TPTP Problem File: SLH0360^1.p

%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : FSM_Tests/0063_Intermediate_Implementations/prob_00925_045367__20853392_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1866 ( 453 unt; 670 typ;   0 def)
%            Number of atoms       : 4265 (1634 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 20740 ( 675   ~;  43   |; 374   &;17356   @)
%                                         (   0 <=>;2292  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   9 avg)
%            Number of types       :  136 ( 135 usr)
%            Number of type conns  : 1456 (1456   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  538 ( 535 usr;  43 con; 0-8 aty)
%            Number of variables   : 4474 ( 290   ^;3968   !; 216   ?;4474   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:30:02.664
%------------------------------------------------------------------------------
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thf(sy_c_FSM_OLS_001t__Set__Oset_Itf__d_J_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS_001tf__d_001tf__b_001tf__c,type,
    lS_d_b_c: fsm_d_b_c > d > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS_092_060_094sub_062i_092_060_094sub_062n_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001t__Product____Type__Oprod_Itf__b_Mtf__c_J_001t__Nat__Onat,type,
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thf(sy_c_FSM_OLS_092_060_094sub_062i_092_060_094sub_062n__rel_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001t__Product____Type__Oprod_Itf__b_Mtf__c_J_001t__Nat__Onat,type,
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thf(sy_c_FSM_OLS__acyclic_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS__acyclic_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS__rel_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS__rel_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oacyclic_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oacyclic_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oafter_001t__Nat__Onat_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oafter_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odefined__inputs_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odefined__inputs_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odistinguishes_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odistinguishes_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odoes__distinguish_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Odoes__distinguish_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ofilter__states_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ofilter__states_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ofrom__FSM_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ofrom__FSM_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oh__from_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oh__obs_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oh__obs_001tf__d_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oindex__states_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oindex__states__integer_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oinitial_001t__Set__Oset_Itf__a_J_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oinputs__as__list_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oio__targets_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_Util_Olinear__order__from__list__position_H__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    linear4366178405326712835od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Util_Olist__ordered__pairs_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    list_o8363625500407931829od_b_c: list_l8907847357763382004od_b_c > list_P205660002400636589od_b_c ).

thf(sy_c_Util_Olist__ordered__pairs_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    list_o804723041229831855od_b_c: list_P903359562653991662od_b_c > list_P7987531494101635245od_b_c ).

thf(sy_c_Util_Olist__ordered__pairs_001tf__a,type,
    list_ordered_pairs_a: list_a > list_P1396940483166286381od_a_a ).

thf(sy_c_Util_Olist__ordered__pairs__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    list_o3318826711941139878od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Util_Olists__of__length_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    lists_2361477089028216131od_b_c: list_P903359562653991662od_b_c > nat > list_l8907847357763382004od_b_c ).

thf(sy_c_Util_Onon__sym__dist__pairs_H_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    non_sy4916969364292876019od_b_c: list_P903359562653991662od_b_c > list_P7987531494101635245od_b_c ).

thf(sy_c_Util_Onon__sym__dist__pairs_H__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    non_sy5902841407094123106od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Util_Opow__list_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    pow_li4341120398627903455od_b_c: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ).

thf(sy_c_Util_Opow__list__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    pow_li3598863925982933110od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Util_Oprefix__pairs_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    prefix5723457598024033902od_b_c: list_P903359562653991662od_b_c > list_P205660002400636589od_b_c ).

thf(sy_c_Util_Oprefix__pairs__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    prefix3768999732699559079od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Util_Oremove__proper__prefixes_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    remove5339202614008355685od_b_c: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c ).

thf(sy_c_Util_Osuffixes_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    suffix2151784340763841114od_b_c: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ).

thf(sy_c_Util_Osuffixes__rel_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    suffix5297622422209064891od_b_c: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    accp_l4654477130474446199od_b_c: ( list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o ) > list_P903359562653991662od_b_c > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mtf__c_J_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    accp_P1924572328958296190od_b_c: ( produc5559707038353031495od_b_c > produc5559707038353031495od_b_c > $o ) > produc5559707038353031495od_b_c > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mtf__c_J_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    accp_P7655262136047134638od_b_c: ( produc6474587151875105527od_b_c > produc6474587151875105527od_b_c > $o ) > produc6474587151875105527od_b_c > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J_J,type,
    accp_P2224188031119546935od_b_c: ( produc9091692362587379584od_b_c > produc9091692362587379584od_b_c > $o ) > produc9091692362587379584od_b_c > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSM__Ofsm_Itf__a_Mtf__b_Mtf__c_J_Mtf__a_J,type,
    accp_P8775296850406592587_b_c_a: ( produc7386240147096006850_b_c_a > produc7386240147096006850_b_c_a > $o ) > produc7386240147096006850_b_c_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSM__Ofsm_Itf__d_Mtf__b_Mtf__c_J_Mtf__d_J,type,
    accp_P3585319936889966987_b_c_d: ( produc2196263233579381250_b_c_d > produc2196263233579381250_b_c_d > $o ) > produc2196263233579381250_b_c_d > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    member1702757119880923450od_b_c: list_P4618364105659340195od_b_c > set_li2758127602597986009od_b_c > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    member6330420149250801815od_b_c: list_P903359562653991662od_b_c > set_li6436108459499378894od_b_c > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_c_member_001t__Option__Ooption_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    member6481636158984118493od_b_c: option7120433447694521524od_b_c > set_op5489718926771074068od_b_c > $o ).

thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
    member_option_a: option_a > set_option_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    member1533839430763132368od_b_c: produc5878855887281848999od_b_c > set_Pr3842837961795859335od_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J_J,type,
    member275807201309088512od_b_c: produc3894960095624370921od_b_c > set_Pr351359260625826719od_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J_J,type,
    member8124909232574984543od_b_c: produc596031391177498678od_b_c > set_Pr571657135400976278od_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    member8899240064043329450od_b_c: produc3246581702073416851od_b_c > set_Pr2622754303974797129od_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mtf__a_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mtf__a_J_J,type,
    member8012203591919427344_b_c_a: produc483325750521941479_b_c_a > set_Pr2844895886267491527_b_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mtf__a_J_J_J,type,
    member3332177101994087840_b_c_a: produc5894170661315020937_b_c_a > set_Pr2458387175352556095_b_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J,type,
    member5502040268208861279od_c_a: produc2669932201312201782od_c_a > set_Pr8357624050790843030od_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    member1426531477525435216od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    member7862447941013992593od_b_c: product_prod_b_c > set_Product_prod_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__d_J_J_J,type,
    member4231278564905875615od_c_d: produc1399170498009216118od_c_d > set_Pr224028844097186518od_c_d > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
    member_set_a: set_a > set_set_a > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_c_member_001tf__c,type,
    member_c: c > set_c > $o ).

thf(sy_c_member_001tf__d,type,
    member_d: d > set_d > $o ).

thf(sy_v_G,type,
    g2: g ).

thf(sy_v_M1,type,
    m1: fsm_a_b_c ).

thf(sy_v_M2,type,
    m2: fsm_d_b_c ).

thf(sy_v_P____,type,
    p: produc3246581702073416851od_b_c > $o ).

thf(sy_v_T,type,
    t: prefix425356687782099470od_b_c ).

thf(sy_v_XY____,type,
    xy: list_P903359562653991662od_b_c ).

thf(sy_v_bestPrefix0____,type,
    bestPrefix0: list_P903359562653991662od_b_c ).

thf(sy_v_cg__lookup,type,
    cg_lookup: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ).

thf(sy_v_e____,type,
    e: nat ).

thf(sy_v_errorValue____,type,
    errorValue: nat ).

thf(sy_v_get__distinguishing__trace,type,
    get_di7968643222313865723_trace: a > a > list_P903359562653991662od_b_c ).

thf(sy_v_ka____,type,
    ka: nat ).

thf(sy_v_minEst0____,type,
    minEst0: nat ).

thf(sy_v_su____,type,
    su: a ).

thf(sy_v_sv____,type,
    sv: a ).

thf(sy_v_tryIO____,type,
    tryIO: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c ).

thf(sy_v_u,type,
    u: list_P903359562653991662od_b_c ).

thf(sy_v_u_H_H____,type,
    u2: list_P903359562653991662od_b_c ).

thf(sy_v_u_H____,type,
    u3: list_P903359562653991662od_b_c ).

thf(sy_v_ua____,type,
    ua: list_P903359562653991662od_b_c ).

thf(sy_v_v,type,
    v: list_P903359562653991662od_b_c ).

thf(sy_v_v_H_H____,type,
    v2: list_P903359562653991662od_b_c ).

thf(sy_v_v_H____,type,
    v3: list_P903359562653991662od_b_c ).

thf(sy_v_va____,type,
    va: list_P903359562653991662od_b_c ).

thf(sy_v_w____,type,
    w: list_P903359562653991662od_b_c ).

thf(sy_v_x____,type,
    x: b ).

thf(sy_v_y____,type,
    y: c ).

% Relevant facts (1190)
thf(fact_0_assms_I3_J,axiom,
    minimal_a_b_c @ m1 ).

% assms(3)
thf(fact_1_assms_I1_J,axiom,
    observable_a_b_c @ m1 ).

% assms(1)
thf(fact_2_assms_I8_J,axiom,
    ( ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ u )
   != ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ v ) ) ).

% assms(8)
thf(fact_3_Suc_Oprems_I1_J,axiom,
    member6330420149250801815od_b_c @ ua @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% Suc.prems(1)
thf(fact_4_Suc_Oprems_I5_J,axiom,
    ( ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua )
   != ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va ) ) ).

% Suc.prems(5)
thf(fact_5_su,axiom,
    ( su
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua ) ) ).

% su
thf(fact_6_f3,axiom,
    ( ( member6330420149250801815od_b_c @ ua @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
    & ( member6330420149250801815od_b_c @ u2 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
    & ( ( lS_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua ) )
      = ( lS_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ u2 ) ) ) ) ).

% f3
thf(fact_7__092_060open_062converge_AM1_Au_Au_H_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ ua @ u2 ).

% \<open>converge M1 u u''\<close>
thf(fact_8_assms_I6_J,axiom,
    member6330420149250801815od_b_c @ v @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% assms(6)
thf(fact_9_assms_I4_J,axiom,
    member6330420149250801815od_b_c @ u @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% assms(4)
thf(fact_10_sv,axiom,
    ( sv
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va ) ) ).

% sv
thf(fact_11_Suc_Oprems_I3_J,axiom,
    member6330420149250801815od_b_c @ va @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% Suc.prems(3)
thf(fact_12_f6,axiom,
    ( ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va )
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ v2 ) ) ).

% f6
thf(fact_13__092_060open_062converge_AM1_Au_H_Au_H_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ u3 @ u2 ).

% \<open>converge M1 u' u''\<close>
thf(fact_14__092_060open_062converge_AM1_Au_Au_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ ua @ u3 ).

% \<open>converge M1 u u'\<close>
thf(fact_15__092_060open_062u_H_A_092_060in_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ u3 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% \<open>u' \<in> L M1\<close>
thf(fact_16__092_060open_062v_H_A_092_060in_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ v3 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% \<open>v' \<in> L M1\<close>
thf(fact_17_f2,axiom,
    ! [F: fsm_a_b_c,Ps: list_P903359562653991662od_b_c,Psa: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ F @ Ps @ Psa )
      = ( ( member6330420149250801815od_b_c @ Ps @ ( lS_a_b_c @ F @ ( initial_a_b_c @ F ) ) )
        & ( member6330420149250801815od_b_c @ Psa @ ( lS_a_b_c @ F @ ( initial_a_b_c @ F ) ) )
        & ( ( lS_a_b_c @ F @ ( after_a_b_c @ F @ ( initial_a_b_c @ F ) @ Ps ) )
          = ( lS_a_b_c @ F @ ( after_a_b_c @ F @ ( initial_a_b_c @ F ) @ Psa ) ) ) ) ) ).

% f2
thf(fact_18__092_060open_062converge_AM1_Av_Av_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ va @ v3 ).

% \<open>converge M1 v v'\<close>
thf(fact_19__092_060open_062converge_AM1_Av_Av_H_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ va @ v2 ).

% \<open>converge M1 v v''\<close>
thf(fact_20__092_060open_062converge_AM1_Av_H_Av_H_H_092_060close_062,axiom,
    converge_a_b_c @ m1 @ v3 @ v2 ).

% \<open>converge M1 v' v''\<close>
thf(fact_21_f5,axiom,
    ( ( member6330420149250801815od_b_c @ va @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
    & ( member6330420149250801815od_b_c @ v2 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
    & ( ( lS_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va ) )
      = ( lS_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ v2 ) ) ) ) ).

% f5
thf(fact_22_f4,axiom,
    ! [F: fsm_a_b_c,Ps: list_P903359562653991662od_b_c,Psa: list_P903359562653991662od_b_c] :
      ( ~ ( minimal_a_b_c @ F )
      | ~ ( observable_a_b_c @ F )
      | ~ ( member6330420149250801815od_b_c @ Ps @ ( lS_a_b_c @ F @ ( initial_a_b_c @ F ) ) )
      | ~ ( member6330420149250801815od_b_c @ Psa @ ( lS_a_b_c @ F @ ( initial_a_b_c @ F ) ) )
      | ( ( converge_a_b_c @ F @ Ps @ Psa )
        = ( ( after_a_b_c @ F @ ( initial_a_b_c @ F ) @ Ps )
          = ( after_a_b_c @ F @ ( initial_a_b_c @ F ) @ Psa ) ) ) ) ).

% f4
thf(fact_23_convergence__minimal,axiom,
    ! [M: fsm_Code_integer_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minima6064407838494594252er_b_c @ M )
     => ( ( observ7524490533585752726er_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_Code_integer_b_c @ M @ ( initia4873860033875475119er_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_Code_integer_b_c @ M @ ( initia4873860033875475119er_b_c @ M ) ) )
           => ( ( conver3908070791346981955er_b_c @ M @ Alpha @ Beta )
              = ( ( after_5090571588895392199er_b_c @ M @ ( initia4873860033875475119er_b_c @ M ) @ Alpha )
                = ( after_5090571588895392199er_b_c @ M @ ( initia4873860033875475119er_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_24_convergence__minimal,axiom,
    ! [M: fsm_set_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_set_d_b_c @ M )
     => ( ( observable_set_d_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_set_d_b_c @ M @ ( initial_set_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_set_d_b_c @ M @ ( initial_set_d_b_c @ M ) ) )
           => ( ( converge_set_d_b_c @ M @ Alpha @ Beta )
              = ( ( after_set_d_b_c @ M @ ( initial_set_d_b_c @ M ) @ Alpha )
                = ( after_set_d_b_c @ M @ ( initial_set_d_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_25_convergence__minimal,axiom,
    ! [M: fsm_set_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_set_a_b_c @ M )
     => ( ( observable_set_a_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_set_a_b_c @ M @ ( initial_set_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_set_a_b_c @ M @ ( initial_set_a_b_c @ M ) ) )
           => ( ( converge_set_a_b_c @ M @ Alpha @ Beta )
              = ( ( after_set_a_b_c @ M @ ( initial_set_a_b_c @ M ) @ Alpha )
                = ( after_set_a_b_c @ M @ ( initial_set_a_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_26_convergence__minimal,axiom,
    ! [M: fsm_nat_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_nat_b_c @ M )
     => ( ( observable_nat_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_nat_b_c @ M @ ( initial_nat_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_nat_b_c @ M @ ( initial_nat_b_c @ M ) ) )
           => ( ( converge_nat_b_c @ M @ Alpha @ Beta )
              = ( ( after_nat_b_c @ M @ ( initial_nat_b_c @ M ) @ Alpha )
                = ( after_nat_b_c @ M @ ( initial_nat_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_27_convergence__minimal,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minima1987601567150520449_c_b_c @ M )
     => ( ( observ6293852833591064631_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
           => ( ( conver6852411701971397450_c_b_c @ M @ Alpha @ Beta )
              = ( ( after_4052058690717316294_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) @ Alpha )
                = ( after_4052058690717316294_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_28_convergence__minimal,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Alpha: list_P4618364105659340195od_b_c,Beta: list_P4618364105659340195od_b_c] :
      ( ( minima427268845184106828od_b_c @ M )
     => ( ( observ667460880479887382od_b_c @ M )
       => ( ( member1702757119880923450od_b_c @ Alpha @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
         => ( ( member1702757119880923450od_b_c @ Beta @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
           => ( ( conver918448029487226435od_b_c @ M @ Alpha @ Beta )
              = ( ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Alpha )
                = ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_29_convergence__minimal,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Alpha: list_P4618364105659340195od_b_c,Beta: list_P4618364105659340195od_b_c] :
      ( ( minima7468704325166659676od_b_c @ M )
     => ( ( observ2194746696072761382od_b_c @ M )
       => ( ( member1702757119880923450od_b_c @ Alpha @ ( lS_lis9220523473116252810od_b_c @ M @ ( initia2755245589554485567od_b_c @ M ) ) )
         => ( ( member1702757119880923450od_b_c @ Beta @ ( lS_lis9220523473116252810od_b_c @ M @ ( initia2755245589554485567od_b_c @ M ) ) )
           => ( ( conver4001532986140499667od_b_c @ M @ Alpha @ Beta )
              = ( ( after_5389876800173013079od_b_c @ M @ ( initia2755245589554485567od_b_c @ M ) @ Alpha )
                = ( after_5389876800173013079od_b_c @ M @ ( initia2755245589554485567od_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_30_convergence__minimal,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_a_b_c @ M )
     => ( ( observable_a_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( converge_a_b_c @ M @ Alpha @ Beta )
              = ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha )
                = ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_31_convergence__minimal,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_d_b_c @ M )
     => ( ( observable_d_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ( converge_d_b_c @ M @ Alpha @ Beta )
              = ( ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Alpha )
                = ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_32_converge_Osimps,axiom,
    ( converge_nat_b_c
    = ( ^ [M2: fsm_nat_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_nat_b_c @ M2 @ ( initial_nat_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_nat_b_c @ M2 @ ( initial_nat_b_c @ M2 ) ) )
          & ( ( lS_nat_b_c @ M2 @ ( after_nat_b_c @ M2 @ ( initial_nat_b_c @ M2 ) @ Pi ) )
            = ( lS_nat_b_c @ M2 @ ( after_nat_b_c @ M2 @ ( initial_nat_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_33_converge_Osimps,axiom,
    ( conver3908070791346981955er_b_c
    = ( ^ [M2: fsm_Code_integer_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_Code_integer_b_c @ M2 @ ( initia4873860033875475119er_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_Code_integer_b_c @ M2 @ ( initia4873860033875475119er_b_c @ M2 ) ) )
          & ( ( lS_Code_integer_b_c @ M2 @ ( after_5090571588895392199er_b_c @ M2 @ ( initia4873860033875475119er_b_c @ M2 ) @ Pi ) )
            = ( lS_Code_integer_b_c @ M2 @ ( after_5090571588895392199er_b_c @ M2 @ ( initia4873860033875475119er_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_34_converge_Osimps,axiom,
    ( converge_set_a_b_c
    = ( ^ [M2: fsm_set_a_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_set_a_b_c @ M2 @ ( initial_set_a_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_set_a_b_c @ M2 @ ( initial_set_a_b_c @ M2 ) ) )
          & ( ( lS_set_a_b_c @ M2 @ ( after_set_a_b_c @ M2 @ ( initial_set_a_b_c @ M2 ) @ Pi ) )
            = ( lS_set_a_b_c @ M2 @ ( after_set_a_b_c @ M2 @ ( initial_set_a_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_35_converge_Osimps,axiom,
    ( conver6852411701971397450_c_b_c
    = ( ^ [M2: fsm_li6801133765522507155_c_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_lis2930931384350476499_c_b_c @ M2 @ ( initia3567573336347591134_c_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_lis2930931384350476499_c_b_c @ M2 @ ( initia3567573336347591134_c_b_c @ M2 ) ) )
          & ( ( lS_lis2930931384350476499_c_b_c @ M2 @ ( after_4052058690717316294_c_b_c @ M2 @ ( initia3567573336347591134_c_b_c @ M2 ) @ Pi ) )
            = ( lS_lis2930931384350476499_c_b_c @ M2 @ ( after_4052058690717316294_c_b_c @ M2 @ ( initia3567573336347591134_c_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_36_converge_Osimps,axiom,
    ( conver918448029487226435od_b_c
    = ( ^ [M2: fsm_a_6390678650791688088od_b_c,Pi: list_P4618364105659340195od_b_c,Tau: list_P4618364105659340195od_b_c] :
          ( ( member1702757119880923450od_b_c @ Pi @ ( lS_a_n6600196584412307578od_b_c @ M2 @ ( initia7582277823139973807od_b_c @ M2 ) ) )
          & ( member1702757119880923450od_b_c @ Tau @ ( lS_a_n6600196584412307578od_b_c @ M2 @ ( initia7582277823139973807od_b_c @ M2 ) ) )
          & ( ( lS_a_n6600196584412307578od_b_c @ M2 @ ( after_7403543103203634631od_b_c @ M2 @ ( initia7582277823139973807od_b_c @ M2 ) @ Pi ) )
            = ( lS_a_n6600196584412307578od_b_c @ M2 @ ( after_7403543103203634631od_b_c @ M2 @ ( initia7582277823139973807od_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_37_converge_Osimps,axiom,
    ( conver4001532986140499667od_b_c
    = ( ^ [M2: fsm_li7789363362239116584od_b_c,Pi: list_P4618364105659340195od_b_c,Tau: list_P4618364105659340195od_b_c] :
          ( ( member1702757119880923450od_b_c @ Pi @ ( lS_lis9220523473116252810od_b_c @ M2 @ ( initia2755245589554485567od_b_c @ M2 ) ) )
          & ( member1702757119880923450od_b_c @ Tau @ ( lS_lis9220523473116252810od_b_c @ M2 @ ( initia2755245589554485567od_b_c @ M2 ) ) )
          & ( ( lS_lis9220523473116252810od_b_c @ M2 @ ( after_5389876800173013079od_b_c @ M2 @ ( initia2755245589554485567od_b_c @ M2 ) @ Pi ) )
            = ( lS_lis9220523473116252810od_b_c @ M2 @ ( after_5389876800173013079od_b_c @ M2 @ ( initia2755245589554485567od_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_38_converge_Osimps,axiom,
    ( converge_a_b_c
    = ( ^ [M2: fsm_a_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
          & ( ( lS_a_b_c @ M2 @ ( after_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ Pi ) )
            = ( lS_a_b_c @ M2 @ ( after_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_39_converge_Osimps,axiom,
    ( converge_d_b_c
    = ( ^ [M2: fsm_d_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) )
          & ( ( lS_d_b_c @ M2 @ ( after_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) @ Pi ) )
            = ( lS_d_b_c @ M2 @ ( after_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_40_converge_Oelims_I1_J,axiom,
    ! [X: fsm_nat_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_nat_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
          & ( ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xa ) )
            = ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_41_converge_Oelims_I1_J,axiom,
    ! [X: fsm_Code_integer_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( conver3908070791346981955er_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
          & ( ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xa ) )
            = ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_42_converge_Oelims_I1_J,axiom,
    ! [X: fsm_set_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_set_a_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
          & ( ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xa ) )
            = ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_43_converge_Oelims_I1_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( conver6852411701971397450_c_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
          & ( ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xa ) )
            = ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_44_converge_Oelims_I1_J,axiom,
    ! [X: fsm_a_6390678650791688088od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c,Y: $o] :
      ( ( ( conver918448029487226435od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member1702757119880923450od_b_c @ Xa @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
          & ( member1702757119880923450od_b_c @ Xb @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
          & ( ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xa ) )
            = ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_45_converge_Oelims_I1_J,axiom,
    ! [X: fsm_li7789363362239116584od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c,Y: $o] :
      ( ( ( conver4001532986140499667od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member1702757119880923450od_b_c @ Xa @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
          & ( member1702757119880923450od_b_c @ Xb @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
          & ( ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xa ) )
            = ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_46_converge_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_a_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_47_converge_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
          & ( ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xa ) )
            = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_48_converge_Oelims_I2_J,axiom,
    ! [X: fsm_nat_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_nat_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
        & ( ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xa ) )
          = ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_49_converge_Oelims_I2_J,axiom,
    ! [X: fsm_Code_integer_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( conver3908070791346981955er_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
        & ( ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xa ) )
          = ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_50_converge_Oelims_I2_J,axiom,
    ! [X: fsm_set_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_set_a_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
        & ( ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xa ) )
          = ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_51_converge_Oelims_I2_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( conver6852411701971397450_c_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
        & ( ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xa ) )
          = ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_52_converge_Oelims_I2_J,axiom,
    ! [X: fsm_a_6390678650791688088od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c] :
      ( ( conver918448029487226435od_b_c @ X @ Xa @ Xb )
     => ( ( member1702757119880923450od_b_c @ Xa @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
        & ( member1702757119880923450od_b_c @ Xb @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
        & ( ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xa ) )
          = ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_53_converge_Oelims_I2_J,axiom,
    ! [X: fsm_li7789363362239116584od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c] :
      ( ( conver4001532986140499667od_b_c @ X @ Xa @ Xb )
     => ( ( member1702757119880923450od_b_c @ Xa @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
        & ( member1702757119880923450od_b_c @ Xb @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
        & ( ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xa ) )
          = ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_54_converge_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
        & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
          = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_55_converge_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_d_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
        & ( ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xa ) )
          = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_56_converge_Oelims_I3_J,axiom,
    ! [X: fsm_nat_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_nat_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_nat_b_c @ X @ ( initial_nat_b_c @ X ) ) )
          & ( ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xa ) )
            = ( lS_nat_b_c @ X @ ( after_nat_b_c @ X @ ( initial_nat_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_57_converge_Oelims_I3_J,axiom,
    ! [X: fsm_Code_integer_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( conver3908070791346981955er_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_Code_integer_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) ) )
          & ( ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xa ) )
            = ( lS_Code_integer_b_c @ X @ ( after_5090571588895392199er_b_c @ X @ ( initia4873860033875475119er_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_58_converge_Oelims_I3_J,axiom,
    ! [X: fsm_set_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_set_a_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) ) )
          & ( ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xa ) )
            = ( lS_set_a_b_c @ X @ ( after_set_a_b_c @ X @ ( initial_set_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_59_converge_Oelims_I3_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( conver6852411701971397450_c_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_lis2930931384350476499_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) ) )
          & ( ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xa ) )
            = ( lS_lis2930931384350476499_c_b_c @ X @ ( after_4052058690717316294_c_b_c @ X @ ( initia3567573336347591134_c_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_60_converge_Oelims_I3_J,axiom,
    ! [X: fsm_a_6390678650791688088od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c] :
      ( ~ ( conver918448029487226435od_b_c @ X @ Xa @ Xb )
     => ~ ( ( member1702757119880923450od_b_c @ Xa @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
          & ( member1702757119880923450od_b_c @ Xb @ ( lS_a_n6600196584412307578od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) ) )
          & ( ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xa ) )
            = ( lS_a_n6600196584412307578od_b_c @ X @ ( after_7403543103203634631od_b_c @ X @ ( initia7582277823139973807od_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_61_converge_Oelims_I3_J,axiom,
    ! [X: fsm_li7789363362239116584od_b_c,Xa: list_P4618364105659340195od_b_c,Xb: list_P4618364105659340195od_b_c] :
      ( ~ ( conver4001532986140499667od_b_c @ X @ Xa @ Xb )
     => ~ ( ( member1702757119880923450od_b_c @ Xa @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
          & ( member1702757119880923450od_b_c @ Xb @ ( lS_lis9220523473116252810od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) ) )
          & ( ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xa ) )
            = ( lS_lis9220523473116252810od_b_c @ X @ ( after_5389876800173013079od_b_c @ X @ ( initia2755245589554485567od_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_62_converge_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_a_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_63_converge_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_d_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) )
          & ( ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xa ) )
            = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_64_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_nat_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_nat_b_c @ M @ ( initial_nat_b_c @ M ) ) )
     => ( converge_nat_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_65_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_Code_integer_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_Code_integer_b_c @ M @ ( initia4873860033875475119er_b_c @ M ) ) )
     => ( conver3908070791346981955er_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_66_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_set_a_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_set_a_b_c @ M @ ( initial_set_a_b_c @ M ) ) )
     => ( converge_set_a_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_67_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
     => ( conver6852411701971397450_c_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_68_converge__refl,axiom,
    ! [Alpha: list_P4618364105659340195od_b_c,M: fsm_a_6390678650791688088od_b_c] :
      ( ( member1702757119880923450od_b_c @ Alpha @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
     => ( conver918448029487226435od_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_69_converge__refl,axiom,
    ! [Alpha: list_P4618364105659340195od_b_c,M: fsm_li7789363362239116584od_b_c] :
      ( ( member1702757119880923450od_b_c @ Alpha @ ( lS_lis9220523473116252810od_b_c @ M @ ( initia2755245589554485567od_b_c @ M ) ) )
     => ( conver4001532986140499667od_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_70_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
     => ( converge_a_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_71_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M: fsm_d_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
     => ( converge_d_b_c @ M @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_72__092_060open_062sv_A_092_060in_062_AFSM_Ostates_AM1_092_060close_062,axiom,
    member_a @ sv @ ( states_a_b_c @ m1 ) ).

% \<open>sv \<in> FSM.states M1\<close>
thf(fact_73__092_060open_062su_A_092_060in_062_AFSM_Ostates_AM1_092_060close_062,axiom,
    member_a @ su @ ( states_a_b_c @ m1 ) ).

% \<open>su \<in> FSM.states M1\<close>
thf(fact_74_bestPrefix0,axiom,
    ( bestPrefix0
    = ( get_di7968643222313865723_trace @ su @ sv ) ) ).

% bestPrefix0
thf(fact_75_a1,axiom,
    ( ( h_obs_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua ) @ x @ y )
   != ( h_obs_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va ) @ x @ y ) ) ).

% a1
thf(fact_76_converge__sym,axiom,
    ( converge_a_b_c
    = ( ^ [M2: fsm_a_b_c,U: list_P903359562653991662od_b_c,V: list_P903359562653991662od_b_c] : ( converge_a_b_c @ M2 @ V @ U ) ) ) ).

% converge_sym
thf(fact_77_converge__sym,axiom,
    ( converge_d_b_c
    = ( ^ [M2: fsm_d_b_c,U: list_P903359562653991662od_b_c,V: list_P903359562653991662od_b_c] : ( converge_d_b_c @ M2 @ V @ U ) ) ) ).

% converge_sym
thf(fact_78_False,axiom,
    ( ( h_obs_a_b_c @ m1 @ su @ x @ y )
   != ( h_obs_a_b_c @ m1 @ sv @ x @ y ) ) ).

% False
thf(fact_79_assms_I2_J,axiom,
    observable_d_b_c @ m2 ).

% assms(2)
thf(fact_80_Suc_Oprems_I4_J,axiom,
    member6330420149250801815od_b_c @ va @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% Suc.prems(4)
thf(fact_81_Suc_Oprems_I2_J,axiom,
    member6330420149250801815od_b_c @ ua @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% Suc.prems(2)
thf(fact_82_assms_I5_J,axiom,
    member6330420149250801815od_b_c @ u @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% assms(5)
thf(fact_83_assms_I7_J,axiom,
    member6330420149250801815od_b_c @ v @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% assms(7)
thf(fact_84_assms_I9_J,axiom,
    ! [Q1: a,Q2: a] :
      ( ( member_a @ Q1 @ ( states_a_b_c @ m1 ) )
     => ( ( member_a @ Q2 @ ( states_a_b_c @ m1 ) )
       => ( ( Q1 != Q2 )
         => ( distinguishes_a_b_c @ m1 @ Q1 @ Q2 @ ( get_di7968643222313865723_trace @ Q1 @ Q2 ) ) ) ) ) ).

% assms(9)
thf(fact_85__092_060open_062FSM_Oh__obs_AM1_Asv_Ax_Ay_A_092_060noteq_062_ANone_092_060close_062,axiom,
    ( ( h_obs_a_b_c @ m1 @ sv @ x @ y )
   != none_a ) ).

% \<open>FSM.h_obs M1 sv x y \<noteq> None\<close>
thf(fact_86__092_060open_062FSM_Oh__obs_AM1_Asu_Ax_Ay_A_092_060noteq_062_ANone_092_060close_062,axiom,
    ( ( h_obs_a_b_c @ m1 @ su @ x @ y )
   != none_a ) ).

% \<open>FSM.h_obs M1 su x y \<noteq> None\<close>
thf(fact_87_fsm__initial,axiom,
    ! [M: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M ) @ ( states_a_b_c @ M ) ) ).

% fsm_initial
thf(fact_88_fsm__initial,axiom,
    ! [M: fsm_d_b_c] : ( member_d @ ( initial_d_b_c @ M ) @ ( states_d_b_c @ M ) ) ).

% fsm_initial
thf(fact_89_after__is__state,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ Q @ Io ) @ ( states7681702920031268536_c_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_90_after__is__state,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ( member_a @ ( after_a_b_c @ M @ Q @ Io ) @ ( states_a_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_91_after__is__state,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) )
       => ( member_d @ ( after_d_b_c @ M @ Q @ Io ) @ ( states_d_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_92_mem__Collect__eq,axiom,
    ! [A: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ A @ ( collec2280997390073109977od_b_c @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_93_mem__Collect__eq,axiom,
    ! [A: a,P: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_94_Collect__mem__eq,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_95_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_96_minimal__alt__def,axiom,
    ( minimal_d_b_c
    = ( ^ [M2: fsm_d_b_c] :
        ! [Q3: d,Q4: d] :
          ( ( member_d @ Q3 @ ( states_d_b_c @ M2 ) )
         => ( ( member_d @ Q4 @ ( states_d_b_c @ M2 ) )
           => ( ( ( lS_d_b_c @ M2 @ Q3 )
                = ( lS_d_b_c @ M2 @ Q4 ) )
             => ( Q3 = Q4 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_97_minimal__alt__def,axiom,
    ( minimal_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q3: a,Q4: a] :
          ( ( member_a @ Q3 @ ( states_a_b_c @ M2 ) )
         => ( ( member_a @ Q4 @ ( states_a_b_c @ M2 ) )
           => ( ( ( lS_a_b_c @ M2 @ Q3 )
                = ( lS_a_b_c @ M2 @ Q4 ) )
             => ( Q3 = Q4 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_98_minimal_Osimps,axiom,
    ( minimal_d_b_c
    = ( ^ [M2: fsm_d_b_c] :
        ! [X2: d] :
          ( ( member_d @ X2 @ ( states_d_b_c @ M2 ) )
         => ! [Y2: d] :
              ( ( member_d @ Y2 @ ( states_d_b_c @ M2 ) )
             => ( ( X2 != Y2 )
               => ( ( lS_d_b_c @ M2 @ X2 )
                 != ( lS_d_b_c @ M2 @ Y2 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_99_minimal_Osimps,axiom,
    ( minimal_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: a] :
          ( ( member_a @ X2 @ ( states_a_b_c @ M2 ) )
         => ! [Y2: a] :
              ( ( member_a @ Y2 @ ( states_a_b_c @ M2 ) )
             => ( ( X2 != Y2 )
               => ( ( lS_a_b_c @ M2 @ X2 )
                 != ( lS_a_b_c @ M2 @ Y2 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_100_minimal_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Y: $o] :
      ( ( ( minimal_d_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: d] :
              ( ( member_d @ X2 @ ( states_d_b_c @ X ) )
             => ! [Y2: d] :
                  ( ( member_d @ Y2 @ ( states_d_b_c @ X ) )
                 => ( ( X2 != Y2 )
                   => ( ( lS_d_b_c @ X @ X2 )
                     != ( lS_d_b_c @ X @ Y2 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_101_minimal_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( minimal_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: a] :
              ( ( member_a @ X2 @ ( states_a_b_c @ X ) )
             => ! [Y2: a] :
                  ( ( member_a @ Y2 @ ( states_a_b_c @ X ) )
                 => ( ( X2 != Y2 )
                   => ( ( lS_a_b_c @ X @ X2 )
                     != ( lS_a_b_c @ X @ Y2 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_102_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ( minimal_d_b_c @ X )
     => ! [X3: d] :
          ( ( member_d @ X3 @ ( states_d_b_c @ X ) )
         => ! [Xa2: d] :
              ( ( member_d @ Xa2 @ ( states_d_b_c @ X ) )
             => ( ( X3 != Xa2 )
               => ( ( lS_d_b_c @ X @ X3 )
                 != ( lS_d_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_103_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( minimal_a_b_c @ X )
     => ! [X3: a] :
          ( ( member_a @ X3 @ ( states_a_b_c @ X ) )
         => ! [Xa2: a] :
              ( ( member_a @ Xa2 @ ( states_a_b_c @ X ) )
             => ( ( X3 != Xa2 )
               => ( ( lS_a_b_c @ X @ X3 )
                 != ( lS_a_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_104_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ~ ( minimal_d_b_c @ X )
     => ~ ! [X4: d] :
            ( ( member_d @ X4 @ ( states_d_b_c @ X ) )
           => ! [Xa3: d] :
                ( ( member_d @ Xa3 @ ( states_d_b_c @ X ) )
               => ( ( X4 != Xa3 )
                 => ( ( lS_d_b_c @ X @ X4 )
                   != ( lS_d_b_c @ X @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_105_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( minimal_a_b_c @ X )
     => ~ ! [X4: a] :
            ( ( member_a @ X4 @ ( states_a_b_c @ X ) )
           => ! [Xa3: a] :
                ( ( member_a @ Xa3 @ ( states_a_b_c @ X ) )
               => ( ( X4 != Xa3 )
                 => ( ( lS_a_b_c @ X @ X4 )
                   != ( lS_a_b_c @ X @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_106__092_060open_062converge_AM2_Au_Au_H_092_060close_062,axiom,
    converge_d_b_c @ m2 @ ua @ u3 ).

% \<open>converge M2 u u'\<close>
thf(fact_107__092_060open_062v_H_A_092_060in_062_AL_AM2_092_060close_062,axiom,
    member6330420149250801815od_b_c @ v3 @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% \<open>v' \<in> L M2\<close>
thf(fact_108__092_060open_062u_H_A_092_060in_062_AL_AM2_092_060close_062,axiom,
    member6330420149250801815od_b_c @ u3 @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% \<open>u' \<in> L M2\<close>
thf(fact_109__092_060open_062converge_AM2_Av_Av_H_092_060close_062,axiom,
    converge_d_b_c @ m2 @ va @ v3 ).

% \<open>converge M2 v v'\<close>
thf(fact_110_distinguishes__sym,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c] :
      ( ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ Io )
     => ( distinguishes_a_b_c @ M @ Q2 @ Q1 @ Io ) ) ).

% distinguishes_sym
thf(fact_111_does__distinguish__correctness,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
       => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
         => ( ( does_d1651467158923735017_d_b_c @ M @ Q1 @ Q2 @ Io )
            = ( distinguishes_d_b_c @ M @ Q1 @ Q2 @ Io ) ) ) ) ) ).

% does_distinguish_correctness
thf(fact_112_does__distinguish__correctness,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
       => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
         => ( ( does_d3309555387068894566_a_b_c @ M @ Q1 @ Q2 @ Io )
            = ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ Io ) ) ) ) ) ).

% does_distinguish_correctness
thf(fact_113_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima8146652644187019584_c_b_c @ M @ Q @ Io ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_114_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_a_b_c,Q: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima1559550560783484624_a_b_c @ M @ Q @ Io ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_115_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_d_b_c,Q: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( states_d_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima9124834369493100883_d_b_c @ M @ Q @ Io ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_116_distinguish__prepend,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( distin2804555989863659119_c_b_c @ M @ ( after_4052058690717316294_c_b_c @ M @ Q1 @ Io ) @ ( after_4052058690717316294_c_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) )
               => ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_117_distinguish__prepend,axiom,
    ! [M: fsm_d_b_c,Q1: d,Io: list_P903359562653991662od_b_c,Q2: d,W: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ Q1 @ Io ) @ ( after_d_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q2 ) )
               => ( distinguishes_d_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_118_distinguish__prepend,axiom,
    ! [M: fsm_a_b_c,Q1: a,Io: list_P903359562653991662od_b_c,Q2: a,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ Q1 @ Io ) @ ( after_a_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q2 ) )
               => ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_119_distinguish__prepend__initial,axiom,
    ! [M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ Io ) ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ Io ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io1 ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io2 ) @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_120_distinguish__prepend__initial,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ Io ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ Io ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io1 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io2 ) @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_121_after__distinguishes__language,axiom,
    ! [M1: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
         => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Alpha ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_122_after__distinguishes__language,axiom,
    ! [M1: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
         => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_123_get__distinguishing__sequence__from__ofsm__tables__distinguishes,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( distinguishes_d_b_c @ M @ Q1 @ Q2 @ ( get_di622774388077934782_d_b_c @ M @ Q1 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_distinguishes
thf(fact_124_get__distinguishing__sequence__from__ofsm__tables__distinguishes,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( get_di2280862616223094331_a_b_c @ M @ Q1 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_distinguishes
thf(fact_125_index__states__language,axiom,
    ! [M: fsm_a_b_c] :
      ( ( lS_nat_b_c @ ( index_states_a_b_c @ M ) @ ( initial_nat_b_c @ ( index_states_a_b_c @ M ) ) )
      = ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ).

% index_states_language
thf(fact_126_index__states__integer__language,axiom,
    ! [M: fsm_a_b_c] :
      ( ( lS_Code_integer_b_c @ ( index_2500966223721395136_a_b_c @ M ) @ ( initia4873860033875475119er_b_c @ ( index_2500966223721395136_a_b_c @ M ) ) )
      = ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ).

% index_states_integer_language
thf(fact_127_diverge__prefix,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ~ ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) )
           => ~ ( converge_a_b_c @ M @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_128_diverge__prefix,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ~ ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) )
           => ~ ( converge_d_b_c @ M @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_129_converge__append,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_130_converge__append,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( converge_d_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_131_converge__extend,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_132_converge__extend,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( converge_d_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_133_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) ) ) ).

% language_prefix
thf(fact_134_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M @ Q ) ) ) ).

% language_prefix
thf(fact_135_converge__append__iff,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha @ Beta )
       => ( ( converge_a_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Alpha @ Omega ) )
          = ( converge_a_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_136_converge__append__iff,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( converge_d_b_c @ M @ Alpha @ Beta )
       => ( ( converge_d_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Alpha @ Omega ) )
          = ( converge_d_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_137_index__states__integer__observable,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( observ7524490533585752726er_b_c @ ( index_2500966223721395136_a_b_c @ M ) ) ) ).

% index_states_integer_observable
thf(fact_138_index__states__observable,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( observable_nat_b_c @ ( index_states_a_b_c @ M ) ) ) ).

% index_states_observable
thf(fact_139_index__states__integer__minimal,axiom,
    ! [M: fsm_a_b_c] :
      ( ( minimal_a_b_c @ M )
     => ( minima6064407838494594252er_b_c @ ( index_2500966223721395136_a_b_c @ M ) ) ) ).

% index_states_integer_minimal
thf(fact_140_index__states__minimal,axiom,
    ! [M: fsm_a_b_c] :
      ( ( minimal_a_b_c @ M )
     => ( minimal_nat_b_c @ ( index_states_a_b_c @ M ) ) ) ).

% index_states_minimal
thf(fact_141_observable__after__language__append,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_append
thf(fact_142_observable__after__language__append,axiom,
    ! [M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q: d,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ Q @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_append
thf(fact_143_observable__after__language__none,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_none
thf(fact_144_observable__after__language__none,axiom,
    ! [M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q: d,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M @ Q ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ Q @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_none
thf(fact_145_observable__after__eq,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( ( after_a_b_c @ M @ Q @ Io1 )
          = ( after_a_b_c @ M @ Q @ Io2 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
         => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_a_b_c @ M @ Q ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_146_observable__after__eq,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( ( after_d_b_c @ M @ Q @ Io1 )
          = ( after_d_b_c @ M @ Q @ Io2 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M @ Q ) )
         => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ Q ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_d_b_c @ M @ Q ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_147_after__language__iff,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Q: a,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Alpha ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% after_language_iff
thf(fact_148_after__language__iff,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Q: d,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ Q @ Alpha ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ).

% after_language_iff
thf(fact_149_after__split,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ Q ) )
       => ( ( after_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Alpha ) @ Gamma )
          = ( after_a_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_150_after__split,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ Q ) )
       => ( ( after_d_b_c @ M @ ( after_d_b_c @ M @ Q @ Alpha ) @ Gamma )
          = ( after_d_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_151_converge__trans__2_I1_J,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U2 @ V2 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ V2 @ W1 ) @ ( append2547753245680614915od_b_c @ V2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_152_converge__trans__2_I1_J,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( converge_d_b_c @ M @ U2 @ V2 )
         => ( ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ V2 @ W1 ) @ ( append2547753245680614915od_b_c @ V2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_153_converge__trans__2_I2_J,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U2 @ V2 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ V2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_154_converge__trans__2_I2_J,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( converge_d_b_c @ M @ U2 @ V2 )
         => ( ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ V2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_155_converge__trans__2_I3_J,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U2 @ V2 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ V2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_156_converge__trans__2_I3_J,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( converge_d_b_c @ M @ U2 @ V2 )
         => ( ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) )
            = ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ V2 @ W1 ) @ ( append2547753245680614915od_b_c @ U2 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_157_after__language__subset,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_158_after__language__subset,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_159_after__language__append__iff,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_160_after__language__append__iff,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_161_converge__append__language__iff,axiom,
    ! [M: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_162_converge__append__language__iff,axiom,
    ! [M: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( converge_d_b_c @ M @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_163_distinguish__converge__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U3: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( converge_a_b_c @ M1 @ U2 @ U3 )
               => ( ( converge_a_b_c @ M1 @ V2 @ V3 )
                 => ( ( converge_a_b_c @ M22 @ U2 @ U3 )
                   => ( ( converge_a_b_c @ M22 @ V2 @ V3 )
                     => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_a_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_164_distinguish__converge__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c,U3: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( converge_a_b_c @ M1 @ U2 @ U3 )
               => ( ( converge_a_b_c @ M1 @ V2 @ V3 )
                 => ( ( converge_d_b_c @ M22 @ U2 @ U3 )
                   => ( ( converge_d_b_c @ M22 @ V2 @ V3 )
                     => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_d_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_165_distinguish__converge__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_a_b_c,U3: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_d_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
             => ( ( converge_d_b_c @ M1 @ U2 @ U3 )
               => ( ( converge_d_b_c @ M1 @ V2 @ V3 )
                 => ( ( converge_a_b_c @ M22 @ U2 @ U3 )
                   => ( ( converge_a_b_c @ M22 @ V2 @ V3 )
                     => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ U2 ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_a_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_166_distinguish__converge__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_d_b_c,U3: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_d_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
             => ( ( converge_d_b_c @ M1 @ U2 @ U3 )
               => ( ( converge_d_b_c @ M1 @ V2 @ V3 )
                 => ( ( converge_d_b_c @ M22 @ U2 @ U3 )
                   => ( ( converge_d_b_c @ M22 @ V2 @ V3 )
                     => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ U2 ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_d_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_167_same__append__eq,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = ( append2547753245680614915od_b_c @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_168_append__same__eq,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Xs )
        = ( append2547753245680614915od_b_c @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_169_append__assoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) @ Zs )
      = ( append2547753245680614915od_b_c @ Xs @ ( append2547753245680614915od_b_c @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_170_append_Oassoc,axiom,
    ! [A: list_P903359562653991662od_b_c,B: list_P903359562653991662od_b_c,C: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( append2547753245680614915od_b_c @ A @ B ) @ C )
      = ( append2547753245680614915od_b_c @ A @ ( append2547753245680614915od_b_c @ B @ C ) ) ) ).

% append.assoc
thf(fact_171_get__distinguishing__sequence__from__ofsm__tables__is__minimally__distinguishing,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ ( get_di2280862616223094331_a_b_c @ M @ Q1 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_minimally_distinguishing
thf(fact_172_get__distinguishing__sequence__from__ofsm__tables__is__minimally__distinguishing,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( minima7808819671940975144_d_b_c @ M @ Q1 @ Q2 @ ( get_di622774388077934782_d_b_c @ M @ Q1 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_minimally_distinguishing
thf(fact_173_distinguish__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ U2 ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_a_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_174_distinguish__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_a_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_175_distinguish__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ U2 ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_d_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_176_distinguish__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_d_b_c @ M22 @ U2 @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_177_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di903557346829177899_c_b_c @ M @ Q1 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_178_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di2280862616223094331_a_b_c @ M @ Q1 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ Q1 ) @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_179_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di622774388077934782_d_b_c @ M @ Q1 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ Q1 ) @ ( lS_d_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_180_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I1_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( get_di903557346829177899_c_b_c @ M @ Q1 @ Q2 ) @ ( sup_su3823046536922626210od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(1)
thf(fact_181_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I1_J,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( get_di2280862616223094331_a_b_c @ M @ Q1 @ Q2 ) @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M @ Q1 ) @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(1)
thf(fact_182_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I1_J,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( get_di622774388077934782_d_b_c @ M @ Q1 @ Q2 ) @ ( sup_su3823046536922626210od_b_c @ ( lS_d_b_c @ M @ Q1 ) @ ( lS_d_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(1)
thf(fact_183__092_060open_062u_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_AL_AM2_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ u2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% \<open>u'' @ [(x, y)] \<in> L M2\<close>
thf(fact_184_list_Oinject,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c,Y21: product_prod_b_c,Y22: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X21 @ X22 )
        = ( cons_P4529483553340347422od_b_c @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_185_append_Oright__neutral,axiom,
    ! [A: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ A @ nil_Product_prod_b_c )
      = A ) ).

% append.right_neutral
thf(fact_186_append__Nil2,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ Xs @ nil_Product_prod_b_c )
      = Xs ) ).

% append_Nil2
thf(fact_187_append__self__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = Xs )
      = ( Ys = nil_Product_prod_b_c ) ) ).

% append_self_conv
thf(fact_188_self__append__conv,axiom,
    ! [Y: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( Y
        = ( append2547753245680614915od_b_c @ Y @ Ys ) )
      = ( Ys = nil_Product_prod_b_c ) ) ).

% self_append_conv
thf(fact_189_append__self__conv2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% append_self_conv2
thf(fact_190_self__append__conv2,axiom,
    ! [Y: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( Y
        = ( append2547753245680614915od_b_c @ Xs @ Y ) )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% self_append_conv2
thf(fact_191_Nil__is__append__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( nil_Product_prod_b_c
        = ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( ( Xs = nil_Product_prod_b_c )
        & ( Ys = nil_Product_prod_b_c ) ) ) ).

% Nil_is_append_conv
thf(fact_192_append__is__Nil__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = nil_Product_prod_b_c )
      = ( ( Xs = nil_Product_prod_b_c )
        & ( Ys = nil_Product_prod_b_c ) ) ) ).

% append_is_Nil_conv
thf(fact_193_append1__eq__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c,Ys: list_P903359562653991662od_b_c,Y: product_prod_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) )
        = ( append2547753245680614915od_b_c @ Ys @ ( cons_P4529483553340347422od_b_c @ Y @ nil_Product_prod_b_c ) ) )
      = ( ( Xs = Ys )
        & ( X = Y ) ) ) ).

% append1_eq_conv
thf(fact_194__092_060open_062v_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ v2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% \<open>v'' @ [(x, y)] \<in> L M1\<close>
thf(fact_195__092_060open_062u_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ u2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ).

% \<open>u'' @ [(x, y)] \<in> L M1\<close>
thf(fact_196__092_060open_062v_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_AL_AM2_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ v2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% \<open>v'' @ [(x, y)] \<in> L M2\<close>
thf(fact_197_rev__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) )
       => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xs2 != nil_Product_prod_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_198_append__eq__Cons__conv,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Zs )
        = ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( ( ( Ys = nil_Product_prod_b_c )
          & ( Zs
            = ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
        | ? [Ys2: list_P903359562653991662od_b_c] :
            ( ( Ys
              = ( cons_P4529483553340347422od_b_c @ X @ Ys2 ) )
            & ( ( append2547753245680614915od_b_c @ Ys2 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_199_Cons__eq__append__conv,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
        = ( append2547753245680614915od_b_c @ Ys @ Zs ) )
      = ( ( ( Ys = nil_Product_prod_b_c )
          & ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
            = Zs ) )
        | ? [Ys2: list_P903359562653991662od_b_c] :
            ( ( ( cons_P4529483553340347422od_b_c @ X @ Ys2 )
              = Ys )
            & ( Xs
              = ( append2547753245680614915od_b_c @ Ys2 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_200_rev__exhaust,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
     => ~ ! [Ys3: list_P903359562653991662od_b_c,Y3: product_prod_b_c] :
            ( Xs
           != ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) ).

% rev_exhaust
thf(fact_201_rev__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( ( P @ Xs2 )
           => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_202_list_Odistinct_I1_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( nil_Product_prod_b_c
     != ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_203_list_OdiscI,axiom,
    ! [List: list_P903359562653991662od_b_c,X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( ( List
        = ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) )
     => ( List != nil_Product_prod_b_c ) ) ).

% list.discI
thf(fact_204_list_Oexhaust,axiom,
    ! [Y: list_P903359562653991662od_b_c] :
      ( ( Y != nil_Product_prod_b_c )
     => ~ ! [X212: product_prod_b_c,X222: list_P903359562653991662od_b_c] :
            ( Y
           != ( cons_P4529483553340347422od_b_c @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_205_min__list_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
          ( X
         != ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
     => ( X = nil_Product_prod_b_c ) ) ).

% min_list.cases
thf(fact_206_transpose_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ( X != nil_li8071162985807626740od_b_c )
     => ( ! [Xss: list_l8907847357763382004od_b_c] :
            ( X
           != ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ Xss ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Xss: list_l8907847357763382004od_b_c] :
              ( X
             != ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_207_remdups__adj_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) )
       => ~ ! [X4: product_prod_b_c,Y3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( cons_P4529483553340347422od_b_c @ X4 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_208_neq__Nil__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
      = ( ? [Y2: product_prod_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( Xs
            = ( cons_P4529483553340347422od_b_c @ Y2 @ Ys4 ) ) ) ) ).

% neq_Nil_conv
thf(fact_209_list__induct2_H,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) )
         => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_210_not__Cons__self2,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_211_list__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) )
       => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xs2 != nil_Product_prod_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_212_maximal__prefix__in__language_Ocases,axiom,
    ! [X: produc5922810228198128439od_b_c] :
      ( ! [M3: fsm_nat_b_c,Q5: nat] :
          ( X
         != ( produc5255539453145639407od_b_c @ M3 @ ( produc8137419655804493381od_b_c @ Q5 @ nil_Product_prod_b_c ) ) )
     => ~ ! [M3: fsm_nat_b_c,Q5: nat,X4: b,Y3: c,Io3: list_P903359562653991662od_b_c] :
            ( X
           != ( produc5255539453145639407od_b_c @ M3 @ ( produc8137419655804493381od_b_c @ Q5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ Io3 ) ) ) ) ) ).

% maximal_prefix_in_language.cases
thf(fact_213_append__Cons,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ Ys )
      = ( cons_P4529483553340347422od_b_c @ X @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ).

% append_Cons
thf(fact_214_Cons__eq__appendI,axiom,
    ! [X: product_prod_b_c,Xs1: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs1 )
        = Ys )
     => ( ( Xs
          = ( append2547753245680614915od_b_c @ Xs1 @ Zs ) )
       => ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
          = ( append2547753245680614915od_b_c @ Ys @ Zs ) ) ) ) ).

% Cons_eq_appendI
thf(fact_215_append__Nil,axiom,
    ! [Ys: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_216_append_Oleft__neutral,axiom,
    ! [A: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ A )
      = A ) ).

% append.left_neutral
thf(fact_217_eq__Nil__appendI,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( Xs = Ys )
     => ( Xs
        = ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_218_distinguishes__def,axiom,
    ( distinguishes_d_b_c
    = ( ^ [M2: fsm_d_b_c,Q12: d,Q22: d,Io4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Io4 @ ( sup_su3823046536922626210od_b_c @ ( lS_d_b_c @ M2 @ Q12 ) @ ( lS_d_b_c @ M2 @ Q22 ) ) )
          & ~ ( member6330420149250801815od_b_c @ Io4 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M2 @ Q12 ) @ ( lS_d_b_c @ M2 @ Q22 ) ) ) ) ) ) ).

% distinguishes_def
thf(fact_219_distinguishes__def,axiom,
    ( distinguishes_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q12: a,Q22: a,Io4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Io4 @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M2 @ Q12 ) @ ( lS_a_b_c @ M2 @ Q22 ) ) )
          & ~ ( member6330420149250801815od_b_c @ Io4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M2 @ Q12 ) @ ( lS_a_b_c @ M2 @ Q22 ) ) ) ) ) ) ).

% distinguishes_def
thf(fact_220_FSM_Oafter_Osimps_I1_J,axiom,
    ! [M: fsm_a_b_c,Q: a] :
      ( ( after_a_b_c @ M @ Q @ nil_Product_prod_b_c )
      = Q ) ).

% FSM.after.simps(1)
thf(fact_221_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( observ6293852833591064631_c_b_c @ M )
         => ~ ! [Io5: list_P903359562653991662od_b_c,X4: b,Y3: c] :
                ( ? [Io6: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) @ Io6 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_222_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( ( observable_a_b_c @ M )
         => ~ ! [Io5: list_P903359562653991662od_b_c,X4: b,Y3: c] :
                ( ? [Io6: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) @ Io6 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_223_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q: d] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) )
     => ( ( member_d @ Q @ ( states_d_b_c @ M ) )
       => ( ( observable_d_b_c @ M )
         => ~ ! [Io5: list_P903359562653991662od_b_c,X4: b,Y3: c] :
                ( ? [Io6: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) @ Io6 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_d_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X4 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_224_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P4618364105659340195od_b_c,M: fsm_li7789363362239116584od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ~ ( member1702757119880923450od_b_c @ Io @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states1638942826817349861od_b_c @ M ) )
       => ( ( observ2194746696072761382od_b_c @ M )
         => ~ ! [Io5: list_P4618364105659340195od_b_c,X4: nat,Y3: list_P903359562653991662od_b_c] :
                ( ? [Io6: list_P4618364105659340195od_b_c] :
                    ( Io
                    = ( append1310559846384609464od_b_c @ Io5 @ ( append1310559846384609464od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X4 @ Y3 ) @ nil_Pr679518533894577677od_b_c ) @ Io6 ) ) )
               => ( ( member1702757119880923450od_b_c @ Io5 @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) )
                 => ( member1702757119880923450od_b_c @ ( append1310559846384609464od_b_c @ Io5 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X4 @ Y3 ) @ nil_Pr679518533894577677od_b_c ) ) @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_225_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P4618364105659340195od_b_c,M: fsm_a_6390678650791688088od_b_c,Q: a] :
      ( ~ ( member1702757119880923450od_b_c @ Io @ ( lS_a_n6600196584412307578od_b_c @ M @ Q ) )
     => ( ( member_a @ Q @ ( states1206967506758974293od_b_c @ M ) )
       => ( ( observ667460880479887382od_b_c @ M )
         => ~ ! [Io5: list_P4618364105659340195od_b_c,X4: nat,Y3: list_P903359562653991662od_b_c] :
                ( ? [Io6: list_P4618364105659340195od_b_c] :
                    ( Io
                    = ( append1310559846384609464od_b_c @ Io5 @ ( append1310559846384609464od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X4 @ Y3 ) @ nil_Pr679518533894577677od_b_c ) @ Io6 ) ) )
               => ( ( member1702757119880923450od_b_c @ Io5 @ ( lS_a_n6600196584412307578od_b_c @ M @ Q ) )
                 => ( member1702757119880923450od_b_c @ ( append1310559846384609464od_b_c @ Io5 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X4 @ Y3 ) @ nil_Pr679518533894577677od_b_c ) ) @ ( lS_a_n6600196584412307578od_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_226_h__obs__language__single__transition__iff,axiom,
    ! [M: fsm_d_b_c,X: b,Y: c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_d_b_c @ M @ Q ) )
        = ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
         != none_d ) ) ) ).

% h_obs_language_single_transition_iff
thf(fact_227_h__obs__language__single__transition__iff,axiom,
    ! [M: fsm_a_b_c,X: b,Y: c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_a_b_c @ M @ Q ) )
        = ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
         != none_a ) ) ) ).

% h_obs_language_single_transition_iff
thf(fact_228_h__obs__language__single__transition__iff,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Q: a] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( member1702757119880923450od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) @ ( lS_a_n6600196584412307578od_b_c @ M @ Q ) )
        = ( ( h_obs_6797610709827923659od_b_c @ M @ Q @ X @ Y )
         != none_a ) ) ) ).

% h_obs_language_single_transition_iff
thf(fact_229_distinguishes__after__prepend,axiom,
    ! [M: fsm_d_b_c,Q1: d,X: b,Y: c,Q2: d,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( ( h_obs_d_b_c @ M @ Q1 @ X @ Y )
         != none_d )
       => ( ( ( h_obs_d_b_c @ M @ Q2 @ X @ Y )
           != none_d )
         => ( ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ Q1 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( after_d_b_c @ M @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ Gamma )
           => ( distinguishes_d_b_c @ M @ Q1 @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ).

% distinguishes_after_prepend
thf(fact_230_distinguishes__after__prepend,axiom,
    ! [M: fsm_a_b_c,Q1: a,X: b,Y: c,Q2: a,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( ( h_obs_a_b_c @ M @ Q1 @ X @ Y )
         != none_a )
       => ( ( ( h_obs_a_b_c @ M @ Q2 @ X @ Y )
           != none_a )
         => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ Q1 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( after_a_b_c @ M @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ Gamma )
           => ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ).

% distinguishes_after_prepend
thf(fact_231_distinguishes__after__prepend,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Q1: a,X: nat,Y: list_P903359562653991662od_b_c,Q2: a,Gamma: list_P4618364105659340195od_b_c] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( ( h_obs_6797610709827923659od_b_c @ M @ Q1 @ X @ Y )
         != none_a )
       => ( ( ( h_obs_6797610709827923659od_b_c @ M @ Q2 @ X @ Y )
           != none_a )
         => ( ( distin240330122477437918od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ Q1 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) @ ( after_7403543103203634631od_b_c @ M @ Q2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) @ Gamma )
           => ( distin240330122477437918od_b_c @ M @ Q1 @ Q2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ).

% distinguishes_after_prepend
thf(fact_232_language__contains__empty__sequence,axiom,
    ! [M: fsm_a_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ).

% language_contains_empty_sequence
thf(fact_233_language__contains__empty__sequence,axiom,
    ! [M: fsm_d_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ).

% language_contains_empty_sequence
thf(fact_234_h__obs__language__append,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,X: b,Y: c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( ( h_obs_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ U2 ) @ X @ Y )
           != none_d )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ).

% h_obs_language_append
thf(fact_235_h__obs__language__append,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,X: b,Y: c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( ( h_obs_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U2 ) @ X @ Y )
           != none_a )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ).

% h_obs_language_append
thf(fact_236_h__obs__language__append,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,U2: list_P4618364105659340195od_b_c,X: nat,Y: list_P903359562653991662od_b_c] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( member1702757119880923450od_b_c @ U2 @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
       => ( ( ( h_obs_6797610709827923659od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ U2 ) @ X @ Y )
           != none_a )
         => ( member1702757119880923450od_b_c @ ( append1310559846384609464od_b_c @ U2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) ) ) ) ) ).

% h_obs_language_append
thf(fact_237_distinguishes__not__Nil,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_238_distinguishes__not__Nil,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c] :
      ( ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
       => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_239_distinguishes__after__initial__prepend,axiom,
    ! [M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,X: b,Y: c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( ( h_obs_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io1 ) @ X @ Y )
             != none_d )
           => ( ( ( h_obs_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io2 ) @ X @ Y )
               != none_d )
             => ( ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) @ Gamma )
               => ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io1 ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io2 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ) ) ).

% distinguishes_after_initial_prepend
thf(fact_240_distinguishes__after__initial__prepend,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,X: b,Y: c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( ( h_obs_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io1 ) @ X @ Y )
             != none_a )
           => ( ( ( h_obs_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io2 ) @ X @ Y )
               != none_a )
             => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) @ Gamma )
               => ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io1 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io2 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ) ) ).

% distinguishes_after_initial_prepend
thf(fact_241_distinguishes__after__initial__prepend,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Io1: list_P4618364105659340195od_b_c,Io2: list_P4618364105659340195od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Gamma: list_P4618364105659340195od_b_c] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( member1702757119880923450od_b_c @ Io1 @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
       => ( ( member1702757119880923450od_b_c @ Io2 @ ( lS_a_n6600196584412307578od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) ) )
         => ( ( ( h_obs_6797610709827923659od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Io1 ) @ X @ Y )
             != none_a )
           => ( ( ( h_obs_6797610709827923659od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Io2 ) @ X @ Y )
               != none_a )
             => ( ( distin240330122477437918od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ ( append1310559846384609464od_b_c @ Io1 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) ) @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ ( append1310559846384609464od_b_c @ Io2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) ) @ Gamma )
               => ( distin240330122477437918od_b_c @ M @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Io1 ) @ ( after_7403543103203634631od_b_c @ M @ ( initia7582277823139973807od_b_c @ M ) @ Io2 ) @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ Gamma ) ) ) ) ) ) ) ) ).

% distinguishes_after_initial_prepend
thf(fact_242_append__eq__appendI,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Xs1: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Us: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Xs1 )
        = Zs )
     => ( ( Ys
          = ( append2547753245680614915od_b_c @ Xs1 @ Us ) )
       => ( ( append2547753245680614915od_b_c @ Xs @ Ys )
          = ( append2547753245680614915od_b_c @ Zs @ Us ) ) ) ) ).

% append_eq_appendI
thf(fact_243_append__eq__append__conv2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,Ts: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = ( append2547753245680614915od_b_c @ Zs @ Ts ) )
      = ( ? [Us2: list_P903359562653991662od_b_c] :
            ( ( ( Xs
                = ( append2547753245680614915od_b_c @ Zs @ Us2 ) )
              & ( ( append2547753245680614915od_b_c @ Us2 @ Ys )
                = Ts ) )
            | ( ( ( append2547753245680614915od_b_c @ Xs @ Us2 )
                = Zs )
              & ( Ys
                = ( append2547753245680614915od_b_c @ Us2 @ Ts ) ) ) ) ) ) ).

% append_eq_append_conv2
thf(fact_244_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( minima9089413714839006869_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima9089413714839006869_c_b_c @ M @ ( after_4052058690717316294_c_b_c @ M @ Q1 @ W ) @ ( after_4052058690717316294_c_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_245_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ Q1 @ W ) @ ( after_a_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_246_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( minima7808819671940975144_d_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima7808819671940975144_d_b_c @ M @ ( after_d_b_c @ M @ Q1 @ W ) @ ( after_d_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_247_minimally__distinguishes__ex,axiom,
    ! [Q1: d,M: fsm_d_b_c,Q2: d] :
      ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
     => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
       => ( ( ( lS_d_b_c @ M @ Q1 )
           != ( lS_d_b_c @ M @ Q2 ) )
         => ~ ! [V4: list_P903359562653991662od_b_c] :
                ~ ( minima7808819671940975144_d_b_c @ M @ Q1 @ Q2 @ V4 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_248_minimally__distinguishes__ex,axiom,
    ! [Q1: a,M: fsm_a_b_c,Q2: a] :
      ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
     => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
       => ( ( ( lS_a_b_c @ M @ Q1 )
           != ( lS_a_b_c @ M @ Q2 ) )
         => ~ ! [V4: list_P903359562653991662od_b_c] :
                ~ ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ V4 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_249_minimally__distinguishes__after__append__initial,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U2 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V2 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ U2 @ W ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ V2 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_250_minimally__distinguishes__after__append__initial,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ( minima7808819671940975144_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ U2 ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ V2 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima7808819671940975144_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ U2 @ W ) ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ V2 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_251_minimally__distinguishes__no__prefix,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ W ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ W ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( minima7808819671940975144_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ U2 ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ V2 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ U2 @ W ) ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2547753245680614915od_b_c @ V2 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_252_minimally__distinguishes__no__prefix,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ W ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V2 @ W ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U2 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V2 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ U2 @ W ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ V2 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_253_list__ee__eq__leel_I1_J,axiom,
    ! [E1: product_prod_b_c,E2: product_prod_b_c,L1: list_P903359562653991662od_b_c,E12: product_prod_b_c,E22: product_prod_b_c,L2: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ E1 @ ( cons_P4529483553340347422od_b_c @ E2 @ nil_Product_prod_b_c ) )
        = ( append2547753245680614915od_b_c @ L1 @ ( cons_P4529483553340347422od_b_c @ E12 @ ( cons_P4529483553340347422od_b_c @ E22 @ L2 ) ) ) )
      = ( ( L1 = nil_Product_prod_b_c )
        & ( E1 = E12 )
        & ( E2 = E22 )
        & ( L2 = nil_Product_prod_b_c ) ) ) ).

% list_ee_eq_leel(1)
thf(fact_254_list__ee__eq__leel_I2_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,E12: product_prod_b_c,E22: product_prod_b_c,L2: list_P903359562653991662od_b_c,E1: product_prod_b_c,E2: product_prod_b_c] :
      ( ( ( append2547753245680614915od_b_c @ L1 @ ( cons_P4529483553340347422od_b_c @ E12 @ ( cons_P4529483553340347422od_b_c @ E22 @ L2 ) ) )
        = ( cons_P4529483553340347422od_b_c @ E1 @ ( cons_P4529483553340347422od_b_c @ E2 @ nil_Product_prod_b_c ) ) )
      = ( ( L1 = nil_Product_prod_b_c )
        & ( E1 = E12 )
        & ( E2 = E22 )
        & ( L2 = nil_Product_prod_b_c ) ) ) ).

% list_ee_eq_leel(2)
thf(fact_255_list__se__match_I1_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,L2: list_P903359562653991662od_b_c,A: product_prod_b_c] :
      ( ( L1 != nil_Product_prod_b_c )
     => ( ( ( append2547753245680614915od_b_c @ L1 @ L2 )
          = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) )
        = ( ( L1
            = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) )
          & ( L2 = nil_Product_prod_b_c ) ) ) ) ).

% list_se_match(1)
thf(fact_256_list__se__match_I2_J,axiom,
    ! [L2: list_P903359562653991662od_b_c,L1: list_P903359562653991662od_b_c,A: product_prod_b_c] :
      ( ( L2 != nil_Product_prod_b_c )
     => ( ( ( append2547753245680614915od_b_c @ L1 @ L2 )
          = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) )
        = ( ( L1 = nil_Product_prod_b_c )
          & ( L2
            = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) ) ) ) ) ).

% list_se_match(2)
thf(fact_257_list__se__match_I3_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,A: product_prod_b_c,L2: list_P903359562653991662od_b_c] :
      ( ( L1 != nil_Product_prod_b_c )
     => ( ( ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c )
          = ( append2547753245680614915od_b_c @ L1 @ L2 ) )
        = ( ( L1
            = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) )
          & ( L2 = nil_Product_prod_b_c ) ) ) ) ).

% list_se_match(3)
thf(fact_258_list__se__match_I4_J,axiom,
    ! [L2: list_P903359562653991662od_b_c,A: product_prod_b_c,L1: list_P903359562653991662od_b_c] :
      ( ( L2 != nil_Product_prod_b_c )
     => ( ( ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c )
          = ( append2547753245680614915od_b_c @ L1 @ L2 ) )
        = ( ( L1 = nil_Product_prod_b_c )
          & ( L2
            = ( cons_P4529483553340347422od_b_c @ A @ nil_Product_prod_b_c ) ) ) ) ) ).

% list_se_match(4)
thf(fact_259_list__e__eq__lel_I1_J,axiom,
    ! [E: product_prod_b_c,L1: list_P903359562653991662od_b_c,E3: product_prod_b_c,L2: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ E @ nil_Product_prod_b_c )
        = ( append2547753245680614915od_b_c @ L1 @ ( cons_P4529483553340347422od_b_c @ E3 @ L2 ) ) )
      = ( ( L1 = nil_Product_prod_b_c )
        & ( E3 = E )
        & ( L2 = nil_Product_prod_b_c ) ) ) ).

% list_e_eq_lel(1)
thf(fact_260_list__e__eq__lel_I2_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,E3: product_prod_b_c,L2: list_P903359562653991662od_b_c,E: product_prod_b_c] :
      ( ( ( append2547753245680614915od_b_c @ L1 @ ( cons_P4529483553340347422od_b_c @ E3 @ L2 ) )
        = ( cons_P4529483553340347422od_b_c @ E @ nil_Product_prod_b_c ) )
      = ( ( L1 = nil_Product_prod_b_c )
        & ( E3 = E )
        & ( L2 = nil_Product_prod_b_c ) ) ) ).

% list_e_eq_lel(2)
thf(fact_261_pass__io__set__maximal__def,axiom,
    ( pass_i5868551379204665570_a_b_c
    = ( ^ [M2: fsm_a_b_c,Ios: set_li6436108459499378894od_b_c] :
        ! [Io4: list_P903359562653991662od_b_c,X2: b,Y2: c,Io7: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io7 ) ) @ Ios )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
             => ? [Io8: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) @ Io8 ) ) @ Ios ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_262_pass__io__set__maximal__def,axiom,
    ( pass_i4210463151059506021_d_b_c
    = ( ^ [M2: fsm_d_b_c,Ios: set_li6436108459499378894od_b_c] :
        ! [Io4: list_P903359562653991662od_b_c,X2: b,Y2: c,Io7: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io7 ) ) @ Ios )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) )
             => ? [Io8: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) @ Io8 ) ) @ Ios ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_263_pass__io__set__def,axiom,
    ( pass_io_set_a_b_c
    = ( ^ [M2: fsm_a_b_c,Ios: set_li6436108459499378894od_b_c] :
        ! [Io4: list_P903359562653991662od_b_c,X2: b,Y2: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ Ios )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ Ios ) ) ) ) ) ).

% pass_io_set_def
thf(fact_264_pass__io__set__def,axiom,
    ( pass_io_set_d_b_c
    = ( ^ [M2: fsm_d_b_c,Ios: set_li6436108459499378894od_b_c] :
        ! [Io4: list_P903359562653991662od_b_c,X2: b,Y2: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ Ios )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ Ios ) ) ) ) ) ).

% pass_io_set_def
thf(fact_265__092_060open_062P_A_Ie_M_Aw_J_092_060close_062,axiom,
    p @ ( produc8137419655804493381od_b_c @ e @ w ) ).

% \<open>P (e, w)\<close>
thf(fact_266_empty__append__eq__id,axiom,
    ( ( append2547753245680614915od_b_c @ nil_Product_prod_b_c )
    = ( ^ [X2: list_P903359562653991662od_b_c] : X2 ) ) ).

% empty_append_eq_id
thf(fact_267_partition__rev_Ocases,axiom,
    ! [X: produc6480465915480880334od_b_c] :
      ( ! [P2: product_prod_b_c > $o,Yes: list_P903359562653991662od_b_c,No: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3614263070280852224od_b_c @ P2 @ ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Yes @ No ) @ nil_Product_prod_b_c ) ) )
     => ~ ! [P2: product_prod_b_c > $o,Yes: list_P903359562653991662od_b_c,No: list_P903359562653991662od_b_c,X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3614263070280852224od_b_c @ P2 @ ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Yes @ No ) @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ).

% partition_rev.cases
thf(fact_268_does__distinguish_Ocases,axiom,
    ! [X: produc3355883267749493558od_b_c] :
      ~ ! [M3: fsm_nat_b_c,Q13: nat,Q23: nat,Io3: list_P903359562653991662od_b_c] :
          ( X
         != ( produc2880123634351411432od_b_c @ M3 @ ( produc5826228540202203260od_b_c @ Q13 @ ( produc8137419655804493381od_b_c @ Q23 @ Io3 ) ) ) ) ).

% does_distinguish.cases
thf(fact_269_mergesort__by__rel__merge_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [R: product_prod_b_c > product_prod_b_c > $o,X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
          ( X
         != ( produc7428879202731100112od_b_c @ R @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) )
     => ( ! [R: product_prod_b_c > product_prod_b_c > $o,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ R @ ( produc3076307724246486423od_b_c @ Xs2 @ nil_Product_prod_b_c ) ) )
       => ~ ! [R: product_prod_b_c > product_prod_b_c > $o,V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( X
             != ( produc7428879202731100112od_b_c @ R @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) ) ) ) ) ).

% mergesort_by_rel_merge.cases
thf(fact_270_quicksort__by__rel_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [R: product_prod_b_c > product_prod_b_c > $o,Sl: list_P903359562653991662od_b_c] :
          ( X
         != ( produc7428879202731100112od_b_c @ R @ ( produc3076307724246486423od_b_c @ Sl @ nil_Product_prod_b_c ) ) )
     => ~ ! [R: product_prod_b_c > product_prod_b_c > $o,Sl: list_P903359562653991662od_b_c,X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ R @ ( produc3076307724246486423od_b_c @ Sl @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ).

% quicksort_by_rel.cases
thf(fact_271_list__all__zip_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [P2: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc7428879202731100112od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ nil_Product_prod_b_c ) ) )
     => ( ! [P2: product_prod_b_c > product_prod_b_c > $o,A3: product_prod_b_c,As: list_P903359562653991662od_b_c,B2: product_prod_b_c,Bs: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ A3 @ As ) @ ( cons_P4529483553340347422od_b_c @ B2 @ Bs ) ) ) )
       => ( ! [P2: product_prod_b_c > product_prod_b_c > $o,V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( X
             != ( produc7428879202731100112od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) @ nil_Product_prod_b_c ) ) )
         => ~ ! [P2: product_prod_b_c > product_prod_b_c > $o,V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
                ( X
               != ( produc7428879202731100112od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) ) ) ) ) ) ).

% list_all_zip.cases
thf(fact_272_mergesort__by__rel__split_Ocases,axiom,
    ! [X: produc1404827273422455342od_b_c] :
      ( ! [Xs12: list_P903359562653991662od_b_c,Xs22: list_P903359562653991662od_b_c] :
          ( X
         != ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Xs12 @ Xs22 ) @ nil_Product_prod_b_c ) )
     => ( ! [Xs12: list_P903359562653991662od_b_c,Xs22: list_P903359562653991662od_b_c,X4: product_prod_b_c] :
            ( X
           != ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Xs12 @ Xs22 ) @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) )
       => ~ ! [Xs12: list_P903359562653991662od_b_c,Xs22: list_P903359562653991662od_b_c,X1: product_prod_b_c,X23: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Xs12 @ Xs22 ) @ ( cons_P4529483553340347422od_b_c @ X1 @ ( cons_P4529483553340347422od_b_c @ X23 @ Xs2 ) ) ) ) ) ) ).

% mergesort_by_rel_split.cases
thf(fact_273_merge_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [L22: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ L22 ) )
     => ( ! [V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) @ nil_Product_prod_b_c ) )
       => ~ ! [X1: product_prod_b_c,L12: list_P903359562653991662od_b_c,X23: product_prod_b_c,L22: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X1 @ L12 ) @ ( cons_P4529483553340347422od_b_c @ X23 @ L22 ) ) ) ) ) ).

% merge.cases
thf(fact_274_successively_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P2: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P2 @ nil_Product_prod_b_c ) )
     => ( ! [P2: product_prod_b_c > product_prod_b_c > $o,X4: product_prod_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) )
       => ~ ! [P2: product_prod_b_c > product_prod_b_c > $o,X4: product_prod_b_c,Y3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc6092892548594537111od_b_c @ P2 @ ( cons_P4529483553340347422od_b_c @ X4 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_275_sorted__wrt_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P2: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P2 @ nil_Product_prod_b_c ) )
     => ~ ! [P2: product_prod_b_c > product_prod_b_c > $o,X4: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P2 @ ( cons_P4529483553340347422od_b_c @ X4 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_276_shuffles_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys3: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys3 ) )
     => ( ! [Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ Xs2 @ nil_Product_prod_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_277_bex2I,axiom,
    ! [A: b,B: c,S: set_Product_prod_b_c,P: b > c > $o] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A @ B ) @ S )
     => ( ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A @ B ) @ S )
         => ( P @ A @ B ) )
       => ? [A3: b,B2: c] :
            ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A3 @ B2 ) @ S )
            & ( P @ A3 @ B2 ) ) ) ) ).

% bex2I
thf(fact_278_bex2I,axiom,
    ! [A: nat,B: list_P903359562653991662od_b_c,S: set_Pr2622754303974797129od_b_c,P: nat > list_P903359562653991662od_b_c > $o] :
      ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ A @ B ) @ S )
     => ( ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ A @ B ) @ S )
         => ( P @ A @ B ) )
       => ? [A3: nat,B2: list_P903359562653991662od_b_c] :
            ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ A3 @ B2 ) @ S )
            & ( P @ A3 @ B2 ) ) ) ) ).

% bex2I
thf(fact_279_list__tail__coinc,axiom,
    ! [N1: product_prod_b_c,R1: list_P903359562653991662od_b_c,N2: product_prod_b_c,R2: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ N1 @ R1 )
        = ( cons_P4529483553340347422od_b_c @ N2 @ R2 ) )
     => ( ( N1 = N2 )
        & ( R1 = R2 ) ) ) ).

% list_tail_coinc
thf(fact_280_mergesort__by__rel__merge__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,R3: product_prod_b_c > product_prod_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ! [Xs2: list_P903359562653991662od_b_c] : ( P @ Xs2 @ nil_Product_prod_b_c )
     => ( ! [X_1: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ X_1 )
       => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
              ( ( R3 @ X4 @ Y3 )
             => ( ( P @ Xs2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) )
         => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
                ( ~ ( R3 @ X4 @ Y3 )
               => ( ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ Ys3 )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% mergesort_by_rel_merge_induct
thf(fact_281_list__induct__first2,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) )
       => ( ! [X1: product_prod_b_c,X23: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( P @ Xs2 )
             => ( P @ ( cons_P4529483553340347422od_b_c @ X1 @ ( cons_P4529483553340347422od_b_c @ X23 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_induct_first2
thf(fact_282_list__2pre__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
     => ( ! [E4: product_prod_b_c,W12: list_P903359562653991662od_b_c,W22: list_P903359562653991662od_b_c] :
            ( ( P @ W12 @ W22 )
           => ( P @ ( cons_P4529483553340347422od_b_c @ E4 @ W12 ) @ W22 ) )
       => ( ! [E4: product_prod_b_c,W13: list_P903359562653991662od_b_c,W23: list_P903359562653991662od_b_c] :
              ( ( P @ W13 @ W23 )
             => ( P @ W13 @ ( cons_P4529483553340347422od_b_c @ E4 @ W23 ) ) )
         => ( P @ W1 @ W2 ) ) ) ) ).

% list_2pre_induct
thf(fact_283_neq__NilE,axiom,
    ! [L: list_P903359562653991662od_b_c] :
      ( ( L != nil_Product_prod_b_c )
     => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( L
           != ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ).

% neq_NilE
thf(fact_284_list__match__lel__lel,axiom,
    ! [C1: list_P903359562653991662od_b_c,Qs: product_prod_b_c,C2: list_P903359562653991662od_b_c,C12: list_P903359562653991662od_b_c,Qs2: product_prod_b_c,C22: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ C1 @ ( cons_P4529483553340347422od_b_c @ Qs @ C2 ) )
        = ( append2547753245680614915od_b_c @ C12 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C22 ) ) )
     => ( ! [C21: list_P903359562653991662od_b_c] :
            ( ( C1
              = ( append2547753245680614915od_b_c @ C12 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C21 ) ) )
           => ( C22
             != ( append2547753245680614915od_b_c @ C21 @ ( cons_P4529483553340347422od_b_c @ Qs @ C2 ) ) ) )
       => ( ( ( C12 = C1 )
           => ( ( Qs2 = Qs )
             => ( C22 != C2 ) ) )
         => ~ ! [C212: list_P903359562653991662od_b_c] :
                ( ( C12
                  = ( append2547753245680614915od_b_c @ C1 @ ( cons_P4529483553340347422od_b_c @ Qs @ C212 ) ) )
               => ( C2
                 != ( append2547753245680614915od_b_c @ C212 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C22 ) ) ) ) ) ) ) ).

% list_match_lel_lel
thf(fact_285_neq__Nil__revE,axiom,
    ! [L: list_P903359562653991662od_b_c] :
      ( ( L != nil_Product_prod_b_c )
     => ~ ! [Ll: list_P903359562653991662od_b_c,E4: product_prod_b_c] :
            ( L
           != ( append2547753245680614915od_b_c @ Ll @ ( cons_P4529483553340347422od_b_c @ E4 @ nil_Product_prod_b_c ) ) ) ) ).

% neq_Nil_revE
thf(fact_286_rev__induct2_H,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
     => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
         => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% rev_induct2'
thf(fact_287_neq__Nil__rev__conv,axiom,
    ! [L: list_P903359562653991662od_b_c] :
      ( ( L != nil_Product_prod_b_c )
      = ( ? [Xs3: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
            ( L
            = ( append2547753245680614915od_b_c @ Xs3 @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) ) ) ) ) ).

% neq_Nil_rev_conv
thf(fact_288_rev__nonempty__induct2_H,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ( Ys != nil_Product_prod_b_c )
       => ( ! [X4: product_prod_b_c,Y3: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) )
         => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c] :
                ( ( Xs2 != nil_Product_prod_b_c )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
           => ( ! [X4: product_prod_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
                  ( ( Ys3 != nil_Product_prod_b_c )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) @ ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
             => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
                    ( ( P @ Xs2 @ Ys3 )
                   => ( ( Xs2 != nil_Product_prod_b_c )
                     => ( ( Ys3 != nil_Product_prod_b_c )
                       => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) ) )
               => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).

% rev_nonempty_induct2'
thf(fact_289_list__Cons__eq__append__cases,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
        = ( append2547753245680614915od_b_c @ Ys @ Zs ) )
     => ( ( ( Ys = nil_Product_prod_b_c )
         => ( Zs
           != ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
       => ~ ! [Ys5: list_P903359562653991662od_b_c] :
              ( ( Ys
                = ( cons_P4529483553340347422od_b_c @ X @ Ys5 ) )
             => ( ( append2547753245680614915od_b_c @ Ys5 @ Zs )
               != Xs ) ) ) ) ).

% list_Cons_eq_append_cases
thf(fact_290_list__append__eq__Cons__cases,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Zs )
        = ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
     => ( ( ( Ys = nil_Product_prod_b_c )
         => ( Zs
           != ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
       => ~ ! [Ys5: list_P903359562653991662od_b_c] :
              ( ( Ys
                = ( cons_P4529483553340347422od_b_c @ X @ Ys5 ) )
             => ( ( append2547753245680614915od_b_c @ Ys5 @ Zs )
               != Xs ) ) ) ) ).

% list_append_eq_Cons_cases
thf(fact_291_Un__Int__eq_I1_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ S @ T ) @ S )
      = S ) ).

% Un_Int_eq(1)
thf(fact_292_Un__Int__eq_I2_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ S @ T ) @ T )
      = T ) ).

% Un_Int_eq(2)
thf(fact_293_Un__Int__eq_I3_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ S @ ( sup_su3823046536922626210od_b_c @ S @ T ) )
      = S ) ).

% Un_Int_eq(3)
thf(fact_294_Un__Int__eq_I4_J,axiom,
    ! [T: set_li6436108459499378894od_b_c,S: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ T @ ( sup_su3823046536922626210od_b_c @ S @ T ) )
      = T ) ).

% Un_Int_eq(4)
thf(fact_295_prod_Oinject,axiom,
    ! [X12: b,X24: c,Y1: b,Y23: c] :
      ( ( ( product_Pair_b_c @ X12 @ X24 )
        = ( product_Pair_b_c @ Y1 @ Y23 ) )
      = ( ( X12 = Y1 )
        & ( X24 = Y23 ) ) ) ).

% prod.inject
thf(fact_296_prod_Oinject,axiom,
    ! [X12: nat,X24: list_P903359562653991662od_b_c,Y1: nat,Y23: list_P903359562653991662od_b_c] :
      ( ( ( produc8137419655804493381od_b_c @ X12 @ X24 )
        = ( produc8137419655804493381od_b_c @ Y1 @ Y23 ) )
      = ( ( X12 = Y1 )
        & ( X24 = Y23 ) ) ) ).

% prod.inject
thf(fact_297_old_Oprod_Oinject,axiom,
    ! [A: b,B: c,A4: b,B3: c] :
      ( ( ( product_Pair_b_c @ A @ B )
        = ( product_Pair_b_c @ A4 @ B3 ) )
      = ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_298_old_Oprod_Oinject,axiom,
    ! [A: nat,B: list_P903359562653991662od_b_c,A4: nat,B3: list_P903359562653991662od_b_c] :
      ( ( ( produc8137419655804493381od_b_c @ A @ B )
        = ( produc8137419655804493381od_b_c @ A4 @ B3 ) )
      = ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
thf(fact_299_IntI,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ A2 )
     => ( ( member_a @ C @ B4 )
       => ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_300_IntI,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ A2 )
     => ( ( member6330420149250801815od_b_c @ C @ B4 )
       => ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_301_Int__iff,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
      = ( ( member_a @ C @ A2 )
        & ( member_a @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_302_Int__iff,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
      = ( ( member6330420149250801815od_b_c @ C @ A2 )
        & ( member6330420149250801815od_b_c @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_303_UnCI,axiom,
    ! [C: list_P903359562653991662od_b_c,B4: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ~ ( member6330420149250801815od_b_c @ C @ B4 )
       => ( member6330420149250801815od_b_c @ C @ A2 ) )
     => ( member6330420149250801815od_b_c @ C @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) ) ) ).

% UnCI
thf(fact_304_UnCI,axiom,
    ! [C: a,B4: set_a,A2: set_a] :
      ( ( ~ ( member_a @ C @ B4 )
       => ( member_a @ C @ A2 ) )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B4 ) ) ) ).

% UnCI
thf(fact_305_Un__iff,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) )
      = ( ( member6330420149250801815od_b_c @ C @ A2 )
        | ( member6330420149250801815od_b_c @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_306_Un__iff,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( sup_sup_set_a @ A2 @ B4 ) )
      = ( ( member_a @ C @ A2 )
        | ( member_a @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_307_Int__Un__eq_I4_J,axiom,
    ! [T: set_li6436108459499378894od_b_c,S: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ T @ ( inf_in4978071631833541052od_b_c @ S @ T ) )
      = T ) ).

% Int_Un_eq(4)
thf(fact_308_Int__Un__eq_I3_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ S @ ( inf_in4978071631833541052od_b_c @ S @ T ) )
      = S ) ).

% Int_Un_eq(3)
thf(fact_309_Int__Un__eq_I2_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ S @ T ) @ T )
      = T ) ).

% Int_Un_eq(2)
thf(fact_310_Int__Un__eq_I1_J,axiom,
    ! [S: set_li6436108459499378894od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ S @ T ) @ S )
      = S ) ).

% Int_Un_eq(1)
thf(fact_311_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_b_c] :
      ~ ! [A3: b,B2: c] :
          ( Y
         != ( product_Pair_b_c @ A3 @ B2 ) ) ).

% old.prod.exhaust
thf(fact_312_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3246581702073416851od_b_c] :
      ~ ! [A3: nat,B2: list_P903359562653991662od_b_c] :
          ( Y
         != ( produc8137419655804493381od_b_c @ A3 @ B2 ) ) ).

% old.prod.exhaust
thf(fact_313_surj__pair,axiom,
    ! [P3: product_prod_b_c] :
    ? [X4: b,Y3: c] :
      ( P3
      = ( product_Pair_b_c @ X4 @ Y3 ) ) ).

% surj_pair
thf(fact_314_surj__pair,axiom,
    ! [P3: produc3246581702073416851od_b_c] :
    ? [X4: nat,Y3: list_P903359562653991662od_b_c] :
      ( P3
      = ( produc8137419655804493381od_b_c @ X4 @ Y3 ) ) ).

% surj_pair
thf(fact_315_prod__cases,axiom,
    ! [P: product_prod_b_c > $o,P3: product_prod_b_c] :
      ( ! [A3: b,B2: c] : ( P @ ( product_Pair_b_c @ A3 @ B2 ) )
     => ( P @ P3 ) ) ).

% prod_cases
thf(fact_316_prod__cases,axiom,
    ! [P: produc3246581702073416851od_b_c > $o,P3: produc3246581702073416851od_b_c] :
      ( ! [A3: nat,B2: list_P903359562653991662od_b_c] : ( P @ ( produc8137419655804493381od_b_c @ A3 @ B2 ) )
     => ( P @ P3 ) ) ).

% prod_cases
thf(fact_317_Pair__inject,axiom,
    ! [A: b,B: c,A4: b,B3: c] :
      ( ( ( product_Pair_b_c @ A @ B )
        = ( product_Pair_b_c @ A4 @ B3 ) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_318_Pair__inject,axiom,
    ! [A: nat,B: list_P903359562653991662od_b_c,A4: nat,B3: list_P903359562653991662od_b_c] :
      ( ( ( produc8137419655804493381od_b_c @ A @ B )
        = ( produc8137419655804493381od_b_c @ A4 @ B3 ) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
thf(fact_319_IntE,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ~ ( ( member_a @ C @ A2 )
         => ~ ( member_a @ C @ B4 ) ) ) ).

% IntE
thf(fact_320_IntE,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
     => ~ ( ( member6330420149250801815od_b_c @ C @ A2 )
         => ~ ( member6330420149250801815od_b_c @ C @ B4 ) ) ) ).

% IntE
thf(fact_321_IntD1,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ( member_a @ C @ A2 ) ) ).

% IntD1
thf(fact_322_IntD1,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
     => ( member6330420149250801815od_b_c @ C @ A2 ) ) ).

% IntD1
thf(fact_323_IntD2,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ( member_a @ C @ B4 ) ) ).

% IntD2
thf(fact_324_IntD2,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
     => ( member6330420149250801815od_b_c @ C @ B4 ) ) ).

% IntD2
thf(fact_325_Int__assoc,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ C3 )
      = ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) ) ) ).

% Int_assoc
thf(fact_326_Int__absorb,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ A2 )
      = A2 ) ).

% Int_absorb
thf(fact_327_Int__commute,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A5: set_li6436108459499378894od_b_c,B5: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ B5 @ A5 ) ) ) ).

% Int_commute
thf(fact_328_Int__left__absorb,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
      = ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) ) ).

% Int_left_absorb
thf(fact_329_Int__left__commute,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) )
      = ( inf_in4978071631833541052od_b_c @ B4 @ ( inf_in4978071631833541052od_b_c @ A2 @ C3 ) ) ) ).

% Int_left_commute
thf(fact_330_UnE,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) )
     => ( ~ ( member6330420149250801815od_b_c @ C @ A2 )
       => ( member6330420149250801815od_b_c @ C @ B4 ) ) ) ).

% UnE
thf(fact_331_UnE,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( sup_sup_set_a @ A2 @ B4 ) )
     => ( ~ ( member_a @ C @ A2 )
       => ( member_a @ C @ B4 ) ) ) ).

% UnE
thf(fact_332_UnI1,axiom,
    ! [C: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ A2 )
     => ( member6330420149250801815od_b_c @ C @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) ) ) ).

% UnI1
thf(fact_333_UnI1,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ A2 )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B4 ) ) ) ).

% UnI1
thf(fact_334_UnI2,axiom,
    ! [C: list_P903359562653991662od_b_c,B4: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ B4 )
     => ( member6330420149250801815od_b_c @ C @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) ) ) ).

% UnI2
thf(fact_335_UnI2,axiom,
    ! [C: a,B4: set_a,A2: set_a] :
      ( ( member_a @ C @ B4 )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B4 ) ) ) ).

% UnI2
thf(fact_336_Un__Int__crazy,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) ) @ ( inf_in4978071631833541052od_b_c @ C3 @ A2 ) )
      = ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) @ ( sup_su3823046536922626210od_b_c @ B4 @ C3 ) ) @ ( sup_su3823046536922626210od_b_c @ C3 @ A2 ) ) ) ).

% Un_Int_crazy
thf(fact_337_Int__Un__distrib,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ ( sup_su3823046536922626210od_b_c @ B4 @ C3 ) )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ ( inf_in4978071631833541052od_b_c @ A2 @ C3 ) ) ) ).

% Int_Un_distrib
thf(fact_338_Un__Int__distrib,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ A2 @ B4 ) @ ( sup_su3823046536922626210od_b_c @ A2 @ C3 ) ) ) ).

% Un_Int_distrib
thf(fact_339_Int__Un__distrib2,axiom,
    ! [B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ B4 @ C3 ) @ A2 )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ B4 @ A2 ) @ ( inf_in4978071631833541052od_b_c @ C3 @ A2 ) ) ) ).

% Int_Un_distrib2
thf(fact_340_Un__Int__distrib2,axiom,
    ! [B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) @ A2 )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ B4 @ A2 ) @ ( sup_su3823046536922626210od_b_c @ C3 @ A2 ) ) ) ).

% Un_Int_distrib2
thf(fact_341__092_060open_062P_A_IminEst0_M_A_091_093_J_092_060close_062,axiom,
    p @ ( produc8137419655804493381od_b_c @ minEst0 @ nil_Product_prod_b_c ) ).

% \<open>P (minEst0, [])\<close>
thf(fact_342_inf__sup__absorb,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( sup_su3823046536922626210od_b_c @ X @ Y ) )
      = X ) ).

% inf_sup_absorb
thf(fact_343_sup__inf__absorb,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ X @ Y ) )
      = X ) ).

% sup_inf_absorb
thf(fact_344_delete__aux_Ocases,axiom,
    ! [X: produc6475121930738208726od_b_c] :
      ( ! [K: b] :
          ( X
         != ( produc561751498933632326od_b_c @ K @ nil_Product_prod_b_c ) )
     => ~ ! [K: b,K2: b,V4: c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc561751498933632326od_b_c @ K @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K2 @ V4 ) @ Xs2 ) ) ) ) ).

% delete_aux.cases
thf(fact_345_delete__aux_Ocases,axiom,
    ! [X: produc2679492274711066452od_b_c] :
      ( ! [K: nat] :
          ( X
         != ( produc3111000275831359756od_b_c @ K @ nil_Pr679518533894577677od_b_c ) )
     => ~ ! [K: nat,K2: nat,V4: list_P903359562653991662od_b_c,Xs2: list_P4618364105659340195od_b_c] :
            ( X
           != ( produc3111000275831359756od_b_c @ K @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ K2 @ V4 ) @ Xs2 ) ) ) ) ).

% delete_aux.cases
thf(fact_346_is__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) )
     => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ nil_Product_prod_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) ) ) ).

% is_prefix.cases
thf(fact_347_inf__right__idem,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ Y )
      = ( inf_in4978071631833541052od_b_c @ X @ Y ) ) ).

% inf_right_idem
thf(fact_348_inf_Oright__idem,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ B )
      = ( inf_in4978071631833541052od_b_c @ A @ B ) ) ).

% inf.right_idem
thf(fact_349_inf__left__idem,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ X @ Y ) )
      = ( inf_in4978071631833541052od_b_c @ X @ Y ) ) ).

% inf_left_idem
thf(fact_350_inf_Oleft__idem,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
      = ( inf_in4978071631833541052od_b_c @ A @ B ) ) ).

% inf.left_idem
thf(fact_351_inf__idem,axiom,
    ! [X: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ X )
      = X ) ).

% inf_idem
thf(fact_352_inf_Oidem,axiom,
    ! [A: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A @ A )
      = A ) ).

% inf.idem
thf(fact_353_inf__left__commute,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
      = ( inf_in4978071631833541052od_b_c @ Y @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) ) ).

% inf_left_commute
thf(fact_354_inf_Oleft__commute,axiom,
    ! [B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ B @ ( inf_in4978071631833541052od_b_c @ A @ C ) )
      = ( inf_in4978071631833541052od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) ) ) ).

% inf.left_commute
thf(fact_355_inf__commute,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [X2: set_li6436108459499378894od_b_c,Y2: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ Y2 @ X2 ) ) ) ).

% inf_commute
thf(fact_356_inf_Ocommute,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B6: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ B6 @ A6 ) ) ) ).

% inf.commute
thf(fact_357_inf__assoc,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ Z )
      = ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) ) ) ).

% inf_assoc
thf(fact_358_inf_Oassoc,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C )
      = ( inf_in4978071631833541052od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) ) ) ).

% inf.assoc
thf(fact_359_inf__sup__aci_I1_J,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [X2: set_li6436108459499378894od_b_c,Y2: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ Y2 @ X2 ) ) ) ).

% inf_sup_aci(1)
thf(fact_360_inf__sup__aci_I2_J,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ Z )
      = ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) ) ) ).

% inf_sup_aci(2)
thf(fact_361_inf__sup__aci_I3_J,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
      = ( inf_in4978071631833541052od_b_c @ Y @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) ) ).

% inf_sup_aci(3)
thf(fact_362_inf__sup__aci_I4_J,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ X @ Y ) )
      = ( inf_in4978071631833541052od_b_c @ X @ Y ) ) ).

% inf_sup_aci(4)
thf(fact_363_find__index_Ocases,axiom,
    ! [X: produc7816210539016439438od_b_c] :
      ( ! [F2: product_prod_b_c > $o] :
          ( X
         != ( produc7392021306980666816od_b_c @ F2 @ nil_Product_prod_b_c ) )
     => ~ ! [F2: product_prod_b_c > $o,X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7392021306980666816od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ).

% find_index.cases
thf(fact_364_linear__order__from__list__position_H_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_365_sup__inf__distrib2,axiom,
    ! [Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) @ X )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ Y @ X ) @ ( sup_su3823046536922626210od_b_c @ Z @ X ) ) ) ).

% sup_inf_distrib2
thf(fact_366_sup__inf__distrib1,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ Y ) @ ( sup_su3823046536922626210od_b_c @ X @ Z ) ) ) ).

% sup_inf_distrib1
thf(fact_367_inf__sup__distrib2,axiom,
    ! [Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) @ X )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ Y @ X ) @ ( inf_in4978071631833541052od_b_c @ Z @ X ) ) ) ).

% inf_sup_distrib2
thf(fact_368_inf__sup__distrib1,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) ) ).

% inf_sup_distrib1
thf(fact_369_distrib__imp2,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ! [X4: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] :
          ( ( sup_su3823046536922626210od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ Y3 @ Z2 ) )
          = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ X4 @ Y3 ) @ ( sup_su3823046536922626210od_b_c @ X4 @ Z2 ) ) )
     => ( ( inf_in4978071631833541052od_b_c @ X @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) )
        = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) ) ) ).

% distrib_imp2
thf(fact_370_distrib__imp1,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ! [X4: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ X4 @ ( sup_su3823046536922626210od_b_c @ Y3 @ Z2 ) )
          = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ X4 @ Y3 ) @ ( inf_in4978071631833541052od_b_c @ X4 @ Z2 ) ) )
     => ( ( sup_su3823046536922626210od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
        = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ Y ) @ ( sup_su3823046536922626210od_b_c @ X @ Z ) ) ) ) ).

% distrib_imp1
thf(fact_371_map__default_Ocases,axiom,
    ! [X: produc2009451851958091931od_b_c] :
      ( ! [K: b,V4: c,F2: c > c] :
          ( X
         != ( produc1384939585547926677od_b_c @ K @ ( produc3590379597927054951od_b_c @ V4 @ ( produc1101678828523717360od_b_c @ F2 @ nil_Product_prod_b_c ) ) ) )
     => ~ ! [K: b,V4: c,F2: c > c,P4: product_prod_b_c,Ps2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1384939585547926677od_b_c @ K @ ( produc3590379597927054951od_b_c @ V4 @ ( produc1101678828523717360od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) ) ) ) ) ) ).

% map_default.cases
thf(fact_372_map__entry_Ocases,axiom,
    ! [X: produc6452300523622238572od_b_c] :
      ( ! [K: b,F2: c > c] :
          ( X
         != ( produc7015427828931889894od_b_c @ K @ ( produc1101678828523717360od_b_c @ F2 @ nil_Product_prod_b_c ) ) )
     => ~ ! [K: b,F2: c > c,P4: product_prod_b_c,Ps2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7015427828931889894od_b_c @ K @ ( produc1101678828523717360od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) ) ) ) ) ).

% map_entry.cases
thf(fact_373_clearjunk_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [P4: product_prod_b_c,Ps2: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) ) ) ).

% clearjunk.cases
thf(fact_374_find__remove_H_Ocases,axiom,
    ! [X: produc5559707038353031495od_b_c] :
      ( ! [P2: product_prod_b_c > $o,Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc1005531610559690873od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) ) )
     => ~ ! [P2: product_prod_b_c > $o,X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Prev: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1005531610559690873od_b_c @ P2 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_375_longest__common__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) )
     => ( ! [Uv: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uv ) )
       => ~ ! [Uu: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ Uu @ nil_Product_prod_b_c ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_376_subset__eq__mset__impl_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys3: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys3 ) )
     => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Ys3: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_377_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ( converge_a_b_c @ X @ X4 @ Xa3 )
                 => ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_378_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser1543909642583041681_b_c_d @ X @ Xa @ Xb )
     => ~ ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ( converge_a_b_c @ X @ X4 @ Xa3 )
                 => ( converge_d_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_379_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser6007795754467437259_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
           => ! [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
               => ( ( converge_d_b_c @ X @ X4 @ Xa3 )
                 => ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_380_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser6007795754467437262_b_c_d @ X @ Xa @ Xb )
     => ~ ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
           => ! [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
               => ( ( converge_d_b_c @ X @ X4 @ Xa3 )
                 => ( converge_d_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_381_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
     => ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ( converge_a_b_c @ X @ X3 @ Xa2 )
               => ( converge_a_b_c @ Xa @ X3 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_382_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser1543909642583041681_b_c_d @ X @ Xa @ Xb )
     => ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ( converge_a_b_c @ X @ X3 @ Xa2 )
               => ( converge_d_b_c @ Xa @ X3 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_383_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser6007795754467437259_b_c_a @ X @ Xa @ Xb )
     => ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
         => ! [Xa2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
             => ( ( converge_d_b_c @ X @ X3 @ Xa2 )
               => ( converge_a_b_c @ Xa @ X3 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_384_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser6007795754467437262_b_c_d @ X @ Xa @ Xb )
     => ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
         => ! [Xa2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
             => ( ( converge_d_b_c @ X @ X3 @ Xa2 )
               => ( converge_d_b_c @ Xa @ X3 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_385_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_a_b_c @ X @ X2 @ Y2 )
                   => ( converge_a_b_c @ Xa @ X2 @ Y2 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_386_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser1543909642583041681_b_c_d @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_a_b_c @ X @ X2 @ Y2 )
                   => ( converge_d_b_c @ Xa @ X2 @ Y2 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_387_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser6007795754467437259_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
             => ! [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_d_b_c @ X @ X2 @ Y2 )
                   => ( converge_a_b_c @ Xa @ X2 @ Y2 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_388_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser6007795754467437262_b_c_d @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
             => ! [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ X @ ( initial_d_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_d_b_c @ X @ X2 @ Y2 )
                   => ( converge_d_b_c @ Xa @ X2 @ Y2 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_389_preserves__convergence_Osimps,axiom,
    ( preser1543909642583041678_b_c_a
    = ( ^ [M12: fsm_a_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_a_b_c @ M12 @ X2 @ Y2 )
               => ( converge_a_b_c @ M23 @ X2 @ Y2 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_390_preserves__convergence_Osimps,axiom,
    ( preser1543909642583041681_b_c_d
    = ( ^ [M12: fsm_a_b_c,M23: fsm_d_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_a_b_c @ M12 @ X2 @ Y2 )
               => ( converge_d_b_c @ M23 @ X2 @ Y2 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_391_preserves__convergence_Osimps,axiom,
    ( preser6007795754467437259_b_c_a
    = ( ^ [M12: fsm_d_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ A5 ) )
         => ! [Y2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_d_b_c @ M12 @ X2 @ Y2 )
               => ( converge_a_b_c @ M23 @ X2 @ Y2 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_392_preserves__convergence_Osimps,axiom,
    ( preser6007795754467437262_b_c_d
    = ( ^ [M12: fsm_d_b_c,M23: fsm_d_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ A5 ) )
         => ! [Y2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_d_b_c @ M12 @ X2 @ Y2 )
               => ( converge_d_b_c @ M23 @ X2 @ Y2 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_393_assms_I11_J,axiom,
    ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) @ ( prefix9085958534787526401od_b_c @ t ) )
    = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) @ ( prefix9085958534787526401od_b_c @ t ) ) ) ).

% assms(11)
thf(fact_394__092_060open_062v_H_H_A_092_060in_062_APrefix__Tree_Oset_AT_A_092_060inter_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ v2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ t ) @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ) ).

% \<open>v'' \<in> Prefix_Tree.set T \<inter> L M1\<close>
thf(fact_395__092_060open_062u_H_H_A_092_060in_062_APrefix__Tree_Oset_AT_A_092_060inter_062_AL_AM1_092_060close_062,axiom,
    member6330420149250801815od_b_c @ u2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ t ) @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) ) ).

% \<open>u'' \<in> Prefix_Tree.set T \<inter> L M1\<close>
thf(fact_396__092_060open_062v_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_APrefix__Tree_Oset_AT_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ v2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ t ) ).

% \<open>v'' @ [(x, y)] \<in> Prefix_Tree.set T\<close>
thf(fact_397__092_060open_062u_H_H_A_064_A_091_Ix_M_Ay_J_093_A_092_060in_062_APrefix__Tree_Oset_AT_092_060close_062,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ u2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ t ) ).

% \<open>u'' @ [(x, y)] \<in> Prefix_Tree.set T\<close>
thf(fact_398_after__distinguishes__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T1: prefix425356687782099470od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_d_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Beta ) ) ) )
                 => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Alpha ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_399_after__distinguishes__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T1: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_400_after__distinguishes__diverge,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T1: prefix425356687782099470od_b_c] :
      ( ( observable_d_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_d_b_c @ M1 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Beta ) ) ) )
                 => ( ( distinguishes_d_b_c @ M1 @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Alpha ) @ ( after_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) ) )
                     => ~ ( converge_d_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_401_after__distinguishes__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T1: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T1 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T1 ) ) )
                     => ~ ( converge_d_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_402_suffixes_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_l8907847357763382004od_b_c] :
      ( ( ( suffix2151784340763841114od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y
           != ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ( Y
               != ( append6992831555715836169od_b_c @ ( suffix2151784340763841114od_b_c @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ nil_li8071162985807626740od_b_c ) ) ) ) ) ) ).

% suffixes.elims
thf(fact_403__092_060open_062e_A_060_AerrorValue_092_060close_062,axiom,
    ord_less_nat @ e @ errorValue ).

% \<open>e < errorValue\<close>
thf(fact_404_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,I: fsm_li6801133765522507155_c_b_c,QM: list_P903359562653991662od_b_c,QI: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( observ6293852833591064631_c_b_c @ I )
       => ( ( member6330420149250801815od_b_c @ QM @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ QI @ ( states7681702920031268536_c_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_405_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,I: fsm_a_b_c,QM: list_P903359562653991662od_b_c,QI: a,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( member6330420149250801815od_b_c @ QM @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member_a @ QI @ ( states_a_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_406_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,I: fsm_d_b_c,QM: list_P903359562653991662od_b_c,QI: d,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( observable_d_b_c @ I )
       => ( ( member6330420149250801815od_b_c @ QM @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member_d @ QI @ ( states_d_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_lis2930931384350476499_c_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_407_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_a_b_c,I: fsm_li6801133765522507155_c_b_c,QM: a,QI: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observ6293852833591064631_c_b_c @ I )
       => ( ( member_a @ QM @ ( states_a_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ QI @ ( states7681702920031268536_c_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_408_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,QM: a,QI: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( member_a @ QM @ ( states_a_b_c @ M ) )
         => ( ( member_a @ QI @ ( states_a_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_409_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_a_b_c,I: fsm_d_b_c,QM: a,QI: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_d_b_c @ I )
       => ( ( member_a @ QM @ ( states_a_b_c @ M ) )
         => ( ( member_d @ QI @ ( states_d_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_a_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_410_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_d_b_c,I: fsm_li6801133765522507155_c_b_c,QM: d,QI: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( observ6293852833591064631_c_b_c @ I )
       => ( ( member_d @ QM @ ( states_d_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ QI @ ( states7681702920031268536_c_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_411_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_d_b_c,I: fsm_a_b_c,QM: d,QI: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( member_d @ QM @ ( states_d_b_c @ M ) )
         => ( ( member_a @ QI @ ( states_a_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_412_minimal__failure__prefix__ob,axiom,
    ! [M: fsm_d_b_c,I: fsm_d_b_c,QM: d,QI: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( observable_d_b_c @ I )
       => ( ( member_d @ QM @ ( states_d_b_c @ M ) )
         => ( ( member_d @ QI @ ( states_d_b_c @ I ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
             => ~ ! [Io5: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
                    ( ? [Io6: list_P903359562653991662od_b_c] :
                        ( Io
                        = ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) @ Io6 ) ) )
                   => ( ( member6330420149250801815od_b_c @ Io5 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) )
                     => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ QI ) @ ( lS_d_b_c @ M @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_413_set__prefix,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,T: prefix425356687782099470od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) @ ( prefix9085958534787526401od_b_c @ T ) )
     => ( member6330420149250801815od_b_c @ Xs @ ( prefix9085958534787526401od_b_c @ T ) ) ) ).

% set_prefix
thf(fact_414_Prefix__Tree_Oafter_Osimps_I1_J,axiom,
    ! [T2: prefix425356687782099470od_b_c] :
      ( ( prefix8037181783833825927od_b_c @ T2 @ nil_Product_prod_b_c )
      = T2 ) ).

% Prefix_Tree.after.simps(1)
thf(fact_415_Diff__Int__distrib2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) @ C3 )
      = ( minus_5375846548645262261od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ C3 ) @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) ) ) ).

% Diff_Int_distrib2
thf(fact_416_Diff__Int__distrib,axiom,
    ! [C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ C3 @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) )
      = ( minus_5375846548645262261od_b_c @ ( inf_in4978071631833541052od_b_c @ C3 @ A2 ) @ ( inf_in4978071631833541052od_b_c @ C3 @ B4 ) ) ) ).

% Diff_Int_distrib
thf(fact_417_Diff__Diff__Int,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( minus_5375846548645262261od_b_c @ A2 @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) )
      = ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) ) ).

% Diff_Diff_Int
thf(fact_418_Diff__Int2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( minus_5375846548645262261od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ C3 ) @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) )
      = ( minus_5375846548645262261od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ C3 ) @ B4 ) ) ).

% Diff_Int2
thf(fact_419_Int__Diff,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( minus_5375846548645262261od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ C3 )
      = ( inf_in4978071631833541052od_b_c @ A2 @ ( minus_5375846548645262261od_b_c @ B4 @ C3 ) ) ) ).

% Int_Diff
thf(fact_420_less__infI1,axiom,
    ! [A: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ A @ X )
     => ( ord_le5653067673530651002od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ X ) ) ).

% less_infI1
thf(fact_421_less__infI1,axiom,
    ! [A: nat,X: nat,B: nat] :
      ( ( ord_less_nat @ A @ X )
     => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).

% less_infI1
thf(fact_422_less__infI2,axiom,
    ! [B: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ B @ X )
     => ( ord_le5653067673530651002od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ X ) ) ).

% less_infI2
thf(fact_423_less__infI2,axiom,
    ! [B: nat,X: nat,A: nat] :
      ( ( ord_less_nat @ B @ X )
     => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).

% less_infI2
thf(fact_424_inf_Oabsorb3,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ A @ B )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = A ) ) ).

% inf.absorb3
thf(fact_425_inf_Oabsorb3,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( inf_inf_nat @ A @ B )
        = A ) ) ).

% inf.absorb3
thf(fact_426_inf_Oabsorb4,axiom,
    ! [B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ B @ A )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = B ) ) ).

% inf.absorb4
thf(fact_427_inf_Oabsorb4,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( inf_inf_nat @ A @ B )
        = B ) ) ).

% inf.absorb4
thf(fact_428_inf_Ostrict__boundedE,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) )
     => ~ ( ( ord_le5653067673530651002od_b_c @ A @ B )
         => ~ ( ord_le5653067673530651002od_b_c @ A @ C ) ) ) ).

% inf.strict_boundedE
thf(fact_429_inf_Ostrict__boundedE,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C ) )
     => ~ ( ( ord_less_nat @ A @ B )
         => ~ ( ord_less_nat @ A @ C ) ) ) ).

% inf.strict_boundedE
thf(fact_430_inf_Ostrict__order__iff,axiom,
    ( ord_le5653067673530651002od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B6: set_li6436108459499378894od_b_c] :
          ( ( A6
            = ( inf_in4978071631833541052od_b_c @ A6 @ B6 ) )
          & ( A6 != B6 ) ) ) ) ).

% inf.strict_order_iff
thf(fact_431_inf_Ostrict__order__iff,axiom,
    ( ord_less_nat
    = ( ^ [A6: nat,B6: nat] :
          ( ( A6
            = ( inf_inf_nat @ A6 @ B6 ) )
          & ( A6 != B6 ) ) ) ) ).

% inf.strict_order_iff
thf(fact_432_inf_Ostrict__coboundedI1,axiom,
    ! [A: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ A @ C )
     => ( ord_le5653067673530651002od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C ) ) ).

% inf.strict_coboundedI1
thf(fact_433_inf_Ostrict__coboundedI1,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_nat @ A @ C )
     => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).

% inf.strict_coboundedI1
thf(fact_434_inf_Ostrict__coboundedI2,axiom,
    ! [B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le5653067673530651002od_b_c @ B @ C )
     => ( ord_le5653067673530651002od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C ) ) ).

% inf.strict_coboundedI2
thf(fact_435_inf_Ostrict__coboundedI2,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).

% inf.strict_coboundedI2
thf(fact_436_less__supI1,axiom,
    ! [X: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ X @ A )
     => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).

% less_supI1
thf(fact_437_less__supI2,axiom,
    ! [X: nat,B: nat,A: nat] :
      ( ( ord_less_nat @ X @ B )
     => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).

% less_supI2
thf(fact_438_sup_Oabsorb3,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( sup_sup_nat @ A @ B )
        = A ) ) ).

% sup.absorb3
thf(fact_439_sup_Oabsorb4,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( sup_sup_nat @ A @ B )
        = B ) ) ).

% sup.absorb4
thf(fact_440_sup_Ostrict__boundedE,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( ord_less_nat @ ( sup_sup_nat @ B @ C ) @ A )
     => ~ ( ( ord_less_nat @ B @ A )
         => ~ ( ord_less_nat @ C @ A ) ) ) ).

% sup.strict_boundedE
thf(fact_441_sup_Ostrict__order__iff,axiom,
    ( ord_less_nat
    = ( ^ [B6: nat,A6: nat] :
          ( ( A6
            = ( sup_sup_nat @ A6 @ B6 ) )
          & ( A6 != B6 ) ) ) ) ).

% sup.strict_order_iff
thf(fact_442_sup_Ostrict__coboundedI1,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ C @ A )
     => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.strict_coboundedI1
thf(fact_443_sup_Ostrict__coboundedI2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.strict_coboundedI2
thf(fact_444_after__set__Cons,axiom,
    ! [Gamma: list_P903359562653991662od_b_c,T: prefix425356687782099470od_b_c,Alpha: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Gamma @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T @ Alpha ) ) )
     => ( ( Gamma != nil_Product_prod_b_c )
       => ( member6330420149250801815od_b_c @ Alpha @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ).

% after_set_Cons
thf(fact_445_Diff__Un,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( minus_5375846548645262261od_b_c @ A2 @ ( sup_su3823046536922626210od_b_c @ B4 @ C3 ) )
      = ( inf_in4978071631833541052od_b_c @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) @ ( minus_5375846548645262261od_b_c @ A2 @ C3 ) ) ) ).

% Diff_Un
thf(fact_446_Diff__Int,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( minus_5375846548645262261od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B4 @ C3 ) )
      = ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) @ ( minus_5375846548645262261od_b_c @ A2 @ C3 ) ) ) ).

% Diff_Int
thf(fact_447_Int__Diff__Un,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) )
      = A2 ) ).

% Int_Diff_Un
thf(fact_448_Un__Diff__Int,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ A2 @ B4 ) @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
      = A2 ) ).

% Un_Diff_Int
thf(fact_449_Util_Osuffixes_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( suffix2151784340763841114od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append6992831555715836169od_b_c @ ( suffix2151784340763841114od_b_c @ Xs ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% Util.suffixes.simps(2)
thf(fact_450_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix2151784340763841114od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% Util.suffixes.simps(1)
thf(fact_451_set__Nil,axiom,
    ! [T2: prefix425356687782099470od_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( prefix9085958534787526401od_b_c @ T2 ) ) ).

% set_Nil
thf(fact_452_Cons__less__Cons,axiom,
    ! [A: product_prod_b_c,X: list_P903359562653991662od_b_c,B: product_prod_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ord_le2870576100876692378od_b_c @ ( cons_P4529483553340347422od_b_c @ A @ X ) @ ( cons_P4529483553340347422od_b_c @ B @ Y ) )
      = ( ( ord_le817911927979441428od_b_c @ A @ B )
        | ( ( A = B )
          & ( ord_le2870576100876692378od_b_c @ X @ Y ) ) ) ) ).

% Cons_less_Cons
thf(fact_453_Cons__less__Cons,axiom,
    ! [A: nat,X: list_nat,B: nat,Y: list_nat] :
      ( ( ord_less_list_nat @ ( cons_nat @ A @ X ) @ ( cons_nat @ B @ Y ) )
      = ( ( ord_less_nat @ A @ B )
        | ( ( A = B )
          & ( ord_less_list_nat @ X @ Y ) ) ) ) ).

% Cons_less_Cons
thf(fact_454_estimate__growth__result,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,Dist_fun: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,X: b,Y: c,ErrorValue: nat] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( ord_less_nat @ ( interm4893020034500811395_c_b_c @ M @ Dist_fun @ Q1 @ Q2 @ X @ Y @ ErrorValue ) @ ErrorValue )
             => ? [Gamma2: list_P903359562653991662od_b_c] : ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ Gamma2 ) ) ) ) ) ) ) ).

% estimate_growth_result
thf(fact_455_estimate__growth__result,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Dist_fun: a > a > list_P903359562653991662od_b_c,X: b,Y: c,ErrorValue: nat] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( ord_less_nat @ ( interm5669867556221419667_a_b_c @ M @ Dist_fun @ Q1 @ Q2 @ X @ Y @ ErrorValue ) @ ErrorValue )
             => ? [Gamma2: list_P903359562653991662od_b_c] : ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ Gamma2 ) ) ) ) ) ) ) ).

% estimate_growth_result
thf(fact_456_estimate__growth__result,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,Dist_fun: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > list_P4618364105659340195od_b_c,X: nat,Y: list_P903359562653991662od_b_c,ErrorValue: nat] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( minima7468704325166659676od_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states1638942826817349861od_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states1638942826817349861od_b_c @ M ) )
           => ( ( ord_less_nat @ ( interm6295471087811638490od_b_c @ M @ Dist_fun @ Q1 @ Q2 @ X @ Y @ ErrorValue ) @ ErrorValue )
             => ? [Gamma2: list_P4618364105659340195od_b_c] : ( distin4121442177538353134od_b_c @ M @ Q1 @ Q2 @ ( append1310559846384609464od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) @ Gamma2 ) ) ) ) ) ) ) ).

% estimate_growth_result
thf(fact_457_estimate__growth__result,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Q1: a,Q2: a,Dist_fun: a > a > list_P4618364105659340195od_b_c,X: nat,Y: list_P903359562653991662od_b_c,ErrorValue: nat] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( minima427268845184106828od_b_c @ M )
       => ( ( member_a @ Q1 @ ( states1206967506758974293od_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states1206967506758974293od_b_c @ M ) )
           => ( ( ord_less_nat @ ( interm483237074649154250od_b_c @ M @ Dist_fun @ Q1 @ Q2 @ X @ Y @ ErrorValue ) @ ErrorValue )
             => ? [Gamma2: list_P4618364105659340195od_b_c] : ( distin240330122477437918od_b_c @ M @ Q1 @ Q2 @ ( append1310559846384609464od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) @ Gamma2 ) ) ) ) ) ) ) ).

% estimate_growth_result
thf(fact_458_errorValue,axiom,
    ( errorValue
    = ( suc @ minEst0 ) ) ).

% errorValue
thf(fact_459__092_060open_0620_A_060_AerrorValue_092_060close_062,axiom,
    ord_less_nat @ zero_zero_nat @ errorValue ).

% \<open>0 < errorValue\<close>
thf(fact_460_defined__inputs__language__diff,axiom,
    ! [X: b,M1: fsm_a_b_c,Q1: a,M22: fsm_a_b_c,Q2: a] :
      ( ( member_b @ X @ ( defined_inputs_a_b_c @ M1 @ Q1 ) )
     => ( ~ ( member_b @ X @ ( defined_inputs_a_b_c @ M22 @ Q2 ) )
       => ~ ! [Y3: c] :
              ~ ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y3 ) @ nil_Product_prod_b_c ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M1 @ Q1 ) @ ( lS_a_b_c @ M22 @ Q2 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_461_defined__inputs__language__diff,axiom,
    ! [X: b,M1: fsm_a_b_c,Q1: a,M22: fsm_d_b_c,Q2: d] :
      ( ( member_b @ X @ ( defined_inputs_a_b_c @ M1 @ Q1 ) )
     => ( ~ ( member_b @ X @ ( defined_inputs_d_b_c @ M22 @ Q2 ) )
       => ~ ! [Y3: c] :
              ~ ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y3 ) @ nil_Product_prod_b_c ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M1 @ Q1 ) @ ( lS_d_b_c @ M22 @ Q2 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_462_defined__inputs__language__diff,axiom,
    ! [X: b,M1: fsm_d_b_c,Q1: d,M22: fsm_a_b_c,Q2: a] :
      ( ( member_b @ X @ ( defined_inputs_d_b_c @ M1 @ Q1 ) )
     => ( ~ ( member_b @ X @ ( defined_inputs_a_b_c @ M22 @ Q2 ) )
       => ~ ! [Y3: c] :
              ~ ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y3 ) @ nil_Product_prod_b_c ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M1 @ Q1 ) @ ( lS_a_b_c @ M22 @ Q2 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_463_defined__inputs__language__diff,axiom,
    ! [X: b,M1: fsm_d_b_c,Q1: d,M22: fsm_d_b_c,Q2: d] :
      ( ( member_b @ X @ ( defined_inputs_d_b_c @ M1 @ Q1 ) )
     => ( ~ ( member_b @ X @ ( defined_inputs_d_b_c @ M22 @ Q2 ) )
       => ~ ! [Y3: c] :
              ~ ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y3 ) @ nil_Product_prod_b_c ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M1 @ Q1 ) @ ( lS_d_b_c @ M22 @ Q2 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_464_less__option__None,axiom,
    ! [X: option_a] :
      ~ ( ord_less_option_a @ X @ none_a ) ).

% less_option_None
thf(fact_465_not__less__Nil,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ~ ( ord_le2870576100876692378od_b_c @ X @ nil_Product_prod_b_c ) ).

% not_less_Nil
thf(fact_466_less__list__code_I1_J,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ~ ( ord_le2870576100876692378od_b_c @ Xs @ nil_Product_prod_b_c ) ).

% less_list_code(1)
thf(fact_467_Nil__less__Cons,axiom,
    ! [A: product_prod_b_c,X: list_P903359562653991662od_b_c] : ( ord_le2870576100876692378od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ A @ X ) ) ).

% Nil_less_Cons
thf(fact_468_less__list__code_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] : ( ord_le2870576100876692378od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) ).

% less_list_code(2)
thf(fact_469_less__list__code_I3_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ord_le2870576100876692378od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) )
      = ( ( ord_le817911927979441428od_b_c @ X @ Y )
        | ( ( X = Y )
          & ( ord_le2870576100876692378od_b_c @ Xs @ Ys ) ) ) ) ).

% less_list_code(3)
thf(fact_470_less__list__code_I3_J,axiom,
    ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
      ( ( ord_less_list_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
      = ( ( ord_less_nat @ X @ Y )
        | ( ( X = Y )
          & ( ord_less_list_nat @ Xs @ Ys ) ) ) ) ).

% less_list_code(3)
thf(fact_471_n__lists__Nil,axiom,
    ! [N: nat] :
      ( ( ( N = zero_zero_nat )
       => ( ( n_list5224936925692304502od_b_c @ N @ nil_Product_prod_b_c )
          = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
      & ( ( N != zero_zero_nat )
       => ( ( n_list5224936925692304502od_b_c @ N @ nil_Product_prod_b_c )
          = nil_li8071162985807626740od_b_c ) ) ) ).

% n_lists_Nil
thf(fact_472_n__lists_Osimps_I1_J,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( n_list5224936925692304502od_b_c @ zero_zero_nat @ Xs )
      = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% n_lists.simps(1)
thf(fact_473_prefixes__snoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = ( append6992831555715836169od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) @ ( cons_l342771267123639716od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% prefixes_snoc
thf(fact_474_h__obs__distinguishes,axiom,
    ! [M: fsm_d_b_c,Q1: d,X: b,Y: c,Q14: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( ( h_obs_d_b_c @ M @ Q1 @ X @ Y )
          = ( some_d @ Q14 ) )
       => ( ( ( h_obs_d_b_c @ M @ Q2 @ X @ Y )
            = none_d )
         => ( distinguishes_d_b_c @ M @ Q1 @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% h_obs_distinguishes
thf(fact_475_h__obs__distinguishes,axiom,
    ! [M: fsm_a_b_c,Q1: a,X: b,Y: c,Q14: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( ( h_obs_a_b_c @ M @ Q1 @ X @ Y )
          = ( some_a @ Q14 ) )
       => ( ( ( h_obs_a_b_c @ M @ Q2 @ X @ Y )
            = none_a )
         => ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% h_obs_distinguishes
thf(fact_476_h__obs__distinguishes,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Q1: a,X: nat,Y: list_P903359562653991662od_b_c,Q14: a,Q2: a] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( ( h_obs_6797610709827923659od_b_c @ M @ Q1 @ X @ Y )
          = ( some_a @ Q14 ) )
       => ( ( ( h_obs_6797610709827923659od_b_c @ M @ Q2 @ X @ Y )
            = none_a )
         => ( distin240330122477437918od_b_c @ M @ Q1 @ Q2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) ) ) ) ).

% h_obs_distinguishes
thf(fact_477_h__obs__distinguishes,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,X: b,Y: c,Q14: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( ( h_obs_593941965179481282_c_b_c @ M @ Q1 @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q14 ) )
       => ( ( ( h_obs_593941965179481282_c_b_c @ M @ Q2 @ X @ Y )
            = none_l1245059289828015823od_b_c )
         => ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% h_obs_distinguishes
thf(fact_478_h__obs__distinguishes,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Q1: list_P903359562653991662od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Q14: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( ( h_obs_2191229059226059611od_b_c @ M @ Q1 @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q14 ) )
       => ( ( ( h_obs_2191229059226059611od_b_c @ M @ Q2 @ X @ Y )
            = none_l1245059289828015823od_b_c )
         => ( distin4121442177538353134od_b_c @ M @ Q1 @ Q2 @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) ) ) ) ) ).

% h_obs_distinguishes
thf(fact_479_not__Some__eq2,axiom,
    ! [V2: option4716579502443089070od_b_c] :
      ( ( ! [X2: b,Y2: c] :
            ( V2
           != ( some_P804611721829158477od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) ) ) )
      = ( V2 = none_P8350622247268937417od_b_c ) ) ).

% not_Some_eq2
thf(fact_480_not__Some__eq2,axiom,
    ! [V2: option6176339638841064419od_b_c] :
      ( ( ! [X2: nat,Y2: list_P903359562653991662od_b_c] :
            ( V2
           != ( some_P1227930929888362734od_b_c @ ( produc8137419655804493381od_b_c @ X2 @ Y2 ) ) ) )
      = ( V2 = none_P2472093661639770994od_b_c ) ) ).

% not_Some_eq2
thf(fact_481_less__option__None__Some__code,axiom,
    ! [X: a] : ( ord_less_option_a @ none_a @ ( some_a @ X ) ) ).

% less_option_None_Some_code
thf(fact_482_less__option__None__Some__code,axiom,
    ! [X: list_P903359562653991662od_b_c] : ( ord_le4843362212862593888od_b_c @ none_l1245059289828015823od_b_c @ ( some_l689282263436086355od_b_c @ X ) ) ).

% less_option_None_Some_code
thf(fact_483_inf__Some,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( inf_in2596389469055639714od_b_c @ ( some_l689282263436086355od_b_c @ X ) @ ( some_l689282263436086355od_b_c @ Y ) )
      = ( some_l689282263436086355od_b_c @ ( inf_in5316438314944203740od_b_c @ X @ Y ) ) ) ).

% inf_Some
thf(fact_484_inf__Some,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( inf_in3747351831089128066od_b_c @ ( some_s3990983904923029043od_b_c @ X ) @ ( some_s3990983904923029043od_b_c @ Y ) )
      = ( some_s3990983904923029043od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) ) ) ).

% inf_Some
thf(fact_485_sup__Some,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( sup_su6750509607737226888od_b_c @ ( some_l689282263436086355od_b_c @ X ) @ ( some_l689282263436086355od_b_c @ Y ) )
      = ( some_l689282263436086355od_b_c @ ( sup_su5036054437528957634od_b_c @ X @ Y ) ) ) ).

% sup_Some
thf(fact_486_less__option__None__is__Some,axiom,
    ! [X: option_a] :
      ( ( ord_less_option_a @ none_a @ X )
     => ? [Z2: a] :
          ( X
          = ( some_a @ Z2 ) ) ) ).

% less_option_None_is_Some
thf(fact_487_less__option__None__is__Some,axiom,
    ! [X: option7120433447694521524od_b_c] :
      ( ( ord_le4843362212862593888od_b_c @ none_l1245059289828015823od_b_c @ X )
     => ? [Z2: list_P903359562653991662od_b_c] :
          ( X
          = ( some_l689282263436086355od_b_c @ Z2 ) ) ) ).

% less_option_None_is_Some
thf(fact_488_less__option__None__Some,axiom,
    ! [X: a] : ( ord_less_option_a @ none_a @ ( some_a @ X ) ) ).

% less_option_None_Some
thf(fact_489_less__option__None__Some,axiom,
    ! [X: list_P903359562653991662od_b_c] : ( ord_le4843362212862593888od_b_c @ none_l1245059289828015823od_b_c @ ( some_l689282263436086355od_b_c @ X ) ) ).

% less_option_None_Some
thf(fact_490_h__obs__state,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c,Q6: a] :
      ( ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
        = ( some_a @ Q6 ) )
     => ( member_a @ Q6 @ ( states_a_b_c @ M ) ) ) ).

% h_obs_state
thf(fact_491_prefixes_Osimps_I1_J,axiom,
    ( ( prefix1131979855692807669od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% prefixes.simps(1)
thf(fact_492_h__obs__language__iff,axiom,
    ! [M: fsm_a_b_c,X: b,Y: c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) @ ( lS_a_b_c @ M @ Q ) )
        = ( ? [Q4: a] :
              ( ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
                = ( some_a @ Q4 ) )
              & ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q4 ) ) ) ) ) ) ).

% h_obs_language_iff
thf(fact_493_h__obs__language__iff,axiom,
    ! [M: fsm_d_b_c,X: b,Y: c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) @ ( lS_d_b_c @ M @ Q ) )
        = ( ? [Q4: d] :
              ( ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
                = ( some_d @ Q4 ) )
              & ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q4 ) ) ) ) ) ) ).

% h_obs_language_iff
thf(fact_494_h__obs__language__iff,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,X: b,Y: c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
        = ( ? [Q4: list_P903359562653991662od_b_c] :
              ( ( ( h_obs_593941965179481282_c_b_c @ M @ Q @ X @ Y )
                = ( some_l689282263436086355od_b_c @ Q4 ) )
              & ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q4 ) ) ) ) ) ) ).

% h_obs_language_iff
thf(fact_495_h__obs__language__iff,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Io: list_P4618364105659340195od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( member1702757119880923450od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ Io ) @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) )
        = ( ? [Q4: list_P903359562653991662od_b_c] :
              ( ( ( h_obs_2191229059226059611od_b_c @ M @ Q @ X @ Y )
                = ( some_l689282263436086355od_b_c @ Q4 ) )
              & ( member1702757119880923450od_b_c @ Io @ ( lS_lis9220523473116252810od_b_c @ M @ Q4 ) ) ) ) ) ) ).

% h_obs_language_iff
thf(fact_496_h__obs__from__LS,axiom,
    ! [M: fsm_a_b_c,X: b,Y: c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_a_b_c @ M @ Q ) )
       => ~ ! [Q7: a] :
              ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
             != ( some_a @ Q7 ) ) ) ) ).

% h_obs_from_LS
thf(fact_497_h__obs__from__LS,axiom,
    ! [M: fsm_d_b_c,X: b,Y: c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_d_b_c @ M @ Q ) )
       => ~ ! [Q7: d] :
              ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
             != ( some_d @ Q7 ) ) ) ) ).

% h_obs_from_LS
thf(fact_498_h__obs__from__LS,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,X: b,Y: c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
       => ~ ! [Q7: list_P903359562653991662od_b_c] :
              ( ( h_obs_593941965179481282_c_b_c @ M @ Q @ X @ Y )
             != ( some_l689282263436086355od_b_c @ Q7 ) ) ) ) ).

% h_obs_from_LS
thf(fact_499_h__obs__from__LS,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( member1702757119880923450od_b_c @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) )
       => ~ ! [Q7: list_P903359562653991662od_b_c] :
              ( ( h_obs_2191229059226059611od_b_c @ M @ Q @ X @ Y )
             != ( some_l689282263436086355od_b_c @ Q7 ) ) ) ) ).

% h_obs_from_LS
thf(fact_500_after__h__obs__prepend,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c,Q6: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
          = ( some_a @ Q6 ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q6 ) )
         => ( ( after_a_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) )
            = ( after_a_b_c @ M @ Q6 @ Io ) ) ) ) ) ).

% after_h_obs_prepend
thf(fact_501_after__h__obs__prepend,axiom,
    ! [M: fsm_d_b_c,Q: d,X: b,Y: c,Q6: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
          = ( some_d @ Q6 ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q6 ) )
         => ( ( after_d_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) )
            = ( after_d_b_c @ M @ Q6 @ Io ) ) ) ) ) ).

% after_h_obs_prepend
thf(fact_502_after__h__obs__prepend,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,X: b,Y: c,Q6: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( ( h_obs_593941965179481282_c_b_c @ M @ Q @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q6 ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q6 ) )
         => ( ( after_4052058690717316294_c_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Io ) )
            = ( after_4052058690717316294_c_b_c @ M @ Q6 @ Io ) ) ) ) ) ).

% after_h_obs_prepend
thf(fact_503_after__h__obs__prepend,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Q: list_P903359562653991662od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Q6: list_P903359562653991662od_b_c,Io: list_P4618364105659340195od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( ( h_obs_2191229059226059611od_b_c @ M @ Q @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q6 ) )
       => ( ( member1702757119880923450od_b_c @ Io @ ( lS_lis9220523473116252810od_b_c @ M @ Q6 ) )
         => ( ( after_5389876800173013079od_b_c @ M @ Q @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ Io ) )
            = ( after_5389876800173013079od_b_c @ M @ Q6 @ Io ) ) ) ) ) ).

% after_h_obs_prepend
thf(fact_504_after__h__obs,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c,Q6: a] :
      ( ( observable_a_b_c @ M )
     => ( ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
          = ( some_a @ Q6 ) )
       => ( ( after_a_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_h_obs
thf(fact_505_after__h__obs,axiom,
    ! [M: fsm_d_b_c,Q: d,X: b,Y: c,Q6: d] :
      ( ( observable_d_b_c @ M )
     => ( ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
          = ( some_d @ Q6 ) )
       => ( ( after_d_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_h_obs
thf(fact_506_after__h__obs,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,X: b,Y: c,Q6: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( ( h_obs_593941965179481282_c_b_c @ M @ Q @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q6 ) )
       => ( ( after_4052058690717316294_c_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_h_obs
thf(fact_507_after__h__obs,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Q: list_P903359562653991662od_b_c,X: nat,Y: list_P903359562653991662od_b_c,Q6: list_P903359562653991662od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( ( h_obs_2191229059226059611od_b_c @ M @ Q @ X @ Y )
          = ( some_l689282263436086355od_b_c @ Q6 ) )
       => ( ( after_5389876800173013079od_b_c @ M @ Q @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ nil_Pr679518533894577677od_b_c ) )
          = Q6 ) ) ) ).

% after_h_obs
thf(fact_508_prefixes__eq__snoc,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ( prefix1131979855692807669od_b_c @ Ys )
        = ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) ) )
      = ( ( ( ( Ys = nil_Product_prod_b_c )
            & ( Xs = nil_li8071162985807626740od_b_c ) )
          | ? [Z3: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
              ( ( Ys
                = ( append2547753245680614915od_b_c @ Zs2 @ ( cons_P4529483553340347422od_b_c @ Z3 @ nil_Product_prod_b_c ) ) )
              & ( Xs
                = ( prefix1131979855692807669od_b_c @ Zs2 ) ) ) )
        & ( X = Ys ) ) ) ).

% prefixes_eq_snoc
thf(fact_509_not__Some__eq,axiom,
    ! [X: option_a] :
      ( ( ! [Y2: a] :
            ( X
           != ( some_a @ Y2 ) ) )
      = ( X = none_a ) ) ).

% not_Some_eq
thf(fact_510_not__Some__eq,axiom,
    ! [X: option7120433447694521524od_b_c] :
      ( ( ! [Y2: list_P903359562653991662od_b_c] :
            ( X
           != ( some_l689282263436086355od_b_c @ Y2 ) ) )
      = ( X = none_l1245059289828015823od_b_c ) ) ).

% not_Some_eq
thf(fact_511_not__None__eq,axiom,
    ! [X: option_a] :
      ( ( X != none_a )
      = ( ? [Y2: a] :
            ( X
            = ( some_a @ Y2 ) ) ) ) ).

% not_None_eq
thf(fact_512_not__None__eq,axiom,
    ! [X: option7120433447694521524od_b_c] :
      ( ( X != none_l1245059289828015823od_b_c )
      = ( ? [Y2: list_P903359562653991662od_b_c] :
            ( X
            = ( some_l689282263436086355od_b_c @ Y2 ) ) ) ) ).

% not_None_eq
thf(fact_513_extract__Nil__code,axiom,
    ! [P: product_prod_b_c > $o] :
      ( ( extrac2790361661052662384od_b_c @ P @ nil_Product_prod_b_c )
      = none_P8002138689083699399od_b_c ) ).

% extract_Nil_code
thf(fact_514_option_Odistinct_I1_J,axiom,
    ! [X24: a] :
      ( none_a
     != ( some_a @ X24 ) ) ).

% option.distinct(1)
thf(fact_515_option_Odistinct_I1_J,axiom,
    ! [X24: list_P903359562653991662od_b_c] :
      ( none_l1245059289828015823od_b_c
     != ( some_l689282263436086355od_b_c @ X24 ) ) ).

% option.distinct(1)
thf(fact_516_option_OdiscI,axiom,
    ! [Option: option_a,X24: a] :
      ( ( Option
        = ( some_a @ X24 ) )
     => ( Option != none_a ) ) ).

% option.discI
thf(fact_517_option_OdiscI,axiom,
    ! [Option: option7120433447694521524od_b_c,X24: list_P903359562653991662od_b_c] :
      ( ( Option
        = ( some_l689282263436086355od_b_c @ X24 ) )
     => ( Option != none_l1245059289828015823od_b_c ) ) ).

% option.discI
thf(fact_518_option_Oexhaust,axiom,
    ! [Y: option_a] :
      ( ( Y != none_a )
     => ~ ! [X23: a] :
            ( Y
           != ( some_a @ X23 ) ) ) ).

% option.exhaust
thf(fact_519_option_Oexhaust,axiom,
    ! [Y: option7120433447694521524od_b_c] :
      ( ( Y != none_l1245059289828015823od_b_c )
     => ~ ! [X23: list_P903359562653991662od_b_c] :
            ( Y
           != ( some_l689282263436086355od_b_c @ X23 ) ) ) ).

% option.exhaust
thf(fact_520_split__option__ex,axiom,
    ( ( ^ [P5: option_a > $o] :
        ? [X5: option_a] : ( P5 @ X5 ) )
    = ( ^ [P6: option_a > $o] :
          ( ( P6 @ none_a )
          | ? [X2: a] : ( P6 @ ( some_a @ X2 ) ) ) ) ) ).

% split_option_ex
thf(fact_521_split__option__ex,axiom,
    ( ( ^ [P5: option7120433447694521524od_b_c > $o] :
        ? [X5: option7120433447694521524od_b_c] : ( P5 @ X5 ) )
    = ( ^ [P6: option7120433447694521524od_b_c > $o] :
          ( ( P6 @ none_l1245059289828015823od_b_c )
          | ? [X2: list_P903359562653991662od_b_c] : ( P6 @ ( some_l689282263436086355od_b_c @ X2 ) ) ) ) ) ).

% split_option_ex
thf(fact_522_split__option__all,axiom,
    ( ( ^ [P5: option_a > $o] :
        ! [X5: option_a] : ( P5 @ X5 ) )
    = ( ^ [P6: option_a > $o] :
          ( ( P6 @ none_a )
          & ! [X2: a] : ( P6 @ ( some_a @ X2 ) ) ) ) ) ).

% split_option_all
thf(fact_523_split__option__all,axiom,
    ( ( ^ [P5: option7120433447694521524od_b_c > $o] :
        ! [X5: option7120433447694521524od_b_c] : ( P5 @ X5 ) )
    = ( ^ [P6: option7120433447694521524od_b_c > $o] :
          ( ( P6 @ none_l1245059289828015823od_b_c )
          & ! [X2: list_P903359562653991662od_b_c] : ( P6 @ ( some_l689282263436086355od_b_c @ X2 ) ) ) ) ) ).

% split_option_all
thf(fact_524_combine__options__cases,axiom,
    ! [X: option_a,P: option_a > option_a > $o,Y: option_a] :
      ( ( ( X = none_a )
       => ( P @ X @ Y ) )
     => ( ( ( Y = none_a )
         => ( P @ X @ Y ) )
       => ( ! [A3: a,B2: a] :
              ( ( X
                = ( some_a @ A3 ) )
             => ( ( Y
                  = ( some_a @ B2 ) )
               => ( P @ X @ Y ) ) )
         => ( P @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_525_combine__options__cases,axiom,
    ! [X: option_a,P: option_a > option7120433447694521524od_b_c > $o,Y: option7120433447694521524od_b_c] :
      ( ( ( X = none_a )
       => ( P @ X @ Y ) )
     => ( ( ( Y = none_l1245059289828015823od_b_c )
         => ( P @ X @ Y ) )
       => ( ! [A3: a,B2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( some_a @ A3 ) )
             => ( ( Y
                  = ( some_l689282263436086355od_b_c @ B2 ) )
               => ( P @ X @ Y ) ) )
         => ( P @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_526_combine__options__cases,axiom,
    ! [X: option7120433447694521524od_b_c,P: option7120433447694521524od_b_c > option_a > $o,Y: option_a] :
      ( ( ( X = none_l1245059289828015823od_b_c )
       => ( P @ X @ Y ) )
     => ( ( ( Y = none_a )
         => ( P @ X @ Y ) )
       => ( ! [A3: list_P903359562653991662od_b_c,B2: a] :
              ( ( X
                = ( some_l689282263436086355od_b_c @ A3 ) )
             => ( ( Y
                  = ( some_a @ B2 ) )
               => ( P @ X @ Y ) ) )
         => ( P @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_527_combine__options__cases,axiom,
    ! [X: option7120433447694521524od_b_c,P: option7120433447694521524od_b_c > option7120433447694521524od_b_c > $o,Y: option7120433447694521524od_b_c] :
      ( ( ( X = none_l1245059289828015823od_b_c )
       => ( P @ X @ Y ) )
     => ( ( ( Y = none_l1245059289828015823od_b_c )
         => ( P @ X @ Y ) )
       => ( ! [A3: list_P903359562653991662od_b_c,B2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( some_l689282263436086355od_b_c @ A3 ) )
             => ( ( Y
                  = ( some_l689282263436086355od_b_c @ B2 ) )
               => ( P @ X @ Y ) ) )
         => ( P @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_528_option_Osize__gen_I1_J,axiom,
    ! [X: a > nat] :
      ( ( size_option_a @ X @ none_a )
      = ( suc @ zero_zero_nat ) ) ).

% option.size_gen(1)
thf(fact_529_distinguishes__diverge__prefix,axiom,
    ! [M: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U2 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V2 ) @ W )
       => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( member6330420149250801815od_b_c @ W3 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ W ) ) )
             => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U2 ) ) )
               => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V2 ) ) )
                 => ~ ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W3 ) @ ( append2547753245680614915od_b_c @ V2 @ W3 ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_530_distinguishes__diverge__prefix,axiom,
    ! [M: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( distinguishes_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ U2 ) @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ V2 ) @ W )
       => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ( member6330420149250801815od_b_c @ W3 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ W ) ) )
             => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ U2 ) ) )
               => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ V2 ) ) )
                 => ~ ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ U2 @ W3 ) @ ( append2547753245680614915od_b_c @ V2 @ W3 ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_531_extract__Some__iff,axiom,
    ! [P: product_prod_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Y: product_prod_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( extrac2790361661052662384od_b_c @ P @ Xs )
        = ( some_P278523132111576139od_b_c @ ( produc1861375773765947862od_b_c @ Ys @ ( produc1467100693395308445od_b_c @ Y @ Zs ) ) ) )
      = ( ( Xs
          = ( append2547753245680614915od_b_c @ Ys @ ( cons_P4529483553340347422od_b_c @ Y @ Zs ) ) )
        & ( P @ Y )
        & ~ ? [X2: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ X2 @ ( set_Product_prod_b_c2 @ Ys ) )
              & ( P @ X2 ) ) ) ) ).

% extract_Some_iff
thf(fact_532_extract__SomeE,axiom,
    ! [P: product_prod_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Y: product_prod_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( extrac2790361661052662384od_b_c @ P @ Xs )
        = ( some_P278523132111576139od_b_c @ ( produc1861375773765947862od_b_c @ Ys @ ( produc1467100693395308445od_b_c @ Y @ Zs ) ) ) )
     => ( ( Xs
          = ( append2547753245680614915od_b_c @ Ys @ ( cons_P4529483553340347422od_b_c @ Y @ Zs ) ) )
        & ( P @ Y )
        & ~ ? [X3: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Ys ) )
              & ( P @ X3 ) ) ) ) ).

% extract_SomeE
thf(fact_533_set__ConsD,axiom,
    ! [Y: list_P903359562653991662od_b_c,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_534_set__ConsD,axiom,
    ! [Y: a,X: a,Xs: list_a] :
      ( ( member_a @ Y @ ( set_a2 @ ( cons_a @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member_a @ Y @ ( set_a2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_535_set__ConsD,axiom,
    ! [Y: product_prod_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_536_list_Oset__cases,axiom,
    ! [E: list_P903359562653991662od_b_c,A: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ E @ ( set_li4480668622519654659od_b_c @ A ) )
     => ( ! [Z22: list_l8907847357763382004od_b_c] :
            ( A
           != ( cons_l342771267123639716od_b_c @ E @ Z22 ) )
       => ~ ! [Z1: list_P903359562653991662od_b_c,Z22: list_l8907847357763382004od_b_c] :
              ( ( A
                = ( cons_l342771267123639716od_b_c @ Z1 @ Z22 ) )
             => ~ ( member6330420149250801815od_b_c @ E @ ( set_li4480668622519654659od_b_c @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_537_list_Oset__cases,axiom,
    ! [E: a,A: list_a] :
      ( ( member_a @ E @ ( set_a2 @ A ) )
     => ( ! [Z22: list_a] :
            ( A
           != ( cons_a @ E @ Z22 ) )
       => ~ ! [Z1: a,Z22: list_a] :
              ( ( A
                = ( cons_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( set_a2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_538_list_Oset__cases,axiom,
    ! [E: product_prod_b_c,A: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ E @ ( set_Product_prod_b_c2 @ A ) )
     => ( ! [Z22: list_P903359562653991662od_b_c] :
            ( A
           != ( cons_P4529483553340347422od_b_c @ E @ Z22 ) )
       => ~ ! [Z1: product_prod_b_c,Z22: list_P903359562653991662od_b_c] :
              ( ( A
                = ( cons_P4529483553340347422od_b_c @ Z1 @ Z22 ) )
             => ~ ( member7862447941013992593od_b_c @ E @ ( set_Product_prod_b_c2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_539_list_Oset__intros_I1_J,axiom,
    ! [X21: list_P903359562653991662od_b_c,X22: list_l8907847357763382004od_b_c] : ( member6330420149250801815od_b_c @ X21 @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_540_list_Oset__intros_I1_J,axiom,
    ! [X21: a,X22: list_a] : ( member_a @ X21 @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_541_list_Oset__intros_I1_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] : ( member7862447941013992593od_b_c @ X21 @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_542_list_Oset__intros_I2_J,axiom,
    ! [Y: list_P903359562653991662od_b_c,X22: list_l8907847357763382004od_b_c,X21: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ X22 ) )
     => ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_543_list_Oset__intros_I2_J,axiom,
    ! [Y: a,X22: list_a,X21: a] :
      ( ( member_a @ Y @ ( set_a2 @ X22 ) )
     => ( member_a @ Y @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_544_list_Oset__intros_I2_J,axiom,
    ! [Y: product_prod_b_c,X22: list_P903359562653991662od_b_c,X21: product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ X22 ) )
     => ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_545_list__concat__non__elem,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_546_list__concat__non__elem,axiom,
    ! [X: a,Xs: list_a,Ys: list_a] :
      ( ~ ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ~ ( member_a @ X @ ( set_a2 @ ( append_a @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_547_list__concat__non__elem,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_548_list__prefix__elem,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_549_list__prefix__elem,axiom,
    ! [X: a,Xs: list_a,Ys: list_a] :
      ( ( member_a @ X @ ( set_a2 @ ( append_a @ Xs @ Ys ) ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ( member_a @ X @ ( set_a2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_550_list__prefix__elem,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_551_list__set__sym,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ X @ Y ) )
      = ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Y @ X ) ) ) ).

% list_set_sym
thf(fact_552_split__list__first__prop__iff,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ( ? [X2: product_prod_b_c] :
            ( ( member7862447941013992593od_b_c @ X2 @ ( set_Product_prod_b_c2 @ Xs ) )
            & ( P @ X2 ) ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
            ( ? [Zs2: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs2 ) ) )
            & ( P @ X2 )
            & ! [Y2: product_prod_b_c] :
                ( ( member7862447941013992593od_b_c @ Y2 @ ( set_Product_prod_b_c2 @ Ys4 ) )
               => ~ ( P @ Y2 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_553_split__list__last__prop__iff,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ( ? [X2: product_prod_b_c] :
            ( ( member7862447941013992593od_b_c @ X2 @ ( set_Product_prod_b_c2 @ Xs ) )
            & ( P @ X2 ) ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,X2: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs2 ) ) )
            & ( P @ X2 )
            & ! [Y2: product_prod_b_c] :
                ( ( member7862447941013992593od_b_c @ Y2 @ ( set_Product_prod_b_c2 @ Zs2 ) )
               => ~ ( P @ Y2 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_554_in__set__conv__decomp__first,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys4: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( ( Xs
              = ( append6992831555715836169od_b_c @ Ys4 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) )
            & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys4 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_555_in__set__conv__decomp__first,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys4: list_a,Zs2: list_a] :
            ( ( Xs
              = ( append_a @ Ys4 @ ( cons_a @ X @ Zs2 ) ) )
            & ~ ( member_a @ X @ ( set_a2 @ Ys4 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_556_in__set__conv__decomp__first,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) )
            & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys4 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_557_in__set__conv__decomp__last,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys4: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( ( Xs
              = ( append6992831555715836169od_b_c @ Ys4 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) )
            & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_558_in__set__conv__decomp__last,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys4: list_a,Zs2: list_a] :
            ( ( Xs
              = ( append_a @ Ys4 @ ( cons_a @ X @ Zs2 ) ) )
            & ~ ( member_a @ X @ ( set_a2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_559_in__set__conv__decomp__last,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) )
            & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_560_split__list__first__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ~ ! [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c] :
            ( ? [Zs3: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa2: product_prod_b_c] :
                    ( ( member7862447941013992593od_b_c @ Xa2 @ ( set_Product_prod_b_c2 @ Ys3 ) )
                   => ~ ( P @ Xa2 ) ) ) ) ) ).

% split_list_first_propE
thf(fact_561_split__list__last__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ~ ! [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa2: product_prod_b_c] :
                    ( ( member7862447941013992593od_b_c @ Xa2 @ ( set_Product_prod_b_c2 @ Zs3 ) )
                   => ~ ( P @ Xa2 ) ) ) ) ) ).

% split_list_last_propE
thf(fact_562_split__list__first__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ? [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c] :
          ( ? [Zs3: list_P903359562653991662od_b_c] :
              ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
          & ( P @ X4 )
          & ! [Xa2: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ Xa2 @ ( set_Product_prod_b_c2 @ Ys3 ) )
             => ~ ( P @ Xa2 ) ) ) ) ).

% split_list_first_prop
thf(fact_563_split__list__last__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ? [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
          & ( P @ X4 )
          & ! [Xa2: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ Xa2 @ ( set_Product_prod_b_c2 @ Zs3 ) )
             => ~ ( P @ Xa2 ) ) ) ) ).

% split_list_last_prop
thf(fact_564_in__set__conv__decomp,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys4: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( Xs
            = ( append6992831555715836169od_b_c @ Ys4 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_565_in__set__conv__decomp,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys4: list_a,Zs2: list_a] :
            ( Xs
            = ( append_a @ Ys4 @ ( cons_a @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_566_in__set__conv__decomp,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( Xs
            = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_567_append__Cons__eq__iff,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,Xs4: list_l8907847357763382004od_b_c,Ys6: list_l8907847357763382004od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ( ( ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ Ys ) )
            = ( append6992831555715836169od_b_c @ Xs4 @ ( cons_l342771267123639716od_b_c @ X @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_568_append__Cons__eq__iff,axiom,
    ! [X: a,Xs: list_a,Ys: list_a,Xs4: list_a,Ys6: list_a] :
      ( ~ ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ( ( ( append_a @ Xs @ ( cons_a @ X @ Ys ) )
            = ( append_a @ Xs4 @ ( cons_a @ X @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_569_append__Cons__eq__iff,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Xs4: list_P903359562653991662od_b_c,Ys6: list_P903359562653991662od_b_c] :
      ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ( ( ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ Ys ) )
            = ( append2547753245680614915od_b_c @ Xs4 @ ( cons_P4529483553340347422od_b_c @ X @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_570_split__list__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ~ ! [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c] :
            ( ? [Zs3: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
           => ~ ( P @ X4 ) ) ) ).

% split_list_propE
thf(fact_571_split__list__first,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys3: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( ( Xs
            = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) )
          & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_572_split__list__first,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys3: list_a,Zs3: list_a] :
          ( ( Xs
            = ( append_a @ Ys3 @ ( cons_a @ X @ Zs3 ) ) )
          & ~ ( member_a @ X @ ( set_a2 @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_573_split__list__first,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys3: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) )
          & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_574_split__list__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X3: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X3 ) )
     => ? [Ys3: list_P903359562653991662od_b_c,X4: product_prod_b_c] :
          ( ? [Zs3: list_P903359562653991662od_b_c] :
              ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X4 @ Zs3 ) ) )
          & ( P @ X4 ) ) ) ).

% split_list_prop
thf(fact_575_split__list__last,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys3: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( ( Xs
            = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) )
          & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_576_split__list__last,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys3: list_a,Zs3: list_a] :
          ( ( Xs
            = ( append_a @ Ys3 @ ( cons_a @ X @ Zs3 ) ) )
          & ~ ( member_a @ X @ ( set_a2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_577_split__list__last,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys3: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) )
          & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_578_split__list,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys3: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( Xs
          = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_579_split__list,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys3: list_a,Zs3: list_a] :
          ( Xs
          = ( append_a @ Ys3 @ ( cons_a @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_580_split__list,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys3: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( Xs
          = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_581_in__set__list__format,axiom,
    ! [E: list_P903359562653991662od_b_c,L: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ E @ ( set_li4480668622519654659od_b_c @ L ) )
     => ~ ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c] :
            ( L
           != ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ E @ L22 ) ) ) ) ).

% in_set_list_format
thf(fact_582_in__set__list__format,axiom,
    ! [E: a,L: list_a] :
      ( ( member_a @ E @ ( set_a2 @ L ) )
     => ~ ! [L12: list_a,L22: list_a] :
            ( L
           != ( append_a @ L12 @ ( cons_a @ E @ L22 ) ) ) ) ).

% in_set_list_format
thf(fact_583_in__set__list__format,axiom,
    ! [E: product_prod_b_c,L: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ E @ ( set_Product_prod_b_c2 @ L ) )
     => ~ ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c] :
            ( L
           != ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ E @ L22 ) ) ) ) ).

% in_set_list_format
thf(fact_584_xy__in__set__cases,axiom,
    ! [X: list_P903359562653991662od_b_c,L: list_l8907847357763382004od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ L ) )
     => ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ L ) )
       => ( ( ( X = Y )
           => ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c] :
                ( L
               != ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ Y @ L22 ) ) ) )
         => ( ( ( X != Y )
             => ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,L3: list_l8907847357763382004od_b_c] :
                  ( L
                 != ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X @ ( append6992831555715836169od_b_c @ L22 @ ( cons_l342771267123639716od_b_c @ Y @ L3 ) ) ) ) ) )
           => ~ ( ( X != Y )
               => ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,L3: list_l8907847357763382004od_b_c] :
                    ( L
                   != ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ Y @ ( append6992831555715836169od_b_c @ L22 @ ( cons_l342771267123639716od_b_c @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).

% xy_in_set_cases
thf(fact_585_xy__in__set__cases,axiom,
    ! [X: a,L: list_a,Y: a] :
      ( ( member_a @ X @ ( set_a2 @ L ) )
     => ( ( member_a @ Y @ ( set_a2 @ L ) )
       => ( ( ( X = Y )
           => ! [L12: list_a,L22: list_a] :
                ( L
               != ( append_a @ L12 @ ( cons_a @ Y @ L22 ) ) ) )
         => ( ( ( X != Y )
             => ! [L12: list_a,L22: list_a,L3: list_a] :
                  ( L
                 != ( append_a @ L12 @ ( cons_a @ X @ ( append_a @ L22 @ ( cons_a @ Y @ L3 ) ) ) ) ) )
           => ~ ( ( X != Y )
               => ! [L12: list_a,L22: list_a,L3: list_a] :
                    ( L
                   != ( append_a @ L12 @ ( cons_a @ Y @ ( append_a @ L22 @ ( cons_a @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).

% xy_in_set_cases
thf(fact_586_xy__in__set__cases,axiom,
    ! [X: product_prod_b_c,L: list_P903359562653991662od_b_c,Y: product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ L ) )
     => ( ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ L ) )
       => ( ( ( X = Y )
           => ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c] :
                ( L
               != ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ Y @ L22 ) ) ) )
         => ( ( ( X != Y )
             => ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,L3: list_P903359562653991662od_b_c] :
                  ( L
                 != ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X @ ( append2547753245680614915od_b_c @ L22 @ ( cons_P4529483553340347422od_b_c @ Y @ L3 ) ) ) ) ) )
           => ~ ( ( X != Y )
               => ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,L3: list_P903359562653991662od_b_c] :
                    ( L
                   != ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ Y @ ( append2547753245680614915od_b_c @ L22 @ ( cons_P4529483553340347422od_b_c @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).

% xy_in_set_cases
thf(fact_587_set__union__code,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( sup_su2554677861087362972od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ Ys ) )
      = ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ).

% set_union_code
thf(fact_588_prefixes__Cons_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) ) ) )
     => ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) ) ) ).

% prefixes_Cons(2)
thf(fact_589_prefixes__Cons_I1_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) ) ) )
     => ( X = Y ) ) ).

% prefixes_Cons(1)
thf(fact_590_prefixes__set__Nil,axiom,
    ! [Xs: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) ) ).

% prefixes_set_Nil
thf(fact_591_prefixes__set__ob,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Xss2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xss2 ) ) )
     => ~ ! [Xs5: list_P903359562653991662od_b_c] :
            ( Xss2
           != ( append2547753245680614915od_b_c @ Xs @ Xs5 ) ) ) ).

% prefixes_set_ob
thf(fact_592_prefixes__prepend,axiom,
    ! [Xs4: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs4 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) )
     => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ys @ Xs4 ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Ys @ Xs ) ) ) ) ) ).

% prefixes_prepend
thf(fact_593_prefixes__prefix__suffix__ob,axiom,
    ! [A: list_P903359562653991662od_b_c,B: list_P903359562653991662od_b_c,C: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ B @ C ) ) ) )
     => ( ~ ( member6330420149250801815od_b_c @ A @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ B ) ) )
       => ~ ! [C4: list_P903359562653991662od_b_c] :
              ( ? [C5: list_P903359562653991662od_b_c] :
                  ( C
                  = ( append2547753245680614915od_b_c @ C4 @ C5 ) )
             => ( ( A
                  = ( append2547753245680614915od_b_c @ B @ C4 ) )
               => ( C4 = nil_Product_prod_b_c ) ) ) ) ) ).

% prefixes_prefix_suffix_ob
thf(fact_594_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c,Io9: list_P903359562653991662od_b_c] :
      ( ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Io9 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) )
       => ( ( Io9 != Io )
         => ( member6330420149250801815od_b_c @ Io9 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ Q1 ) @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_595_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d,Io: list_P903359562653991662od_b_c,Io9: list_P903359562653991662od_b_c] :
      ( ( minima7808819671940975144_d_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Io9 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) )
       => ( ( Io9 != Io )
         => ( member6330420149250801815od_b_c @ Io9 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ Q1 ) @ ( lS_d_b_c @ M @ Q2 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_596_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima8146652644187019584_c_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_597_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_a_b_c,Q: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima1559550560783484624_a_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_598_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_d_b_c,Q: d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( states_d_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima9124834369493100883_d_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_599_lists__of__length_Osimps_I1_J,axiom,
    ! [T: list_P903359562653991662od_b_c] :
      ( ( lists_2361477089028216131od_b_c @ T @ zero_zero_nat )
      = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% lists_of_length.simps(1)
thf(fact_600_option_Osize_I3_J,axiom,
    ( ( size_size_option_a @ none_a )
    = ( suc @ zero_zero_nat ) ) ).

% option.size(3)
thf(fact_601_boolean__algebra_Oconj__disj__distrib,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) ) ).

% boolean_algebra.conj_disj_distrib
thf(fact_602_boolean__algebra__cancel_Oinf2,axiom,
    ! [B4: set_li6436108459499378894od_b_c,K3: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( B4
        = ( inf_in4978071631833541052od_b_c @ K3 @ B ) )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B4 )
        = ( inf_in4978071631833541052od_b_c @ K3 @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_603_boolean__algebra__cancel_Oinf1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,K3: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A2
        = ( inf_in4978071631833541052od_b_c @ K3 @ A ) )
     => ( ( inf_in4978071631833541052od_b_c @ A2 @ B )
        = ( inf_in4978071631833541052od_b_c @ K3 @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_604_boolean__algebra_Odisj__conj__distrib2,axiom,
    ! [Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) @ X )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ Y @ X ) @ ( sup_su3823046536922626210od_b_c @ Z @ X ) ) ) ).

% boolean_algebra.disj_conj_distrib2
thf(fact_605_boolean__algebra_Oconj__disj__distrib2,axiom,
    ! [Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) @ X )
      = ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ Y @ X ) @ ( inf_in4978071631833541052od_b_c @ Z @ X ) ) ) ).

% boolean_algebra.conj_disj_distrib2
thf(fact_606_boolean__algebra_Odisj__conj__distrib,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( sup_su3823046536922626210od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
      = ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ Y ) @ ( sup_su3823046536922626210od_b_c @ X @ Z ) ) ) ).

% boolean_algebra.disj_conj_distrib
thf(fact_607_after__transition,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c,Q6: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q @ ( produc3440865914000881661od_c_a @ X @ ( product_Pair_c_a @ Y @ Q6 ) ) ) @ ( transitions_a_b_c @ M ) )
       => ( ( after_a_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_transition
thf(fact_608_after__transition,axiom,
    ! [M: fsm_d_b_c,Q: d,X: b,Y: c,Q6: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q @ ( produc3440865926910568064od_c_d @ X @ ( product_Pair_c_d @ Y @ Q6 ) ) ) @ ( transitions_d_b_c @ M ) )
       => ( ( after_d_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_transition
thf(fact_609_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I3_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( butlas5354910156707045818od_b_c @ ( get_di903557346829177899_c_b_c @ M @ Q1 @ Q2 ) ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(3)
thf(fact_610_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I3_J,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( butlas5354910156707045818od_b_c @ ( get_di2280862616223094331_a_b_c @ M @ Q1 @ Q2 ) ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ Q1 ) @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(3)
thf(fact_611_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I3_J,axiom,
    ! [M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( member6330420149250801815od_b_c @ ( butlas5354910156707045818od_b_c @ ( get_di622774388077934782_d_b_c @ M @ Q1 @ Q2 ) ) @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ Q1 ) @ ( lS_d_b_c @ M @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(3)
thf(fact_612_quicksort_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ).

% quicksort.cases
thf(fact_613_butlast__snoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( butlas5354910156707045818od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = Xs ) ).

% butlast_snoc
thf(fact_614_in__set__butlastD,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( butlas2026940317822895424od_b_c @ Xs ) ) )
     => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ).

% in_set_butlastD
thf(fact_615_in__set__butlastD,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ ( butlast_a @ Xs ) ) )
     => ( member_a @ X @ ( set_a2 @ Xs ) ) ) ).

% in_set_butlastD
thf(fact_616_butlast_Osimps_I1_J,axiom,
    ( ( butlas5354910156707045818od_b_c @ nil_Product_prod_b_c )
    = nil_Product_prod_b_c ) ).

% butlast.simps(1)
thf(fact_617_butlast_Osimps_I2_J,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( ( Xs = nil_Product_prod_b_c )
       => ( ( butlas5354910156707045818od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
          = nil_Product_prod_b_c ) )
      & ( ( Xs != nil_Product_prod_b_c )
       => ( ( butlas5354910156707045818od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
          = ( cons_P4529483553340347422od_b_c @ X @ ( butlas5354910156707045818od_b_c @ Xs ) ) ) ) ) ).

% butlast.simps(2)
thf(fact_618_butlast__append,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( Ys = nil_Product_prod_b_c )
       => ( ( butlas5354910156707045818od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
          = ( butlas5354910156707045818od_b_c @ Xs ) ) )
      & ( ( Ys != nil_Product_prod_b_c )
       => ( ( butlas5354910156707045818od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
          = ( append2547753245680614915od_b_c @ Xs @ ( butlas5354910156707045818od_b_c @ Ys ) ) ) ) ) ).

% butlast_append
thf(fact_619_in__set__butlast__appendI,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( butlas2026940317822895424od_b_c @ Xs ) ) )
        | ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( butlas2026940317822895424od_b_c @ Ys ) ) ) )
     => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( butlas2026940317822895424od_b_c @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_620_in__set__butlast__appendI,axiom,
    ! [X: a,Xs: list_a,Ys: list_a] :
      ( ( ( member_a @ X @ ( set_a2 @ ( butlast_a @ Xs ) ) )
        | ( member_a @ X @ ( set_a2 @ ( butlast_a @ Ys ) ) ) )
     => ( member_a @ X @ ( set_a2 @ ( butlast_a @ ( append_a @ Xs @ Ys ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_621_in__set__butlast__appendI,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( butlas5354910156707045818od_b_c @ Xs ) ) )
        | ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( butlas5354910156707045818od_b_c @ Ys ) ) ) )
     => ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( butlas5354910156707045818od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_622_butlast__eq__cons__conv,axiom,
    ! [L: list_P903359562653991662od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( butlas5354910156707045818od_b_c @ L )
        = ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( ? [Xl: product_prod_b_c] :
            ( L
            = ( cons_P4529483553340347422od_b_c @ X @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ Xl @ nil_Product_prod_b_c ) ) ) ) ) ) ).

% butlast_eq_cons_conv
thf(fact_623_butlast__eq__consE,axiom,
    ! [L: list_P903359562653991662od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( butlas5354910156707045818od_b_c @ L )
        = ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
     => ~ ! [Xl2: product_prod_b_c] :
            ( L
           != ( cons_P4529483553340347422od_b_c @ X @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ Xl2 @ nil_Product_prod_b_c ) ) ) ) ) ).

% butlast_eq_consE
thf(fact_624_observable__alt__def,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q12: a,X2: b,Y2: c,Q15: a,Q16: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q12 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q15 ) ) ) @ ( transitions_a_b_c @ M2 ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q12 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q16 ) ) ) @ ( transitions_a_b_c @ M2 ) ) )
         => ( Q15 = Q16 ) ) ) ) ).

% observable_alt_def
thf(fact_625_observable__alt__def,axiom,
    ( observable_d_b_c
    = ( ^ [M2: fsm_d_b_c] :
        ! [Q12: d,X2: b,Y2: c,Q15: d,Q16: d] :
          ( ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q12 @ ( produc3440865926910568064od_c_d @ X2 @ ( product_Pair_c_d @ Y2 @ Q15 ) ) ) @ ( transitions_d_b_c @ M2 ) )
            & ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q12 @ ( produc3440865926910568064od_c_d @ X2 @ ( product_Pair_c_d @ Y2 @ Q16 ) ) ) @ ( transitions_d_b_c @ M2 ) ) )
         => ( Q15 = Q16 ) ) ) ) ).

% observable_alt_def
thf(fact_626_h__obs__None,axiom,
    ! [M: fsm_d_b_c,Q: d,X: b,Y: c] :
      ( ( observable_d_b_c @ M )
     => ( ( ( h_obs_d_b_c @ M @ Q @ X @ Y )
          = none_d )
        = ( ~ ? [Q4: d] : ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q @ ( produc3440865926910568064od_c_d @ X @ ( product_Pair_c_d @ Y @ Q4 ) ) ) @ ( transitions_d_b_c @ M ) ) ) ) ) ).

% h_obs_None
thf(fact_627_h__obs__None,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c] :
      ( ( observable_a_b_c @ M )
     => ( ( ( h_obs_a_b_c @ M @ Q @ X @ Y )
          = none_a )
        = ( ~ ? [Q4: a] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q @ ( produc3440865914000881661od_c_a @ X @ ( product_Pair_c_a @ Y @ Q4 ) ) ) @ ( transitions_a_b_c @ M ) ) ) ) ) ).

% h_obs_None
thf(fact_628_suffixes__eq__snoc,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ( suffix3867853578027978934od_b_c @ Ys )
        = ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) ) )
      = ( ( ( ( Ys = nil_Product_prod_b_c )
            & ( Xs = nil_li8071162985807626740od_b_c ) )
          | ? [Z3: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
              ( ( Ys
                = ( cons_P4529483553340347422od_b_c @ Z3 @ Zs2 ) )
              & ( Xs
                = ( suffix3867853578027978934od_b_c @ Zs2 ) ) ) )
        & ( X = Ys ) ) ) ).

% suffixes_eq_snoc
thf(fact_629_Sublist_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix3867853578027978934od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% Sublist.suffixes.simps(1)
thf(fact_630_Sublist_Osuffixes_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( suffix3867853578027978934od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append6992831555715836169od_b_c @ ( suffix3867853578027978934od_b_c @ Xs ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% Sublist.suffixes.simps(2)
thf(fact_631_language__equivalence__from__isomorphism,axiom,
    ! [F3: list_P903359562653991662od_b_c > a,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F3 @ ( states7681702920031268536_c_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( states7681702920031268536_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M1 ) )
           => ( ( lS_lis2930931384350476499_c_b_c @ M1 @ Q )
              = ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_632_language__equivalence__from__isomorphism,axiom,
    ! [F3: list_P903359562653991662od_b_c > d,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F3 @ ( states7681702920031268536_c_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( states7681702920031268536_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M1 ) )
           => ( ( lS_lis2930931384350476499_c_b_c @ M1 @ Q )
              = ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_633_language__equivalence__from__isomorphism,axiom,
    ! [F3: a > a,M1: fsm_a_b_c,M22: fsm_a_b_c,Q: a] :
      ( ( bij_betw_a_a @ F3 @ ( states_a_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( states_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q @ ( states_a_b_c @ M1 ) )
           => ( ( lS_a_b_c @ M1 @ Q )
              = ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_634_language__equivalence__from__isomorphism,axiom,
    ! [F3: a > d,M1: fsm_a_b_c,M22: fsm_d_b_c,Q: a] :
      ( ( bij_betw_a_d @ F3 @ ( states_a_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( states_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q @ ( states_a_b_c @ M1 ) )
           => ( ( lS_a_b_c @ M1 @ Q )
              = ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_635_language__equivalence__from__isomorphism,axiom,
    ! [F3: d > a,M1: fsm_d_b_c,M22: fsm_a_b_c,Q: d] :
      ( ( bij_betw_d_a @ F3 @ ( states_d_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( states_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q @ ( states_d_b_c @ M1 ) )
           => ( ( lS_d_b_c @ M1 @ Q )
              = ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_636_language__equivalence__from__isomorphism,axiom,
    ! [F3: d > d,M1: fsm_d_b_c,M22: fsm_d_b_c,Q: d] :
      ( ( bij_betw_d_d @ F3 @ ( states_d_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( states_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q @ ( states_d_b_c @ M1 ) )
           => ( ( lS_d_b_c @ M1 @ Q )
              = ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_637_bind__simps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,F3: product_prod_b_c > list_P903359562653991662od_b_c] :
      ( ( bind_P6820369299258290311od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ F3 )
      = ( append2547753245680614915od_b_c @ ( F3 @ X ) @ ( bind_P6820369299258290311od_b_c @ Xs @ F3 ) ) ) ).

% bind_simps(2)
thf(fact_638_pow__list_Osimps_I1_J,axiom,
    ( ( pow_li4341120398627903455od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% pow_list.simps(1)
thf(fact_639_sublists_Osimps_I1_J,axiom,
    ( ( sublis8706766506341057792od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% sublists.simps(1)
thf(fact_640_bind__simps_I1_J,axiom,
    ! [F3: product_prod_b_c > list_P903359562653991662od_b_c] :
      ( ( bind_P6820369299258290311od_b_c @ nil_Product_prod_b_c @ F3 )
      = nil_Product_prod_b_c ) ).

% bind_simps(1)
thf(fact_641_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: list_P903359562653991662od_b_c > a,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F3 @ ( states7681702920031268536_c_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( states7681702920031268536_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M1 @ Q ) @ ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_642_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: list_P903359562653991662od_b_c > d,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F3 @ ( states7681702920031268536_c_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( states7681702920031268536_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M1 @ Q ) @ ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_643_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: a > a,M1: fsm_a_b_c,M22: fsm_a_b_c,Q: a] :
      ( ( bij_betw_a_a @ F3 @ ( states_a_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( states_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q @ ( states_a_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M1 @ Q ) @ ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_644_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: a > d,M1: fsm_a_b_c,M22: fsm_d_b_c,Q: a] :
      ( ( bij_betw_a_d @ F3 @ ( states_a_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( states_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q @ ( states_a_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M1 @ Q ) @ ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_645_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: d > a,M1: fsm_d_b_c,M22: fsm_a_b_c,Q: d] :
      ( ( bij_betw_d_a @ F3 @ ( states_d_b_c @ M1 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( states_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q @ ( states_d_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M1 @ Q ) @ ( lS_a_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_646_language__equivalence__from__isomorphism__helper,axiom,
    ! [F3: d > d,M1: fsm_d_b_c,M22: fsm_d_b_c,Q: d] :
      ( ( bij_betw_d_d @ F3 @ ( states_d_b_c @ M1 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( states_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q @ ( states_d_b_c @ M1 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M1 @ Q ) @ ( lS_d_b_c @ M22 @ ( F3 @ Q ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_647_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: list_P903359562653991662od_b_c > a,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F3 @ ( reacha8116992257183400179_c_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_lis2930931384350476499_c_b_c @ M1 @ ( initia3567573336347591134_c_b_c @ M1 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_648_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: list_P903359562653991662od_b_c > d,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F3 @ ( reacha8116992257183400179_c_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_lis2930931384350476499_c_b_c @ M1 @ ( initia3567573336347591134_c_b_c @ M1 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_649_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: a > a,M1: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_a_a @ F3 @ ( reacha1620305530751930115_a_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_650_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: a > d,M1: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_a_d @ F3 @ ( reacha1620305530751930115_a_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_651_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: d > a,M1: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_d_a @ F3 @ ( reacha9185589339461546374_d_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_652_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F3: d > d,M1: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_d_d @ F3 @ ( reacha9185589339461546374_d_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_653_find__remove__2__set_I2_J,axiom,
    ! [P: product_prod_b_c > nat > $o,Xs: list_P903359562653991662od_b_c,Ys: list_nat,X: product_prod_b_c,Y: nat,Xs4: list_P903359562653991662od_b_c] :
      ( ( ( find_r9196408498688822641_c_nat @ P @ Xs @ Ys )
        = ( some_P7286244805943011973od_b_c @ ( produc4507202783310137636od_b_c @ X @ ( produc8137419655804493381od_b_c @ Y @ Xs4 ) ) ) )
     => ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) ) ) ).

% find_remove_2_set(2)
thf(fact_654_find__remove__2__set_I3_J,axiom,
    ! [P: product_prod_b_c > nat > $o,Xs: list_P903359562653991662od_b_c,Ys: list_nat,X: product_prod_b_c,Y: nat,Xs4: list_P903359562653991662od_b_c] :
      ( ( ( find_r9196408498688822641_c_nat @ P @ Xs @ Ys )
        = ( some_P7286244805943011973od_b_c @ ( produc4507202783310137636od_b_c @ X @ ( produc8137419655804493381od_b_c @ Y @ Xs4 ) ) ) )
     => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).

% find_remove_2_set(3)
thf(fact_655_inf_Obounded__iff,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) )
      = ( ( ord_le282488521294790766od_b_c @ A @ B )
        & ( ord_le282488521294790766od_b_c @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_656_le__inf__iff,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) )
      = ( ( ord_le282488521294790766od_b_c @ X @ Y )
        & ( ord_le282488521294790766od_b_c @ X @ Z ) ) ) ).

% le_inf_iff
thf(fact_657_Int__subset__iff,axiom,
    ! [C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C3 @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) )
      = ( ( ord_le282488521294790766od_b_c @ C3 @ A2 )
        & ( ord_le282488521294790766od_b_c @ C3 @ B4 ) ) ) ).

% Int_subset_iff
thf(fact_658_Int__Collect__mono,axiom,
    ! [A2: set_a,B4: set_a,P: a > $o,Q8: a > $o] :
      ( ( ord_less_eq_set_a @ A2 @ B4 )
     => ( ! [X4: a] :
            ( ( member_a @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q8 @ X4 ) ) )
       => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A2 @ ( collect_a @ P ) ) @ ( inf_inf_set_a @ B4 @ ( collect_a @ Q8 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_659_Int__Collect__mono,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,P: list_P903359562653991662od_b_c > $o,Q8: list_P903359562653991662od_b_c > $o] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B4 )
     => ( ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ A2 )
           => ( ( P @ X4 )
             => ( Q8 @ X4 ) ) )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ ( collec2280997390073109977od_b_c @ P ) ) @ ( inf_in4978071631833541052od_b_c @ B4 @ ( collec2280997390073109977od_b_c @ Q8 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_660_Int__greatest,axiom,
    ! [C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C3 @ A2 )
     => ( ( ord_le282488521294790766od_b_c @ C3 @ B4 )
       => ( ord_le282488521294790766od_b_c @ C3 @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) ) ) ) ).

% Int_greatest
thf(fact_661_Int__absorb2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B4 )
     => ( ( inf_in4978071631833541052od_b_c @ A2 @ B4 )
        = A2 ) ) ).

% Int_absorb2
thf(fact_662_Int__absorb1,axiom,
    ! [B4: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B4 @ A2 )
     => ( ( inf_in4978071631833541052od_b_c @ A2 @ B4 )
        = B4 ) ) ).

% Int_absorb1
thf(fact_663_Int__lower2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ B4 ) ).

% Int_lower2
thf(fact_664_Int__lower1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ A2 ) ).

% Int_lower1
thf(fact_665_Int__mono,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,D: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ C3 )
     => ( ( ord_le282488521294790766od_b_c @ B4 @ D )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ ( inf_in4978071631833541052od_b_c @ C3 @ D ) ) ) ) ).

% Int_mono
thf(fact_666_inter__eq__subsetI,axiom,
    ! [S: set_li6436108459499378894od_b_c,S2: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ S @ S2 )
     => ( ( ( inf_in4978071631833541052od_b_c @ A2 @ S2 )
          = ( inf_in4978071631833541052od_b_c @ B4 @ S2 ) )
       => ( ( inf_in4978071631833541052od_b_c @ A2 @ S )
          = ( inf_in4978071631833541052od_b_c @ B4 @ S ) ) ) ) ).

% inter_eq_subsetI
thf(fact_667_inf__sup__ord_I2_J,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_668_inf__sup__ord_I1_J,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ X ) ).

% inf_sup_ord(1)
thf(fact_669_inf__le1,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ X ) ).

% inf_le1
thf(fact_670_inf__le2,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ Y ) ).

% inf_le2
thf(fact_671_le__infE,axiom,
    ! [X: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
     => ~ ( ( ord_le282488521294790766od_b_c @ X @ A )
         => ~ ( ord_le282488521294790766od_b_c @ X @ B ) ) ) ).

% le_infE
thf(fact_672_le__infI,axiom,
    ! [X: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ A )
     => ( ( ord_le282488521294790766od_b_c @ X @ B )
       => ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ) ).

% le_infI
thf(fact_673_inf__mono,axiom,
    ! [A: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,D2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ C )
     => ( ( ord_le282488521294790766od_b_c @ B @ D2 )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ ( inf_in4978071631833541052od_b_c @ C @ D2 ) ) ) ) ).

% inf_mono
thf(fact_674_le__infI1,axiom,
    ! [A: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ X )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ X ) ) ).

% le_infI1
thf(fact_675_le__infI2,axiom,
    ! [B: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ X )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ X ) ) ).

% le_infI2
thf(fact_676_inf_OorderE,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( A
        = ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ).

% inf.orderE
thf(fact_677_inf_OorderI,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A
        = ( inf_in4978071631833541052od_b_c @ A @ B ) )
     => ( ord_le282488521294790766od_b_c @ A @ B ) ) ).

% inf.orderI
thf(fact_678_inf__unique,axiom,
    ! [F3: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ! [X4: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( F3 @ X4 @ Y3 ) @ X4 )
     => ( ! [X4: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( F3 @ X4 @ Y3 ) @ Y3 )
       => ( ! [X4: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X4 @ Y3 )
             => ( ( ord_le282488521294790766od_b_c @ X4 @ Z2 )
               => ( ord_le282488521294790766od_b_c @ X4 @ ( F3 @ Y3 @ Z2 ) ) ) )
         => ( ( inf_in4978071631833541052od_b_c @ X @ Y )
            = ( F3 @ X @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_679_le__iff__inf,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [X2: set_li6436108459499378894od_b_c,Y2: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ X2 @ Y2 )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_680_inf_Oabsorb1,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = A ) ) ).

% inf.absorb1
thf(fact_681_inf_Oabsorb2,axiom,
    ! [B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ A )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = B ) ) ).

% inf.absorb2
thf(fact_682_inf__absorb1,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ Y )
     => ( ( inf_in4978071631833541052od_b_c @ X @ Y )
        = X ) ) ).

% inf_absorb1
thf(fact_683_inf__absorb2,axiom,
    ! [Y: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ Y @ X )
     => ( ( inf_in4978071631833541052od_b_c @ X @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_684_inf_OboundedE,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) )
     => ~ ( ( ord_le282488521294790766od_b_c @ A @ B )
         => ~ ( ord_le282488521294790766od_b_c @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_685_inf_OboundedI,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( ord_le282488521294790766od_b_c @ A @ C )
       => ( ord_le282488521294790766od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C ) ) ) ) ).

% inf.boundedI
thf(fact_686_inf__greatest,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ Y )
     => ( ( ord_le282488521294790766od_b_c @ X @ Z )
       => ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) ) ) ) ).

% inf_greatest
thf(fact_687_inf_Oorder__iff,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B6: set_li6436108459499378894od_b_c] :
          ( A6
          = ( inf_in4978071631833541052od_b_c @ A6 @ B6 ) ) ) ) ).

% inf.order_iff
thf(fact_688_inf_Ocobounded1,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ A ) ).

% inf.cobounded1
thf(fact_689_inf_Ocobounded2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ B ) ).

% inf.cobounded2
thf(fact_690_inf_Oabsorb__iff1,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B6: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ A6 @ B6 )
          = A6 ) ) ) ).

% inf.absorb_iff1
thf(fact_691_inf_Oabsorb__iff2,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [B6: set_li6436108459499378894od_b_c,A6: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ A6 @ B6 )
          = B6 ) ) ) ).

% inf.absorb_iff2
thf(fact_692_inf_OcoboundedI1,axiom,
    ! [A: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ C )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_693_inf_OcoboundedI2,axiom,
    ! [B: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ C )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_694_reachable__state__is__state,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( member_a @ Q @ ( states_a_b_c @ M ) ) ) ).

% reachable_state_is_state
thf(fact_695_reachable__states__initial,axiom,
    ! [M: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ).

% reachable_states_initial
thf(fact_696_reachable__states__initial,axiom,
    ! [M: fsm_d_b_c] : ( member_d @ ( initial_d_b_c @ M ) @ ( reacha9185589339461546374_d_b_c @ M ) ) ).

% reachable_states_initial
thf(fact_697_subset__code_I1_J,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ Xs ) @ B4 )
      = ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( set_li4480668622519654659od_b_c @ Xs ) )
           => ( member6330420149250801815od_b_c @ X2 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_698_subset__code_I1_J,axiom,
    ! [Xs: list_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ ( set_a2 @ Xs ) @ B4 )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
           => ( member_a @ X2 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_699_set__subset__Cons,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] : ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) ) ).

% set_subset_Cons
thf(fact_700_distrib__sup__le,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ Y @ Z ) ) @ ( inf_in4978071631833541052od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ Y ) @ ( sup_su3823046536922626210od_b_c @ X @ Z ) ) ) ).

% distrib_sup_le
thf(fact_701_distrib__inf__le,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ X @ Y ) @ ( inf_in4978071631833541052od_b_c @ X @ Z ) ) @ ( inf_in4978071631833541052od_b_c @ X @ ( sup_su3823046536922626210od_b_c @ Y @ Z ) ) ) ).

% distrib_inf_le
thf(fact_702_list__prefix__subset,axiom,
    ! [Ts: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ? [Ys7: list_P903359562653991662od_b_c] :
          ( Ts
          = ( append2547753245680614915od_b_c @ Xs @ Ys7 ) )
     => ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ Ts ) ) ) ).

% list_prefix_subset
thf(fact_703_list__append__subset3,axiom,
    ! [Xs1: list_P903359562653991662od_b_c,Ys1: list_P903359562653991662od_b_c,Xs23: list_P903359562653991662od_b_c,Ys22: list_P903359562653991662od_b_c,Xs32: list_P903359562653991662od_b_c,Ys32: list_P903359562653991662od_b_c] :
      ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs1 ) @ ( set_Product_prod_b_c2 @ Ys1 ) )
     => ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs23 ) @ ( set_Product_prod_b_c2 @ Ys22 ) )
       => ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs32 ) @ ( set_Product_prod_b_c2 @ Ys32 ) )
         => ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs1 @ ( append2547753245680614915od_b_c @ Xs23 @ Xs32 ) ) ) @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Ys1 @ ( append2547753245680614915od_b_c @ Ys22 @ Ys32 ) ) ) ) ) ) ) ).

% list_append_subset3
thf(fact_704_Un__Int__assoc__eq,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( ( sup_su3823046536922626210od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) @ C3 )
        = ( inf_in4978071631833541052od_b_c @ A2 @ ( sup_su3823046536922626210od_b_c @ B4 @ C3 ) ) )
      = ( ord_le282488521294790766od_b_c @ C3 @ A2 ) ) ).

% Un_Int_assoc_eq
thf(fact_705_after__reachable,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ Q @ Io ) @ ( reacha8116992257183400179_c_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_706_after__reachable,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( member_a @ ( after_a_b_c @ M @ Q @ Io ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_707_after__reachable,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) )
       => ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ( member_d @ ( after_d_b_c @ M @ Q @ Io ) @ ( reacha9185589339461546374_d_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_708_butlast__subset,axiom,
    ! [Xs: list_P903359562653991662od_b_c,A2: set_Product_prod_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ A2 )
       => ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ ( butlas5354910156707045818od_b_c @ Xs ) ) @ A2 ) ) ) ).

% butlast_subset
thf(fact_709_prefixes__set__subset,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] : ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ) ).

% prefixes_set_subset
thf(fact_710_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: list_P903359562653991662od_b_c > a,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F3 @ ( reacha8116992257183400179_c_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M1 @ ( initia3567573336347591134_c_b_c @ M1 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_711_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: list_P903359562653991662od_b_c > d,M1: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F3 @ ( reacha8116992257183400179_c_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X4: b,Y3: c,Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
             => ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M1 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X4 @ ( produc4268225641733455109od_b_c @ Y3 @ Q7 ) ) ) @ ( transi3161963839906981764_c_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M1 @ ( initia3567573336347591134_c_b_c @ M1 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_712_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: a > a,M1: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_a_a @ F3 @ ( reacha1620305530751930115_a_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_713_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: a > d,M1: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_a_d @ F3 @ ( reacha1620305530751930115_a_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_a_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X4: b,Y3: c,Q7: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
             => ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M1 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ Q7 ) ) ) @ ( transitions_a_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_714_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: d > a,M1: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_d_a @ F3 @ ( reacha9185589339461546374_d_b_c @ M1 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F3 @ Q5 ) @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_715_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F3: d > d,M1: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_d_d @ F3 @ ( reacha9185589339461546374_d_b_c @ M1 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F3 @ ( initial_d_b_c @ M1 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X4: b,Y3: c,Q7: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
             => ( ( member_d @ Q7 @ ( reacha9185589339461546374_d_b_c @ M1 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ Q7 ) ) ) @ ( transitions_d_b_c @ M1 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F3 @ Q5 ) @ ( produc3440865926910568064od_c_d @ X4 @ ( product_Pair_c_d @ Y3 @ ( F3 @ Q7 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_716_after__reachable__initial,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) @ Io ) @ ( reacha8116992257183400179_c_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_717_after__reachable__initial,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( member_a @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_718_after__reachable__initial,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
       => ( member_d @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Io ) @ ( reacha9185589339461546374_d_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_719_find__remove__2__strengthening,axiom,
    ! [P: product_prod_b_c > nat > $o,Xs: list_P903359562653991662od_b_c,Ys: list_nat,X: product_prod_b_c,Y: nat,Xs4: list_P903359562653991662od_b_c,P7: product_prod_b_c > nat > $o] :
      ( ( ( find_r9196408498688822641_c_nat @ P @ Xs @ Ys )
        = ( some_P7286244805943011973od_b_c @ ( produc4507202783310137636od_b_c @ X @ ( produc8137419655804493381od_b_c @ Y @ Xs4 ) ) ) )
     => ( ( P7 @ X @ Y )
       => ( ! [X6: product_prod_b_c,Y5: nat] :
              ( ( P7 @ X6 @ Y5 )
             => ( P @ X6 @ Y5 ) )
         => ( ( find_r9196408498688822641_c_nat @ P7 @ Xs @ Ys )
            = ( some_P7286244805943011973od_b_c @ ( produc4507202783310137636od_b_c @ X @ ( produc8137419655804493381od_b_c @ Y @ Xs4 ) ) ) ) ) ) ) ).

% find_remove_2_strengthening
thf(fact_720_find__remove__2__set_I1_J,axiom,
    ! [P: product_prod_b_c > nat > $o,Xs: list_P903359562653991662od_b_c,Ys: list_nat,X: product_prod_b_c,Y: nat,Xs4: list_P903359562653991662od_b_c] :
      ( ( ( find_r9196408498688822641_c_nat @ P @ Xs @ Ys )
        = ( some_P7286244805943011973od_b_c @ ( produc4507202783310137636od_b_c @ X @ ( produc8137419655804493381od_b_c @ Y @ Xs4 ) ) ) )
     => ( P @ X @ Y ) ) ).

% find_remove_2_set(1)
thf(fact_721_less__prod__simp,axiom,
    ! [X12: b,Y1: c,X24: b,Y23: c] :
      ( ( ord_le817911927979441428od_b_c @ ( product_Pair_b_c @ X12 @ Y1 ) @ ( product_Pair_b_c @ X24 @ Y23 ) )
      = ( ( ord_less_b @ X12 @ X24 )
        | ( ( ord_less_eq_b @ X12 @ X24 )
          & ( ord_less_c @ Y1 @ Y23 ) ) ) ) ).

% less_prod_simp
thf(fact_722_less__prod__simp,axiom,
    ! [X12: nat,Y1: list_P903359562653991662od_b_c,X24: nat,Y23: list_P903359562653991662od_b_c] :
      ( ( ord_le7571209501266857191od_b_c @ ( produc8137419655804493381od_b_c @ X12 @ Y1 ) @ ( produc8137419655804493381od_b_c @ X24 @ Y23 ) )
      = ( ( ord_less_nat @ X12 @ X24 )
        | ( ( ord_less_eq_nat @ X12 @ X24 )
          & ( ord_le2870576100876692378od_b_c @ Y1 @ Y23 ) ) ) ) ).

% less_prod_simp
thf(fact_723_less__prod__simp,axiom,
    ! [X12: nat,Y1: nat,X24: nat,Y23: nat] :
      ( ( ord_le1203424502768444845at_nat @ ( product_Pair_nat_nat @ X12 @ Y1 ) @ ( product_Pair_nat_nat @ X24 @ Y23 ) )
      = ( ( ord_less_nat @ X12 @ X24 )
        | ( ( ord_less_eq_nat @ X12 @ X24 )
          & ( ord_less_nat @ Y1 @ Y23 ) ) ) ) ).

% less_prod_simp
thf(fact_724_less__eq__prod__simp,axiom,
    ! [X12: b,Y1: c,X24: b,Y23: c] :
      ( ( ord_le5491865407852299784od_b_c @ ( product_Pair_b_c @ X12 @ Y1 ) @ ( product_Pair_b_c @ X24 @ Y23 ) )
      = ( ( ord_less_b @ X12 @ X24 )
        | ( ( ord_less_eq_b @ X12 @ X24 )
          & ( ord_less_eq_c @ Y1 @ Y23 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_725_less__eq__prod__simp,axiom,
    ! [X12: nat,Y1: list_P903359562653991662od_b_c,X24: nat,Y23: list_P903359562653991662od_b_c] :
      ( ( ord_le1421968755357256947od_b_c @ ( produc8137419655804493381od_b_c @ X12 @ Y1 ) @ ( produc8137419655804493381od_b_c @ X24 @ Y23 ) )
      = ( ( ord_less_nat @ X12 @ X24 )
        | ( ( ord_less_eq_nat @ X12 @ X24 )
          & ( ord_le8780369363890727566od_b_c @ Y1 @ Y23 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_726_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ! [Q5: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M ) )
             => ( member6330420149250801815od_b_c @ Q5 @ ( io_tar7088883562557314310_c_b_c @ M @ ( F3 @ Q5 ) @ ( initia3567573336347591134_c_b_c @ M ) ) ) )
         => ( ! [Q5: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F3 @ Q5 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) ) )
           => ( ( member6330420149250801815od_b_c @ Q1 @ ( reacha8116992257183400179_c_b_c @ M ) )
             => ( ( member6330420149250801815od_b_c @ Q2 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( conver6852411701971397450_c_b_c @ M @ ( F3 @ Q1 ) @ ( F3 @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_727_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_a_b_c,F3: a > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ! [Q5: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( member_a @ Q5 @ ( io_targets_a_b_c @ M @ ( F3 @ Q5 ) @ ( initial_a_b_c @ M ) ) ) )
         => ( ! [Q5: a] :
                ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F3 @ Q5 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) ) )
           => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_a_b_c @ M @ ( F3 @ Q1 ) @ ( F3 @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_728_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_d_b_c,F3: d > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ! [Q5: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M ) )
             => ( member_d @ Q5 @ ( io_targets_d_b_c @ M @ ( F3 @ Q5 ) @ ( initial_d_b_c @ M ) ) ) )
         => ( ! [Q5: d] :
                ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F3 @ Q5 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ SC ) ) )
           => ( ( member_d @ Q1 @ ( reacha9185589339461546374_d_b_c @ M ) )
             => ( ( member_d @ Q2 @ ( reacha9185589339461546374_d_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_d_b_c @ M @ ( F3 @ Q1 ) @ ( F3 @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_729_le__Nil,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( ord_le8780369363890727566od_b_c @ X @ nil_Product_prod_b_c )
      = ( X = nil_Product_prod_b_c ) ) ).

% le_Nil
thf(fact_730_less__eq__option__None__code,axiom,
    ! [X: option_a] : ( ord_less_eq_option_a @ none_a @ X ) ).

% less_eq_option_None_code
thf(fact_731_Cons__le__Cons,axiom,
    ! [A: product_prod_b_c,X: list_P903359562653991662od_b_c,B: product_prod_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ord_le8780369363890727566od_b_c @ ( cons_P4529483553340347422od_b_c @ A @ X ) @ ( cons_P4529483553340347422od_b_c @ B @ Y ) )
      = ( ( ord_le817911927979441428od_b_c @ A @ B )
        | ( ( A = B )
          & ( ord_le8780369363890727566od_b_c @ X @ Y ) ) ) ) ).

% Cons_le_Cons
thf(fact_732_Cons__le__Cons,axiom,
    ! [A: nat,X: list_nat,B: nat,Y: list_nat] :
      ( ( ord_less_eq_list_nat @ ( cons_nat @ A @ X ) @ ( cons_nat @ B @ Y ) )
      = ( ( ord_less_nat @ A @ B )
        | ( ( A = B )
          & ( ord_less_eq_list_nat @ X @ Y ) ) ) ) ).

% Cons_le_Cons
thf(fact_733_less__eq__option__Some__None,axiom,
    ! [X: a] :
      ~ ( ord_less_eq_option_a @ ( some_a @ X ) @ none_a ) ).

% less_eq_option_Some_None
thf(fact_734_less__eq__option__Some__None,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ~ ( ord_le2305922816848743508od_b_c @ ( some_l689282263436086355od_b_c @ X ) @ none_l1245059289828015823od_b_c ) ).

% less_eq_option_Some_None
thf(fact_735_less__eq__option__None__is__None,axiom,
    ! [X: option_a] :
      ( ( ord_less_eq_option_a @ X @ none_a )
     => ( X = none_a ) ) ).

% less_eq_option_None_is_None
thf(fact_736_less__eq__option__None,axiom,
    ! [X: option_a] : ( ord_less_eq_option_a @ none_a @ X ) ).

% less_eq_option_None
thf(fact_737_less__eq__list__code_I2_J,axiom,
    ! [Xs: list_P903359562653991662od_b_c] : ( ord_le8780369363890727566od_b_c @ nil_Product_prod_b_c @ Xs ) ).

% less_eq_list_code(2)
thf(fact_738_Nil__le__Cons,axiom,
    ! [X: list_P903359562653991662od_b_c] : ( ord_le8780369363890727566od_b_c @ nil_Product_prod_b_c @ X ) ).

% Nil_le_Cons
thf(fact_739_io__targets__language,axiom,
    ! [Q6: d,M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( member_d @ Q6 @ ( io_targets_d_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_740_io__targets__language,axiom,
    ! [Q6: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q6 @ ( io_tar7088883562557314310_c_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_741_io__targets__language,axiom,
    ! [Q6: a,M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( member_a @ Q6 @ ( io_targets_a_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_742_less__eq__list__code_I3_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ord_le8780369363890727566od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) )
      = ( ( ord_le817911927979441428od_b_c @ X @ Y )
        | ( ( X = Y )
          & ( ord_le8780369363890727566od_b_c @ Xs @ Ys ) ) ) ) ).

% less_eq_list_code(3)
thf(fact_743_less__eq__list__code_I3_J,axiom,
    ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
      ( ( ord_less_eq_list_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
      = ( ( ord_less_nat @ X @ Y )
        | ( ( X = Y )
          & ( ord_less_eq_list_nat @ Xs @ Ys ) ) ) ) ).

% less_eq_list_code(3)
thf(fact_744_less__eq__list__code_I1_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ~ ( ord_le8780369363890727566od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ nil_Product_prod_b_c ) ).

% less_eq_list_code(1)
thf(fact_745_io__targets__states,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] : ( ord_less_eq_set_a @ ( io_targets_a_b_c @ M @ Io @ Q ) @ ( states_a_b_c @ M ) ) ).

% io_targets_states
thf(fact_746_language__io__target__append,axiom,
    ! [Q6: d,M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q: d,Io2: list_P903359562653991662od_b_c] :
      ( ( member_d @ Q6 @ ( io_targets_d_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_747_language__io__target__append,axiom,
    ! [Q6: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io1: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q6 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_748_language__io__target__append,axiom,
    ! [Q6: a,M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( member_a @ Q6 @ ( io_targets_a_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_749_io__targets__language__append,axiom,
    ! [Q1: d,M: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q: d,Io2: list_P903359562653991662od_b_c] :
      ( ( member_d @ Q1 @ ( io_targets_d_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_750_io__targets__language__append,axiom,
    ! [Q1: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io1: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q1 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_751_io__targets__language__append,axiom,
    ! [Q1: a,M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( member_a @ Q1 @ ( io_targets_a_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_752_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
     => ( ( observ6293852833591064631_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q2 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_753_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q1 ) )
     => ( ( observable_a_b_c @ M )
       => ( ( member_a @ Q2 @ ( io_targets_a_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_754_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q1: d,Q2: d] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q1 ) )
     => ( ( observable_d_b_c @ M )
       => ( ( member_d @ Q2 @ ( io_targets_d_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_755_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q5: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ? [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) )
              & ( member6330420149250801815od_b_c @ Q5 @ ( io_tar7088883562557314310_c_b_c @ M @ X3 @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
     => ~ ! [F2: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
            ( ! [Q9: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ Q9 @ ( io_tar7088883562557314310_c_b_c @ M @ ( F2 @ Q9 ) @ ( initia3567573336347591134_c_b_c @ M ) ) ) )
           => ~ ! [Q9: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_756_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_a_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q5: a] :
          ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ? [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) )
              & ( member_a @ Q5 @ ( io_targets_a_b_c @ M @ X3 @ ( initial_a_b_c @ M ) ) ) ) )
     => ~ ! [F2: a > list_P903359562653991662od_b_c] :
            ( ! [Q9: a] :
                ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( member_a @ Q9 @ ( io_targets_a_b_c @ M @ ( F2 @ Q9 ) @ ( initial_a_b_c @ M ) ) ) )
           => ~ ! [Q9: a] :
                  ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_757_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_d_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q5: d] :
          ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ? [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ SC ) )
              & ( member_d @ Q5 @ ( io_targets_d_b_c @ M @ X3 @ ( initial_d_b_c @ M ) ) ) ) )
     => ~ ! [F2: d > list_P903359562653991662od_b_c] :
            ( ! [Q9: d] :
                ( ( member_d @ Q9 @ ( reacha9185589339461546374_d_b_c @ M ) )
               => ( member_d @ Q9 @ ( io_targets_d_b_c @ M @ ( F2 @ Q9 ) @ ( initial_d_b_c @ M ) ) ) )
           => ~ ! [Q9: d] :
                  ( ( member_d @ Q9 @ ( reacha9185589339461546374_d_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_758_observable__language__target,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_759_observable__language__target,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_760_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: list_P903359562653991662od_b_c,T: fsm_li6801133765522507155_c_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ T2 @ ( io_tar7088883562557314310_c_b_c @ T @ Io1 @ ( initia3567573336347591134_c_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ ( initia3567573336347591134_c_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_761_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_762_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_763_observable__language__target,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: list_P903359562653991662od_b_c,T: fsm_li6801133765522507155_c_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ T2 @ ( io_tar7088883562557314310_c_b_c @ T @ Io1 @ ( initia3567573336347591134_c_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ ( initia3567573336347591134_c_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_764_observable__language__target,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_765_observable__language__target,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_766_observable__language__target__failure,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_767_observable__language__target__failure,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_768_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: list_P903359562653991662od_b_c,T: fsm_li6801133765522507155_c_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ T2 @ ( io_tar7088883562557314310_c_b_c @ T @ Io1 @ ( initia3567573336347591134_c_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ ( initia3567573336347591134_c_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_769_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_770_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_771_observable__language__target__failure,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: list_P903359562653991662od_b_c,T: fsm_li6801133765522507155_c_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ T2 @ ( io_tar7088883562557314310_c_b_c @ T @ Io1 @ ( initia3567573336347591134_c_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ T @ ( initia3567573336347591134_c_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_772_observable__language__target__failure,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: a,T: fsm_a_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member_a @ T2 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_773_observable__language__target__failure,axiom,
    ! [M: fsm_d_b_c,Q: d,Io1: list_P903359562653991662od_b_c,T2: d,T: fsm_d_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member_d @ Q @ ( io_targets_d_b_c @ M @ Io1 @ ( initial_d_b_c @ M ) ) )
       => ( ( member_d @ T2 @ ( io_targets_d_b_c @ T @ Io1 @ ( initial_d_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ T2 ) @ ( lS_d_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ T @ ( initial_d_b_c @ T ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_774_LS__from__LS__acyclic,axiom,
    ! [M: fsm_a_b_c] :
      ( ( acyclic_a_b_c @ M )
     => ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
        = ( lS_acyclic_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_775_LS__from__LS__acyclic,axiom,
    ! [M: fsm_d_b_c] :
      ( ( acyclic_d_b_c @ M )
     => ( ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) )
        = ( lS_acyclic_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_776_is__state__cover_Osimps,axiom,
    ( state_6970031540555430092_c_b_c
    = ( ^ [M2: fsm_li6801133765522507155_c_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ M2 ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ SC2 )
                  & ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ M2 @ Y2 @ ( initia3567573336347591134_c_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_777_is__state__cover_Osimps,axiom,
    ( state_2795256216244586588_a_b_c
    = ( ^ [M2: fsm_a_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ M2 ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ SC2 )
                  & ( member_a @ X2 @ ( io_targets_a_b_c @ M2 @ Y2 @ ( initial_a_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_778_is__state__cover_Osimps,axiom,
    ( state_1137167988099427039_d_b_c
    = ( ^ [M2: fsm_d_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X2: d] :
              ( ( member_d @ X2 @ ( reacha9185589339461546374_d_b_c @ M2 ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ SC2 )
                  & ( member_d @ X2 @ ( io_targets_d_b_c @ M2 @ Y2 @ ( initial_d_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_779_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_6970031540555430092_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ Xa )
                  & ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ X @ Y2 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_780_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_2795256216244586588_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ Xa )
                  & ( member_a @ X2 @ ( io_targets_a_b_c @ X @ Y2 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_781_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_1137167988099427039_d_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: d] :
              ( ( member_d @ X2 @ ( reacha9185589339461546374_d_b_c @ X ) )
             => ? [Y2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y2 @ Xa )
                  & ( member_d @ X2 @ ( io_targets_d_b_c @ X @ Y2 @ ( initial_d_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_782_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_6970031540555430092_c_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ? [Xa2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                  & ( member6330420149250801815od_b_c @ X4 @ ( io_tar7088883562557314310_c_b_c @ X @ Xa2 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_783_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_2795256216244586588_a_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X4: a] :
              ( ( member_a @ X4 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ? [Xa2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                  & ( member_a @ X4 @ ( io_targets_a_b_c @ X @ Xa2 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_784_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_1137167988099427039_d_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X4: d] :
              ( ( member_d @ X4 @ ( reacha9185589339461546374_d_b_c @ X ) )
             => ? [Xa2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                  & ( member_d @ X4 @ ( io_targets_d_b_c @ X @ Xa2 @ ( initial_d_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_785_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_6970031540555430092_c_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ X ) )
           => ? [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                & ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ X @ Xa3 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_786_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_2795256216244586588_a_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X3: a] :
            ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ X ) )
           => ? [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                & ( member_a @ X3 @ ( io_targets_a_b_c @ X @ Xa3 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_787_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_1137167988099427039_d_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X3: d] :
            ( ( member_d @ X3 @ ( reacha9185589339461546374_d_b_c @ X ) )
           => ? [Xa3: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                & ( member_d @ X3 @ ( io_targets_d_b_c @ X @ Xa3 @ ( initial_d_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_788_after__io__targets,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ( ( after_a_b_c @ M @ Q @ Io )
          = ( the_elem_a @ ( io_targets_a_b_c @ M @ Io @ Q ) ) ) ) ) ).

% after_io_targets
thf(fact_789_after__io__targets,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) )
       => ( ( after_d_b_c @ M @ Q @ Io )
          = ( the_elem_d @ ( io_targets_d_b_c @ M @ Io @ Q ) ) ) ) ) ).

% after_io_targets
thf(fact_790_observable__minimal__size__r__language__distinct,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ord_less_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) ) @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) )
             => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
               != ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% observable_minimal_size_r_language_distinct
thf(fact_791_observable__minimal__size__r__language__distinct,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_d_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_d_b_c @ M22 )
           => ( ( ord_less_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) ) @ ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M22 ) ) )
             => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
               != ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ) ) ).

% observable_minimal_size_r_language_distinct
thf(fact_792_observable__minimal__size__r__language__distinct,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( minimal_d_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_d_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ord_less_nat @ ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M1 ) ) @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) )
             => ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
               != ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% observable_minimal_size_r_language_distinct
thf(fact_793_observable__minimal__size__r__language__distinct,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( minimal_d_b_c @ M1 )
     => ( ( minimal_d_b_c @ M22 )
       => ( ( observable_d_b_c @ M1 )
         => ( ( observable_d_b_c @ M22 )
           => ( ( ord_less_nat @ ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M1 ) ) @ ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M22 ) ) )
             => ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
               != ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ) ) ).

% observable_minimal_size_r_language_distinct
thf(fact_794_find__remove_H_Oelims,axiom,
    ! [X: product_prod_b_c > $o,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: option1643449060076316019od_b_c] :
      ( ( ( find_r3073053696315353587od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_Product_prod_b_c )
         => ( Y != none_P5298055089671475982od_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xa
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ~ ( ( ( X @ X4 )
                   => ( Y
                      = ( some_P1625066591076178066od_b_c @ ( produc1467100693395308445od_b_c @ X4 @ ( append2547753245680614915od_b_c @ Xb @ Xs2 ) ) ) ) )
                  & ( ~ ( X @ X4 )
                   => ( Y
                      = ( find_r3073053696315353587od_b_c @ X @ Xs2 @ ( append2547753245680614915od_b_c @ Xb @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) ) ) ) ) ) ) ) ).

% find_remove'.elims
thf(fact_795_find__remove_H_Osimps_I1_J,axiom,
    ! [P: product_prod_b_c > $o,Uu2: list_P903359562653991662od_b_c] :
      ( ( find_r3073053696315353587od_b_c @ P @ nil_Product_prod_b_c @ Uu2 )
      = none_P5298055089671475982od_b_c ) ).

% find_remove'.simps(1)
thf(fact_796_find__remove_H__set_I2_J,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Prev2: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c,Xs4: list_l8907847357763382004od_b_c] :
      ( ( ( find_r4611264938487749881od_b_c @ P @ Xs @ Prev2 )
        = ( some_P6329742247110290194od_b_c @ ( produc169793319869648157od_b_c @ X @ Xs4 ) ) )
     => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ).

% find_remove'_set(2)
thf(fact_797_find__remove_H__set_I2_J,axiom,
    ! [P: a > $o,Xs: list_a,Prev2: list_a,X: a,Xs4: list_a] :
      ( ( ( find_remove_a2 @ P @ Xs @ Prev2 )
        = ( some_P8471903096582035730list_a @ ( produc6670463072477821725list_a @ X @ Xs4 ) ) )
     => ( member_a @ X @ ( set_a2 @ Xs ) ) ) ).

% find_remove'_set(2)
thf(fact_798_the__elem__set,axiom,
    ! [X: product_prod_b_c] :
      ( ( the_el5801713635627447133od_b_c @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = X ) ).

% the_elem_set
thf(fact_799_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) )
                = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_800_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_d_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_d_b_c @ M22 )
           => ( ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
             => ( ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) )
                = ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_801_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( minimal_d_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_d_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
                = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M1 ) )
                = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_802_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( minimal_d_b_c @ M1 )
     => ( ( minimal_d_b_c @ M22 )
       => ( ( observable_d_b_c @ M1 )
         => ( ( observable_d_b_c @ M22 )
           => ( ( ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) )
                = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
             => ( ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M1 ) )
                = ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_803_find__remove_H_Osimps_I2_J,axiom,
    ! [P: product_prod_b_c > $o,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Prev2: list_P903359562653991662od_b_c] :
      ( ( ( P @ X )
       => ( ( find_r3073053696315353587od_b_c @ P @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ Prev2 )
          = ( some_P1625066591076178066od_b_c @ ( produc1467100693395308445od_b_c @ X @ ( append2547753245680614915od_b_c @ Prev2 @ Xs ) ) ) ) )
      & ( ~ ( P @ X )
       => ( ( find_r3073053696315353587od_b_c @ P @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ Prev2 )
          = ( find_r3073053696315353587od_b_c @ P @ Xs @ ( append2547753245680614915od_b_c @ Prev2 @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) ) ) ) ) ).

% find_remove'.simps(2)
thf(fact_804_find__remove_H_Opelims,axiom,
    ! [X: product_prod_b_c > $o,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: option1643449060076316019od_b_c] :
      ( ( ( find_r3073053696315353587od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( ( accp_P1924572328958296190od_b_c @ find_r5358976936226027362od_b_c @ ( produc1005531610559690873od_b_c @ X @ ( produc3076307724246486423od_b_c @ Xa @ Xb ) ) )
       => ( ( ( Xa = nil_Product_prod_b_c )
           => ( ( Y = none_P5298055089671475982od_b_c )
             => ~ ( accp_P1924572328958296190od_b_c @ find_r5358976936226027362od_b_c @ ( produc1005531610559690873od_b_c @ X @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Xb ) ) ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( Xa
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( ( ( X @ X4 )
                     => ( Y
                        = ( some_P1625066591076178066od_b_c @ ( produc1467100693395308445od_b_c @ X4 @ ( append2547753245680614915od_b_c @ Xb @ Xs2 ) ) ) ) )
                    & ( ~ ( X @ X4 )
                     => ( Y
                        = ( find_r3073053696315353587od_b_c @ X @ Xs2 @ ( append2547753245680614915od_b_c @ Xb @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) ) ) ) )
                 => ~ ( accp_P1924572328958296190od_b_c @ find_r5358976936226027362od_b_c @ ( produc1005531610559690873od_b_c @ X @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ Xb ) ) ) ) ) ) ) ) ).

% find_remove'.pelims
thf(fact_805_find__remove__set_I2_J,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c,Xs4: list_l8907847357763382004od_b_c] :
      ( ( ( find_r7089894180088904034od_b_c @ P @ Xs )
        = ( some_P6329742247110290194od_b_c @ ( produc169793319869648157od_b_c @ X @ Xs4 ) ) )
     => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ).

% find_remove_set(2)
thf(fact_806_find__remove__set_I2_J,axiom,
    ! [P: a > $o,Xs: list_a,X: a,Xs4: list_a] :
      ( ( ( find_remove_a @ P @ Xs )
        = ( some_P8471903096582035730list_a @ ( produc6670463072477821725list_a @ X @ Xs4 ) ) )
     => ( member_a @ X @ ( set_a2 @ Xs ) ) ) ).

% find_remove_set(2)
thf(fact_807_enumerate__simps_I2_J,axiom,
    ! [N: nat,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( enumer6465649393455563597od_b_c @ N @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( cons_P4210672686487023319od_b_c @ ( produc4238952992575422783od_b_c @ N @ X ) @ ( enumer6465649393455563597od_b_c @ ( suc @ N ) @ Xs ) ) ) ).

% enumerate_simps(2)
thf(fact_808_enumerate__simps_I2_J,axiom,
    ! [N: nat,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( enumer6060834047297110355od_b_c @ N @ ( cons_l342771267123639716od_b_c @ X @ Xs ) )
      = ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ N @ X ) @ ( enumer6060834047297110355od_b_c @ ( suc @ N ) @ Xs ) ) ) ).

% enumerate_simps(2)
thf(fact_809_enumerate__simps_I1_J,axiom,
    ! [N: nat] :
      ( ( enumer6465649393455563597od_b_c @ N @ nil_Product_prod_b_c )
      = nil_Pr7533291033639376519od_b_c ) ).

% enumerate_simps(1)
thf(fact_810_find__remove_Osimps,axiom,
    ( find_r398788227580841692od_b_c
    = ( ^ [P6: product_prod_b_c > $o,Xs3: list_P903359562653991662od_b_c] : ( find_r3073053696315353587od_b_c @ P6 @ Xs3 @ nil_Product_prod_b_c ) ) ) ).

% find_remove.simps
thf(fact_811_find__remove_Oelims,axiom,
    ! [X: product_prod_b_c > $o,Xa: list_P903359562653991662od_b_c,Y: option1643449060076316019od_b_c] :
      ( ( ( find_r398788227580841692od_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( find_r3073053696315353587od_b_c @ X @ Xa @ nil_Product_prod_b_c ) ) ) ).

% find_remove.elims
thf(fact_812_product__lists_Osimps_I1_J,axiom,
    ( ( produc3104363228908302167od_b_c @ nil_li8071162985807626740od_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% product_lists.simps(1)
thf(fact_813_inter__list__set,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( inter_5071192024096513505od_b_c @ Xs @ Ys ) )
      = ( inf_in4978071631833541052od_b_c @ ( set_li4480668622519654659od_b_c @ Xs ) @ ( set_li4480668622519654659od_b_c @ Ys ) ) ) ).

% inter_list_set
thf(fact_814_list__ordered__pairs__set__containment,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ Xs ) )
       => ( ( X != Y )
         => ( ( member1533839430763132368od_b_c @ ( produc3076307724246486423od_b_c @ X @ Y ) @ ( set_Pr292865031892111420od_b_c @ ( list_o8363625500407931829od_b_c @ Xs ) ) )
            | ( member1533839430763132368od_b_c @ ( produc3076307724246486423od_b_c @ Y @ X ) @ ( set_Pr292865031892111420od_b_c @ ( list_o8363625500407931829od_b_c @ Xs ) ) ) ) ) ) ) ).

% list_ordered_pairs_set_containment
thf(fact_815_list__ordered__pairs__set__containment,axiom,
    ! [X: a,Xs: list_a,Y: a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ( member_a @ Y @ ( set_a2 @ Xs ) )
       => ( ( X != Y )
         => ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( set_Product_prod_a_a2 @ ( list_ordered_pairs_a @ Xs ) ) )
            | ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( set_Product_prod_a_a2 @ ( list_ordered_pairs_a @ Xs ) ) ) ) ) ) ) ).

% list_ordered_pairs_set_containment
thf(fact_816_update__with__aux_Osimps_I1_J,axiom,
    ! [V2: c,K3: b,F3: c > c] :
      ( ( update_with_aux_c_b @ V2 @ K3 @ F3 @ nil_Product_prod_b_c )
      = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F3 @ V2 ) ) @ nil_Product_prod_b_c ) ) ).

% update_with_aux.simps(1)
thf(fact_817_update__with__aux_Osimps_I1_J,axiom,
    ! [V2: list_P903359562653991662od_b_c,K3: nat,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( update3547200019653564_c_nat @ V2 @ K3 @ F3 @ nil_Pr679518533894577677od_b_c )
      = ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ K3 @ ( F3 @ V2 ) ) @ nil_Pr679518533894577677od_b_c ) ) ).

% update_with_aux.simps(1)
thf(fact_818_map__tailrec__rev_Opelims,axiom,
    ! [X: product_prod_b_c > product_prod_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( map_ta2658900722513622261od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( ( accp_P7655262136047134638od_b_c @ map_ta3552191613423382852od_b_c @ ( produc5829777284606927017od_b_c @ X @ ( produc3076307724246486423od_b_c @ Xa @ Xb ) ) )
       => ( ( ( Xa = nil_Product_prod_b_c )
           => ( ( Y = Xb )
             => ~ ( accp_P7655262136047134638od_b_c @ map_ta3552191613423382852od_b_c @ ( produc5829777284606927017od_b_c @ X @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Xb ) ) ) ) )
         => ~ ! [A3: product_prod_b_c,As: list_P903359562653991662od_b_c] :
                ( ( Xa
                  = ( cons_P4529483553340347422od_b_c @ A3 @ As ) )
               => ( ( Y
                    = ( map_ta2658900722513622261od_b_c @ X @ As @ ( cons_P4529483553340347422od_b_c @ ( X @ A3 ) @ Xb ) ) )
                 => ~ ( accp_P7655262136047134638od_b_c @ map_ta3552191613423382852od_b_c @ ( produc5829777284606927017od_b_c @ X @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ A3 @ As ) @ Xb ) ) ) ) ) ) ) ) ).

% map_tailrec_rev.pelims
thf(fact_819_map__tailrec__rev_Osimps_I2_J,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,A: product_prod_b_c,As2: list_P903359562653991662od_b_c,Bs2: list_P903359562653991662od_b_c] :
      ( ( map_ta2658900722513622261od_b_c @ F3 @ ( cons_P4529483553340347422od_b_c @ A @ As2 ) @ Bs2 )
      = ( map_ta2658900722513622261od_b_c @ F3 @ As2 @ ( cons_P4529483553340347422od_b_c @ ( F3 @ A ) @ Bs2 ) ) ) ).

% map_tailrec_rev.simps(2)
thf(fact_820_map__tailrec__rev_Oelims,axiom,
    ! [X: product_prod_b_c > product_prod_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( map_ta2658900722513622261od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_Product_prod_b_c )
         => ( Y != Xb ) )
       => ~ ! [A3: product_prod_b_c,As: list_P903359562653991662od_b_c] :
              ( ( Xa
                = ( cons_P4529483553340347422od_b_c @ A3 @ As ) )
             => ( Y
               != ( map_ta2658900722513622261od_b_c @ X @ As @ ( cons_P4529483553340347422od_b_c @ ( X @ A3 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_821_list__ordered__pairs_Osimps_I1_J,axiom,
    ( ( list_o804723041229831855od_b_c @ nil_Product_prod_b_c )
    = nil_Pr2945457328363356077od_b_c ) ).

% list_ordered_pairs.simps(1)
thf(fact_822_list__ordered__pairs_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( list_o804723041229831855od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y != nil_Pr2945457328363356077od_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ( Y
               != ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( list_o804723041229831855od_b_c @ Xs2 ) ) ) ) ) ) ).

% list_ordered_pairs.elims
thf(fact_823_convergence__graph__lookup__invar__def,axiom,
    ( conver7089555221631485247_c_d_g
    = ( ^ [M12: fsm_a_b_c,M23: fsm_d_b_c,Cg_lookup: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G: g] :
        ! [Alpha2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
         => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_d_b_c @ M23 @ ( initial_d_b_c @ M23 ) ) )
           => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup @ G @ Alpha2 ) ) )
              & ! [Beta2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Beta2 @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup @ G @ Alpha2 ) ) )
                 => ( ( converge_a_b_c @ M12 @ Alpha2 @ Beta2 )
                    & ( converge_d_b_c @ M23 @ Alpha2 @ Beta2 ) ) ) ) ) ) ) ) ).

% convergence_graph_lookup_invar_def
thf(fact_824_convergence__graph__lookup__invar__simp_I1_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( conver7089555221631485247_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup2 @ G2 @ Alpha ) ) )
           => ( converge_a_b_c @ M1 @ Alpha @ Beta ) ) ) ) ) ).

% convergence_graph_lookup_invar_simp(1)
thf(fact_825_list_Omap__disc__iff,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,A: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ A )
        = nil_Product_prod_b_c )
      = ( A = nil_Product_prod_b_c ) ) ).

% list.map_disc_iff
thf(fact_826_Nil__is__map__conv,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( nil_Product_prod_b_c
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Xs ) )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% Nil_is_map_conv
thf(fact_827_map__is__Nil__conv,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Xs )
        = nil_Product_prod_b_c )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% map_is_Nil_conv
thf(fact_828_map__append,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( map_Pr6384634858812015940od_b_c @ F3 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( append2547753245680614915od_b_c @ ( map_Pr6384634858812015940od_b_c @ F3 @ Xs ) @ ( map_Pr6384634858812015940od_b_c @ F3 @ Ys ) ) ) ).

% map_append
thf(fact_829_map__idI,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( set_li4480668622519654659od_b_c @ Xs ) )
         => ( ( F3 @ X4 )
            = X4 ) )
     => ( ( map_li8081432502061035332od_b_c @ F3 @ Xs )
        = Xs ) ) ).

% map_idI
thf(fact_830_map__idI,axiom,
    ! [Xs: list_a,F3: a > a] :
      ( ! [X4: a] :
          ( ( member_a @ X4 @ ( set_a2 @ Xs ) )
         => ( ( F3 @ X4 )
            = X4 ) )
     => ( ( map_a_a @ F3 @ Xs )
        = Xs ) ) ).

% map_idI
thf(fact_831_list_Omap__ident__strong,axiom,
    ! [T2: list_l8907847357763382004od_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ! [Z2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Z2 @ ( set_li4480668622519654659od_b_c @ T2 ) )
         => ( ( F3 @ Z2 )
            = Z2 ) )
     => ( ( map_li8081432502061035332od_b_c @ F3 @ T2 )
        = T2 ) ) ).

% list.map_ident_strong
thf(fact_832_list_Omap__ident__strong,axiom,
    ! [T2: list_a,F3: a > a] :
      ( ! [Z2: a] :
          ( ( member_a @ Z2 @ ( set_a2 @ T2 ) )
         => ( ( F3 @ Z2 )
            = Z2 ) )
     => ( ( map_a_a @ F3 @ T2 )
        = T2 ) ) ).

% list.map_ident_strong
thf(fact_833_append__eq__mapE,axiom,
    ! [Fl: list_P903359562653991662od_b_c,Fl2: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ls: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Fl @ Fl2 )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Ls ) )
     => ~ ! [L4: list_P903359562653991662od_b_c,L5: list_P903359562653991662od_b_c] :
            ( ( Ls
              = ( append2547753245680614915od_b_c @ L4 @ L5 ) )
           => ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ L4 )
                = Fl )
             => ( ( map_Pr6384634858812015940od_b_c @ F3 @ L5 )
               != Fl2 ) ) ) ) ).

% append_eq_mapE
thf(fact_834_map__eq__appendE,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Ls: list_P903359562653991662od_b_c,Fl: list_P903359562653991662od_b_c,Fl2: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Ls )
        = ( append2547753245680614915od_b_c @ Fl @ Fl2 ) )
     => ~ ! [L4: list_P903359562653991662od_b_c,L5: list_P903359562653991662od_b_c] :
            ( ( Ls
              = ( append2547753245680614915od_b_c @ L4 @ L5 ) )
           => ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ L4 )
                = Fl )
             => ( ( map_Pr6384634858812015940od_b_c @ F3 @ L5 )
               != Fl2 ) ) ) ) ).

% map_eq_appendE
thf(fact_835_Misc_Oappend__eq__map__conv,axiom,
    ! [Fl: list_P903359562653991662od_b_c,Fl2: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ls: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Fl @ Fl2 )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Ls ) )
      = ( ? [L6: list_P903359562653991662od_b_c,L7: list_P903359562653991662od_b_c] :
            ( ( Ls
              = ( append2547753245680614915od_b_c @ L6 @ L7 ) )
            & ( ( map_Pr6384634858812015940od_b_c @ F3 @ L6 )
              = Fl )
            & ( ( map_Pr6384634858812015940od_b_c @ F3 @ L7 )
              = Fl2 ) ) ) ) ).

% Misc.append_eq_map_conv
thf(fact_836_Misc_Omap__eq__append__conv,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Ls: list_P903359562653991662od_b_c,Fl: list_P903359562653991662od_b_c,Fl2: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Ls )
        = ( append2547753245680614915od_b_c @ Fl @ Fl2 ) )
      = ( ? [L6: list_P903359562653991662od_b_c,L7: list_P903359562653991662od_b_c] :
            ( ( Ls
              = ( append2547753245680614915od_b_c @ L6 @ L7 ) )
            & ( ( map_Pr6384634858812015940od_b_c @ F3 @ L6 )
              = Fl )
            & ( ( map_Pr6384634858812015940od_b_c @ F3 @ L7 )
              = Fl2 ) ) ) ) ).

% Misc.map_eq_append_conv
thf(fact_837_List_Omap__eq__append__conv,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Xs )
        = ( append2547753245680614915od_b_c @ Ys @ Zs ) )
      = ( ? [Us2: list_P903359562653991662od_b_c,Vs: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Pr6384634858812015940od_b_c @ F3 @ Us2 ) )
            & ( Zs
              = ( map_Pr6384634858812015940od_b_c @ F3 @ Vs ) ) ) ) ) ).

% List.map_eq_append_conv
thf(fact_838_List_Oappend__eq__map__conv,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Zs )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Xs ) )
      = ( ? [Us2: list_P903359562653991662od_b_c,Vs: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Pr6384634858812015940od_b_c @ F3 @ Us2 ) )
            & ( Zs
              = ( map_Pr6384634858812015940od_b_c @ F3 @ Vs ) ) ) ) ) ).

% List.append_eq_map_conv
thf(fact_839_list_Osimps_I8_J,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c] :
      ( ( map_Pr6384634858812015940od_b_c @ F3 @ nil_Product_prod_b_c )
      = nil_Product_prod_b_c ) ).

% list.simps(8)
thf(fact_840_map__consI_I2_J,axiom,
    ! [W: list_P903359562653991662od_b_c,L: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ww: list_P903359562653991662od_b_c,A: product_prod_b_c] :
      ( ( ( append2547753245680614915od_b_c @ W @ L )
        = ( append2547753245680614915od_b_c @ ( map_Pr6384634858812015940od_b_c @ F3 @ Ww ) @ L ) )
     => ( ( cons_P4529483553340347422od_b_c @ ( F3 @ A ) @ ( append2547753245680614915od_b_c @ W @ L ) )
        = ( append2547753245680614915od_b_c @ ( map_Pr6384634858812015940od_b_c @ F3 @ ( cons_P4529483553340347422od_b_c @ A @ Ww ) ) @ L ) ) ) ).

% map_consI(2)
thf(fact_841_list_Osimps_I9_J,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( ( map_Pr6384634858812015940od_b_c @ F3 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) )
      = ( cons_P4529483553340347422od_b_c @ ( F3 @ X21 ) @ ( map_Pr6384634858812015940od_b_c @ F3 @ X22 ) ) ) ).

% list.simps(9)
thf(fact_842_Cons__eq__map__D,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Ys ) )
     => ? [Z2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Ys
            = ( cons_P4529483553340347422od_b_c @ Z2 @ Zs3 ) )
          & ( X
            = ( F3 @ Z2 ) )
          & ( Xs
            = ( map_Pr6384634858812015940od_b_c @ F3 @ Zs3 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_843_map__eq__Cons__D,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Xs )
        = ( cons_P4529483553340347422od_b_c @ Y @ Ys ) )
     => ? [Z2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( cons_P4529483553340347422od_b_c @ Z2 @ Zs3 ) )
          & ( ( F3 @ Z2 )
            = Y )
          & ( ( map_Pr6384634858812015940od_b_c @ F3 @ Zs3 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_844_Cons__eq__map__conv,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Ys ) )
      = ( ? [Z3: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Ys
              = ( cons_P4529483553340347422od_b_c @ Z3 @ Zs2 ) )
            & ( X
              = ( F3 @ Z3 ) )
            & ( Xs
              = ( map_Pr6384634858812015940od_b_c @ F3 @ Zs2 ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_845_map__eq__Cons__conv,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Xs )
        = ( cons_P4529483553340347422od_b_c @ Y @ Ys ) )
      = ( ? [Z3: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( cons_P4529483553340347422od_b_c @ Z3 @ Zs2 ) )
            & ( ( F3 @ Z3 )
              = Y )
            & ( ( map_Pr6384634858812015940od_b_c @ F3 @ Zs2 )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_846_map__eq__consE,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Ls: list_P903359562653991662od_b_c,Fa: product_prod_b_c,Fl: list_P903359562653991662od_b_c] :
      ( ( ( map_Pr6384634858812015940od_b_c @ F3 @ Ls )
        = ( cons_P4529483553340347422od_b_c @ Fa @ Fl ) )
     => ~ ! [A3: product_prod_b_c,L4: list_P903359562653991662od_b_c] :
            ( ( Ls
              = ( cons_P4529483553340347422od_b_c @ A3 @ L4 ) )
           => ( ( ( F3 @ A3 )
                = Fa )
             => ( ( map_Pr6384634858812015940od_b_c @ F3 @ L4 )
               != Fl ) ) ) ) ).

% map_eq_consE
thf(fact_847_map__consI_I1_J,axiom,
    ! [W: list_P903359562653991662od_b_c,F3: product_prod_b_c > product_prod_b_c,Ww: list_P903359562653991662od_b_c,A: product_prod_b_c] :
      ( ( W
        = ( map_Pr6384634858812015940od_b_c @ F3 @ Ww ) )
     => ( ( cons_P4529483553340347422od_b_c @ ( F3 @ A ) @ W )
        = ( map_Pr6384634858812015940od_b_c @ F3 @ ( cons_P4529483553340347422od_b_c @ A @ Ww ) ) ) ) ).

% map_consI(1)
thf(fact_848_set__map__subset,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,T2: list_P903359562653991662od_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_li8081432502061035332od_b_c @ F3 @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) ) ) )
       => ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_li8081432502061035332od_b_c @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_849_set__map__subset,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,T2: a,F3: list_P903359562653991662od_b_c > a] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ( member_a @ T2 @ ( set_a2 @ ( map_li642343614954829908_b_c_a @ F3 @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) ) ) )
       => ( member_a @ T2 @ ( set_a2 @ ( map_li642343614954829908_b_c_a @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_850_set__map__subset,axiom,
    ! [X: a,Xs: list_a,T2: list_P903359562653991662od_b_c,F3: a > list_P903359562653991662od_b_c] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_a_6125361980051820212od_b_c @ F3 @ ( cons_a @ X @ nil_a ) ) ) )
       => ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_a_6125361980051820212od_b_c @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_851_set__map__subset,axiom,
    ! [X: a,Xs: list_a,T2: a,F3: a > a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ( member_a @ T2 @ ( set_a2 @ ( map_a_a @ F3 @ ( cons_a @ X @ nil_a ) ) ) )
       => ( member_a @ T2 @ ( set_a2 @ ( map_a_a @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_852_set__map__subset,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,T2: list_P903359562653991662od_b_c,F3: product_prod_b_c > list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_Pr719690668591373258od_b_c @ F3 @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) ) )
       => ( member6330420149250801815od_b_c @ T2 @ ( set_li4480668622519654659od_b_c @ ( map_Pr719690668591373258od_b_c @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_853_set__map__subset,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,T2: a,F3: product_prod_b_c > a] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ( member_a @ T2 @ ( set_a2 @ ( map_Pr8222292247188198874_b_c_a @ F3 @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) ) )
       => ( member_a @ T2 @ ( set_a2 @ ( map_Pr8222292247188198874_b_c_a @ F3 @ Xs ) ) ) ) ) ).

% set_map_subset
thf(fact_854_list__ordered__pairs_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( list_o804723041229831855od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X ) @ Xs ) @ ( list_o804723041229831855od_b_c @ Xs ) ) ) ).

% list_ordered_pairs.simps(2)
thf(fact_855_convergence__graph__lookup__invar__simp_I2_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( conver7089555221631485247_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup2 @ G2 @ Alpha ) ) )
           => ( converge_d_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ).

% convergence_graph_lookup_invar_simp(2)
thf(fact_856_linear__order__from__list__position_H_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( linear5647500195961616402od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y != nil_Pr2945457328363356077od_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ( Y
               != ( cons_P1038846555276421981od_b_c @ ( produc6366901981060558487od_b_c @ X4 @ X4 ) @ ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( linear5647500195961616402od_b_c @ Xs2 ) ) ) ) ) ) ) ).

% linear_order_from_list_position'.elims
thf(fact_857_get__extension__result_I3_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver6228549930694737538_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ) ) ).

% get_extension_result(3)
thf(fact_858_get__extension__result_I3_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver8229248357314462597_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ) ) ).

% get_extension_result(3)
thf(fact_859_get__extension__result_I3_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver9090253648251210306_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ) ) ).

% get_extension_result(3)
thf(fact_860_get__extension__result_I3_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver7089555221631485247_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ) ) ).

% get_extension_result(3)
thf(fact_861_linear__order__from__list__position_H_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( linear5647500195961616402od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( cons_P1038846555276421981od_b_c @ ( produc6366901981060558487od_b_c @ X @ X ) @ ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X ) @ Xs ) @ ( linear5647500195961616402od_b_c @ Xs ) ) ) ) ).

% linear_order_from_list_position'.simps(2)
thf(fact_862_prefixes_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ ( map_li8081432502061035332od_b_c @ ( cons_P4529483553340347422od_b_c @ X ) @ ( prefix1131979855692807669od_b_c @ Xs ) ) ) ) ).

% prefixes.simps(2)
thf(fact_863_linear__order__from__list__position_H_Osimps_I1_J,axiom,
    ( ( linear5647500195961616402od_b_c @ nil_Product_prod_b_c )
    = nil_Pr2945457328363356077od_b_c ) ).

% linear_order_from_list_position'.simps(1)
thf(fact_864_sublists_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( sublis8706766506341057792od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append6992831555715836169od_b_c @ ( sublis8706766506341057792od_b_c @ Xs ) @ ( map_li8081432502061035332od_b_c @ ( cons_P4529483553340347422od_b_c @ X ) @ ( prefix1131979855692807669od_b_c @ Xs ) ) ) ) ).

% sublists.simps(2)
thf(fact_865_get__extension__result_I2_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver6228549930694737538_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( converge_a_b_c @ M22 @ U2 @ U3 ) ) ) ) ) ) ).

% get_extension_result(2)
thf(fact_866_get__extension__result_I2_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver8229248357314462597_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( converge_a_b_c @ M22 @ U2 @ U3 ) ) ) ) ) ) ).

% get_extension_result(2)
thf(fact_867_get__extension__result_I2_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver9090253648251210306_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
             => ( converge_d_b_c @ M22 @ U2 @ U3 ) ) ) ) ) ) ).

% get_extension_result(2)
thf(fact_868_get__extension__result_I2_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver7089555221631485247_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
             => ( converge_d_b_c @ M22 @ U2 @ U3 ) ) ) ) ) ) ).

% get_extension_result(2)
thf(fact_869_get__extension__result_I1_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver6228549930694737538_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( converge_a_b_c @ M1 @ U2 @ U3 ) ) ) ) ) ).

% get_extension_result(1)
thf(fact_870_get__extension__result_I1_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_a_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
       => ( ( conver8229248357314462597_c_a_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( converge_d_b_c @ M1 @ U2 @ U3 ) ) ) ) ) ).

% get_extension_result(1)
thf(fact_871_get__extension__result_I1_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_d_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M1 @ ( initial_d_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver9090253648251210306_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( converge_d_b_c @ M1 @ U2 @ U3 ) ) ) ) ) ).

% get_extension_result(1)
thf(fact_872_get__extension__result_I1_J,axiom,
    ! [U2: list_P903359562653991662od_b_c,M1: fsm_a_b_c,M22: fsm_d_b_c,Cg_lookup2: g > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: g,T: prefix425356687782099470od_b_c,X: b,Y: c,U3: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) )
       => ( ( conver7089555221631485247_c_d_g @ M1 @ M22 @ Cg_lookup2 @ G2 )
         => ( ( ( interm365466133665009373_b_c_g @ T @ G2 @ Cg_lookup2 @ U2 @ X @ Y )
              = ( some_l689282263436086355od_b_c @ U3 ) )
           => ( converge_a_b_c @ M1 @ U2 @ U3 ) ) ) ) ) ).

% get_extension_result(1)
thf(fact_873_Some,axiom,
    ( ( interm365466133665009373_b_c_g @ t @ g2 @ cg_lookup @ v3 @ x @ y )
    = ( some_l689282263436086355od_b_c @ v2 ) ) ).

% Some
thf(fact_874_non__sym__dist__pairs_H_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( non_sy4916969364292876019od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y != nil_Pr2945457328363356077od_b_c ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ( Y
               != ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( non_sy4916969364292876019od_b_c @ Xs2 ) ) ) ) ) ) ).

% non_sym_dist_pairs'.elims
thf(fact_875_linear__order__from__list__position_H_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( linear5647500195961616402od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ linear4366178405326712835od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y = nil_Pr2945457328363356077od_b_c )
             => ~ ( accp_l4654477130474446199od_b_c @ linear4366178405326712835od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( Y
                    = ( cons_P1038846555276421981od_b_c @ ( produc6366901981060558487od_b_c @ X4 @ X4 ) @ ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( linear5647500195961616402od_b_c @ Xs2 ) ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ linear4366178405326712835od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ) ) ).

% linear_order_from_list_position'.pelims
thf(fact_876_assms_I10_J,axiom,
    conver7089555221631485247_c_d_g @ m1 @ m2 @ cg_lookup @ g2 ).

% assms(10)
thf(fact_877_non__sym__dist__pairs_H_Osimps_I1_J,axiom,
    ( ( non_sy4916969364292876019od_b_c @ nil_Product_prod_b_c )
    = nil_Pr2945457328363356077od_b_c ) ).

% non_sym_dist_pairs'.simps(1)
thf(fact_878_non__sym__dist__pairs_H_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( non_sy4916969364292876019od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X ) @ Xs ) @ ( non_sy4916969364292876019od_b_c @ Xs ) ) ) ).

% non_sym_dist_pairs'.simps(2)
thf(fact_879_u_H,axiom,
    ( u3
    = ( interm7381356855087595981od_b_c @ ( cg_lookup @ g2 @ ua ) @ ua ) ) ).

% u'
thf(fact_880_v_H,axiom,
    ( v3
    = ( interm7381356855087595981od_b_c @ ( cg_lookup @ g2 @ va ) @ va ) ) ).

% v'
thf(fact_881_list__ordered__pairs_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( list_o804723041229831855od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ list_o3318826711941139878od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y = nil_Pr2945457328363356077od_b_c )
             => ~ ( accp_l4654477130474446199od_b_c @ list_o3318826711941139878od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( Y
                    = ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( list_o804723041229831855od_b_c @ Xs2 ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ list_o3318826711941139878od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ) ) ).

% list_ordered_pairs.pelims
thf(fact_882_non__sym__dist__pairs_H_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P7987531494101635245od_b_c] :
      ( ( ( non_sy4916969364292876019od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ non_sy5902841407094123106od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y = nil_Pr2945457328363356077od_b_c )
             => ~ ( accp_l4654477130474446199od_b_c @ non_sy5902841407094123106od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( Y
                    = ( append5486846175084624706od_b_c @ ( map_Pr8917322328026853507od_b_c @ ( produc6366901981060558487od_b_c @ X4 ) @ Xs2 ) @ ( non_sy4916969364292876019od_b_c @ Xs2 ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ non_sy5902841407094123106od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ) ) ).

% non_sym_dist_pairs'.pelims
thf(fact_883_suffixes_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_l8907847357763382004od_b_c] :
      ( ( ( suffix2151784340763841114od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ suffix5297622422209064891od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y
                = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) )
             => ~ ( accp_l4654477130474446199od_b_c @ suffix5297622422209064891od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( Y
                    = ( append6992831555715836169od_b_c @ ( suffix2151784340763841114od_b_c @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ nil_li8071162985807626740od_b_c ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ suffix5297622422209064891od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ) ) ).

% suffixes.pelims
thf(fact_884_res,axiom,
    ( ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ ua @ va @ ( suc @ ka ) )
    = ( foldl_4971804256590438578od_b_c @ tryIO @ ( produc8137419655804493381od_b_c @ minEst0 @ nil_Product_prod_b_c ) @ xy ) ) ).

% res
thf(fact_885_minEst0,axiom,
    ( minEst0
    = ( plus_plus_nat @ ( plus_plus_nat @ ( size_s3392097710323735898od_b_c @ bestPrefix0 ) @ ( if_nat @ ( interm5195843386759618246_b_c_g @ t @ g2 @ cg_lookup @ u3 ) @ zero_zero_nat @ ( size_s3392097710323735898od_b_c @ u3 ) ) ) @ ( if_nat @ ( interm5195843386759618246_b_c_g @ t @ g2 @ cg_lookup @ v3 ) @ zero_zero_nat @ ( size_s3392097710323735898od_b_c @ v3 ) ) ) ) ).

% minEst0
thf(fact_886_append__eq__append__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Us: list_P903359562653991662od_b_c,Vs2: list_P903359562653991662od_b_c] :
      ( ( ( ( size_s3392097710323735898od_b_c @ Xs )
          = ( size_s3392097710323735898od_b_c @ Ys ) )
        | ( ( size_s3392097710323735898od_b_c @ Us )
          = ( size_s3392097710323735898od_b_c @ Vs2 ) ) )
     => ( ( ( append2547753245680614915od_b_c @ Xs @ Us )
          = ( append2547753245680614915od_b_c @ Ys @ Vs2 ) )
        = ( ( Xs = Ys )
          & ( Us = Vs2 ) ) ) ) ).

% append_eq_append_conv
thf(fact_887_length__map,axiom,
    ! [F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ ( map_Pr6384634858812015940od_b_c @ F3 @ Xs ) )
      = ( size_s3392097710323735898od_b_c @ Xs ) ) ).

% length_map
thf(fact_888_foldl__append,axiom,
    ! [F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,A: produc3246581702073416851od_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( foldl_4971804256590438578od_b_c @ F3 @ A @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( foldl_4971804256590438578od_b_c @ F3 @ ( foldl_4971804256590438578od_b_c @ F3 @ A @ Xs ) @ Ys ) ) ).

% foldl_append
thf(fact_889_length__enumerate,axiom,
    ! [N: nat,Xs: list_P903359562653991662od_b_c] :
      ( ( size_s6608733560997646641od_b_c @ ( enumer6465649393455563597od_b_c @ N @ Xs ) )
      = ( size_s3392097710323735898od_b_c @ Xs ) ) ).

% length_enumerate
thf(fact_890_length__0__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = zero_zero_nat )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% length_0_conv
thf(fact_891_length__append,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( plus_plus_nat @ ( size_s3392097710323735898od_b_c @ Xs ) @ ( size_s3392097710323735898od_b_c @ Ys ) ) ) ).

% length_append
thf(fact_892_length__ge__1__conv,axiom,
    ! [L: list_P903359562653991662od_b_c] :
      ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s3392097710323735898od_b_c @ L ) )
      = ( L != nil_Product_prod_b_c ) ) ).

% length_ge_1_conv
thf(fact_893_length__greater__0__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s3392097710323735898od_b_c @ Xs ) )
      = ( Xs != nil_Product_prod_b_c ) ) ).

% length_greater_0_conv
thf(fact_894_length__compl__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,L: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [E4: product_prod_b_c,L4: list_P903359562653991662od_b_c] :
            ( ! [Ll2: list_P903359562653991662od_b_c] :
                ( ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ Ll2 ) @ ( size_s3392097710323735898od_b_c @ L4 ) )
               => ( P @ Ll2 ) )
           => ( P @ ( cons_P4529483553340347422od_b_c @ E4 @ L4 ) ) )
       => ( P @ L ) ) ) ).

% length_compl_induct
thf(fact_895_list__induct2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
       => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
              ( ( ( size_s3392097710323735898od_b_c @ Xs2 )
                = ( size_s3392097710323735898od_b_c @ Ys3 ) )
             => ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% list_induct2
thf(fact_896_list__induct3,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( ( ( size_s3392097710323735898od_b_c @ Ys )
          = ( size_s3392097710323735898od_b_c @ Zs ) )
       => ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
         => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c,Z2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
                ( ( ( size_s3392097710323735898od_b_c @ Xs2 )
                  = ( size_s3392097710323735898od_b_c @ Ys3 ) )
               => ( ( ( size_s3392097710323735898od_b_c @ Ys3 )
                    = ( size_s3392097710323735898od_b_c @ Zs3 ) )
                 => ( ( P @ Xs2 @ Ys3 @ Zs3 )
                   => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) @ ( cons_P4529483553340347422od_b_c @ Z2 @ Zs3 ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).

% list_induct3
thf(fact_897_list__induct4,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,Ws: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( ( ( size_s3392097710323735898od_b_c @ Ys )
          = ( size_s3392097710323735898od_b_c @ Zs ) )
       => ( ( ( size_s3392097710323735898od_b_c @ Zs )
            = ( size_s3392097710323735898od_b_c @ Ws ) )
         => ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
           => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c,Z2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c,W5: product_prod_b_c,Ws2: list_P903359562653991662od_b_c] :
                  ( ( ( size_s3392097710323735898od_b_c @ Xs2 )
                    = ( size_s3392097710323735898od_b_c @ Ys3 ) )
                 => ( ( ( size_s3392097710323735898od_b_c @ Ys3 )
                      = ( size_s3392097710323735898od_b_c @ Zs3 ) )
                   => ( ( ( size_s3392097710323735898od_b_c @ Zs3 )
                        = ( size_s3392097710323735898od_b_c @ Ws2 ) )
                     => ( ( P @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
                       => ( P @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) @ ( cons_P4529483553340347422od_b_c @ Z2 @ Zs3 ) @ ( cons_P4529483553340347422od_b_c @ W5 @ Ws2 ) ) ) ) ) )
             => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).

% list_induct4
thf(fact_898_foldl__Cons,axiom,
    ! [F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,A: produc3246581702073416851od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( foldl_4971804256590438578od_b_c @ F3 @ A @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( foldl_4971804256590438578od_b_c @ F3 @ ( F3 @ A @ X ) @ Xs ) ) ).

% foldl_Cons
thf(fact_899_list_Osize_I4_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) )
      = ( plus_plus_nat @ ( size_s3392097710323735898od_b_c @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).

% list.size(4)
thf(fact_900_impossible__Cons,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ Xs ) @ ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( Xs
       != ( cons_P4529483553340347422od_b_c @ X @ Ys ) ) ) ).

% impossible_Cons
thf(fact_901_in__set__product__lists__length,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Xss2: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( produc3104363228908302167od_b_c @ Xss2 ) ) )
     => ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( size_s4150533072628932448od_b_c @ Xss2 ) ) ) ).

% in_set_product_lists_length
thf(fact_902_foldl__Nil,axiom,
    ! [F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,A: produc3246581702073416851od_b_c] :
      ( ( foldl_4971804256590438578od_b_c @ F3 @ A @ nil_Product_prod_b_c )
      = A ) ).

% foldl_Nil
thf(fact_903_length__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ! [Xs2: list_P903359562653991662od_b_c] :
          ( ! [Ys7: list_P903359562653991662od_b_c] :
              ( ( ord_less_nat @ ( size_s3392097710323735898od_b_c @ Ys7 ) @ ( size_s3392097710323735898od_b_c @ Xs2 ) )
             => ( P @ Ys7 ) )
         => ( P @ Xs2 ) )
     => ( P @ Xs ) ) ).

% length_induct
thf(fact_904_neq__if__length__neq,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
       != ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( Xs != Ys ) ) ).

% neq_if_length_neq
thf(fact_905_Ex__list__of__length,axiom,
    ! [N: nat] :
    ? [Xs2: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ Xs2 )
      = N ) ).

% Ex_list_of_length
thf(fact_906_foldl__cong,axiom,
    ! [A: produc3246581702073416851od_b_c,B: produc3246581702073416851od_b_c,L: list_P903359562653991662od_b_c,K3: list_P903359562653991662od_b_c,F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,G3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c] :
      ( ( A = B )
     => ( ( L = K3 )
       => ( ! [A3: produc3246581702073416851od_b_c,X4: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ L ) )
             => ( ( F3 @ A3 @ X4 )
                = ( G3 @ A3 @ X4 ) ) )
         => ( ( foldl_4971804256590438578od_b_c @ F3 @ A @ L )
            = ( foldl_4971804256590438578od_b_c @ G3 @ B @ K3 ) ) ) ) ) ).

% foldl_cong
thf(fact_907_list__rest__coinc,axiom,
    ! [S22: list_P903359562653991662od_b_c,S1: list_P903359562653991662od_b_c,R1: list_P903359562653991662od_b_c,R2: list_P903359562653991662od_b_c] :
      ( ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ S22 ) @ ( size_s3392097710323735898od_b_c @ S1 ) )
     => ( ( ( append2547753245680614915od_b_c @ S1 @ R1 )
          = ( append2547753245680614915od_b_c @ S22 @ R2 ) )
       => ? [R1p: list_P903359562653991662od_b_c] :
            ( R2
            = ( append2547753245680614915od_b_c @ R1p @ R1 ) ) ) ) ).

% list_rest_coinc
thf(fact_908_enumerate__append__eq,axiom,
    ! [N: nat,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( enumer6465649393455563597od_b_c @ N @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( append2730124374675813042od_b_c @ ( enumer6465649393455563597od_b_c @ N @ Xs ) @ ( enumer6465649393455563597od_b_c @ ( plus_plus_nat @ N @ ( size_s3392097710323735898od_b_c @ Xs ) ) @ Ys ) ) ) ).

% enumerate_append_eq
thf(fact_909_card__length,axiom,
    ! [Xs: list_P903359562653991662od_b_c] : ( ord_less_eq_nat @ ( finite2007600076630979216od_b_c @ ( set_Product_prod_b_c2 @ Xs ) ) @ ( size_s3392097710323735898od_b_c @ Xs ) ) ).

% card_length
thf(fact_910_len__greater__imp__nonempty,axiom,
    ! [X: nat,L: list_P903359562653991662od_b_c] :
      ( ( ord_less_nat @ X @ ( size_s3392097710323735898od_b_c @ L ) )
     => ( L != nil_Product_prod_b_c ) ) ).

% len_greater_imp_nonempty
thf(fact_911_list_Osize_I3_J,axiom,
    ( ( size_s3392097710323735898od_b_c @ nil_Product_prod_b_c )
    = zero_zero_nat ) ).

% list.size(3)
thf(fact_912_Suc__le__length__iff,axiom,
    ! [N: nat,Xs: list_P903359562653991662od_b_c] :
      ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s3392097710323735898od_b_c @ Xs ) )
      = ( ? [X2: product_prod_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( cons_P4529483553340347422od_b_c @ X2 @ Ys4 ) )
            & ( ord_less_eq_nat @ N @ ( size_s3392097710323735898od_b_c @ Ys4 ) ) ) ) ) ).

% Suc_le_length_iff
thf(fact_913_length__Suc__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,N: nat] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( suc @ N ) )
      = ( ? [Y2: product_prod_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( cons_P4529483553340347422od_b_c @ Y2 @ Ys4 ) )
            & ( ( size_s3392097710323735898od_b_c @ Ys4 )
              = N ) ) ) ) ).

% length_Suc_conv
thf(fact_914_Suc__length__conv,axiom,
    ! [N: nat,Xs: list_P903359562653991662od_b_c] :
      ( ( ( suc @ N )
        = ( size_s3392097710323735898od_b_c @ Xs ) )
      = ( ? [Y2: product_prod_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( cons_P4529483553340347422od_b_c @ Y2 @ Ys4 ) )
            & ( ( size_s3392097710323735898od_b_c @ Ys4 )
              = N ) ) ) ) ).

% Suc_length_conv
thf(fact_915_length__n__lists__elem,axiom,
    ! [Ys: list_P903359562653991662od_b_c,N: nat,Xs: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Ys @ ( set_li4480668622519654659od_b_c @ ( n_list5224936925692304502od_b_c @ N @ Xs ) ) )
     => ( ( size_s3392097710323735898od_b_c @ Ys )
        = N ) ) ).

% length_n_lists_elem
thf(fact_916_minimally__distinguishes__def,axiom,
    ( minima243535863231358885_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q12: a,Q22: a,Io4: list_P903359562653991662od_b_c] :
          ( ( distinguishes_a_b_c @ M2 @ Q12 @ Q22 @ Io4 )
          & ! [Io7: list_P903359562653991662od_b_c] :
              ( ( distinguishes_a_b_c @ M2 @ Q12 @ Q22 @ Io7 )
             => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ Io4 ) @ ( size_s3392097710323735898od_b_c @ Io7 ) ) ) ) ) ) ).

% minimally_distinguishes_def
thf(fact_917_rev__induct2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
       => ( ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
              ( ( ( size_s3392097710323735898od_b_c @ Xs2 )
                = ( size_s3392097710323735898od_b_c @ Ys3 ) )
             => ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% rev_induct2
thf(fact_918_same__length__different,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( Xs != Ys )
     => ( ( ( size_s3392097710323735898od_b_c @ Xs )
          = ( size_s3392097710323735898od_b_c @ Ys ) )
       => ? [Pre: list_P903359562653991662od_b_c,X4: product_prod_b_c,Xs5: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys5: list_P903359562653991662od_b_c] :
            ( ( X4 != Y3 )
            & ( Xs
              = ( append2547753245680614915od_b_c @ Pre @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) @ Xs5 ) ) )
            & ( Ys
              = ( append2547753245680614915od_b_c @ Pre @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) @ Ys5 ) ) ) ) ) ) ).

% same_length_different
thf(fact_919_length__compl__rev__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,L: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [L4: list_P903359562653991662od_b_c,E4: product_prod_b_c] :
            ( ! [Ll2: list_P903359562653991662od_b_c] :
                ( ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ Ll2 ) @ ( size_s3392097710323735898od_b_c @ L4 ) )
               => ( P @ Ll2 ) )
           => ( P @ ( append2547753245680614915od_b_c @ L4 @ ( cons_P4529483553340347422od_b_c @ E4 @ nil_Product_prod_b_c ) ) ) )
       => ( P @ L ) ) ) ).

% length_compl_rev_induct
thf(fact_920_length__pos__if__in__set,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ord_less_nat @ zero_zero_nat @ ( size_s4150533072628932448od_b_c @ Xs ) ) ) ).

% length_pos_if_in_set
thf(fact_921_length__pos__if__in__set,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) ) ) ).

% length_pos_if_in_set
thf(fact_922_length__pos__if__in__set,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ord_less_nat @ zero_zero_nat @ ( size_s3392097710323735898od_b_c @ Xs ) ) ) ).

% length_pos_if_in_set
thf(fact_923_foldl__rule,axiom,
    ! [I: produc3246581702073416851od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Sigma_0: produc3246581702073416851od_b_c,L0: list_P903359562653991662od_b_c,F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c] :
      ( ( I @ Sigma_0 @ nil_Product_prod_b_c @ L0 )
     => ( ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,X4: product_prod_b_c,Sigma: produc3246581702073416851od_b_c] :
            ( ( L0
              = ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) ) )
           => ( ( I @ Sigma @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) )
             => ( I @ ( F3 @ Sigma @ X4 ) @ ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ L22 ) ) )
       => ( I @ ( foldl_4971804256590438578od_b_c @ F3 @ Sigma_0 @ L0 ) @ L0 @ nil_Product_prod_b_c ) ) ) ).

% foldl_rule
thf(fact_924_foldl__rule__P,axiom,
    ! [I: produc3246581702073416851od_b_c > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Sigma_0: produc3246581702073416851od_b_c,L0: list_P903359562653991662od_b_c,F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,P: produc3246581702073416851od_b_c > $o] :
      ( ( I @ Sigma_0 @ nil_Product_prod_b_c @ L0 )
     => ( ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,X4: product_prod_b_c,Sigma: produc3246581702073416851od_b_c] :
            ( ( L0
              = ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) ) )
           => ( ( I @ Sigma @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) )
             => ( I @ ( F3 @ Sigma @ X4 ) @ ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ nil_Product_prod_b_c ) ) @ L22 ) ) )
       => ( ! [Sigma: produc3246581702073416851od_b_c] :
              ( ( I @ Sigma @ L0 @ nil_Product_prod_b_c )
             => ( P @ Sigma ) )
         => ( P @ ( foldl_4971804256590438578od_b_c @ F3 @ Sigma_0 @ L0 ) ) ) ) ) ).

% foldl_rule_P
thf(fact_925_foldl__rule__aux,axiom,
    ! [I: produc3246581702073416851od_b_c > list_P903359562653991662od_b_c > $o,Sigma_0: produc3246581702073416851od_b_c,L0: list_P903359562653991662od_b_c,F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c] :
      ( ( I @ Sigma_0 @ L0 )
     => ( ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,X4: product_prod_b_c,Sigma: produc3246581702073416851od_b_c] :
            ( ( L0
              = ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) ) )
           => ( ( I @ Sigma @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) )
             => ( I @ ( F3 @ Sigma @ X4 ) @ L22 ) ) )
       => ( I @ ( foldl_4971804256590438578od_b_c @ F3 @ Sigma_0 @ L0 ) @ nil_Product_prod_b_c ) ) ) ).

% foldl_rule_aux
thf(fact_926_foldl__rule__aux__P,axiom,
    ! [I: produc3246581702073416851od_b_c > list_P903359562653991662od_b_c > $o,Sigma_0: produc3246581702073416851od_b_c,L0: list_P903359562653991662od_b_c,F3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,P: produc3246581702073416851od_b_c > $o] :
      ( ( I @ Sigma_0 @ L0 )
     => ( ! [L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,X4: product_prod_b_c,Sigma: produc3246581702073416851od_b_c] :
            ( ( L0
              = ( append2547753245680614915od_b_c @ L12 @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) ) )
           => ( ( I @ Sigma @ ( cons_P4529483553340347422od_b_c @ X4 @ L22 ) )
             => ( I @ ( F3 @ Sigma @ X4 ) @ L22 ) ) )
       => ( ! [Sigma: produc3246581702073416851od_b_c] :
              ( ( I @ Sigma @ nil_Product_prod_b_c )
             => ( P @ Sigma ) )
         => ( P @ ( foldl_4971804256590438578od_b_c @ F3 @ Sigma_0 @ L0 ) ) ) ) ) ).

% foldl_rule_aux_P
thf(fact_927_length__Suc__rev__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,N: nat] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( suc @ N ) )
      = ( ? [Ys4: list_P903359562653991662od_b_c,Y2: product_prod_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ Y2 @ nil_Product_prod_b_c ) ) )
            & ( ( size_s3392097710323735898od_b_c @ Ys4 )
              = N ) ) ) ) ).

% length_Suc_rev_conv
thf(fact_928_length__Suc__conv__rev,axiom,
    ! [Xs: list_P903359562653991662od_b_c,N: nat] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
        = ( suc @ N ) )
      = ( ? [Y2: product_prod_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ Y2 @ nil_Product_prod_b_c ) ) )
            & ( ( size_s3392097710323735898od_b_c @ Ys4 )
              = N ) ) ) ) ).

% length_Suc_conv_rev
thf(fact_929_res_H,axiom,
    ( ( ( ~ ( prefix4064274009650901372od_b_c @ t @ u3 )
        | ~ ( prefix4064274009650901372od_b_c @ t @ v3 ) )
     => ( ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ ua @ va @ ( suc @ ka ) )
        = ( produc8137419655804493381od_b_c @ errorValue @ nil_Product_prod_b_c ) ) )
    & ( ~ ( ~ ( prefix4064274009650901372od_b_c @ t @ u3 )
          | ~ ( prefix4064274009650901372od_b_c @ t @ v3 ) )
     => ( ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ ua @ va @ ( suc @ ka ) )
        = ( foldl_4971804256590438578od_b_c @ tryIO @ ( produc8137419655804493381od_b_c @ minEst0 @ nil_Product_prod_b_c ) @ xy ) ) ) ) ).

% res'
thf(fact_930_length__append__singleton,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( size_s3392097710323735898od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = ( suc @ ( size_s3392097710323735898od_b_c @ Xs ) ) ) ).

% length_append_singleton
thf(fact_931_foldl__conc__empty__eq,axiom,
    ! [I2: list_P903359562653991662od_b_c,Ww: list_l8907847357763382004od_b_c] :
      ( ( foldl_8708832512819626401od_b_c @ append2547753245680614915od_b_c @ I2 @ Ww )
      = ( append2547753245680614915od_b_c @ I2 @ ( foldl_8708832512819626401od_b_c @ append2547753245680614915od_b_c @ nil_Product_prod_b_c @ Ww ) ) ) ).

% foldl_conc_empty_eq
thf(fact_932_isin__prefix,axiom,
    ! [T2: prefix425356687782099470od_b_c,Xs: list_P903359562653991662od_b_c,Xs4: list_P903359562653991662od_b_c] :
      ( ( prefix4064274009650901372od_b_c @ T2 @ ( append2547753245680614915od_b_c @ Xs @ Xs4 ) )
     => ( prefix4064274009650901372od_b_c @ T2 @ Xs ) ) ).

% isin_prefix
thf(fact_933_isin_Osimps_I1_J,axiom,
    ! [T2: prefix425356687782099470od_b_c] : ( prefix4064274009650901372od_b_c @ T2 @ nil_Product_prod_b_c ) ).

% isin.simps(1)
thf(fact_934_length__Cons,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( suc @ ( size_s3392097710323735898od_b_c @ Xs ) ) ) ).

% length_Cons
thf(fact_935_XY,axiom,
    ( xy
    = ( product_b_c @ ( inputs_as_list_a_b_c @ m1 ) @ ( output4084235763626582864_a_b_c @ m1 ) ) ) ).

% XY
thf(fact_936_List_Oproduct_Osimps_I1_J,axiom,
    ! [Uu2: list_c] :
      ( ( product_b_c @ nil_b @ Uu2 )
      = nil_Product_prod_b_c ) ).

% List.product.simps(1)
thf(fact_937_List_Oproduct_Osimps_I2_J,axiom,
    ! [X: b,Xs: list_b,Ys: list_c] :
      ( ( product_b_c @ ( cons_b @ X @ Xs ) @ Ys )
      = ( append2547753245680614915od_b_c @ ( map_c_3793715988870728620od_b_c @ ( product_Pair_b_c @ X ) @ Ys ) @ ( product_b_c @ Xs @ Ys ) ) ) ).

% List.product.simps(2)
thf(fact_938_List_Oproduct_Osimps_I2_J,axiom,
    ! [X: nat,Xs: list_nat,Ys: list_l8907847357763382004od_b_c] :
      ( ( produc6636321582557677079od_b_c @ ( cons_nat @ X @ Xs ) @ Ys )
      = ( append1310559846384609464od_b_c @ ( map_li472403623484853437od_b_c @ ( produc8137419655804493381od_b_c @ X ) @ Ys ) @ ( produc6636321582557677079od_b_c @ Xs @ Ys ) ) ) ).

% List.product.simps(2)
thf(fact_939_Suc_OIH,axiom,
    ! [U2: list_P903359562653991662od_b_c,V2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
     => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) )
       => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) )
         => ( ( member6330420149250801815od_b_c @ V2 @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) )
           => ( ( ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ U2 )
               != ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ V2 ) )
             => ( ( ( ( produc3608113002378536793od_b_c @ ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ U2 @ V2 @ ka ) )
                    = zero_zero_nat )
                 => ~ ( converge_d_b_c @ m2 @ U2 @ V2 ) )
                & ( ( ( produc3608113002378536793od_b_c @ ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ U2 @ V2 @ ka ) )
                   != zero_zero_nat )
                 => ? [Gamma2: list_P903359562653991662od_b_c] : ( distinguishes_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ U2 ) @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ V2 ) @ ( append2547753245680614915od_b_c @ ( produc2468146899304044183od_b_c @ ( interm5402096062465699177_b_c_g @ m1 @ t @ g2 @ cg_lookup @ get_di7968643222313865723_trace @ U2 @ V2 @ ka ) ) @ Gamma2 ) ) ) ) ) ) ) ) ) ).

% Suc.IH
thf(fact_940_prod_Ocollapse,axiom,
    ! [Prod: product_prod_b_c] :
      ( ( product_Pair_b_c @ ( product_fst_b_c @ Prod ) @ ( product_snd_b_c @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_941_prod_Ocollapse,axiom,
    ! [Prod: produc3246581702073416851od_b_c] :
      ( ( produc8137419655804493381od_b_c @ ( produc3608113002378536793od_b_c @ Prod ) @ ( produc2468146899304044183od_b_c @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_942_map__snd__enumerate,axiom,
    ! [N: nat,Xs: list_l8907847357763382004od_b_c] :
      ( ( map_Pr5536700448928023253od_b_c @ produc2468146899304044183od_b_c @ ( enumer6060834047297110355od_b_c @ N @ Xs ) )
      = Xs ) ).

% map_snd_enumerate
thf(fact_943_fsm__transition__target,axiom,
    ! [T2: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
     => ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) @ ( states_a_b_c @ M ) ) ) ).

% fsm_transition_target
thf(fact_944_map__snd__mk__fst,axiom,
    ! [K3: b,L: list_c] :
      ( ( map_Pr8222292247188198876_b_c_c @ product_snd_b_c @ ( map_c_3793715988870728620od_b_c @ ( product_Pair_b_c @ K3 ) @ L ) )
      = L ) ).

% map_snd_mk_fst
thf(fact_945_map__snd__mk__fst,axiom,
    ! [K3: nat,L: list_l8907847357763382004od_b_c] :
      ( ( map_Pr5536700448928023253od_b_c @ produc2468146899304044183od_b_c @ ( map_li472403623484853437od_b_c @ ( produc8137419655804493381od_b_c @ K3 ) @ L ) )
      = L ) ).

% map_snd_mk_fst
thf(fact_946_map__fst__mk__snd,axiom,
    ! [K3: c,L: list_b] :
      ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c
        @ ( map_b_4433156289202544749od_b_c
          @ ^ [X2: b] : ( product_Pair_b_c @ X2 @ K3 )
          @ L ) )
      = L ) ).

% map_fst_mk_snd
thf(fact_947_map__fst__mk__snd,axiom,
    ! [K3: list_P903359562653991662od_b_c,L: list_nat] :
      ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c
        @ ( map_na7852381390595483433od_b_c
          @ ^ [X2: nat] : ( produc8137419655804493381od_b_c @ X2 @ K3 )
          @ L ) )
      = L ) ).

% map_fst_mk_snd
thf(fact_948_suffixes__snoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( suffix3867853578027978934od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c
        @ ( map_li8081432502061035332od_b_c
          @ ^ [Ys4: list_P903359562653991662od_b_c] : ( append2547753245680614915od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) )
          @ ( suffix3867853578027978934od_b_c @ Xs ) ) ) ) ).

% suffixes_snoc
thf(fact_949_foldl__map,axiom,
    ! [G3: produc3246581702073416851od_b_c > product_prod_b_c > produc3246581702073416851od_b_c,A: produc3246581702073416851od_b_c,F3: product_prod_b_c > product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( foldl_4971804256590438578od_b_c @ G3 @ A @ ( map_Pr6384634858812015940od_b_c @ F3 @ Xs ) )
      = ( foldl_4971804256590438578od_b_c
        @ ^ [A6: produc3246581702073416851od_b_c,X2: product_prod_b_c] : ( G3 @ A6 @ ( F3 @ X2 ) )
        @ A
        @ Xs ) ) ).

% foldl_map
thf(fact_950_shortest__list__or__default_Osimps,axiom,
    ( interm7381356855087595981od_b_c
    = ( ^ [Xs3: list_l8907847357763382004od_b_c,X2: list_P903359562653991662od_b_c] :
          ( foldl_8708832512819626401od_b_c
          @ ^ [A6: list_P903359562653991662od_b_c,B6: list_P903359562653991662od_b_c] : ( if_lis437861846949295796od_b_c @ ( ord_less_nat @ ( size_s3392097710323735898od_b_c @ A6 ) @ ( size_s3392097710323735898od_b_c @ B6 ) ) @ A6 @ B6 )
          @ X2
          @ Xs3 ) ) ) ).

% shortest_list_or_default.simps
thf(fact_951_shortest__list__or__default_Oelims,axiom,
    ! [X: list_l8907847357763382004od_b_c,Xa: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( interm7381356855087595981od_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( foldl_8708832512819626401od_b_c
          @ ^ [A6: list_P903359562653991662od_b_c,B6: list_P903359562653991662od_b_c] : ( if_lis437861846949295796od_b_c @ ( ord_less_nat @ ( size_s3392097710323735898od_b_c @ A6 ) @ ( size_s3392097710323735898od_b_c @ B6 ) ) @ A6 @ B6 )
          @ Xa
          @ X ) ) ) ).

% shortest_list_or_default.elims
thf(fact_952_update__with__aux_Osimps_I2_J,axiom,
    ! [P3: product_prod_b_c,K3: b,V2: c,F3: c > c,Ps3: list_P903359562653991662od_b_c] :
      ( ( ( ( product_fst_b_c @ P3 )
          = K3 )
       => ( ( update_with_aux_c_b @ V2 @ K3 @ F3 @ ( cons_P4529483553340347422od_b_c @ P3 @ Ps3 ) )
          = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F3 @ ( product_snd_b_c @ P3 ) ) ) @ Ps3 ) ) )
      & ( ( ( product_fst_b_c @ P3 )
         != K3 )
       => ( ( update_with_aux_c_b @ V2 @ K3 @ F3 @ ( cons_P4529483553340347422od_b_c @ P3 @ Ps3 ) )
          = ( cons_P4529483553340347422od_b_c @ P3 @ ( update_with_aux_c_b @ V2 @ K3 @ F3 @ Ps3 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_953_update__with__aux_Osimps_I2_J,axiom,
    ! [P3: produc3246581702073416851od_b_c,K3: nat,V2: list_P903359562653991662od_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Ps3: list_P4618364105659340195od_b_c] :
      ( ( ( ( produc3608113002378536793od_b_c @ P3 )
          = K3 )
       => ( ( update3547200019653564_c_nat @ V2 @ K3 @ F3 @ ( cons_P8134328817602661981od_b_c @ P3 @ Ps3 ) )
          = ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ K3 @ ( F3 @ ( produc2468146899304044183od_b_c @ P3 ) ) ) @ Ps3 ) ) )
      & ( ( ( produc3608113002378536793od_b_c @ P3 )
         != K3 )
       => ( ( update3547200019653564_c_nat @ V2 @ K3 @ F3 @ ( cons_P8134328817602661981od_b_c @ P3 @ Ps3 ) )
          = ( cons_P8134328817602661981od_b_c @ P3 @ ( update3547200019653564_c_nat @ V2 @ K3 @ F3 @ Ps3 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_954_Collect__conj__eq,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Q8: list_P903359562653991662od_b_c > $o] :
      ( ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] :
            ( ( P @ X2 )
            & ( Q8 @ X2 ) ) )
      = ( inf_in4978071631833541052od_b_c @ ( collec2280997390073109977od_b_c @ P ) @ ( collec2280997390073109977od_b_c @ Q8 ) ) ) ).

% Collect_conj_eq
thf(fact_955_inf__set__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A5: set_a,B5: set_a] :
          ( collect_a
          @ ( inf_inf_a_o
            @ ^ [X2: a] : ( member_a @ X2 @ A5 )
            @ ^ [X2: a] : ( member_a @ X2 @ B5 ) ) ) ) ) ).

% inf_set_def
thf(fact_956_inf__set__def,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A5: set_li6436108459499378894od_b_c,B5: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ( inf_in3324677931821484577_b_c_o
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A5 )
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ B5 ) ) ) ) ) ).

% inf_set_def
thf(fact_957_Int__Collect,axiom,
    ! [X: a,A2: set_a,P: a > $o] :
      ( ( member_a @ X @ ( inf_inf_set_a @ A2 @ ( collect_a @ P ) ) )
      = ( ( member_a @ X @ A2 )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_958_Int__Collect,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ A2 @ ( collec2280997390073109977od_b_c @ P ) ) )
      = ( ( member6330420149250801815od_b_c @ X @ A2 )
        & ( P @ X ) ) ) ).

% Int_Collect
thf(fact_959_Int__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A5: set_a,B5: set_a] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ A5 )
              & ( member_a @ X2 @ B5 ) ) ) ) ) ).

% Int_def
thf(fact_960_Int__def,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A5: set_li6436108459499378894od_b_c,B5: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A5 )
              & ( member6330420149250801815od_b_c @ X2 @ B5 ) ) ) ) ) ).

% Int_def
thf(fact_961_Un__def,axiom,
    ( sup_su3823046536922626210od_b_c
    = ( ^ [A5: set_li6436108459499378894od_b_c,B5: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A5 )
              | ( member6330420149250801815od_b_c @ X2 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_962_Un__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A5: set_a,B5: set_a] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ A5 )
              | ( member_a @ X2 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_963_sup__set__def,axiom,
    ( sup_su3823046536922626210od_b_c
    = ( ^ [A5: set_li6436108459499378894od_b_c,B5: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ( sup_su1384278580622331579_b_c_o
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A5 )
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_964_sup__set__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A5: set_a,B5: set_a] :
          ( collect_a
          @ ( sup_sup_a_o
            @ ^ [X2: a] : ( member_a @ X2 @ A5 )
            @ ^ [X2: a] : ( member_a @ X2 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_965_observable__transition__target__language__eq,axiom,
    ! [M: fsm_a_b_c,T12: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T12 ) )
        = ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T12 @ ( transitions_a_b_c @ M ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M )
               => ( ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) ) ) )
                  = ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_966_observable__transition__target__language__eq,axiom,
    ! [M: fsm_d_b_c,T12: produc1399170498009216118od_c_d,T22: produc1399170498009216118od_c_d] :
      ( ( ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T12 ) )
        = ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T22 ) ) )
     => ( ( member4231278564905875615od_c_d @ T12 @ ( transitions_d_b_c @ M ) )
       => ( ( member4231278564905875615od_c_d @ T22 @ ( transitions_d_b_c @ M ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) ) )
                = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) )
             => ( ( observable_d_b_c @ M )
               => ( ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) ) ) )
                  = ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_967_observable_Osimps,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Y2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_968_observable_Osimps,axiom,
    ( observable_d_b_c
    = ( ^ [M2: fsm_d_b_c] :
        ! [X2: produc1399170498009216118od_c_d] :
          ( ( member4231278564905875615od_c_d @ X2 @ ( transitions_d_b_c @ M2 ) )
         => ! [Y2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ Y2 @ ( transitions_d_b_c @ M2 ) )
             => ( ( ( ( produc1508465569166014290od_c_d @ X2 )
                    = ( produc1508465569166014290od_c_d @ Y2 ) )
                  & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) )
                    = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) )
                  & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) ) )
                    = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) ) ) )
               => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) ) )
                  = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_969_observable_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( observable_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
             => ! [Y2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ X ) )
                 => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                        = ( produc4225943634317630866od_c_a @ Y2 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) )
                      & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                        = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) )
                   => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                      = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_970_observable_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Y: $o] :
      ( ( ( observable_d_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ X2 @ ( transitions_d_b_c @ X ) )
             => ! [Y2: produc1399170498009216118od_c_d] :
                  ( ( member4231278564905875615od_c_d @ Y2 @ ( transitions_d_b_c @ X ) )
                 => ( ( ( ( produc1508465569166014290od_c_d @ X2 )
                        = ( produc1508465569166014290od_c_d @ Y2 ) )
                      & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) )
                        = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) )
                      & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) ) )
                        = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) ) ) )
                   => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) ) )
                      = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_971_observable_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( observable_a_b_c @ X )
     => ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                    = ( produc4225943634317630866od_c_a @ Xa2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_972_observable_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ( observable_d_b_c @ X )
     => ! [X3: produc1399170498009216118od_c_d] :
          ( ( member4231278564905875615od_c_d @ X3 @ ( transitions_d_b_c @ X ) )
         => ! [Xa2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ Xa2 @ ( transitions_d_b_c @ X ) )
             => ( ( ( ( produc1508465569166014290od_c_d @ X3 )
                    = ( produc1508465569166014290od_c_d @ Xa2 ) )
                  & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) )
                    = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) )
                  & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
                    = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
                  = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_973_observable_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( observable_a_b_c @ X )
     => ~ ! [X4: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ X ) )
           => ! [Xa3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X4 )
                      = ( produc4225943634317630866od_c_a @ Xa3 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) )
                 => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_974_observable_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ~ ( observable_d_b_c @ X )
     => ~ ! [X4: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X4 @ ( transitions_d_b_c @ X ) )
           => ! [Xa3: produc1399170498009216118od_c_d] :
                ( ( member4231278564905875615od_c_d @ Xa3 @ ( transitions_d_b_c @ X ) )
               => ( ( ( ( produc1508465569166014290od_c_d @ X4 )
                      = ( produc1508465569166014290od_c_d @ Xa3 ) )
                    & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) )
                      = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Xa3 ) ) )
                    & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) ) )
                      = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa3 ) ) ) ) )
                 => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) ) )
                    = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_975_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_b_c] :
      ( Prod
      = ( product_Pair_b_c @ ( product_fst_b_c @ Prod ) @ ( product_snd_b_c @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_976_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3246581702073416851od_b_c] :
      ( Prod
      = ( produc8137419655804493381od_b_c @ ( produc3608113002378536793od_b_c @ Prod ) @ ( produc2468146899304044183od_b_c @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_977_surjective__pairing,axiom,
    ! [T2: product_prod_b_c] :
      ( T2
      = ( product_Pair_b_c @ ( product_fst_b_c @ T2 ) @ ( product_snd_b_c @ T2 ) ) ) ).

% surjective_pairing
thf(fact_978_surjective__pairing,axiom,
    ! [T2: produc3246581702073416851od_b_c] :
      ( T2
      = ( produc8137419655804493381od_b_c @ ( produc3608113002378536793od_b_c @ T2 ) @ ( produc2468146899304044183od_b_c @ T2 ) ) ) ).

% surjective_pairing
thf(fact_979_sndE,axiom,
    ! [X: product_prod_b_c,A: b,B: c,P: c > $o] :
      ( ( X
        = ( product_Pair_b_c @ A @ B ) )
     => ( ( P @ ( product_snd_b_c @ X ) )
       => ( P @ B ) ) ) ).

% sndE
thf(fact_980_sndE,axiom,
    ! [X: produc3246581702073416851od_b_c,A: nat,B: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( X
        = ( produc8137419655804493381od_b_c @ A @ B ) )
     => ( ( P @ ( produc2468146899304044183od_b_c @ X ) )
       => ( P @ B ) ) ) ).

% sndE
thf(fact_981_snd__eqD,axiom,
    ! [X: b,Y: c,A: c] :
      ( ( ( product_snd_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_982_snd__eqD,axiom,
    ! [X: nat,Y: list_P903359562653991662od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( ( produc2468146899304044183od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_983_snd__conv,axiom,
    ! [X12: b,X24: c] :
      ( ( product_snd_b_c @ ( product_Pair_b_c @ X12 @ X24 ) )
      = X24 ) ).

% snd_conv
thf(fact_984_snd__conv,axiom,
    ! [X12: nat,X24: list_P903359562653991662od_b_c] :
      ( ( produc2468146899304044183od_b_c @ ( produc8137419655804493381od_b_c @ X12 @ X24 ) )
      = X24 ) ).

% snd_conv
thf(fact_985_fstE,axiom,
    ! [X: product_prod_b_c,A: b,B: c,P: b > $o] :
      ( ( X
        = ( product_Pair_b_c @ A @ B ) )
     => ( ( P @ ( product_fst_b_c @ X ) )
       => ( P @ A ) ) ) ).

% fstE
thf(fact_986_fstE,axiom,
    ! [X: produc3246581702073416851od_b_c,A: nat,B: list_P903359562653991662od_b_c,P: nat > $o] :
      ( ( X
        = ( produc8137419655804493381od_b_c @ A @ B ) )
     => ( ( P @ ( produc3608113002378536793od_b_c @ X ) )
       => ( P @ A ) ) ) ).

% fstE
thf(fact_987_fst__eqD,axiom,
    ! [X: b,Y: c,A: b] :
      ( ( ( product_fst_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_988_fst__eqD,axiom,
    ! [X: nat,Y: list_P903359562653991662od_b_c,A: nat] :
      ( ( ( produc3608113002378536793od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_989_fst__conv,axiom,
    ! [X12: b,X24: c] :
      ( ( product_fst_b_c @ ( product_Pair_b_c @ X12 @ X24 ) )
      = X12 ) ).

% fst_conv
thf(fact_990_fst__conv,axiom,
    ! [X12: nat,X24: list_P903359562653991662od_b_c] :
      ( ( produc3608113002378536793od_b_c @ ( produc8137419655804493381od_b_c @ X12 @ X24 ) )
      = X12 ) ).

% fst_conv
thf(fact_991_after__transition__exhaust,axiom,
    ! [M: fsm_a_b_c,T2: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
       => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) )
          = ( after_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T2 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_992_after__transition__exhaust,axiom,
    ! [M: fsm_d_b_c,T2: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
       => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) )
          = ( after_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T2 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_993_observable__language__transition__target,axiom,
    ! [M: fsm_a_b_c,T2: produc2669932201312201782od_c_a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ Io ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T2 ) ) )
         => ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_994_observable__language__transition__target,axiom,
    ! [M: fsm_d_b_c,T2: produc1399170498009216118od_c_d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ Io ) @ ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T2 ) ) )
         => ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_995_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios2 ) @ ( lS_a_b_c @ M @ Q ) )
     => ~ ! [T3: produc2669932201312201782od_c_a] :
            ( ( ( produc4225943634317630866od_c_a @ T3 )
              = Q )
           => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
             => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) )
                  = X )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios2 @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_996_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios2: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios2 ) @ ( lS_d_b_c @ M @ Q ) )
     => ~ ! [T3: produc1399170498009216118od_c_d] :
            ( ( ( produc1508465569166014290od_c_d @ T3 )
              = Q )
           => ( ( member4231278564905875615od_c_d @ T3 @ ( transitions_d_b_c @ M ) )
             => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) )
                  = X )
               => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios2 @ ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_997_LS__prepend__transition,axiom,
    ! [T2: produc2669932201312201782od_c_a,M: fsm_a_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ Io ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T2 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_998_LS__prepend__transition,axiom,
    ! [T2: produc1399170498009216118od_c_d,M: fsm_d_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ Io ) @ ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T2 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_999_map__pair__fst,axiom,
    ! [F3: b > c,Xs: list_b] :
      ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c
        @ ( map_b_4433156289202544749od_b_c
          @ ^ [X2: b] : ( product_Pair_b_c @ X2 @ ( F3 @ X2 ) )
          @ Xs ) )
      = Xs ) ).

% map_pair_fst
thf(fact_1000_map__pair__fst,axiom,
    ! [F3: nat > list_P903359562653991662od_b_c,Xs: list_nat] :
      ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c
        @ ( map_na7852381390595483433od_b_c
          @ ^ [X2: nat] : ( produc8137419655804493381od_b_c @ X2 @ ( F3 @ X2 ) )
          @ Xs ) )
      = Xs ) ).

% map_pair_fst
thf(fact_1001_pair__list__eqI,axiom,
    ! [Xs: list_P4618364105659340195od_b_c,Ys: list_P4618364105659340195od_b_c] :
      ( ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c @ Xs )
        = ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c @ Ys ) )
     => ( ( ( map_Pr5536700448928023253od_b_c @ produc2468146899304044183od_b_c @ Xs )
          = ( map_Pr5536700448928023253od_b_c @ produc2468146899304044183od_b_c @ Ys ) )
       => ( Xs = Ys ) ) ) ).

% pair_list_eqI
thf(fact_1002_set__n__lists,axiom,
    ! [N: nat,Xs: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( n_list5224936925692304502od_b_c @ N @ Xs ) )
      = ( collec2280997390073109977od_b_c
        @ ^ [Ys4: list_P903359562653991662od_b_c] :
            ( ( ( size_s3392097710323735898od_b_c @ Ys4 )
              = N )
            & ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Ys4 ) @ ( set_Product_prod_b_c2 @ Xs ) ) ) ) ) ).

% set_n_lists
thf(fact_1003_pow__list_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( pow_li4341120398627903455od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append6992831555715836169od_b_c @ ( pow_li4341120398627903455od_b_c @ Xs ) @ ( map_li8081432502061035332od_b_c @ ( cons_P4529483553340347422od_b_c @ X ) @ ( pow_li4341120398627903455od_b_c @ Xs ) ) ) ) ).

% pow_list.simps(2)
thf(fact_1004_observable__io__targets__next,axiom,
    ! [M: fsm_a_b_c,T2: produc2669932201312201782od_c_a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
       => ( ( io_targets_a_b_c @ M
            @ ( append2547753245680614915od_b_c
              @ ( map_Pr776894537227705078od_b_c
                @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                @ ( cons_P8659537020926305772od_c_a @ T2 @ nil_Pr1342775757158464060od_c_a ) )
              @ Io )
            @ ( produc4225943634317630866od_c_a @ T2 ) )
          = ( io_targets_a_b_c @ M @ Io @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ).

% observable_io_targets_next
thf(fact_1005_observable__io__targets__next,axiom,
    ! [M: fsm_d_b_c,T2: produc1399170498009216118od_c_d,Io: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
       => ( ( io_targets_d_b_c @ M
            @ ( append2547753245680614915od_b_c
              @ ( map_Pr2083123184184746678od_b_c
                @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                @ ( cons_P7388775317623320108od_c_d @ T2 @ nil_Pr72014053855478396od_c_d ) )
              @ Io )
            @ ( produc1508465569166014290od_c_d @ T2 ) )
          = ( io_targets_d_b_c @ M @ Io @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) ) ).

% observable_io_targets_next
thf(fact_1006_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: b > c > $o,X: b,Y: c,A: product_prod_b_c] :
      ( ( P @ X @ Y )
     => ( ( A
          = ( product_Pair_b_c @ X @ Y ) )
       => ( P @ ( product_fst_b_c @ A ) @ ( product_snd_b_c @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_1007_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: nat > list_P903359562653991662od_b_c > $o,X: nat,Y: list_P903359562653991662od_b_c,A: produc3246581702073416851od_b_c] :
      ( ( P @ X @ Y )
     => ( ( A
          = ( produc8137419655804493381od_b_c @ X @ Y ) )
       => ( P @ ( produc3608113002378536793od_b_c @ A ) @ ( produc2468146899304044183od_b_c @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_1008_observable__transition__target__language__subset,axiom,
    ! [M: fsm_a_b_c,T12: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T12 ) ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T12 @ ( transitions_a_b_c @ M ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M )
               => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T12 ) ) ) ) @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_1009_observable__transition__target__language__subset,axiom,
    ! [M: fsm_d_b_c,T12: produc1399170498009216118od_c_d,T22: produc1399170498009216118od_c_d] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T12 ) ) @ ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T22 ) ) )
     => ( ( member4231278564905875615od_c_d @ T12 @ ( transitions_d_b_c @ M ) )
       => ( ( member4231278564905875615od_c_d @ T22 @ ( transitions_d_b_c @ M ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) ) )
                = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) )
             => ( ( observable_d_b_c @ M )
               => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T12 ) ) ) ) @ ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_1010_pow__list_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_l8907847357763382004od_b_c] :
      ( ( ( pow_li4341120398627903455od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y
           != ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
             => ( Y
               != ( append6992831555715836169od_b_c @ ( pow_li4341120398627903455od_b_c @ Xs2 ) @ ( map_li8081432502061035332od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 ) @ ( pow_li4341120398627903455od_b_c @ Xs2 ) ) ) ) ) ) ) ).

% pow_list.elims
thf(fact_1011_P,axiom,
    ( p
    = ( ^ [Ew: produc3246581702073416851od_b_c] :
          ( ( ( ( produc3608113002378536793od_b_c @ Ew )
              = zero_zero_nat )
           => ~ ( converge_d_b_c @ m2 @ ua @ va ) )
          & ( ( ( produc3608113002378536793od_b_c @ Ew )
             != zero_zero_nat )
           => ? [Gamma3: list_P903359562653991662od_b_c] : ( distinguishes_a_b_c @ m1 @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua ) @ ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ va ) @ ( append2547753245680614915od_b_c @ ( produc2468146899304044183od_b_c @ Ew ) @ Gamma3 ) ) ) ) ) ) ).

% P
thf(fact_1012_pow__list_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_l8907847357763382004od_b_c] :
      ( ( ( pow_li4341120398627903455od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ pow_li3598863925982933110od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y
                = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) )
             => ~ ( accp_l4654477130474446199od_b_c @ pow_li3598863925982933110od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [X4: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) )
               => ( ( Y
                    = ( append6992831555715836169od_b_c @ ( pow_li4341120398627903455od_b_c @ Xs2 ) @ ( map_li8081432502061035332od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 ) @ ( pow_li4341120398627903455od_b_c @ Xs2 ) ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ pow_li3598863925982933110od_b_c @ ( cons_P4529483553340347422od_b_c @ X4 @ Xs2 ) ) ) ) ) ) ) ).

% pow_list.pelims
thf(fact_1013_fsm__transition__source,axiom,
    ! [T2: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
     => ( member_a @ ( produc4225943634317630866od_c_a @ T2 ) @ ( states_a_b_c @ M ) ) ) ).

% fsm_transition_source
thf(fact_1014_observable__transition__unique,axiom,
    ! [M: fsm_a_b_c,T2: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
       => ? [X4: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ M ) )
            & ( ( produc4225943634317630866od_c_a @ X4 )
              = ( produc4225943634317630866od_c_a @ T2 ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
              = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
            & ! [Y6: produc2669932201312201782od_c_a] :
                ( ( ( member5502040268208861279od_c_a @ Y6 @ ( transitions_a_b_c @ M ) )
                  & ( ( produc4225943634317630866od_c_a @ Y6 )
                    = ( produc4225943634317630866od_c_a @ T2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y6 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y6 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) )
               => ( Y6 = X4 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_1015_observable__transition__unique,axiom,
    ! [M: fsm_d_b_c,T2: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
       => ? [X4: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X4 @ ( transitions_d_b_c @ M ) )
            & ( ( produc1508465569166014290od_c_d @ X4 )
              = ( produc1508465569166014290od_c_d @ T2 ) )
            & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) )
            & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) ) )
              = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) )
            & ! [Y6: produc1399170498009216118od_c_d] :
                ( ( ( member4231278564905875615od_c_d @ Y6 @ ( transitions_d_b_c @ M ) )
                  & ( ( produc1508465569166014290od_c_d @ Y6 )
                    = ( produc1508465569166014290od_c_d @ T2 ) )
                  & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Y6 ) )
                    = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) )
                  & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y6 ) ) )
                    = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) )
               => ( Y6 = X4 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_1016_LS__single__transition,axiom,
    ! [X: b,Y: c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_a_b_c @ M @ Q ) )
      = ( ? [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
            & ( ( produc4225943634317630866od_c_a @ X2 )
              = Q )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
              = X )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
              = Y ) ) ) ) ).

% LS_single_transition
thf(fact_1017_LS__single__transition,axiom,
    ! [X: b,Y: c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_d_b_c @ M @ Q ) )
      = ( ? [X2: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X2 @ ( transitions_d_b_c @ M ) )
            & ( ( produc1508465569166014290od_c_d @ X2 )
              = Q )
            & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) )
              = X )
            & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X2 ) ) )
              = Y ) ) ) ) ).

% LS_single_transition
thf(fact_1018_prefixes__set,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) )
      = ( collec2280997390073109977od_b_c
        @ ^ [Xs6: list_P903359562653991662od_b_c] :
          ? [Xs7: list_P903359562653991662od_b_c] :
            ( ( append2547753245680614915od_b_c @ Xs6 @ Xs7 )
            = Xs ) ) ) ).

% prefixes_set
thf(fact_1019_suffixes__set,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( suffix2151784340763841114od_b_c @ Xs ) )
      = ( collec2280997390073109977od_b_c
        @ ^ [Zs2: list_P903359562653991662od_b_c] :
          ? [Ys4: list_P903359562653991662od_b_c] :
            ( ( append2547753245680614915od_b_c @ Ys4 @ Zs2 )
            = Xs ) ) ) ).

% suffixes_set
thf(fact_1020_reachable__states__cases,axiom,
    ! [Q: a,M: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( P @ ( initial_a_b_c @ M ) )
       => ( ! [T3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T3 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_cases
thf(fact_1021_reachable__states__cases,axiom,
    ! [Q: d,M: fsm_d_b_c,P: d > $o] :
      ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
     => ( ( P @ ( initial_d_b_c @ M ) )
       => ( ! [T3: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ T3 @ ( transitions_d_b_c @ M ) )
             => ( ( member_d @ ( produc1508465569166014290od_c_d @ T3 ) @ ( reacha9185589339461546374_d_b_c @ M ) )
               => ( P @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_cases
thf(fact_1022_reachable__states__induct,axiom,
    ! [Q: a,M: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( P @ ( initial_a_b_c @ M ) )
       => ( ! [T3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T3 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( ( P @ ( produc4225943634317630866od_c_a @ T3 ) )
                 => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_induct
thf(fact_1023_reachable__states__induct,axiom,
    ! [Q: d,M: fsm_d_b_c,P: d > $o] :
      ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
     => ( ( P @ ( initial_d_b_c @ M ) )
       => ( ! [T3: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ T3 @ ( transitions_d_b_c @ M ) )
             => ( ( member_d @ ( produc1508465569166014290od_c_d @ T3 ) @ ( reacha9185589339461546374_d_b_c @ M ) )
               => ( ( P @ ( produc1508465569166014290od_c_d @ T3 ) )
                 => ( P @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_induct
thf(fact_1024_reachable__states__initial__or__target,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( Q
          = ( initial_a_b_c @ M ) )
        | ? [X4: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ M ) )
            & ( member_a @ ( produc4225943634317630866od_c_a @ X4 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
            & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
              = Q ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_1025_reachable__states__initial__or__target,axiom,
    ! [Q: d,M: fsm_d_b_c] :
      ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
     => ( ( Q
          = ( initial_d_b_c @ M ) )
        | ? [X4: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X4 @ ( transitions_d_b_c @ M ) )
            & ( member_d @ ( produc1508465569166014290od_c_d @ X4 ) @ ( reacha9185589339461546374_d_b_c @ M ) )
            & ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) ) )
              = Q ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_1026_prefixes__butlast,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( butlas2026940317822895424od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) )
      = ( collec2280997390073109977od_b_c
        @ ^ [Ys4: list_P903359562653991662od_b_c] :
          ? [Zs2: list_P903359562653991662od_b_c] :
            ( ( ( append2547753245680614915od_b_c @ Ys4 @ Zs2 )
              = Xs )
            & ( Zs2 != nil_Product_prod_b_c ) ) ) ) ).

% prefixes_butlast
thf(fact_1027_set__prefixes__append,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) )
      = ( sup_su3823046536922626210od_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) )
        @ ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [Ys2: list_P903359562653991662od_b_c] :
              ( ( Uu3
                = ( append2547753245680614915od_b_c @ Xs @ Ys2 ) )
              & ( member6330420149250801815od_b_c @ Ys2 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) ) ) ) ) ) ).

% set_prefixes_append
thf(fact_1028_set__suffixes__append,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( suffix3867853578027978934od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) )
      = ( sup_su3823046536922626210od_b_c @ ( set_li4480668622519654659od_b_c @ ( suffix3867853578027978934od_b_c @ Ys ) )
        @ ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [Xs6: list_P903359562653991662od_b_c] :
              ( ( Uu3
                = ( append2547753245680614915od_b_c @ Xs6 @ Ys ) )
              & ( member6330420149250801815od_b_c @ Xs6 @ ( set_li4480668622519654659od_b_c @ ( suffix3867853578027978934od_b_c @ Xs ) ) ) ) ) ) ) ).

% set_suffixes_append
thf(fact_1029_language__state__prepend__transition,axiom,
    ! [Io: list_P903359562653991662od_b_c,A2: fsm_a_b_c,T2: produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ ( from_FSM_a_b_c @ A2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ A2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) )
     => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ A2 ) )
       => ( member6330420149250801815od_b_c
          @ ( append2547753245680614915od_b_c
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
              @ ( cons_P8659537020926305772od_c_a @ T2 @ nil_Pr1342775757158464060od_c_a ) )
            @ Io )
          @ ( lS_a_b_c @ A2 @ ( produc4225943634317630866od_c_a @ T2 ) ) ) ) ) ).

% language_state_prepend_transition
thf(fact_1030_language__state__prepend__transition,axiom,
    ! [Io: list_P903359562653991662od_b_c,A2: fsm_d_b_c,T2: produc1399170498009216118od_c_d] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ ( from_FSM_d_b_c @ A2 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ A2 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) )
     => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ A2 ) )
       => ( member6330420149250801815od_b_c
          @ ( append2547753245680614915od_b_c
            @ ( map_Pr2083123184184746678od_b_c
              @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
              @ ( cons_P7388775317623320108od_c_d @ T2 @ nil_Pr72014053855478396od_c_d ) )
            @ Io )
          @ ( lS_d_b_c @ A2 @ ( produc1508465569166014290od_c_d @ T2 ) ) ) ) ) ).

% language_state_prepend_transition
thf(fact_1031_from__from,axiom,
    ! [Q1: a,M: fsm_a_b_c,Q14: a] :
      ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
     => ( ( member_a @ Q14 @ ( states_a_b_c @ M ) )
       => ( ( from_FSM_a_b_c @ ( from_FSM_a_b_c @ M @ Q1 ) @ Q14 )
          = ( from_FSM_a_b_c @ M @ Q14 ) ) ) ) ).

% from_from
thf(fact_1032_from__FSM__simps_I5_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( states_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = ( states_a_b_c @ M ) ) ) ).

% from_FSM_simps(5)
thf(fact_1033_from__FSM__simps_I1_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = Q ) ) ).

% from_FSM_simps(1)
thf(fact_1034_from__FSM__simps_I1_J,axiom,
    ! [Q: d,M: fsm_d_b_c] :
      ( ( member_d @ Q @ ( states_d_b_c @ M ) )
     => ( ( initial_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) )
        = Q ) ) ).

% from_FSM_simps(1)
thf(fact_1035_from__FSM__simps_I4_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( transitions_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = ( transitions_a_b_c @ M ) ) ) ).

% from_FSM_simps(4)
thf(fact_1036_from__FSM__observable,axiom,
    ! [M: fsm_a_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( observable_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) ) ).

% from_FSM_observable
thf(fact_1037_from__FSM__observable,axiom,
    ! [M: fsm_d_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( observable_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) ) ) ).

% from_FSM_observable
thf(fact_1038_from__FSM__language,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( lS_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) )
        = ( lS_a_b_c @ M @ Q ) ) ) ).

% from_FSM_language
thf(fact_1039_from__FSM__language,axiom,
    ! [Q: d,M: fsm_d_b_c] :
      ( ( member_d @ Q @ ( states_d_b_c @ M ) )
     => ( ( lS_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) ) )
        = ( lS_d_b_c @ M @ Q ) ) ) ).

% from_FSM_language
thf(fact_1040_observable__language__next,axiom,
    ! [Io: product_prod_b_c,Ios2: list_P903359562653991662od_b_c,M: fsm_a_b_c,T2: produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io @ Ios2 ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T2 ) ) )
     => ( ( observable_a_b_c @ M )
       => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) )
              = ( product_fst_b_c @ Io ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) )
                = ( product_snd_b_c @ Io ) )
             => ( member6330420149250801815od_b_c @ Ios2 @ ( lS_a_b_c @ ( from_FSM_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_1041_observable__language__next,axiom,
    ! [Io: product_prod_b_c,Ios2: list_P903359562653991662od_b_c,M: fsm_d_b_c,T2: produc1399170498009216118od_c_d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io @ Ios2 ) @ ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T2 ) ) )
     => ( ( observable_d_b_c @ M )
       => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) )
              = ( product_fst_b_c @ Io ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) )
                = ( product_snd_b_c @ Io ) )
             => ( member6330420149250801815od_b_c @ Ios2 @ ( lS_d_b_c @ ( from_FSM_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_1042_state__cover__transition__converges,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V5: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,T2: produc596031391177498678od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( state_2362830510734323903_c_b_c @ M @ V5 )
       => ( ( member8124909232574984543od_b_c @ T2 @ ( transi3161963839906981764_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ ( produc5084291339869529746od_b_c @ T2 ) @ ( reacha8116992257183400179_c_b_c @ M ) )
           => ( conver6852411701971397450_c_b_c @ M @ ( append2547753245680614915od_b_c @ ( V5 @ ( produc5084291339869529746od_b_c @ T2 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc4488652850390612441od_b_c @ ( produc829356566976367572od_b_c @ T2 ) ) @ ( produc5388473464130769137od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T2 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V5 @ ( produc8475728678562477363od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T2 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_1043_state__cover__transition__converges,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,V5: list_P903359562653991662od_b_c > list_P4618364105659340195od_b_c,T2: produc3894960095624370921od_b_c] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( state_7436225829948223902od_b_c @ M @ V5 )
       => ( ( member275807201309088512od_b_c @ T2 @ ( transi4631474696376506137od_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ ( produc9192024162703516791od_b_c @ T2 ) @ ( reacha7795901668899977834od_b_c @ M ) )
           => ( conver4001532986140499667od_b_c @ M @ ( append1310559846384609464od_b_c @ ( V5 @ ( produc9192024162703516791od_b_c @ T2 ) ) @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ ( produc861206492263493522od_b_c @ ( produc4509980026417360309od_b_c @ T2 ) ) @ ( produc1807356612421382019od_b_c @ ( produc7935499289977867216od_b_c @ ( produc4509980026417360309od_b_c @ T2 ) ) ) ) @ nil_Pr679518533894577677od_b_c ) ) @ ( V5 @ ( produc8256383748742478021od_b_c @ ( produc7935499289977867216od_b_c @ ( produc4509980026417360309od_b_c @ T2 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_1044_state__cover__transition__converges,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,V5: a > list_P4618364105659340195od_b_c,T2: produc5894170661315020937_b_c_a] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( state_4039615241003423118od_b_c @ M @ V5 )
       => ( ( member3332177101994087840_b_c_a @ T2 @ ( transi4954505071500765065od_b_c @ M ) )
         => ( ( member_a @ ( produc4356466802063587095_b_c_a @ T2 ) @ ( reacha1783724991602909274od_b_c @ M ) )
           => ( conver918448029487226435od_b_c @ M @ ( append1310559846384609464od_b_c @ ( V5 @ ( produc4356466802063587095_b_c_a @ T2 ) ) @ ( cons_P8134328817602661981od_b_c @ ( produc8137419655804493381od_b_c @ ( produc1343630566382188834_b_c_a @ ( produc1179498357986986581_b_c_a @ T2 ) ) @ ( produc1715878850288909075_b_c_a @ ( produc210687423892126304_b_c_a @ ( produc1179498357986986581_b_c_a @ T2 ) ) ) ) @ nil_Pr679518533894577677od_b_c ) ) @ ( V5 @ ( produc4803134064720617301_b_c_a @ ( produc210687423892126304_b_c_a @ ( produc1179498357986986581_b_c_a @ T2 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_1045_state__cover__transition__converges,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,T2: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
         => ( ( member_a @ ( produc4225943634317630866od_c_a @ T2 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ ( V5 @ ( produc4225943634317630866od_c_a @ T2 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V5 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_1046_state__cover__transition__converges,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c,T2: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( state_6014242345326633810_d_b_c @ M @ V5 )
       => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M ) )
         => ( ( member_d @ ( produc1508465569166014290od_c_d @ T2 ) @ ( reacha9185589339461546374_d_b_c @ M ) )
           => ( converge_d_b_c @ M @ ( append2547753245680614915od_b_c @ ( V5 @ ( produc1508465569166014290od_c_d @ T2 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V5 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_1047_state__cover__assignment__inj,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,Q1: a,Q2: a] :
      ( ( state_7672330573471793359_a_b_c @ M @ V5 )
     => ( ( observable_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( ( V5 @ Q1 )
               != ( V5 @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_1048_state__cover__assignment__inj,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c,Q1: d,Q2: d] :
      ( ( state_6014242345326633810_d_b_c @ M @ V5 )
     => ( ( observable_d_b_c @ M )
       => ( ( member_d @ Q1 @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ( ( member_d @ Q2 @ ( reacha9185589339461546374_d_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( ( V5 @ Q1 )
               != ( V5 @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_1049_is__state__cover__assignment__language,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V5: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( state_2362830510734323903_c_b_c @ M @ V5 )
     => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_1050_is__state__cover__assignment__language,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( state_7672330573471793359_a_b_c @ M @ V5 )
     => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_1051_is__state__cover__assignment__language,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c,Q: d] :
      ( ( state_6014242345326633810_d_b_c @ M @ V5 )
     => ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_1052_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V5: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( state_2362830510734323903_c_b_c @ M @ V5 )
       => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_1053_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_1054_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( state_6014242345326633810_d_b_c @ M @ V5 )
       => ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V5 @ Q ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_1055_is__state__cover__assignment__observable__after,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( V5 @ Q ) )
            = Q ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_1056_is__state__cover__assignment__observable__after,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( state_6014242345326633810_d_b_c @ M @ V5 )
       => ( ( member_d @ Q @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ( ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( V5 @ Q ) )
            = Q ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_1057_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ~ ( state_2362830510734323903_c_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ( member6330420149250801815od_b_c @ X4 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X4 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_1058_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c] :
      ( ~ ( state_7672330573471793359_a_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_a_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X4: a] :
              ( ( member_a @ X4 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ( member_a @ X4 @ ( io_targets_a_b_c @ X @ ( Xa @ X4 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_1059_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa: d > list_P903359562653991662od_b_c] :
      ( ~ ( state_6014242345326633810_d_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_d_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X4: d] :
              ( ( member_d @ X4 @ ( reacha9185589339461546374_d_b_c @ X ) )
             => ( member_d @ X4 @ ( io_targets_d_b_c @ X @ ( Xa @ X4 ) @ ( initial_d_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_1060_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( state_2362830510734323903_c_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ X ) )
           => ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X3 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_1061_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_a_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X3: a] :
            ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ X ) )
           => ( member_a @ X3 @ ( io_targets_a_b_c @ X @ ( Xa @ X3 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_1062_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa: d > list_P903359562653991662od_b_c] :
      ( ( state_6014242345326633810_d_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_d_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X3: d] :
            ( ( member_d @ X3 @ ( reacha9185589339461546374_d_b_c @ X ) )
           => ( member_d @ X3 @ ( io_targets_d_b_c @ X @ ( Xa @ X3 ) @ ( initial_d_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_1063_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_2362830510734323903_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X2 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_1064_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_7672330573471793359_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_a_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ( member_a @ X2 @ ( io_targets_a_b_c @ X @ ( Xa @ X2 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_1065_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa: d > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_6014242345326633810_d_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_d_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: d] :
              ( ( member_d @ X2 @ ( reacha9185589339461546374_d_b_c @ X ) )
             => ( member_d @ X2 @ ( io_targets_d_b_c @ X @ ( Xa @ X2 ) @ ( initial_d_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_1066_is__state__cover__assignment_Osimps,axiom,
    ( state_2362830510734323903_c_b_c
    = ( ^ [M2: fsm_li6801133765522507155_c_b_c,F4: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
          ( ( ( F4 @ ( initia3567573336347591134_c_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ M2 ) )
             => ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ M2 @ ( F4 @ X2 ) @ ( initia3567573336347591134_c_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_1067_is__state__cover__assignment_Osimps,axiom,
    ( state_7672330573471793359_a_b_c
    = ( ^ [M2: fsm_a_b_c,F4: a > list_P903359562653991662od_b_c] :
          ( ( ( F4 @ ( initial_a_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ M2 ) )
             => ( member_a @ X2 @ ( io_targets_a_b_c @ M2 @ ( F4 @ X2 ) @ ( initial_a_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_1068_is__state__cover__assignment_Osimps,axiom,
    ( state_6014242345326633810_d_b_c
    = ( ^ [M2: fsm_d_b_c,F4: d > list_P903359562653991662od_b_c] :
          ( ( ( F4 @ ( initial_d_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X2: d] :
              ( ( member_d @ X2 @ ( reacha9185589339461546374_d_b_c @ M2 ) )
             => ( member_d @ X2 @ ( io_targets_d_b_c @ M2 @ ( F4 @ X2 ) @ ( initial_d_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_1069_state__cover__assignment__diverges,axiom,
    ! [M: fsm_a_b_c,F3: a > list_P903359562653991662od_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( state_7672330573471793359_a_b_c @ M @ F3 )
         => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( ( Q1 != Q2 )
               => ~ ( converge_a_b_c @ M @ ( F3 @ Q1 ) @ ( F3 @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_1070_state__cover__assignment__diverges,axiom,
    ! [M: fsm_d_b_c,F3: d > list_P903359562653991662od_b_c,Q1: d,Q2: d] :
      ( ( observable_d_b_c @ M )
     => ( ( minimal_d_b_c @ M )
       => ( ( state_6014242345326633810_d_b_c @ M @ F3 )
         => ( ( member_d @ Q1 @ ( reacha9185589339461546374_d_b_c @ M ) )
           => ( ( member_d @ Q2 @ ( reacha9185589339461546374_d_b_c @ M ) )
             => ( ( Q1 != Q2 )
               => ~ ( converge_d_b_c @ M @ ( F3 @ Q1 ) @ ( F3 @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_1071_get__pairs__H__set_I2_J,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c,Alpha: list_P903359562653991662od_b_c,Q6: a,Beta: list_P903359562653991662od_b_c,Q10: a,M4: nat] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( member8012203591919427344_b_c_a @ ( produc4725704460314280791_b_c_a @ ( produc595631027891595047_b_c_a @ Alpha @ Q6 ) @ ( produc595631027891595047_b_c_a @ Beta @ Q10 ) ) @ ( set_Pr2718271725578035580_b_c_a @ ( interm5402289259522850805_a_b_c @ V5 @ M @ M4 ) ) )
         => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
            & ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
            & ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha )
             != ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Beta ) )
            & ( Q6
              = ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha ) )
            & ( Q10
              = ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Beta ) ) ) ) ) ) ).

% get_pairs_H_set(2)
thf(fact_1072_language__path__append__transition__observable,axiom,
    ! [P3: list_P6327159017948738492od_c_a,X: b,Y: c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c
        @ ( append2547753245680614915od_b_c
          @ ( map_Pr776894537227705078od_b_c
            @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
            @ P3 )
          @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
        @ ( lS_a_b_c @ M @ Q ) )
     => ( ( path_a_b_c @ M @ Q @ P3 )
       => ( ( observable_a_b_c @ M )
         => ~ ! [T3: produc2669932201312201782od_c_a] :
                ( ( path_a_b_c @ M @ Q @ ( append3884164603879732689od_c_a @ P3 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) )
                    = X )
                 => ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
                   != Y ) ) ) ) ) ) ).

% language_path_append_transition_observable
thf(fact_1073_language__path__append__transition__observable,axiom,
    ! [P3: list_P7416935848109857788od_c_d,X: b,Y: c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c
        @ ( append2547753245680614915od_b_c
          @ ( map_Pr2083123184184746678od_b_c
            @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
            @ P3 )
          @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
        @ ( lS_d_b_c @ M @ Q ) )
     => ( ( path_d_b_c @ M @ Q @ P3 )
       => ( ( observable_d_b_c @ M )
         => ~ ! [T3: produc1399170498009216118od_c_d] :
                ( ( path_d_b_c @ M @ Q @ ( append2613402900576747025od_c_d @ P3 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
               => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) )
                    = X )
                 => ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) )
                   != Y ) ) ) ) ) ) ).

% language_path_append_transition_observable
thf(fact_1074_nil,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( path_a_b_c @ M @ Q @ nil_Pr1342775757158464060od_c_a ) ) ).

% nil
thf(fact_1075_path__nil__elim,axiom,
    ! [M: fsm_a_b_c,Q: a] :
      ( ( path_a_b_c @ M @ Q @ nil_Pr1342775757158464060od_c_a )
     => ( member_a @ Q @ ( states_a_b_c @ M ) ) ) ).

% path_nil_elim
thf(fact_1076_path__begin__state,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q @ P3 )
     => ( member_a @ Q @ ( states_a_b_c @ M ) ) ) ).

% path_begin_state
thf(fact_1077_transition__subset__path,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ A2 ) @ ( transitions_a_b_c @ B4 ) )
     => ( ( path_a_b_c @ A2 @ Q @ P3 )
       => ( ( member_a @ Q @ ( states_a_b_c @ B4 ) )
         => ( path_a_b_c @ B4 @ Q @ P3 ) ) ) ) ).

% transition_subset_path
thf(fact_1078_from__FSM__path,axiom,
    ! [Q: a,M: fsm_a_b_c,Q6: a,P3: list_P6327159017948738492od_c_a] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( path_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) @ Q6 @ P3 )
       => ( path_a_b_c @ M @ Q6 @ P3 ) ) ) ).

% from_FSM_path
thf(fact_1079_from__FSM__path__initial,axiom,
    ! [Q: a,M: fsm_a_b_c,P3: list_P6327159017948738492od_c_a] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( path_a_b_c @ M @ Q @ P3 )
        = ( path_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) @ P3 ) ) ) ).

% from_FSM_path_initial
thf(fact_1080_from__FSM__path__initial,axiom,
    ! [Q: d,M: fsm_d_b_c,P3: list_P7416935848109857788od_c_d] :
      ( ( member_d @ Q @ ( states_d_b_c @ M ) )
     => ( ( path_d_b_c @ M @ Q @ P3 )
        = ( path_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ M @ Q ) ) @ P3 ) ) ) ).

% from_FSM_path_initial
thf(fact_1081_LS_Oelims,axiom,
    ! [X: fsm_a_b_c,Xa: a,Y: set_li6436108459499378894od_b_c] :
      ( ( ( lS_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [P8: list_P6327159017948738492od_c_a] :
              ( ( Uu3
                = ( map_Pr776894537227705078od_b_c
                  @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_a_b_c @ X @ Xa @ P8 ) ) ) ) ) ).

% LS.elims
thf(fact_1082_LS_Oelims,axiom,
    ! [X: fsm_d_b_c,Xa: d,Y: set_li6436108459499378894od_b_c] :
      ( ( ( lS_d_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [P8: list_P7416935848109857788od_c_d] :
              ( ( Uu3
                = ( map_Pr2083123184184746678od_b_c
                  @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_d_b_c @ X @ Xa @ P8 ) ) ) ) ) ).

% LS.elims
thf(fact_1083_LS_Osimps,axiom,
    ( lS_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q3: a] :
          ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [P8: list_P6327159017948738492od_c_a] :
              ( ( Uu3
                = ( map_Pr776894537227705078od_b_c
                  @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_a_b_c @ M2 @ Q3 @ P8 ) ) ) ) ) ).

% LS.simps
thf(fact_1084_LS_Osimps,axiom,
    ( lS_d_b_c
    = ( ^ [M2: fsm_d_b_c,Q3: d] :
          ( collec2280997390073109977od_b_c
          @ ^ [Uu3: list_P903359562653991662od_b_c] :
            ? [P8: list_P7416935848109857788od_c_d] :
              ( ( Uu3
                = ( map_Pr2083123184184746678od_b_c
                  @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_d_b_c @ M2 @ Q3 @ P8 ) ) ) ) ) ).

% LS.simps
thf(fact_1085_language__intro,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q @ P3 )
     => ( member6330420149250801815od_b_c
        @ ( map_Pr776894537227705078od_b_c
          @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
          @ P3 )
        @ ( lS_a_b_c @ M @ Q ) ) ) ).

% language_intro
thf(fact_1086_language__intro,axiom,
    ! [M: fsm_d_b_c,Q: d,P3: list_P7416935848109857788od_c_d] :
      ( ( path_d_b_c @ M @ Q @ P3 )
     => ( member6330420149250801815od_b_c
        @ ( map_Pr2083123184184746678od_b_c
          @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
          @ P3 )
        @ ( lS_d_b_c @ M @ Q ) ) ) ).

% language_intro
thf(fact_1087_language__state__containment,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
      ( ( path_a_b_c @ M @ Q @ P3 )
     => ( ( ( map_Pr776894537227705078od_b_c
            @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
            @ P3 )
          = Io )
       => ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% language_state_containment
thf(fact_1088_language__state__containment,axiom,
    ! [M: fsm_d_b_c,Q: d,P3: list_P7416935848109857788od_c_d,Io: list_P903359562653991662od_b_c] :
      ( ( path_d_b_c @ M @ Q @ P3 )
     => ( ( ( map_Pr2083123184184746678od_b_c
            @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
            @ P3 )
          = Io )
       => ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) ) ) ) ).

% language_state_containment
thf(fact_1089_observable__path__unique,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a,P9: list_P6327159017948738492od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( path_a_b_c @ M @ Q @ P3 )
       => ( ( path_a_b_c @ M @ Q @ P9 )
         => ( ( ( map_Pr776894537227705078od_b_c
                @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                @ P3 )
              = ( map_Pr776894537227705078od_b_c
                @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                @ P9 ) )
           => ( P3 = P9 ) ) ) ) ) ).

% observable_path_unique
thf(fact_1090_observable__path__unique,axiom,
    ! [M: fsm_d_b_c,Q: d,P3: list_P7416935848109857788od_c_d,P9: list_P7416935848109857788od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( path_d_b_c @ M @ Q @ P3 )
       => ( ( path_d_b_c @ M @ Q @ P9 )
         => ( ( ( map_Pr2083123184184746678od_b_c
                @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                @ P3 )
              = ( map_Pr2083123184184746678od_b_c
                @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                @ P9 ) )
           => ( P3 = P9 ) ) ) ) ) ).

% observable_path_unique
thf(fact_1091_path_Osimps,axiom,
    ( path_a_b_c
    = ( ^ [A1: fsm_a_b_c,A22: a,A32: list_P6327159017948738492od_c_a] :
          ( ? [Q3: a,M2: fsm_a_b_c] :
              ( ( A1 = M2 )
              & ( A22 = Q3 )
              & ( A32 = nil_Pr1342775757158464060od_c_a )
              & ( member_a @ Q3 @ ( states_a_b_c @ M2 ) ) )
          | ? [T4: produc2669932201312201782od_c_a,M2: fsm_a_b_c,Ts2: list_P6327159017948738492od_c_a] :
              ( ( A1 = M2 )
              & ( A22
                = ( produc4225943634317630866od_c_a @ T4 ) )
              & ( A32
                = ( cons_P8659537020926305772od_c_a @ T4 @ Ts2 ) )
              & ( member5502040268208861279od_c_a @ T4 @ ( transitions_a_b_c @ M2 ) )
              & ( path_a_b_c @ M2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Ts2 ) ) ) ) ) ).

% path.simps
thf(fact_1092_path_Ocases,axiom,
    ! [A12: fsm_a_b_c,A23: a,A33: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ A12 @ A23 @ A33 )
     => ( ( ( A33 = nil_Pr1342775757158464060od_c_a )
         => ~ ( member_a @ A23 @ ( states_a_b_c @ A12 ) ) )
       => ~ ! [T3: produc2669932201312201782od_c_a] :
              ( ( A23
                = ( produc4225943634317630866od_c_a @ T3 ) )
             => ! [Ts3: list_P6327159017948738492od_c_a] :
                  ( ( A33
                    = ( cons_P8659537020926305772od_c_a @ T3 @ Ts3 ) )
                 => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ A12 ) )
                   => ~ ( path_a_b_c @ A12 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) @ Ts3 ) ) ) ) ) ) ).

% path.cases
thf(fact_1093_language__split,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
     => ~ ! [P1: list_P6327159017948738492od_c_a,P22: list_P6327159017948738492od_c_a] :
            ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append3884164603879732689od_c_a @ P1 @ P22 ) )
           => ( ( ( map_Pr776894537227705078od_b_c
                  @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                  @ P1 )
                = Io1 )
             => ( ( map_Pr776894537227705078od_b_c
                  @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                  @ P22 )
               != Io2 ) ) ) ) ).

% language_split
thf(fact_1094_language__split,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_d_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
     => ~ ! [P1: list_P7416935848109857788od_c_d,P22: list_P7416935848109857788od_c_d] :
            ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2613402900576747025od_c_d @ P1 @ P22 ) )
           => ( ( ( map_Pr2083123184184746678od_b_c
                  @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                  @ P1 )
                = Io1 )
             => ( ( map_Pr2083123184184746678od_b_c
                  @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                  @ P22 )
               != Io2 ) ) ) ) ).

% language_split
thf(fact_1095_language__path__append__transition,axiom,
    ! [Ios2: list_P903359562653991662od_b_c,Io: product_prod_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ Q ) )
     => ~ ! [P4: list_P6327159017948738492od_c_a,T3: produc2669932201312201782od_c_a] :
            ( ( path_a_b_c @ M @ Q @ ( append3884164603879732689od_c_a @ P4 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
           => ( ( map_Pr776894537227705078od_b_c
                @ ^ [U: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) ) )
                @ ( append3884164603879732689od_c_a @ P4 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
             != ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) ) ) ) ).

% language_path_append_transition
thf(fact_1096_language__path__append__transition,axiom,
    ! [Ios2: list_P903359562653991662od_b_c,Io: product_prod_b_c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ Q ) )
     => ~ ! [P4: list_P7416935848109857788od_c_d,T3: produc1399170498009216118od_c_d] :
            ( ( path_d_b_c @ M @ Q @ ( append2613402900576747025od_c_d @ P4 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
           => ( ( map_Pr2083123184184746678od_b_c
                @ ^ [U: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) ) )
                @ ( append2613402900576747025od_c_d @ P4 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
             != ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) ) ) ) ).

% language_path_append_transition
thf(fact_1097_language__append__path__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,X: b,Y: c,M: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
     => ~ ! [P4: list_P6327159017948738492od_c_a,T3: produc2669932201312201782od_c_a] :
            ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append3884164603879732689od_c_a @ P4 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
           => ( ( ( map_Pr776894537227705078od_b_c
                  @ ^ [U: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) ) )
                  @ P4 )
                = Io )
             => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) )
                  = X )
               => ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
                 != Y ) ) ) ) ) ).

% language_append_path_ob
thf(fact_1098_language__append__path__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,X: b,Y: c,M: fsm_d_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
     => ~ ! [P4: list_P7416935848109857788od_c_d,T3: produc1399170498009216118od_c_d] :
            ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2613402900576747025od_c_d @ P4 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
           => ( ( ( map_Pr2083123184184746678od_b_c
                  @ ^ [U: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) ) )
                  @ P4 )
                = Io )
             => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) )
                  = X )
               => ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T3 ) ) )
                 != Y ) ) ) ) ) ).

% language_append_path_ob
thf(fact_1099_language__initial__path__append__transition,axiom,
    ! [Ios2: list_P903359562653991662od_b_c,Io: product_prod_b_c,M: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
     => ~ ! [P4: list_P6327159017948738492od_c_a,T3: produc2669932201312201782od_c_a] :
            ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append3884164603879732689od_c_a @ P4 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
           => ( ( map_Pr776894537227705078od_b_c
                @ ^ [U: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ U ) ) ) )
                @ ( append3884164603879732689od_c_a @ P4 @ ( cons_P8659537020926305772od_c_a @ T3 @ nil_Pr1342775757158464060od_c_a ) ) )
             != ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) ) ) ) ).

% language_initial_path_append_transition
thf(fact_1100_language__initial__path__append__transition,axiom,
    ! [Ios2: list_P903359562653991662od_b_c,Io: product_prod_b_c,M: fsm_d_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
     => ~ ! [P4: list_P7416935848109857788od_c_d,T3: produc1399170498009216118od_c_d] :
            ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ ( append2613402900576747025od_c_d @ P4 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
           => ( ( map_Pr2083123184184746678od_b_c
                @ ^ [U: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ U ) ) ) )
                @ ( append2613402900576747025od_c_d @ P4 @ ( cons_P7388775317623320108od_c_d @ T3 @ nil_Pr72014053855478396od_c_d ) ) )
             != ( append2547753245680614915od_b_c @ Ios2 @ ( cons_P4529483553340347422od_b_c @ Io @ nil_Product_prod_b_c ) ) ) ) ) ).

% language_initial_path_append_transition
thf(fact_1101_reachable__states__intro,axiom,
    ! [M: fsm_a_b_c,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ P3 )
     => ( member_a @ ( target_a_b_c @ ( initial_a_b_c @ M ) @ P3 ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ).

% reachable_states_intro
thf(fact_1102_reachable__states__intro,axiom,
    ! [M: fsm_d_b_c,P3: list_P7416935848109857788od_c_d] :
      ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ P3 )
     => ( member_d @ ( target_d_b_c @ ( initial_d_b_c @ M ) @ P3 ) @ ( reacha9185589339461546374_d_b_c @ M ) ) ) ).

% reachable_states_intro
thf(fact_1103_path__target__is__state,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q @ P3 )
     => ( member_a @ ( target_a_b_c @ Q @ P3 ) @ ( states_a_b_c @ M ) ) ) ).

% path_target_is_state
thf(fact_1104_cyclic__cycle__rev,axiom,
    ! [M: fsm_a_b_c,P9: list_P6327159017948738492od_c_a,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ P9 )
     => ( ( ( target_a_b_c @ ( initial_a_b_c @ M ) @ P9 )
          = Q )
       => ( ( path_a_b_c @ M @ Q @ P3 )
         => ( ( P3 != nil_Pr1342775757158464060od_c_a )
           => ( ( ( target_a_b_c @ Q @ P3 )
                = Q )
             => ~ ( acyclic_a_b_c @ M ) ) ) ) ) ) ).

% cyclic_cycle_rev
thf(fact_1105_cyclic__cycle__rev,axiom,
    ! [M: fsm_d_b_c,P9: list_P7416935848109857788od_c_d,Q: d,P3: list_P7416935848109857788od_c_d] :
      ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ P9 )
     => ( ( ( target_d_b_c @ ( initial_d_b_c @ M ) @ P9 )
          = Q )
       => ( ( path_d_b_c @ M @ Q @ P3 )
         => ( ( P3 != nil_Pr72014053855478396od_c_d )
           => ( ( ( target_d_b_c @ Q @ P3 )
                = Q )
             => ~ ( acyclic_d_b_c @ M ) ) ) ) ) ) ).

% cyclic_cycle_rev
thf(fact_1106_reachable__states__def,axiom,
    ( reacha1620305530751930115_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
          ( collect_a
          @ ^ [Uu3: a] :
            ? [P8: list_P6327159017948738492od_c_a] :
              ( ( Uu3
                = ( target_a_b_c @ ( initial_a_b_c @ M2 ) @ P8 ) )
              & ( path_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ P8 ) ) ) ) ) ).

% reachable_states_def
thf(fact_1107_reachable__states__def,axiom,
    ( reacha9185589339461546374_d_b_c
    = ( ^ [M2: fsm_d_b_c] :
          ( collect_d
          @ ^ [Uu3: d] :
            ? [P8: list_P7416935848109857788od_c_d] :
              ( ( Uu3
                = ( target_d_b_c @ ( initial_d_b_c @ M2 ) @ P8 ) )
              & ( path_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) @ P8 ) ) ) ) ) ).

% reachable_states_def
thf(fact_1108_acyclic__initial,axiom,
    ! [M: fsm_a_b_c] :
      ( ( acyclic_a_b_c @ M )
     => ~ ? [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M ) )
            & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
              = ( initial_a_b_c @ M ) )
            & ? [P10: list_P6327159017948738492od_c_a] :
                ( ( path_a_b_c @ M @ ( initial_a_b_c @ M ) @ P10 )
                & ( ( target_a_b_c @ ( initial_a_b_c @ M ) @ P10 )
                  = ( produc4225943634317630866od_c_a @ X3 ) ) ) ) ) ).

% acyclic_initial
thf(fact_1109_acyclic__initial,axiom,
    ! [M: fsm_d_b_c] :
      ( ( acyclic_d_b_c @ M )
     => ~ ? [X3: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X3 @ ( transitions_d_b_c @ M ) )
            & ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
              = ( initial_d_b_c @ M ) )
            & ? [P10: list_P7416935848109857788od_c_d] :
                ( ( path_d_b_c @ M @ ( initial_d_b_c @ M ) @ P10 )
                & ( ( target_d_b_c @ ( initial_d_b_c @ M ) @ P10 )
                  = ( produc1508465569166014290od_c_d @ X3 ) ) ) ) ) ).

% acyclic_initial
thf(fact_1110_language__state__split,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q1: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q1 ) )
     => ~ ! [P1: list_P6327159017948738492od_c_a] :
            ( ( path_a_b_c @ M @ Q1 @ P1 )
           => ! [P22: list_P6327159017948738492od_c_a] :
                ( ( path_a_b_c @ M @ ( target_a_b_c @ Q1 @ P1 ) @ P22 )
               => ( ( ( map_Pr776894537227705078od_b_c
                      @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                      @ P1 )
                    = Io1 )
                 => ( ( map_Pr776894537227705078od_b_c
                      @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                      @ P22 )
                   != Io2 ) ) ) ) ) ).

% language_state_split
thf(fact_1111_language__state__split,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q1: d] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M @ Q1 ) )
     => ~ ! [P1: list_P7416935848109857788od_c_d] :
            ( ( path_d_b_c @ M @ Q1 @ P1 )
           => ! [P22: list_P7416935848109857788od_c_d] :
                ( ( path_d_b_c @ M @ ( target_d_b_c @ Q1 @ P1 ) @ P22 )
               => ( ( ( map_Pr2083123184184746678od_b_c
                      @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                      @ P1 )
                    = Io1 )
                 => ( ( map_Pr2083123184184746678od_b_c
                      @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                      @ P22 )
                   != Io2 ) ) ) ) ) ).

% language_state_split
thf(fact_1112_language__path__append,axiom,
    ! [M1: fsm_a_b_c,Q1: a,P12: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
      ( ( path_a_b_c @ M1 @ Q1 @ P12 )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M1 @ ( target_a_b_c @ Q1 @ P12 ) ) )
       => ( member6330420149250801815od_b_c
          @ ( append2547753245680614915od_b_c
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
              @ P12 )
            @ Io )
          @ ( lS_a_b_c @ M1 @ Q1 ) ) ) ) ).

% language_path_append
thf(fact_1113_language__path__append,axiom,
    ! [M1: fsm_d_b_c,Q1: d,P12: list_P7416935848109857788od_c_d,Io: list_P903359562653991662od_b_c] :
      ( ( path_d_b_c @ M1 @ Q1 @ P12 )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M1 @ ( target_d_b_c @ Q1 @ P12 ) ) )
       => ( member6330420149250801815od_b_c
          @ ( append2547753245680614915od_b_c
            @ ( map_Pr2083123184184746678od_b_c
              @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
              @ P12 )
            @ Io )
          @ ( lS_d_b_c @ M1 @ Q1 ) ) ) ) ).

% language_path_append
thf(fact_1114_after__path,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( path_a_b_c @ M @ Q @ P3 )
       => ( ( after_a_b_c @ M @ Q
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
              @ P3 ) )
          = ( target_a_b_c @ Q @ P3 ) ) ) ) ).

% after_path
thf(fact_1115_after__path,axiom,
    ! [M: fsm_d_b_c,Q: d,P3: list_P7416935848109857788od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( path_d_b_c @ M @ Q @ P3 )
       => ( ( after_d_b_c @ M @ Q
            @ ( map_Pr2083123184184746678od_b_c
              @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
              @ P3 ) )
          = ( target_d_b_c @ Q @ P3 ) ) ) ) ).

% after_path
thf(fact_1116_observable__path__suffix,axiom,
    ! [P3: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c
        @ ( append2547753245680614915od_b_c
          @ ( map_Pr776894537227705078od_b_c
            @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
            @ P3 )
          @ Io )
        @ ( lS_a_b_c @ M @ Q ) )
     => ( ( path_a_b_c @ M @ Q @ P3 )
       => ( ( observable_a_b_c @ M )
         => ~ ! [P11: list_P6327159017948738492od_c_a] :
                ( ( path_a_b_c @ M @ ( target_a_b_c @ Q @ P3 ) @ P11 )
               => ( ( map_Pr776894537227705078od_b_c
                    @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                    @ P11 )
                 != Io ) ) ) ) ) ).

% observable_path_suffix
thf(fact_1117_observable__path__suffix,axiom,
    ! [P3: list_P7416935848109857788od_c_d,Io: list_P903359562653991662od_b_c,M: fsm_d_b_c,Q: d] :
      ( ( member6330420149250801815od_b_c
        @ ( append2547753245680614915od_b_c
          @ ( map_Pr2083123184184746678od_b_c
            @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
            @ P3 )
          @ Io )
        @ ( lS_d_b_c @ M @ Q ) )
     => ( ( path_d_b_c @ M @ Q @ P3 )
       => ( ( observable_d_b_c @ M )
         => ~ ! [P11: list_P7416935848109857788od_c_d] :
                ( ( path_d_b_c @ M @ ( target_d_b_c @ Q @ P3 ) @ P11 )
               => ( ( map_Pr2083123184184746678od_b_c
                    @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                    @ P11 )
                 != Io ) ) ) ) ) ).

% observable_path_suffix
thf(fact_1118_observable__after__path,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ~ ! [P4: list_P6327159017948738492od_c_a] :
              ( ( path_a_b_c @ M @ Q @ P4 )
             => ( ( ( map_Pr776894537227705078od_b_c
                    @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                    @ P4 )
                  = Io )
               => ( ( target_a_b_c @ Q @ P4 )
                 != ( after_a_b_c @ M @ Q @ Io ) ) ) ) ) ) ).

% observable_after_path
thf(fact_1119_observable__after__path,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Q: d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_d_b_c @ M @ Q ) )
       => ~ ! [P4: list_P7416935848109857788od_c_d] :
              ( ( path_d_b_c @ M @ Q @ P4 )
             => ( ( ( map_Pr2083123184184746678od_b_c
                    @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                    @ P4 )
                  = Io )
               => ( ( target_d_b_c @ Q @ P4 )
                 != ( after_d_b_c @ M @ Q @ Io ) ) ) ) ) ) ).

% observable_after_path
thf(fact_1120_observable__after__target,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Io9: list_P903359562653991662od_b_c,Q: a,P3: list_P6327159017948738492od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ Io9 ) @ ( lS_a_b_c @ M @ Q ) )
       => ( ( path_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Io ) @ P3 )
         => ( ( ( map_Pr776894537227705078od_b_c
                @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                @ P3 )
              = Io9 )
           => ( ( target_a_b_c @ ( after_a_b_c @ M @ Q @ Io ) @ P3 )
              = ( after_a_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Io @ Io9 ) ) ) ) ) ) ) ).

% observable_after_target
thf(fact_1121_observable__after__target,axiom,
    ! [M: fsm_d_b_c,Io: list_P903359562653991662od_b_c,Io9: list_P903359562653991662od_b_c,Q: d,P3: list_P7416935848109857788od_c_d] :
      ( ( observable_d_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ Io9 ) @ ( lS_d_b_c @ M @ Q ) )
       => ( ( path_d_b_c @ M @ ( after_d_b_c @ M @ Q @ Io ) @ P3 )
         => ( ( ( map_Pr2083123184184746678od_b_c
                @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                @ P3 )
              = Io9 )
           => ( ( target_d_b_c @ ( after_d_b_c @ M @ Q @ Io ) @ P3 )
              = ( after_d_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Io @ Io9 ) ) ) ) ) ) ) ).

% observable_after_target
thf(fact_1122_observable__path__language__step,axiom,
    ! [M: fsm_a_b_c,Q: a,P3: list_P6327159017948738492od_c_a,X: b,Y: c] :
      ( ( observable_a_b_c @ M )
     => ( ( path_a_b_c @ M @ Q @ P3 )
       => ( ~ ? [X4: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ M ) )
                & ( ( produc4225943634317630866od_c_a @ X4 )
                  = ( target_a_b_c @ Q @ P3 ) )
                & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                  = X )
                & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                  = Y ) )
         => ~ ( member6330420149250801815od_b_c
              @ ( append2547753245680614915od_b_c
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                  @ P3 )
                @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
              @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% observable_path_language_step
thf(fact_1123_observable__path__language__step,axiom,
    ! [M: fsm_d_b_c,Q: d,P3: list_P7416935848109857788od_c_d,X: b,Y: c] :
      ( ( observable_d_b_c @ M )
     => ( ( path_d_b_c @ M @ Q @ P3 )
       => ( ~ ? [X4: produc1399170498009216118od_c_d] :
                ( ( member4231278564905875615od_c_d @ X4 @ ( transitions_d_b_c @ M ) )
                & ( ( produc1508465569166014290od_c_d @ X4 )
                  = ( target_d_b_c @ Q @ P3 ) )
                & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) )
                  = X )
                & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X4 ) ) )
                  = Y ) )
         => ~ ( member6330420149250801815od_b_c
              @ ( append2547753245680614915od_b_c
                @ ( map_Pr2083123184184746678od_b_c
                  @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                  @ P3 )
                @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
              @ ( lS_d_b_c @ M @ Q ) ) ) ) ) ).

% observable_path_language_step
thf(fact_1124_reachable__def,axiom,
    ( reachable_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q3: a] :
        ? [P8: list_P6327159017948738492od_c_a] :
          ( ( path_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ P8 )
          & ( ( target_a_b_c @ ( initial_a_b_c @ M2 ) @ P8 )
            = Q3 ) ) ) ) ).

% reachable_def
thf(fact_1125_reachable__def,axiom,
    ( reachable_d_b_c
    = ( ^ [M2: fsm_d_b_c,Q3: d] :
        ? [P8: list_P7416935848109857788od_c_d] :
          ( ( path_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) @ P8 )
          & ( ( target_d_b_c @ ( initial_d_b_c @ M2 ) @ P8 )
            = Q3 ) ) ) ) ).

% reachable_def
thf(fact_1126_LS_092_060_094sub_062i_092_060_094sub_062n_Oelims,axiom,
    ! [X: fsm_li2029469768545131004_c_nat,Xa: list_P903359562653991662od_b_c,Xb: set_li6436108459499378894od_b_c,Y: set_li4639764580484544813_c_nat] :
      ( ( ( lS_i_n6924076591458517989_c_nat @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collec1199358614461328332_c_nat
          @ ^ [Uu3: list_P3641384893615913079_c_nat] :
            ? [P8: list_P5293700762493941463od_b_c] :
              ( ( Uu3
                = ( map_Pr3201276518747544052_c_nat
                  @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_l8745066325403190020_c_nat @ X @ Xa @ P8 )
              & ( member6330420149250801815od_b_c
                @ ( map_Pr3740398654890430971od_b_c @ produc8698072664305447413_c_nat
                  @ ( map_Pr3201276518747544052_c_nat
                    @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                    @ P8 ) )
                @ Xb ) ) ) ) ) ).

% LS\<^sub>i\<^sub>n.elims
thf(fact_1127_LS_092_060_094sub_062i_092_060_094sub_062n_Osimps,axiom,
    ( lS_i_n6924076591458517989_c_nat
    = ( ^ [M2: fsm_li2029469768545131004_c_nat,Q3: list_P903359562653991662od_b_c,Xss3: set_li6436108459499378894od_b_c] :
          ( collec1199358614461328332_c_nat
          @ ^ [Uu3: list_P3641384893615913079_c_nat] :
            ? [P8: list_P5293700762493941463od_b_c] :
              ( ( Uu3
                = ( map_Pr3201276518747544052_c_nat
                  @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                  @ P8 ) )
              & ( path_l8745066325403190020_c_nat @ M2 @ Q3 @ P8 )
              & ( member6330420149250801815od_b_c
                @ ( map_Pr3740398654890430971od_b_c @ produc8698072664305447413_c_nat
                  @ ( map_Pr3201276518747544052_c_nat
                    @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                    @ P8 ) )
                @ Xss3 ) ) ) ) ) ).

% LS\<^sub>i\<^sub>n.simps
thf(fact_1128_remove__proper__prefixes__def,axiom,
    ( remove5339202614008355685od_b_c
    = ( ^ [Xs3: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ Xs3 )
              & ~ ? [X7: list_P903359562653991662od_b_c] :
                    ( ( X7 != nil_Product_prod_b_c )
                    & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ X2 @ X7 ) @ Xs3 ) ) ) ) ) ) ).

% remove_proper_prefixes_def
thf(fact_1129_prefix__pairs_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P205660002400636589od_b_c] :
      ( ( ( prefix5723457598024033902od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y != nil_Pr894548836149926573od_b_c ) )
       => ~ ! [V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ V4 @ Va ) )
             => ( Y
               != ( append3867215013846006082od_b_c @ ( prefix5723457598024033902od_b_c @ ( butlas5354910156707045818od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) )
                  @ ( map_li1896284803375742973od_b_c
                    @ ^ [Ys4: list_P903359562653991662od_b_c] : ( produc3076307724246486423od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) )
                    @ ( butlas2026940317822895424od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) ) ) ) ) ) ) ) ).

% prefix_pairs.elims
thf(fact_1130_prefix__pairs_Osimps_I1_J,axiom,
    ( ( prefix5723457598024033902od_b_c @ nil_Product_prod_b_c )
    = nil_Pr894548836149926573od_b_c ) ).

% prefix_pairs.simps(1)
thf(fact_1131_prefix__pairs__set,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( set_Pr292865031892111420od_b_c @ ( prefix5723457598024033902od_b_c @ Xs ) )
      = ( collec4655644190068631058od_b_c
        @ ^ [Uu3: produc5878855887281848999od_b_c] :
          ? [Zs2: list_P903359562653991662od_b_c,Ys4: list_P903359562653991662od_b_c] :
            ( ( Uu3
              = ( produc3076307724246486423od_b_c @ Zs2 @ Ys4 ) )
            & ? [Xs13: list_P903359562653991662od_b_c,Xs24: list_P903359562653991662od_b_c] :
                ( ( ( append2547753245680614915od_b_c @ Zs2 @ Xs13 )
                  = Ys4 )
                & ( ( append2547753245680614915od_b_c @ Ys4 @ Xs24 )
                  = Xs )
                & ( Xs13 != nil_Product_prod_b_c ) ) ) ) ) ).

% prefix_pairs_set
thf(fact_1132_prefix__pairs__set__alt,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( set_Pr292865031892111420od_b_c @ ( prefix5723457598024033902od_b_c @ Xs ) )
      = ( collec4655644190068631058od_b_c
        @ ^ [Uu3: produc5878855887281848999od_b_c] :
          ? [Xs13: list_P903359562653991662od_b_c,Xs24: list_P903359562653991662od_b_c] :
            ( ( Uu3
              = ( produc3076307724246486423od_b_c @ Xs13 @ ( append2547753245680614915od_b_c @ Xs13 @ Xs24 ) ) )
            & ( Xs24 != nil_Product_prod_b_c )
            & ? [Xs33: list_P903359562653991662od_b_c] :
                ( ( append2547753245680614915od_b_c @ Xs13 @ ( append2547753245680614915od_b_c @ Xs24 @ Xs33 ) )
                = Xs ) ) ) ) ).

% prefix_pairs_set_alt
thf(fact_1133_prefix__pairs_Osimps_I2_J,axiom,
    ! [V2: product_prod_b_c,Va2: list_P903359562653991662od_b_c] :
      ( ( prefix5723457598024033902od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va2 ) )
      = ( append3867215013846006082od_b_c @ ( prefix5723457598024033902od_b_c @ ( butlas5354910156707045818od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va2 ) ) )
        @ ( map_li1896284803375742973od_b_c
          @ ^ [Ys4: list_P903359562653991662od_b_c] : ( produc3076307724246486423od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ V2 @ Va2 ) )
          @ ( butlas2026940317822895424od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va2 ) ) ) ) ) ) ).

% prefix_pairs.simps(2)
thf(fact_1134_prefix__pairs_Opelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P205660002400636589od_b_c] :
      ( ( ( prefix5723457598024033902od_b_c @ X )
        = Y )
     => ( ( accp_l4654477130474446199od_b_c @ prefix3768999732699559079od_b_c @ X )
       => ( ( ( X = nil_Product_prod_b_c )
           => ( ( Y = nil_Pr894548836149926573od_b_c )
             => ~ ( accp_l4654477130474446199od_b_c @ prefix3768999732699559079od_b_c @ nil_Product_prod_b_c ) ) )
         => ~ ! [V4: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
                ( ( X
                  = ( cons_P4529483553340347422od_b_c @ V4 @ Va ) )
               => ( ( Y
                    = ( append3867215013846006082od_b_c @ ( prefix5723457598024033902od_b_c @ ( butlas5354910156707045818od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) )
                      @ ( map_li1896284803375742973od_b_c
                        @ ^ [Ys4: list_P903359562653991662od_b_c] : ( produc3076307724246486423od_b_c @ Ys4 @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) )
                        @ ( butlas2026940317822895424od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) ) ) ) )
                 => ~ ( accp_l4654477130474446199od_b_c @ prefix3768999732699559079od_b_c @ ( cons_P4529483553340347422od_b_c @ V4 @ Va ) ) ) ) ) ) ) ).

% prefix_pairs.pelims
thf(fact_1135_shortest__list__in__tree__or__default_Oelims,axiom,
    ! [X: list_l8907847357763382004od_b_c,Xa: prefix425356687782099470od_b_c,Xb: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( interm1404143555434137040od_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( foldl_8708832512819626401od_b_c
          @ ^ [A6: list_P903359562653991662od_b_c,B6: list_P903359562653991662od_b_c] :
              ( if_lis437861846949295796od_b_c
              @ ( ( prefix4064274009650901372od_b_c @ Xa @ A6 )
                & ( ord_less_nat @ ( size_s3392097710323735898od_b_c @ A6 ) @ ( size_s3392097710323735898od_b_c @ B6 ) ) )
              @ A6
              @ B6 )
          @ Xb
          @ X ) ) ) ).

% shortest_list_in_tree_or_default.elims
thf(fact_1136_shortest__list__in__tree__or__default_Osimps,axiom,
    ( interm1404143555434137040od_b_c
    = ( ^ [Xs3: list_l8907847357763382004od_b_c,T5: prefix425356687782099470od_b_c,X2: list_P903359562653991662od_b_c] :
          ( foldl_8708832512819626401od_b_c
          @ ^ [A6: list_P903359562653991662od_b_c,B6: list_P903359562653991662od_b_c] :
              ( if_lis437861846949295796od_b_c
              @ ( ( prefix4064274009650901372od_b_c @ T5 @ A6 )
                & ( ord_less_nat @ ( size_s3392097710323735898od_b_c @ A6 ) @ ( size_s3392097710323735898od_b_c @ B6 ) ) )
              @ A6
              @ B6 )
          @ X2
          @ Xs3 ) ) ) ).

% shortest_list_in_tree_or_default.simps
thf(fact_1137_language__for__input__set,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Xs: list_b] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( set_li4480668622519654659od_b_c @ ( langua1163729730700701121_c_b_c @ M @ Q @ Xs ) )
          = ( collec2280997390073109977od_b_c
            @ ^ [Io4: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Io4 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
                & ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c @ Io4 )
                  = Xs ) ) ) ) ) ) ).

% language_for_input_set
thf(fact_1138_language__for__input__set,axiom,
    ! [M: fsm_a_b_c,Q: a,Xs: list_b] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( ( set_li4480668622519654659od_b_c @ ( langua5143504920213240017_a_b_c @ M @ Q @ Xs ) )
          = ( collec2280997390073109977od_b_c
            @ ^ [Io4: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Io4 @ ( lS_a_b_c @ M @ Q ) )
                & ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c @ Io4 )
                  = Xs ) ) ) ) ) ) ).

% language_for_input_set
thf(fact_1139_language__for__input__set,axiom,
    ! [M: fsm_li7789363362239116584od_b_c,Q: list_P903359562653991662od_b_c,Xs: list_nat] :
      ( ( observ2194746696072761382od_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states1638942826817349861od_b_c @ M ) )
       => ( ( set_li1782360227516047310od_b_c @ ( langua7622801871917929244od_b_c @ M @ Q @ Xs ) )
          = ( collec2289857514644937336od_b_c
            @ ^ [Io4: list_P4618364105659340195od_b_c] :
                ( ( member1702757119880923450od_b_c @ Io4 @ ( lS_lis9220523473116252810od_b_c @ M @ Q ) )
                & ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c @ Io4 )
                  = Xs ) ) ) ) ) ) ).

% language_for_input_set
thf(fact_1140_language__for__input__set,axiom,
    ! [M: fsm_a_6390678650791688088od_b_c,Q: a,Xs: list_nat] :
      ( ( observ667460880479887382od_b_c @ M )
     => ( ( member_a @ Q @ ( states1206967506758974293od_b_c @ M ) )
       => ( ( set_li1782360227516047310od_b_c @ ( langua8398761482416667660od_b_c @ M @ Q @ Xs ) )
          = ( collec2289857514644937336od_b_c
            @ ^ [Io4: list_P4618364105659340195od_b_c] :
                ( ( member1702757119880923450od_b_c @ Io4 @ ( lS_a_n6600196584412307578od_b_c @ M @ Q ) )
                & ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c @ Io4 )
                  = Xs ) ) ) ) ) ) ).

% language_for_input_set
thf(fact_1141_filter__states__simps_I5_J,axiom,
    ! [P: a > $o,M: fsm_a_b_c] :
      ( ( P @ ( initial_a_b_c @ M ) )
     => ( ( transitions_a_b_c @ ( filter_states_a_b_c @ M @ P ) )
        = ( collec8405073525749625505od_c_a
          @ ^ [T4: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T4 @ ( transitions_a_b_c @ M ) )
              & ( P @ ( produc4225943634317630866od_c_a @ T4 ) )
              & ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) ) ) ) ).

% filter_states_simps(5)
thf(fact_1142_filter__states__simps_I5_J,axiom,
    ! [P: d > $o,M: fsm_d_b_c] :
      ( ( P @ ( initial_d_b_c @ M ) )
     => ( ( transitions_d_b_c @ ( filter_states_d_b_c @ M @ P ) )
        = ( collec7134311822446639841od_c_d
          @ ^ [T4: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ T4 @ ( transitions_d_b_c @ M ) )
              & ( P @ ( produc1508465569166014290od_c_d @ T4 ) )
              & ( P @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) ) ) ) ) ) ).

% filter_states_simps(5)
thf(fact_1143_filter__states__simps_I1_J,axiom,
    ! [P: a > $o,M: fsm_a_b_c] :
      ( ( P @ ( initial_a_b_c @ M ) )
     => ( ( initial_a_b_c @ ( filter_states_a_b_c @ M @ P ) )
        = ( initial_a_b_c @ M ) ) ) ).

% filter_states_simps(1)
thf(fact_1144_filter__states__simps_I1_J,axiom,
    ! [P: d > $o,M: fsm_d_b_c] :
      ( ( P @ ( initial_d_b_c @ M ) )
     => ( ( initial_d_b_c @ ( filter_states_d_b_c @ M @ P ) )
        = ( initial_d_b_c @ M ) ) ) ).

% filter_states_simps(1)
thf(fact_1145_filter__states__simps_I2_J,axiom,
    ! [P: a > $o,M: fsm_a_b_c] :
      ( ( P @ ( initial_a_b_c @ M ) )
     => ( ( states_a_b_c @ ( filter_states_a_b_c @ M @ P ) )
        = ( filter_a @ P @ ( states_a_b_c @ M ) ) ) ) ).

% filter_states_simps(2)
thf(fact_1146_filter__states__simps_I2_J,axiom,
    ! [P: d > $o,M: fsm_d_b_c] :
      ( ( P @ ( initial_d_b_c @ M ) )
     => ( ( states_d_b_c @ ( filter_states_d_b_c @ M @ P ) )
        = ( filter_d @ P @ ( states_d_b_c @ M ) ) ) ) ).

% filter_states_simps(2)
thf(fact_1147_paths__up__to__length__set,axiom,
    ! [Q: a,M: fsm_a_b_c,K3: nat] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( paths_5655032219139660648_a_b_c @ M @ Q @ K3 )
        = ( collec6273869032445462695od_c_a
          @ ^ [P8: list_P6327159017948738492od_c_a] :
              ( ( path_a_b_c @ M @ Q @ P8 )
              & ( ord_less_eq_nat @ ( size_s3386368156187063848od_c_a @ P8 ) @ K3 ) ) ) ) ) ).

% paths_up_to_length_set
thf(fact_1148_paths__for__input_H__set,axiom,
    ! [Q: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Xs: list_b,Prev2: list_P8364599791545511612od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
     => ( ( paths_2402314502658583498_c_b_c @ ( h_from2122548697928753168_c_b_c @ M ) @ Xs @ Q @ Prev2 )
        = ( collec1242728128799169191od_b_c
          @ ^ [Uu3: list_P8364599791545511612od_b_c] :
            ? [P8: list_P8364599791545511612od_b_c] :
              ( ( Uu3
                = ( append8574118600258580689od_b_c @ Prev2 @ P8 ) )
              & ( path_l6977963524759401717_c_b_c @ M @ Q @ P8 )
              & ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c
                  @ ( map_Pr4814182253694984182od_b_c
                    @ ^ [T4: produc596031391177498678od_b_c] : ( product_Pair_b_c @ ( produc4488652850390612441od_b_c @ ( produc829356566976367572od_b_c @ T4 ) ) @ ( produc5388473464130769137od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T4 ) ) ) )
                    @ P8 ) )
                = Xs ) ) ) ) ) ).

% paths_for_input'_set
thf(fact_1149_paths__for__input_H__set,axiom,
    ! [Q: a,M: fsm_a_b_c,Xs: list_b,Prev2: list_P6327159017948738492od_c_a] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( paths_6276656153717473370_a_b_c @ ( h_from_a_b_c @ M ) @ Xs @ Q @ Prev2 )
        = ( collec6273869032445462695od_c_a
          @ ^ [Uu3: list_P6327159017948738492od_c_a] :
            ? [P8: list_P6327159017948738492od_c_a] :
              ( ( Uu3
                = ( append3884164603879732689od_c_a @ Prev2 @ P8 ) )
              & ( path_a_b_c @ M @ Q @ P8 )
              & ( ( map_Pr8222292247188198875_b_c_b @ product_fst_b_c
                  @ ( map_Pr776894537227705078od_b_c
                    @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                    @ P8 ) )
                = Xs ) ) ) ) ) ).

% paths_for_input'_set
thf(fact_1150_paths__for__input_H__set,axiom,
    ! [Q: list_P903359562653991662od_b_c,M: fsm_li7789363362239116584od_b_c,Xs: list_nat,Prev2: list_P8892595561428699129od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q @ ( states1638942826817349861od_b_c @ M ) )
     => ( ( paths_8577358193962876499od_b_c @ ( h_from3744152339648312717od_b_c @ M ) @ Xs @ Q @ Prev2 )
        = ( collec9003323369204841422od_b_c
          @ ^ [Uu3: list_P8892595561428699129od_b_c] :
            ? [P8: list_P8892595561428699129od_b_c] :
              ( ( Uu3
                = ( append6326602238407583246od_b_c @ Prev2 @ P8 ) )
              & ( path_l3297086352762299624od_b_c @ M @ Q @ P8 )
              & ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c
                  @ ( map_Pr3385157932045932098od_b_c
                    @ ^ [T4: produc3894960095624370921od_b_c] : ( produc8137419655804493381od_b_c @ ( produc861206492263493522od_b_c @ ( produc4509980026417360309od_b_c @ T4 ) ) @ ( produc1807356612421382019od_b_c @ ( produc7935499289977867216od_b_c @ ( produc4509980026417360309od_b_c @ T4 ) ) ) )
                    @ P8 ) )
                = Xs ) ) ) ) ) ).

% paths_for_input'_set
thf(fact_1151_paths__for__input_H__set,axiom,
    ! [Q: a,M: fsm_a_6390678650791688088od_b_c,Xs: list_nat,Prev2: list_P1010261849227979929_b_c_a] :
      ( ( member_a @ Q @ ( states1206967506758974293od_b_c @ M ) )
     => ( ( paths_7417869917651172803od_b_c @ ( h_from2640343883176879101od_b_c @ M ) @ Xs @ Q @ Prev2 )
        = ( collec667911008590165870_b_c_a
          @ ^ [Uu3: list_P1010261849227979929_b_c_a] :
            ? [P8: list_P1010261849227979929_b_c_a] :
              ( ( Uu3
                = ( append8046498633336543918_b_c_a @ Prev2 @ P8 ) )
              & ( path_a4443415204092530648od_b_c @ M @ Q @ P8 )
              & ( ( map_Pr7981408659186842025_c_nat @ produc3608113002378536793od_b_c
                  @ ( map_Pr3124327934517951202od_b_c
                    @ ^ [T4: produc5894170661315020937_b_c_a] : ( produc8137419655804493381od_b_c @ ( produc1343630566382188834_b_c_a @ ( produc1179498357986986581_b_c_a @ T4 ) ) @ ( produc1715878850288909075_b_c_a @ ( produc210687423892126304_b_c_a @ ( produc1179498357986986581_b_c_a @ T4 ) ) ) )
                    @ P8 ) )
                = Xs ) ) ) ) ) ).

% paths_for_input'_set
thf(fact_1152_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,I: fsm_a_b_c,V5: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) )
       != ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
     => ( ( state_2362830510734323903_c_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: list_P903359562653991662od_b_c] :
                          ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1153_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,I: fsm_d_b_c,V5: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) )
       != ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
     => ( ( state_2362830510734323903_c_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_2850395784482391045od_b_c @ V5 @ ( reacha8116992257183400179_c_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: list_P903359562653991662od_b_c] :
                          ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1154_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c] :
      ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
       != ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: a] :
                          ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1155_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_a_b_c,I: fsm_d_b_c,V5: a > list_P903359562653991662od_b_c] :
      ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
       != ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
     => ( ( state_7672330573471793359_a_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: a] :
                          ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1156_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_d_b_c,I: fsm_a_b_c,V5: d > list_P903359562653991662od_b_c] :
      ( ( ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) )
       != ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
     => ( ( state_6014242345326633810_d_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: d] :
                          ( ( member_d @ Q9 @ ( reacha9185589339461546374_d_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1157_minimal__sequence__to__failure__from__state__cover__assignment__ob,axiom,
    ! [M: fsm_d_b_c,I: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c] :
      ( ( ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) )
       != ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
     => ( ( state_6014242345326633810_d_b_c @ M @ V5 )
       => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) ) )
         => ~ ! [IoT: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ IoT @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) )
               => ! [IoX: list_P903359562653991662od_b_c] :
                    ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ IoX ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) )
                   => ~ ! [Io10: list_P903359562653991662od_b_c,Q9: d] :
                          ( ( member_d @ Q9 @ ( reacha9185589339461546374_d_b_c @ M ) )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( V5 @ Q9 ) @ Io10 ) @ ( sup_su3823046536922626210od_b_c @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) ) @ ( minus_5375846548645262261od_b_c @ ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) )
                           => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ IoX ) @ ( size_s3392097710323735898od_b_c @ Io10 ) ) ) ) ) ) ) ) ) ).

% minimal_sequence_to_failure_from_state_cover_assignment_ob
thf(fact_1158_image__Int__subset,axiom,
    ! [F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F3 @ ( inf_in4978071631833541052od_b_c @ A2 @ B4 ) ) @ ( inf_in4978071631833541052od_b_c @ ( image_2850395784482391045od_b_c @ F3 @ A2 ) @ ( image_2850395784482391045od_b_c @ F3 @ B4 ) ) ) ).

% image_Int_subset
thf(fact_1159_state__cover__assignment__card,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ M @ V5 )
     => ( ( observable_a_b_c @ M )
       => ( ( finite5583770498833199894od_b_c @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) )
          = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ) ).

% state_cover_assignment_card
thf(fact_1160_state__cover__assignment__card,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c] :
      ( ( state_6014242345326633810_d_b_c @ M @ V5 )
     => ( ( observable_d_b_c @ M )
       => ( ( finite5583770498833199894od_b_c @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) )
          = ( finite_card_d @ ( reacha9185589339461546374_d_b_c @ M ) ) ) ) ) ).

% state_cover_assignment_card
thf(fact_1161_state__cover__assignment__language,axiom,
    ! [M: fsm_a_b_c,V5: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ M @ V5 )
     => ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ V5 @ ( reacha1620305530751930115_a_b_c @ M ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% state_cover_assignment_language
thf(fact_1162_state__cover__assignment__language,axiom,
    ! [M: fsm_d_b_c,V5: d > list_P903359562653991662od_b_c] :
      ( ( state_6014242345326633810_d_b_c @ M @ V5 )
     => ( ord_le282488521294790766od_b_c @ ( image_1329551058250833970od_b_c @ V5 @ ( reacha9185589339461546374_d_b_c @ M ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) ) ) ).

% state_cover_assignment_language
thf(fact_1163_LS_Opelims,axiom,
    ! [X: fsm_a_b_c,Xa: a,Y: set_li6436108459499378894od_b_c] :
      ( ( ( lS_a_b_c @ X @ Xa )
        = Y )
     => ( ( accp_P8775296850406592587_b_c_a @ lS_rel_a_b_c @ ( produc1330280085856475698_b_c_a @ X @ Xa ) )
       => ~ ( ( Y
              = ( collec2280997390073109977od_b_c
                @ ^ [Uu3: list_P903359562653991662od_b_c] :
                  ? [P8: list_P6327159017948738492od_c_a] :
                    ( ( Uu3
                      = ( map_Pr776894537227705078od_b_c
                        @ ^ [T4: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) )
                        @ P8 ) )
                    & ( path_a_b_c @ X @ Xa @ P8 ) ) ) )
           => ~ ( accp_P8775296850406592587_b_c_a @ lS_rel_a_b_c @ ( produc1330280085856475698_b_c_a @ X @ Xa ) ) ) ) ) ).

% LS.pelims
thf(fact_1164_LS_Opelims,axiom,
    ! [X: fsm_d_b_c,Xa: d,Y: set_li6436108459499378894od_b_c] :
      ( ( ( lS_d_b_c @ X @ Xa )
        = Y )
     => ( ( accp_P3585319936889966987_b_c_d @ lS_rel_d_b_c @ ( produc5363675196284939506_b_c_d @ X @ Xa ) )
       => ~ ( ( Y
              = ( collec2280997390073109977od_b_c
                @ ^ [Uu3: list_P903359562653991662od_b_c] :
                  ? [P8: list_P7416935848109857788od_c_d] :
                    ( ( Uu3
                      = ( map_Pr2083123184184746678od_b_c
                        @ ^ [T4: produc1399170498009216118od_c_d] : ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) )
                        @ P8 ) )
                    & ( path_d_b_c @ X @ Xa @ P8 ) ) ) )
           => ~ ( accp_P3585319936889966987_b_c_d @ lS_rel_d_b_c @ ( produc5363675196284939506_b_c_d @ X @ Xa ) ) ) ) ) ).

% LS.pelims
thf(fact_1165_img__snd,axiom,
    ! [A: b,B: c,S: set_Product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A @ B ) @ S )
     => ( member_c @ B @ ( image_7762865866877615261_b_c_c @ product_snd_b_c @ S ) ) ) ).

% img_snd
thf(fact_1166_img__snd,axiom,
    ! [A: nat,B: list_P903359562653991662od_b_c,S: set_Pr2622754303974797129od_b_c] :
      ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ A @ B ) @ S )
     => ( member6330420149250801815od_b_c @ B @ ( image_30863409318222036od_b_c @ produc2468146899304044183od_b_c @ S ) ) ) ).

% img_snd
thf(fact_1167_img__fst,axiom,
    ! [A: b,B: c,S: set_Product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A @ B ) @ S )
     => ( member_b @ A @ ( image_7762865866877615260_b_c_b @ product_fst_b_c @ S ) ) ) ).

% img_fst
thf(fact_1168_img__fst,axiom,
    ! [A: nat,B: list_P903359562653991662od_b_c,S: set_Pr2622754303974797129od_b_c] :
      ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ A @ B ) @ S )
     => ( member_nat @ A @ ( image_7089917280164999018_c_nat @ produc3608113002378536793od_b_c @ S ) ) ) ).

% img_fst
thf(fact_1169_op__conc__empty__img__id,axiom,
    ! [L8: set_li6436108459499378894od_b_c] :
      ( ( image_2850395784482391045od_b_c @ ( append2547753245680614915od_b_c @ nil_Product_prod_b_c ) @ L8 )
      = L8 ) ).

% op_conc_empty_img_id
thf(fact_1170_snd__image__mp,axiom,
    ! [A2: set_Product_prod_b_c,B4: set_c,X: b,Y: c] :
      ( ( ord_less_eq_set_c @ ( image_7762865866877615261_b_c_c @ product_snd_b_c @ A2 ) @ B4 )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ A2 )
       => ( member_c @ Y @ B4 ) ) ) ).

% snd_image_mp
thf(fact_1171_snd__image__mp,axiom,
    ! [A2: set_Pr2622754303974797129od_b_c,B4: set_li6436108459499378894od_b_c,X: nat,Y: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( image_30863409318222036od_b_c @ produc2468146899304044183od_b_c @ A2 ) @ B4 )
     => ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ A2 )
       => ( member6330420149250801815od_b_c @ Y @ B4 ) ) ) ).

% snd_image_mp
thf(fact_1172_fst__image__mp,axiom,
    ! [A2: set_Product_prod_b_c,B4: set_b,X: b,Y: c] :
      ( ( ord_less_eq_set_b @ ( image_7762865866877615260_b_c_b @ product_fst_b_c @ A2 ) @ B4 )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ A2 )
       => ( member_b @ X @ B4 ) ) ) ).

% fst_image_mp
thf(fact_1173_fst__image__mp,axiom,
    ! [A2: set_Pr2622754303974797129od_b_c,B4: set_nat,X: nat,Y: list_P903359562653991662od_b_c] :
      ( ( ord_less_eq_set_nat @ ( image_7089917280164999018_c_nat @ produc3608113002378536793od_b_c @ A2 ) @ B4 )
     => ( ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y ) @ A2 )
       => ( member_nat @ X @ B4 ) ) ) ).

% fst_image_mp
thf(fact_1174_None__notin__image__Some,axiom,
    ! [A2: set_a] :
      ~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A2 ) ) ).

% None_notin_image_Some
thf(fact_1175_None__notin__image__Some,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ~ ( member6481636158984118493od_b_c @ none_l1245059289828015823od_b_c @ ( image_3124369808113985355od_b_c @ some_l689282263436086355od_b_c @ A2 ) ) ).

% None_notin_image_Some
thf(fact_1176_in__snd__imageE,axiom,
    ! [Y: c,S: set_Product_prod_b_c] :
      ( ( member_c @ Y @ ( image_7762865866877615261_b_c_c @ product_snd_b_c @ S ) )
     => ~ ! [X4: b] :
            ~ ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X4 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_1177_in__snd__imageE,axiom,
    ! [Y: list_P903359562653991662od_b_c,S: set_Pr2622754303974797129od_b_c] :
      ( ( member6330420149250801815od_b_c @ Y @ ( image_30863409318222036od_b_c @ produc2468146899304044183od_b_c @ S ) )
     => ~ ! [X4: nat] :
            ~ ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ X4 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_1178_in__fst__imageE,axiom,
    ! [X: b,S: set_Product_prod_b_c] :
      ( ( member_b @ X @ ( image_7762865866877615260_b_c_b @ product_fst_b_c @ S ) )
     => ~ ! [Y3: c] :
            ~ ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_1179_in__fst__imageE,axiom,
    ! [X: nat,S: set_Pr2622754303974797129od_b_c] :
      ( ( member_nat @ X @ ( image_7089917280164999018_c_nat @ produc3608113002378536793od_b_c @ S ) )
     => ~ ! [Y3: list_P903359562653991662od_b_c] :
            ~ ( member8899240064043329450od_b_c @ ( produc8137419655804493381od_b_c @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_1180_observable__after__reachable__surj,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( image_3173854338463926933_b_c_a @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
        = ( reacha1620305530751930115_a_b_c @ M ) ) ) ).

% observable_after_reachable_surj
thf(fact_1181_observable__after__reachable__surj,axiom,
    ! [M: fsm_d_b_c] :
      ( ( observable_d_b_c @ M )
     => ( ( image_3173854338463926936_b_c_d @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
        = ( reacha9185589339461546374_d_b_c @ M ) ) ) ).

% observable_after_reachable_surj
thf(fact_1182_language__equivalence__classes__preserve__observability,axiom,
    ! [M5: fsm_set_a_b_c,M: fsm_a_b_c] :
      ( ( ( transi8205445899535437940_a_b_c @ M5 )
        = ( image_5400094664181065349_set_a
          @ ^ [T4: produc2669932201312201782od_c_a] :
              ( produc3915556858435501990_set_a
              @ ( collect_a
                @ ^ [Q3: a] :
                    ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
                    & ( ( lS_a_b_c @ M @ Q3 )
                      = ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T4 ) ) ) ) )
              @ ( produc799526633598312797_set_a @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) )
                @ ( product_Pair_c_set_a @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) )
                  @ ( collect_a
                    @ ^ [Q3: a] :
                        ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
                        & ( ( lS_a_b_c @ M @ Q3 )
                          = ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) ) ) ) ) )
          @ ( transitions_a_b_c @ M ) ) )
     => ( ( observable_a_b_c @ M )
       => ( observable_set_a_b_c @ M5 ) ) ) ).

% language_equivalence_classes_preserve_observability
thf(fact_1183_language__equivalence__classes__preserve__observability,axiom,
    ! [M5: fsm_set_d_b_c,M: fsm_d_b_c] :
      ( ( ( transi9092705012810146167_d_b_c @ M5 )
        = ( image_7053377148799312517_set_d
          @ ^ [T4: produc1399170498009216118od_c_d] :
              ( produc1042816977955784038_set_d
              @ ( collect_d
                @ ^ [Q3: d] :
                    ( ( member_d @ Q3 @ ( states_d_b_c @ M ) )
                    & ( ( lS_d_b_c @ M @ Q3 )
                      = ( lS_d_b_c @ M @ ( produc1508465569166014290od_c_d @ T4 ) ) ) ) )
              @ ( produc1012628753737350752_set_d @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) )
                @ ( product_Pair_c_set_d @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) )
                  @ ( collect_d
                    @ ^ [Q3: d] :
                        ( ( member_d @ Q3 @ ( states_d_b_c @ M ) )
                        & ( ( lS_d_b_c @ M @ Q3 )
                          = ( lS_d_b_c @ M @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T4 ) ) ) ) ) ) ) ) ) )
          @ ( transitions_d_b_c @ M ) ) )
     => ( ( observable_d_b_c @ M )
       => ( observable_set_d_b_c @ M5 ) ) ) ).

% language_equivalence_classes_preserve_observability
thf(fact_1184_LS_092_060_094sub_062i_092_060_094sub_062n_Opelims,axiom,
    ! [X: fsm_li2029469768545131004_c_nat,Xa: list_P903359562653991662od_b_c,Xb: set_li6436108459499378894od_b_c,Y: set_li4639764580484544813_c_nat] :
      ( ( ( lS_i_n6924076591458517989_c_nat @ X @ Xa @ Xb )
        = Y )
     => ( ( accp_P2224188031119546935od_b_c @ lS_i_n3139218242678872554_c_nat @ ( produc6581266043806648114od_b_c @ X @ ( produc3398925745557389175od_b_c @ Xa @ Xb ) ) )
       => ~ ( ( Y
              = ( collec1199358614461328332_c_nat
                @ ^ [Uu3: list_P3641384893615913079_c_nat] :
                  ? [P8: list_P5293700762493941463od_b_c] :
                    ( ( Uu3
                      = ( map_Pr3201276518747544052_c_nat
                        @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                        @ P8 ) )
                    & ( path_l8745066325403190020_c_nat @ X @ Xa @ P8 )
                    & ( member6330420149250801815od_b_c
                      @ ( map_Pr3740398654890430971od_b_c @ produc8698072664305447413_c_nat
                        @ ( map_Pr3201276518747544052_c_nat
                          @ ^ [T4: produc6787499024992510535od_b_c] : ( produc573923733243432673_c_nat @ ( produc4463163520150497848od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) @ ( produc3608113002378536793od_b_c @ ( produc1286195076073897334od_b_c @ ( produc4910823246647749523od_b_c @ T4 ) ) ) )
                          @ P8 ) )
                      @ Xb ) ) ) )
           => ~ ( accp_P2224188031119546935od_b_c @ lS_i_n3139218242678872554_c_nat @ ( produc6581266043806648114od_b_c @ X @ ( produc3398925745557389175od_b_c @ Xa @ Xb ) ) ) ) ) ) ).

% LS\<^sub>i\<^sub>n.pelims
thf(fact_1185_minimise__props_I5_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( transi8205445899535437940_a_b_c @ ( minimise_a_b_c @ M ) )
        = ( image_5400094664181065349_set_a
          @ ^ [T4: produc2669932201312201782od_c_a] :
              ( produc3915556858435501990_set_a
              @ ( collect_a
                @ ^ [Q3: a] :
                    ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
                    & ( ( lS_a_b_c @ M @ Q3 )
                      = ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T4 ) ) ) ) )
              @ ( produc799526633598312797_set_a @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) )
                @ ( product_Pair_c_set_a @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) )
                  @ ( collect_a
                    @ ^ [Q3: a] :
                        ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
                        & ( ( lS_a_b_c @ M @ Q3 )
                          = ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) ) ) ) ) )
          @ ( transitions_a_b_c @ M ) ) ) ) ).

% minimise_props(5)
thf(fact_1186_minimise__minimal,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( minimal_set_a_b_c @ ( minimise_a_b_c @ M ) ) ) ).

% minimise_minimal
thf(fact_1187_minimise__observable,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( observable_set_a_b_c @ ( minimise_a_b_c @ M ) ) ) ).

% minimise_observable
thf(fact_1188_minimise__states__subset,axiom,
    ! [M: fsm_a_b_c,Q: set_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member_set_a @ Q @ ( states_set_a_b_c @ ( minimise_a_b_c @ M ) ) )
       => ( ord_less_eq_set_a @ Q @ ( states_a_b_c @ M ) ) ) ) ).

% minimise_states_subset
thf(fact_1189_minimise__props_I1_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( initial_set_a_b_c @ ( minimise_a_b_c @ M ) )
        = ( collect_a
          @ ^ [Q4: a] :
              ( ( member_a @ Q4 @ ( states_a_b_c @ M ) )
              & ( ( lS_a_b_c @ M @ Q4 )
                = ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% minimise_props(1)

% Helper facts (5)
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $true @ X @ Y )
      = X ) ).

thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_T,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( if_lis437861846949295796od_b_c @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_T,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( if_lis437861846949295796od_b_c @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ua )
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ u2 ) ) ).

%------------------------------------------------------------------------------