 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK57(X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK58 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK58(X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK59 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK59(X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK60 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK60(X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK61 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK61(X0_'A_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK62 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK62(X0_'D_update',X0_'A_update_b_update_fun',X0_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK63 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK63(X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK64 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK64(X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK65 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK65(X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK66 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK66(X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK67 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK67(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK68 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK68(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK69 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK69(X0_'C_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK70 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK70(X0_'D_update',X0_'C_update_a_update_fun',X0_'D_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK71 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_d_prod_update',X0_'C_d_prod_update_set',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK71(X0_'C_d_prod_update',X0_'C_d_prod_update_set',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK72 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_a_update_fun',X0_'C_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK72(X0_'C_update',X0_'C_update_a_update_fun',X0_'C_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK73 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK73(X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK74 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK74(X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK75 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK75(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK76 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK76(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK77 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK77(X0_'C_update',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK78 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK78(X0_'D_update',X0_'C_d_prod_update_b_update_fun',X1_'C_d_prod_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK79 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK79(X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK80 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK80(X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK81 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update_a_update_fun',X0_'C_update_a_update_fun_bool_fun',X1_'C_update_a_update_fun_bool_fun'] : 4.35/1.89 ( iProver_Flat_sK81(X0_'C_update_a_update_fun',X0_'C_update_a_update_fun_bool_fun',X1_'C_update_a_update_fun_bool_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK82 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_d_prod_update',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK82(X0_'C_d_prod_update',X0_'C_d_prod_update_a_update_fun',X0_'C_d_prod_update_set',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_d_prod_update'=iProver_Domain_'C_d_prod_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK83 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK83(X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK84 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK84(X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK85 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK85(X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK86 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK86(X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK87 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'B_update',X0_'B_update_set',X0_'B_update_b_update_fun',X1_'B_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK87(X0_'B_update',X0_'B_update_set',X0_'B_update_b_update_fun',X1_'B_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'B_update'=iProver_Domain_'B_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK88 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'B_update_b_update_fun',X0_'B_update_set'] : 4.35/1.89 ( iProver_Flat_sK88(X0_'B_update_b_update_fun',X0_'B_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK89 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'B_update_b_update_fun',X0_'B_update_set'] : 4.35/1.89 ( iProver_Flat_sK89(X0_'B_update_b_update_fun',X0_'B_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'B_update_b_update_fun'=iProver_Domain_'B_update_b_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK90 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK90(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK91 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK91(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK92 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK92(X0_'C_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK93 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK93(X0_'A_update',X0_'C_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK94 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK94(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK95 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK95(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK96 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK96(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK97 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK97(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK98 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update_a_update_fun',X0_'C_update_set'] : 4.35/1.89 ( iProver_Flat_sK98(X0_'C_update_a_update_fun',X0_'C_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK99 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update_a_update_fun',X0_'C_update_set'] : 4.35/1.89 ( iProver_Flat_sK99(X0_'C_update_a_update_fun',X0_'C_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update_a_update_fun'=iProver_Domain_'C_update_a_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK100 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_set',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun'] : 4.35/1.89 ( iProver_Flat_sK100(X0_'C_update',X0_'C_update_set',X0_'C_update_a_update_fun',X1_'C_update_a_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK101 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK101(X0_'D_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK102 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK102(X0_'C_update',X0_'D_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK103 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK103(X0_'A_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK104 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK104(X0_'C_update',X0_'A_update_b_update_fun',X0_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK105 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK105(X0_'A_update',X0_'C_d_prod_update_a_update_fun',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK106 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK106(X0_'D_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK107 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK107(X0_'A_update',X0_'D_update_b_update_fun',X0_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK108 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK108(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK109 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK109(X0_'A_update',X0_'A_update_b_update_fun',X1_'A_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'A_update'=iProver_Domain_'A_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK110 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK110(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK111 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK111(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK112 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK112(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK113 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK113(X0_'C_update',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK114 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update_b_update_fun',X0_'C_update_set'] : 4.35/1.89 ( iProver_Flat_sK114(X0_'C_update_b_update_fun',X0_'C_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK115 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update_b_update_fun',X0_'C_update_set'] : 4.35/1.89 ( iProver_Flat_sK115(X0_'C_update_b_update_fun',X0_'C_update_set') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update_b_update_fun'=iProver_Domain_'C_update_b_update_fun'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK116 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'C_update',X0_'C_update_set',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK116(X0_'C_update',X0_'C_update_set',X0_'C_update_b_update_fun',X1_'C_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'C_update'=iProver_Domain_'C_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK117 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK117(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 4.35/1.89 %------ Positive definition of iProver_Flat_sK118 4.35/1.89 fof(lit_def,axiom, 4.35/1.89 (! [X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun'] : 4.35/1.89 ( iProver_Flat_sK118(X0_'D_update',X0_'D_update_b_update_fun',X1_'D_update_b_update_fun') <=> 4.35/1.89 ( 4.35/1.89 ( 4.35/1.89 ( X0_'D_update'=iProver_Domain_'D_update'_1 ) 4.35/1.89 ) 4.35/1.89 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ) 4.35/1.89 ). 4.35/1.89 % SZS output end Model for theBenchmark.p 4.35/1.89 4.35/1.97 EOF