%------------------------------------------------------------------------------
% 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_04869_263192__20971606_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1458 ( 269 unt; 537 typ;   0 def)
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%            Maximal formula atoms :   14 (   3 avg)
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%            Maximal formula depth :   26 (   9 avg)
%            Number of types       :  121 ( 120 usr)
%            Number of type conns  : 1299 (1299   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  418 ( 417 usr;  20 con; 0-9 aty)
%            Number of variables   : 3522 ( 140   ^;3299   !;  83   ?;3522   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:30:19.360
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thf(sy_c_Set_Oimage_001tf__d_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    image_1329551058250833970od_b_c: ( d > list_P903359562653991662od_b_c ) > set_d > set_li6436108459499378894od_b_c ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__e,type,
    state_500947992327884274_b_c_e: fsm_li553205354899133766_b_c_e > ( list_P903359562653991662od_b_c > list_P268689088907702561_b_c_e ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__b_001tf__c,type,
    state_2362830510734323903_c_b_c: fsm_li6801133765522507155_c_b_c > ( list_P903359562653991662od_b_c > list_P903359562653991662od_b_c ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__e,type,
    state_785075175243941690_b_c_e: fsm_Pr379724744552003854_b_c_e > ( produc2669932201312201782od_c_a > list_P268689088907702561_b_c_e ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_001tf__b_001tf__c,type,
    state_1238012481214864903_a_b_c: fsm_Pr6425204305901329755_a_b_c > ( produc2669932201312201782od_c_a > list_P903359562653991662od_b_c ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001t__Product____Type__Oprod_Itf__c_Mtf__a_J_001tf__a_001tf__b,type,
    state_7248828479493717430_a_a_b: fsm_Pr1886043760914421514_a_a_b > ( product_prod_c_a > list_P1467974523212632366od_a_b ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001tf__a_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__e,type,
    state_8320733454665479682_b_c_e: fsm_a_8518373703003225814_b_c_e > ( a > list_P268689088907702561_b_c_e ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001tf__a_001tf__b_001tf__c,type,
    state_7672330573471793359_a_b_c: fsm_a_b_c > ( a > list_P903359562653991662od_b_c ) > $o ).

thf(sy_c_State__Cover_Ois__state__cover__assignment_001tf__d_001tf__b_001tf__c,type,
    state_6014242345326633810_d_b_c: fsm_d_b_c > ( d > list_P903359562653991662od_b_c ) > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mtf__e_J_J,type,
    member8329588800322848842_b_c_e: list_P268689088907702561_b_c_e > set_li197352544483416321_b_c_e > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member6895035109809442519od_a_b: list_P1467974523212632366od_a_b > set_li6306622547289818894od_a_b > $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__List__Olist_It__Product____Type__Oprod_Itf__c_Mtf__a_J_J,type,
    member5552703068553123156od_c_a: list_P125642481956313003od_c_a > set_li4905775889721270027od_c_a > $o ).

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

thf(sy_c_member_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    member2378525361814473399od_b_c: prefix425356687782099470od_b_c > set_Pr4395803880006080238od_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__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_Itf__e_Mt__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J_J,type,
    member106767767543922318od_b_c: produc4773341515281486821od_b_c > set_Pr7034415387153991493od_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__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mtf__e_J,type,
    member323891770073680196_b_c_e: produc4534891796109904283_b_c_e > set_Pr3237851069733663483_b_c_e > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_Mt__Product____Type__Oprod_It__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_J_J_J,type,
    member7595321081310302990od_c_a: produc5653889938759785317od_c_a > set_Pr4541457668242118597od_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_J_J_J,type,
    member6671621370117864543od_c_a: produc1415087868921929270od_c_a > set_Pr429956822316910230od_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_Mt__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_J_J,type,
    member5500486793640445664od_c_a: produc3729687299602777783od_c_a > set_Pr7664180988061153431od_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__c_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_J,type,
    member6508725278956418977od_c_a: produc3205353004677322104od_c_a > set_Pr2640428967771533528od_c_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_Itf__e_Mtf__a_J_J_J,type,
    member8958573442437681166od_e_a: produc8570131207859728997od_e_a > set_Pr4321813372295601349od_e_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__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J,type,
    member1160383752307813046od_c_a: produc2133359284458116493od_c_a > set_Pr272002107461315949od_c_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__c_Mtf__a_J,type,
    member5074992350434858958od_c_a: product_prod_c_a > set_Product_prod_c_a > $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_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_c_member_001tf__e,type,
    member_e: e > set_e > $o ).

thf(sy_v_G,type,
    g: e ).

thf(sy_v_M1,type,
    m1: fsm_a_b_c ).

thf(sy_v_M2,type,
    m2: fsm_d_b_c ).

thf(sy_v_T,type,
    t: prefix425356687782099470od_b_c ).

thf(sy_v_V,type,
    v: a > list_P903359562653991662od_b_c ).

thf(sy_v__092_060alpha_062____,type,
    alpha: list_P903359562653991662od_b_c ).

thf(sy_v__092_060beta_062____,type,
    beta: list_P903359562653991662od_b_c ).

thf(sy_v_cg__insert,type,
    cg_insert: e > list_P903359562653991662od_b_c > e ).

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

thf(sy_v_dist__fun,type,
    dist_fun: nat > a > prefix425356687782099470od_b_c ).

thf(sy_v_handleTrace____,type,
    handleTrace: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e ).

thf(sy_v_k____,type,
    k: nat ).

thf(sy_v_m,type,
    m: nat ).

thf(sy_v_qSource____,type,
    qSource: a ).

thf(sy_v_qTarget____,type,
    qTarget: a ).

thf(sy_v_t,type,
    t2: produc2669932201312201782od_c_a ).

thf(sy_v_ttc____,type,
    ttc: list_l8907847357763382004od_b_c ).

thf(sy_v_xy____,type,
    xy: product_prod_b_c ).

% Relevant facts (920)
thf(fact_0_assms_I1_J,axiom,
    observable_a_b_c @ m1 ).

% assms(1)
thf(fact_1_assms_I2_J,axiom,
    observable_d_b_c @ m2 ).

% assms(2)
thf(fact_2_assms_I3_J,axiom,
    minimal_a_b_c @ m1 ).

% assms(3)
thf(fact_3_assms_I4_J,axiom,
    minimal_d_b_c @ m2 ).

% assms(4)
thf(fact_4_result,axiom,
    ( ( interm821963860068034213_b_c_e @ dist_fun @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ m @ t2 )
    = ( foldl_2934561762154836916od_b_c @ handleTrace @ ( produc2511600812177743883_b_c_e @ t @ g ) @ ttc ) ) ).

% result
thf(fact_5_assms_I13_J,axiom,
    conver7089555221631485245_c_d_e @ m1 @ m2 @ cg_lookup @ g ).

% assms(13)
thf(fact_6_assms_I14_J,axiom,
    conver2727675425255806140_c_d_e @ m1 @ m2 @ cg_lookup @ cg_insert ).

% assms(14)
thf(fact_7_assms_I18_J,axiom,
    ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm821963860068034213_b_c_e @ dist_fun @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ m @ t2 ) ) ) )
    = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm821963860068034213_b_c_e @ dist_fun @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ m @ t2 ) ) ) ) ) ).

% assms(18)
thf(fact_8_assms_I9_J,axiom,
    state_7672330573471793359_a_b_c @ m1 @ v ).

% assms(9)
thf(fact_9_assms_I7_J,axiom,
    member5502040268208861279od_c_a @ t2 @ ( transitions_a_b_c @ m1 ) ).

% assms(7)
thf(fact_10_IntI,axiom,
    ! [C: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ C @ A )
     => ( ( member5502040268208861279od_c_a @ C @ B )
       => ( member5502040268208861279od_c_a @ C @ ( inf_in3815988127369930372od_c_a @ A @ B ) ) ) ) ).

% IntI
thf(fact_11_IntI,axiom,
    ! [C: a,A: set_a,B: set_a] :
      ( ( member_a @ C @ A )
     => ( ( member_a @ C @ B )
       => ( member_a @ C @ ( inf_inf_set_a @ A @ B ) ) ) ) ).

% IntI
thf(fact_12_IntI,axiom,
    ! [C: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ A )
     => ( ( member6330420149250801815od_b_c @ C @ B )
       => ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ) ).

% IntI
thf(fact_13_Int__iff,axiom,
    ! [C: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ C @ ( inf_in3815988127369930372od_c_a @ A @ B ) )
      = ( ( member5502040268208861279od_c_a @ C @ A )
        & ( member5502040268208861279od_c_a @ C @ B ) ) ) ).

% Int_iff
thf(fact_14_Int__iff,axiom,
    ! [C: a,A: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B ) )
      = ( ( member_a @ C @ A )
        & ( member_a @ C @ B ) ) ) ).

% Int_iff
thf(fact_15_Int__iff,axiom,
    ! [C: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
      = ( ( member6330420149250801815od_b_c @ C @ A )
        & ( member6330420149250801815od_b_c @ C @ B ) ) ) ).

% Int_iff
thf(fact_16_inf_Oidem,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ A2 )
      = A2 ) ).

% inf.idem
thf(fact_17_inf__idem,axiom,
    ! [X: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ X @ X )
      = X ) ).

% inf_idem
thf(fact_18_inf_Oleft__idem,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) )
      = ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) ) ).

% inf.left_idem
thf(fact_19_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_20_inf_Oright__idem,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ B2 )
      = ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) ) ).

% inf.right_idem
thf(fact_21_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_22_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_23_inf_Oleft__commute,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ B2 @ ( inf_in4978071631833541052od_b_c @ A2 @ C ) )
      = ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B2 @ C ) ) ) ).

% inf.left_commute
thf(fact_24_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_25_inf_Ocommute,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A3: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ B3 @ A3 ) ) ) ).

% inf.commute
thf(fact_26_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_27_inf_Oassoc,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ C )
      = ( inf_in4978071631833541052od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B2 @ C ) ) ) ).

% inf.assoc
thf(fact_28_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_29_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_30_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_31_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_32_Int__left__commute,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C2 ) )
      = ( inf_in4978071631833541052od_b_c @ B @ ( inf_in4978071631833541052od_b_c @ A @ C2 ) ) ) ).

% Int_left_commute
thf(fact_33_Int__left__absorb,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 ) ) ).

% Int_left_absorb
thf(fact_34_Int__commute,axiom,
    ( inf_in4978071631833541052od_b_c
    = ( ^ [A4: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] : ( inf_in4978071631833541052od_b_c @ B4 @ A4 ) ) ) ).

% Int_commute
thf(fact_35_Int__absorb,axiom,
    ! [A: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ A @ A )
      = A ) ).

% Int_absorb
thf(fact_36_Int__assoc,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( inf_in4978071631833541052od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ C2 )
      = ( inf_in4978071631833541052od_b_c @ A @ ( inf_in4978071631833541052od_b_c @ B @ C2 ) ) ) ).

% Int_assoc
thf(fact_37_IntD2,axiom,
    ! [C: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ C @ ( inf_in3815988127369930372od_c_a @ A @ B ) )
     => ( member5502040268208861279od_c_a @ C @ B ) ) ).

% IntD2
thf(fact_38_IntD2,axiom,
    ! [C: a,A: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B ) )
     => ( member_a @ C @ B ) ) ).

% IntD2
thf(fact_39_IntD2,axiom,
    ! [C: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
     => ( member6330420149250801815od_b_c @ C @ B ) ) ).

% IntD2
thf(fact_40_IntD1,axiom,
    ! [C: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ C @ ( inf_in3815988127369930372od_c_a @ A @ B ) )
     => ( member5502040268208861279od_c_a @ C @ A ) ) ).

% IntD1
thf(fact_41_IntD1,axiom,
    ! [C: a,A: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B ) )
     => ( member_a @ C @ A ) ) ).

% IntD1
thf(fact_42_IntD1,axiom,
    ! [C: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
     => ( member6330420149250801815od_b_c @ C @ A ) ) ).

% IntD1
thf(fact_43_IntE,axiom,
    ! [C: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ C @ ( inf_in3815988127369930372od_c_a @ A @ B ) )
     => ~ ( ( member5502040268208861279od_c_a @ C @ A )
         => ~ ( member5502040268208861279od_c_a @ C @ B ) ) ) ).

% IntE
thf(fact_44_IntE,axiom,
    ! [C: a,A: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A @ B ) )
     => ~ ( ( member_a @ C @ A )
         => ~ ( member_a @ C @ B ) ) ) ).

% IntE
thf(fact_45_IntE,axiom,
    ! [C: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
     => ~ ( ( member6330420149250801815od_b_c @ C @ A )
         => ~ ( member6330420149250801815od_b_c @ C @ B ) ) ) ).

% IntE
thf(fact_46_observable__alt__def,axiom,
    ( observable_d_b_c
    = ( ^ [M: fsm_d_b_c] :
        ! [Q1: d,X2: b,Y2: c,Q12: d,Q13: d] :
          ( ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q1 @ ( produc3440865926910568064od_c_d @ X2 @ ( product_Pair_c_d @ Y2 @ Q12 ) ) ) @ ( transitions_d_b_c @ M ) )
            & ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q1 @ ( produc3440865926910568064od_c_d @ X2 @ ( product_Pair_c_d @ Y2 @ Q13 ) ) ) @ ( transitions_d_b_c @ M ) ) )
         => ( Q12 = Q13 ) ) ) ) ).

% observable_alt_def
thf(fact_47_observable__alt__def,axiom,
    ( observable_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [Q1: a,X2: b,Y2: c,Q12: a,Q13: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q12 ) ) ) @ ( transitions_a_b_c @ M ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q13 ) ) ) @ ( transitions_a_b_c @ M ) ) )
         => ( Q12 = Q13 ) ) ) ) ).

% observable_alt_def
thf(fact_48_convergence__graph__insert__invar__def,axiom,
    ( conver2727675425255806140_c_d_e
    = ( ^ [M1: fsm_a_b_c,M2: fsm_d_b_c,Cg_lookup: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,Cg_insert: e > list_P903359562653991662od_b_c > e] :
        ! [G: e,Gamma: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
         => ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) )
           => ( ( conver7089555221631485245_c_d_e @ M1 @ M2 @ Cg_lookup @ G )
             => ( conver7089555221631485245_c_d_e @ M1 @ M2 @ Cg_lookup @ ( Cg_insert @ G @ Gamma ) ) ) ) ) ) ) ).

% convergence_graph_insert_invar_def
thf(fact_49_mem__Collect__eq,axiom,
    ! [A2: produc2669932201312201782od_c_a,P: produc2669932201312201782od_c_a > $o] :
      ( ( member5502040268208861279od_c_a @ A2 @ ( collec8405073525749625505od_c_a @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_50_mem__Collect__eq,axiom,
    ! [A2: a,P: a > $o] :
      ( ( member_a @ A2 @ ( collect_a @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_51_mem__Collect__eq,axiom,
    ! [A2: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ A2 @ ( collec2280997390073109977od_b_c @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_52_Collect__mem__eq,axiom,
    ! [A: set_Pr8357624050790843030od_c_a] :
      ( ( collec8405073525749625505od_c_a
        @ ^ [X2: produc2669932201312201782od_c_a] : ( member5502040268208861279od_c_a @ X2 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_53_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X2: a] : ( member_a @ X2 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_54_Collect__mem__eq,axiom,
    ! [A: set_li6436108459499378894od_b_c] :
      ( ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_55_old_Oprod_Oinject,axiom,
    ! [A2: prefix425356687782099470od_b_c,B2: e,A5: prefix425356687782099470od_b_c,B5: e] :
      ( ( ( produc2511600812177743883_b_c_e @ A2 @ B2 )
        = ( produc2511600812177743883_b_c_e @ A5 @ B5 ) )
      = ( ( A2 = A5 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_56_old_Oprod_Oinject,axiom,
    ! [A2: b,B2: c,A5: b,B5: c] :
      ( ( ( product_Pair_b_c @ A2 @ B2 )
        = ( product_Pair_b_c @ A5 @ B5 ) )
      = ( ( A2 = A5 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_57_prod_Oinject,axiom,
    ! [X1: prefix425356687782099470od_b_c,X22: e,Y1: prefix425356687782099470od_b_c,Y22: e] :
      ( ( ( produc2511600812177743883_b_c_e @ X1 @ X22 )
        = ( produc2511600812177743883_b_c_e @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_58_prod_Oinject,axiom,
    ! [X1: b,X22: c,Y1: b,Y22: c] :
      ( ( ( product_Pair_b_c @ X1 @ X22 )
        = ( product_Pair_b_c @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_59_old_Oprod_Oexhaust,axiom,
    ! [Y: produc4534891796109904283_b_c_e] :
      ~ ! [A6: prefix425356687782099470od_b_c,B6: e] :
          ( Y
         != ( produc2511600812177743883_b_c_e @ A6 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_60_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_b_c] :
      ~ ! [A6: b,B6: c] :
          ( Y
         != ( product_Pair_b_c @ A6 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_61_surj__pair,axiom,
    ! [P2: produc4534891796109904283_b_c_e] :
    ? [X3: prefix425356687782099470od_b_c,Y3: e] :
      ( P2
      = ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_62_surj__pair,axiom,
    ! [P2: product_prod_b_c] :
    ? [X3: b,Y3: c] :
      ( P2
      = ( product_Pair_b_c @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_63_prod__cases,axiom,
    ! [P: produc4534891796109904283_b_c_e > $o,P2: produc4534891796109904283_b_c_e] :
      ( ! [A6: prefix425356687782099470od_b_c,B6: e] : ( P @ ( produc2511600812177743883_b_c_e @ A6 @ B6 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_64_prod__cases,axiom,
    ! [P: product_prod_b_c > $o,P2: product_prod_b_c] :
      ( ! [A6: b,B6: c] : ( P @ ( product_Pair_b_c @ A6 @ B6 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_65_Pair__inject,axiom,
    ! [A2: prefix425356687782099470od_b_c,B2: e,A5: prefix425356687782099470od_b_c,B5: e] :
      ( ( ( produc2511600812177743883_b_c_e @ A2 @ B2 )
        = ( produc2511600812177743883_b_c_e @ A5 @ B5 ) )
     => ~ ( ( A2 = A5 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_66_Pair__inject,axiom,
    ! [A2: b,B2: c,A5: b,B5: c] :
      ( ( ( product_Pair_b_c @ A2 @ B2 )
        = ( product_Pair_b_c @ A5 @ B5 ) )
     => ~ ( ( A2 = A5 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_67_fst__eqD,axiom,
    ! [X: b,Y: c,A2: b] :
      ( ( ( product_fst_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_68_fst__eqD,axiom,
    ! [X: prefix425356687782099470od_b_c,Y: e,A2: prefix425356687782099470od_b_c] :
      ( ( ( produc1447154562020694007_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_69_fst__eqD,axiom,
    ! [X: a,Y: produc2133359284458116493od_c_a,A2: a] :
      ( ( ( produc4225943634317630866od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_70_fst__eqD,axiom,
    ! [X: b,Y: product_prod_c_a,A2: b] :
      ( ( ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_71_fst__eqD,axiom,
    ! [X: c,Y: a,A2: c] :
      ( ( ( product_fst_c_a @ ( product_Pair_c_a @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_72_fst__conv,axiom,
    ! [X1: b,X22: c] :
      ( ( product_fst_b_c @ ( product_Pair_b_c @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_73_fst__conv,axiom,
    ! [X1: prefix425356687782099470od_b_c,X22: e] :
      ( ( produc1447154562020694007_b_c_e @ ( produc2511600812177743883_b_c_e @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_74_fst__conv,axiom,
    ! [X1: a,X22: produc2133359284458116493od_c_a] :
      ( ( produc4225943634317630866od_c_a @ ( produc5762801557034676134od_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_75_fst__conv,axiom,
    ! [X1: b,X22: product_prod_c_a] :
      ( ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_76_fst__conv,axiom,
    ! [X1: c,X22: a] :
      ( ( product_fst_c_a @ ( product_Pair_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_77_deterministic__alt__def,axiom,
    ( deterministic_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [Q1: a,X2: b,Y4: c,Y5: c,Q12: a,Q13: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y4 @ Q12 ) ) ) @ ( transitions_a_b_c @ M ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y5 @ Q13 ) ) ) @ ( transitions_a_b_c @ M ) ) )
         => ( ( Y4 = Y5 )
            & ( Q12 = Q13 ) ) ) ) ) ).

% deterministic_alt_def
thf(fact_78_single__input__alt__def,axiom,
    ( single_input_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [Q1: a,X2: b,X4: b,Y2: c,Y4: c,Q12: a,Q13: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q12 ) ) ) @ ( transitions_a_b_c @ M ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y4 @ Q13 ) ) ) @ ( transitions_a_b_c @ M ) ) )
         => ( X2 = X4 ) ) ) ) ).

% single_input_alt_def
thf(fact_79_fstE,axiom,
    ! [X: product_prod_b_c,A2: b,B2: c,P: b > $o] :
      ( ( X
        = ( product_Pair_b_c @ A2 @ B2 ) )
     => ( ( P @ ( product_fst_b_c @ X ) )
       => ( P @ A2 ) ) ) ).

% fstE
thf(fact_80_fstE,axiom,
    ! [X: produc4534891796109904283_b_c_e,A2: prefix425356687782099470od_b_c,B2: e,P: prefix425356687782099470od_b_c > $o] :
      ( ( X
        = ( produc2511600812177743883_b_c_e @ A2 @ B2 ) )
     => ( ( P @ ( produc1447154562020694007_b_c_e @ X ) )
       => ( P @ A2 ) ) ) ).

% fstE
thf(fact_81_fstE,axiom,
    ! [X: produc2669932201312201782od_c_a,A2: a,B2: produc2133359284458116493od_c_a,P: a > $o] :
      ( ( X
        = ( produc5762801557034676134od_c_a @ A2 @ B2 ) )
     => ( ( P @ ( produc4225943634317630866od_c_a @ X ) )
       => ( P @ A2 ) ) ) ).

% fstE
thf(fact_82_fstE,axiom,
    ! [X: produc2133359284458116493od_c_a,A2: b,B2: product_prod_c_a,P: b > $o] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ A2 @ B2 ) )
     => ( ( P @ ( produc301949074746585577od_c_a @ X ) )
       => ( P @ A2 ) ) ) ).

% fstE
thf(fact_83_fstE,axiom,
    ! [X: product_prod_c_a,A2: c,B2: a,P: c > $o] :
      ( ( X
        = ( product_Pair_c_a @ A2 @ B2 ) )
     => ( ( P @ ( product_fst_c_a @ X ) )
       => ( P @ A2 ) ) ) ).

% fstE
thf(fact_84_fstI,axiom,
    ! [X: product_prod_b_c,Y: b,Z: c] :
      ( ( X
        = ( product_Pair_b_c @ Y @ Z ) )
     => ( ( product_fst_b_c @ X )
        = Y ) ) ).

% fstI
thf(fact_85_fstI,axiom,
    ! [X: produc4534891796109904283_b_c_e,Y: prefix425356687782099470od_b_c,Z: e] :
      ( ( X
        = ( produc2511600812177743883_b_c_e @ Y @ Z ) )
     => ( ( produc1447154562020694007_b_c_e @ X )
        = Y ) ) ).

% fstI
thf(fact_86_fstI,axiom,
    ! [X: produc2669932201312201782od_c_a,Y: a,Z: produc2133359284458116493od_c_a] :
      ( ( X
        = ( produc5762801557034676134od_c_a @ Y @ Z ) )
     => ( ( produc4225943634317630866od_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_87_fstI,axiom,
    ! [X: produc2133359284458116493od_c_a,Y: b,Z: product_prod_c_a] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ Y @ Z ) )
     => ( ( produc301949074746585577od_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_88_fstI,axiom,
    ! [X: product_prod_c_a,Y: c,Z: a] :
      ( ( X
        = ( product_Pair_c_a @ Y @ Z ) )
     => ( ( product_fst_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_89_eq__fst__iff,axiom,
    ! [A2: b,P2: product_prod_b_c] :
      ( ( A2
        = ( product_fst_b_c @ P2 ) )
      = ( ? [B3: c] :
            ( P2
            = ( product_Pair_b_c @ A2 @ B3 ) ) ) ) ).

% eq_fst_iff
thf(fact_90_eq__fst__iff,axiom,
    ! [A2: prefix425356687782099470od_b_c,P2: produc4534891796109904283_b_c_e] :
      ( ( A2
        = ( produc1447154562020694007_b_c_e @ P2 ) )
      = ( ? [B3: e] :
            ( P2
            = ( produc2511600812177743883_b_c_e @ A2 @ B3 ) ) ) ) ).

% eq_fst_iff
thf(fact_91_eq__fst__iff,axiom,
    ! [A2: a,P2: produc2669932201312201782od_c_a] :
      ( ( A2
        = ( produc4225943634317630866od_c_a @ P2 ) )
      = ( ? [B3: produc2133359284458116493od_c_a] :
            ( P2
            = ( produc5762801557034676134od_c_a @ A2 @ B3 ) ) ) ) ).

% eq_fst_iff
thf(fact_92_eq__fst__iff,axiom,
    ! [A2: b,P2: produc2133359284458116493od_c_a] :
      ( ( A2
        = ( produc301949074746585577od_c_a @ P2 ) )
      = ( ? [B3: product_prod_c_a] :
            ( P2
            = ( produc3440865914000881661od_c_a @ A2 @ B3 ) ) ) ) ).

% eq_fst_iff
thf(fact_93_eq__fst__iff,axiom,
    ! [A2: c,P2: product_prod_c_a] :
      ( ( A2
        = ( product_fst_c_a @ P2 ) )
      = ( ? [B3: a] :
            ( P2
            = ( product_Pair_c_a @ A2 @ B3 ) ) ) ) ).

% eq_fst_iff
thf(fact_94_assms_I15_J,axiom,
    ! [Q14: a,Q2: a] :
      ( ( member_a @ Q14 @ ( states_a_b_c @ m1 ) )
     => ( ( member_a @ Q2 @ ( states_a_b_c @ m1 ) )
       => ( ( Q14 != Q2 )
         => ? [Io: list_P903359562653991662od_b_c] :
            ! [K1: nat,K2: nat] :
              ( ( member6330420149250801815od_b_c @ Io @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( dist_fun @ K1 @ Q14 ) ) @ ( prefix9085958534787526401od_b_c @ ( dist_fun @ K2 @ Q2 ) ) ) )
              & ( distinguishes_a_b_c @ m1 @ Q14 @ Q2 @ Io ) ) ) ) ) ).

% assms(15)
thf(fact_95_abstract__h__condition__soundness,axiom,
    ! [M3: fsm_d_b_c,I: fsm_a_b_c,V: d > list_P903359562653991662od_b_c,M4: nat] :
      ( ( observable_d_b_c @ M3 )
     => ( ( observable_a_b_c @ I )
       => ( ( state_6014242345326633810_d_b_c @ M3 @ V )
         => ( ( ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) )
              = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
           => ( h_sati4005454913823510672_b_c_a @ M3 @ I @ V @ M4 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_96_abstract__h__condition__soundness,axiom,
    ! [M3: fsm_d_b_c,I: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,M4: nat] :
      ( ( observable_d_b_c @ M3 )
     => ( ( observable_d_b_c @ I )
       => ( ( state_6014242345326633810_d_b_c @ M3 @ V )
         => ( ( ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) )
              = ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
           => ( h_sati4005454913823510675_b_c_d @ M3 @ I @ V @ M4 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_97_abstract__h__condition__soundness,axiom,
    ! [M3: fsm_a_b_c,I: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,M4: nat] :
      ( ( observable_a_b_c @ M3 )
     => ( ( observable_a_b_c @ I )
       => ( ( state_7672330573471793359_a_b_c @ M3 @ V )
         => ( ( ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) )
              = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
           => ( h_sati8764940838793890899_b_c_a @ M3 @ I @ V @ M4 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_98_abstract__h__condition__soundness,axiom,
    ! [M3: fsm_a_b_c,I: fsm_d_b_c,V: a > list_P903359562653991662od_b_c,M4: nat] :
      ( ( observable_a_b_c @ M3 )
     => ( ( observable_d_b_c @ I )
       => ( ( state_7672330573471793359_a_b_c @ M3 @ V )
         => ( ( ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) )
              = ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
           => ( h_sati8764940838793890902_b_c_d @ M3 @ I @ V @ M4 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_99__092_060alpha_062,axiom,
    ( alpha
    = ( v @ ( produc4225943634317630866od_c_a @ t2 ) ) ) ).

% \<alpha>
thf(fact_100_fsm__initial,axiom,
    ! [M3: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M3 ) @ ( states_a_b_c @ M3 ) ) ).

% fsm_initial
thf(fact_101_fsm__initial,axiom,
    ! [M3: fsm_d_b_c] : ( member_d @ ( initial_d_b_c @ M3 ) @ ( states_d_b_c @ M3 ) ) ).

% fsm_initial
thf(fact_102_fsm__transition__source,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
     => ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M3 ) ) ) ).

% fsm_transition_source
thf(fact_103_assms_I8_J,axiom,
    member_a @ ( produc4225943634317630866od_c_a @ t2 ) @ ( reacha1620305530751930115_a_b_c @ m1 ) ).

% assms(8)
thf(fact_104_distinguishes__sym,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a,Io2: list_P903359562653991662od_b_c] :
      ( ( distinguishes_a_b_c @ M3 @ Q14 @ Q2 @ Io2 )
     => ( distinguishes_a_b_c @ M3 @ Q2 @ Q14 @ Io2 ) ) ).

% distinguishes_sym
thf(fact_105_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( minimal_a_b_c @ X )
     => ~ ! [X3: a] :
            ( ( member_a @ X3 @ ( states_a_b_c @ X ) )
           => ! [Xa: a] :
                ( ( member_a @ Xa @ ( states_a_b_c @ X ) )
               => ( ( X3 != Xa )
                 => ( ( lS_a_b_c @ X @ X3 )
                   != ( lS_a_b_c @ X @ Xa ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_106_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ~ ( minimal_d_b_c @ X )
     => ~ ! [X3: d] :
            ( ( member_d @ X3 @ ( states_d_b_c @ X ) )
           => ! [Xa: d] :
                ( ( member_d @ Xa @ ( states_d_b_c @ X ) )
               => ( ( X3 != Xa )
                 => ( ( lS_d_b_c @ X @ X3 )
                   != ( lS_d_b_c @ X @ Xa ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_107_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( minimal_a_b_c @ X )
     => ! [X5: a] :
          ( ( member_a @ X5 @ ( states_a_b_c @ X ) )
         => ! [Xa2: a] :
              ( ( member_a @ Xa2 @ ( states_a_b_c @ X ) )
             => ( ( X5 != Xa2 )
               => ( ( lS_a_b_c @ X @ X5 )
                 != ( lS_a_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_108_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ( minimal_d_b_c @ X )
     => ! [X5: d] :
          ( ( member_d @ X5 @ ( states_d_b_c @ X ) )
         => ! [Xa2: d] :
              ( ( member_d @ Xa2 @ ( states_d_b_c @ X ) )
             => ( ( X5 != Xa2 )
               => ( ( lS_d_b_c @ X @ X5 )
                 != ( lS_d_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_109_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_110_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_111_minimal_Osimps,axiom,
    ( minimal_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [X2: a] :
          ( ( member_a @ X2 @ ( states_a_b_c @ M ) )
         => ! [Y2: a] :
              ( ( member_a @ Y2 @ ( states_a_b_c @ M ) )
             => ( ( X2 != Y2 )
               => ( ( lS_a_b_c @ M @ X2 )
                 != ( lS_a_b_c @ M @ Y2 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_112_minimal_Osimps,axiom,
    ( minimal_d_b_c
    = ( ^ [M: fsm_d_b_c] :
        ! [X2: d] :
          ( ( member_d @ X2 @ ( states_d_b_c @ M ) )
         => ! [Y2: d] :
              ( ( member_d @ Y2 @ ( states_d_b_c @ M ) )
             => ( ( X2 != Y2 )
               => ( ( lS_d_b_c @ M @ X2 )
                 != ( lS_d_b_c @ M @ Y2 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_113_minimal__alt__def,axiom,
    ( minimal_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [Q: a,Q3: a] :
          ( ( member_a @ Q @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
           => ( ( ( lS_a_b_c @ M @ Q )
                = ( lS_a_b_c @ M @ Q3 ) )
             => ( Q = Q3 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_114_minimal__alt__def,axiom,
    ( minimal_d_b_c
    = ( ^ [M: fsm_d_b_c] :
        ! [Q: d,Q3: d] :
          ( ( member_d @ Q @ ( states_d_b_c @ M ) )
         => ( ( member_d @ Q3 @ ( states_d_b_c @ M ) )
           => ( ( ( lS_d_b_c @ M @ Q )
                = ( lS_d_b_c @ M @ Q3 ) )
             => ( Q = Q3 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_115_bex2I,axiom,
    ! [A2: a,B2: produc2133359284458116493od_c_a,S: set_Pr8357624050790843030od_c_a,P: a > produc2133359284458116493od_c_a > $o] :
      ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ A2 @ B2 ) @ S )
     => ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ A2 @ B2 ) @ S )
         => ( P @ A2 @ B2 ) )
       => ? [A6: a,B6: produc2133359284458116493od_c_a] :
            ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ A6 @ B6 ) @ S )
            & ( P @ A6 @ B6 ) ) ) ) ).

% bex2I
thf(fact_116_bex2I,axiom,
    ! [A2: prefix425356687782099470od_b_c,B2: e,S: set_Pr3237851069733663483_b_c_e,P: prefix425356687782099470od_b_c > e > $o] :
      ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ A2 @ B2 ) @ S )
     => ( ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ A2 @ B2 ) @ S )
         => ( P @ A2 @ B2 ) )
       => ? [A6: prefix425356687782099470od_b_c,B6: e] :
            ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ A6 @ B6 ) @ S )
            & ( P @ A6 @ B6 ) ) ) ) ).

% bex2I
thf(fact_117_bex2I,axiom,
    ! [A2: b,B2: c,S: set_Product_prod_b_c,P: b > c > $o] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A2 @ B2 ) @ S )
     => ( ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A2 @ B2 ) @ S )
         => ( P @ A2 @ B2 ) )
       => ? [A6: b,B6: c] :
            ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A6 @ B6 ) @ S )
            & ( P @ A6 @ B6 ) ) ) ) ).

% bex2I
thf(fact_118_assms_I17_J,axiom,
    ! [Q4: a,K: nat] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ m1 ) )
     => ( prefix6767660319289835678od_b_c @ ( dist_fun @ K @ Q4 ) ) ) ).

% assms(17)
thf(fact_119_qSource,axiom,
    ( qSource
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ( v @ ( produc4225943634317630866od_c_a @ t2 ) ) ) ) ).

% qSource
thf(fact_120_language__equivalence__from__isomorphism,axiom,
    ! [F: produc2669932201312201782od_c_a > d,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_d_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( bij_be5632368444736963777_c_a_d @ F @ ( states895637122477222528_a_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( states895637122477222528_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( states895637122477222528_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M12 ) )
           => ( ( lS_Pro3731892891411965979_a_b_c @ M12 @ Q4 )
              = ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_121_language__equivalence__from__isomorphism,axiom,
    ! [F: list_P903359562653991662od_b_c > d,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F @ ( states7681702920031268536_c_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( states7681702920031268536_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M12 ) )
           => ( ( lS_lis2930931384350476499_c_b_c @ M12 @ Q4 )
              = ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_122_language__equivalence__from__isomorphism,axiom,
    ! [F: d > d,M12: fsm_d_b_c,M22: fsm_d_b_c,Q4: d] :
      ( ( bij_betw_d_d @ F @ ( states_d_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( states_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q4 @ ( states_d_b_c @ M12 ) )
           => ( ( lS_d_b_c @ M12 @ Q4 )
              = ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_123_language__equivalence__from__isomorphism,axiom,
    ! [F: produc2669932201312201782od_c_a > a,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_a_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( bij_be5632368444736963774_c_a_a @ F @ ( states895637122477222528_a_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( states895637122477222528_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( states895637122477222528_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M12 ) )
           => ( ( lS_Pro3731892891411965979_a_b_c @ M12 @ Q4 )
              = ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_124_language__equivalence__from__isomorphism,axiom,
    ! [F: list_P903359562653991662od_b_c > a,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F @ ( states7681702920031268536_c_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( states7681702920031268536_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M12 ) )
           => ( ( lS_lis2930931384350476499_c_b_c @ M12 @ Q4 )
              = ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_125_language__equivalence__from__isomorphism,axiom,
    ! [F: d > a,M12: fsm_d_b_c,M22: fsm_a_b_c,Q4: d] :
      ( ( bij_betw_d_a @ F @ ( states_d_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( states_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q4 @ ( states_d_b_c @ M12 ) )
           => ( ( lS_d_b_c @ M12 @ Q4 )
              = ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_126_language__equivalence__from__isomorphism,axiom,
    ! [F: a > d,M12: fsm_a_b_c,M22: fsm_d_b_c,Q4: a] :
      ( ( bij_betw_a_d @ F @ ( states_a_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( states_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q4 @ ( states_a_b_c @ M12 ) )
           => ( ( lS_a_b_c @ M12 @ Q4 )
              = ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_127_language__equivalence__from__isomorphism,axiom,
    ! [F: a > a,M12: fsm_a_b_c,M22: fsm_a_b_c,Q4: a] :
      ( ( bij_betw_a_a @ F @ ( states_a_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( states_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q4 @ ( states_a_b_c @ M12 ) )
           => ( ( lS_a_b_c @ M12 @ Q4 )
              = ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_128_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Q14: produc2669932201312201782od_c_a,Q2: produc2669932201312201782od_c_a] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( minima5859589491558189769_a_b_c @ M3 )
       => ( ( member5502040268208861279od_c_a @ Q14 @ ( states895637122477222528_a_b_c @ M3 ) )
         => ( ( member5502040268208861279od_c_a @ Q2 @ ( states895637122477222528_a_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di6791261883501465459_a_b_c @ M3 @ Q14 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q14 ) @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_129_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Q14: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( minima1987601567150520449_c_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ Q14 @ ( states7681702920031268536_c_b_c @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di903557346829177899_c_b_c @ M3 @ Q14 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q14 ) @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_130_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di2280862616223094331_a_b_c @ M3 @ Q14 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M3 @ Q14 ) @ ( lS_a_b_c @ M3 @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_131_get__distinguishing__sequence__from__ofsm__tables__is__distinguishing__trace_I2_J,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Q2: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ~ ( member6330420149250801815od_b_c @ ( get_di622774388077934782_d_b_c @ M3 @ Q14 @ Q2 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M3 @ Q14 ) @ ( lS_d_b_c @ M3 @ Q2 ) ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_distinguishing_trace(2)
thf(fact_132_does__distinguish__correctness,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Q2: d,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
       => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
         => ( ( does_d1651467158923735017_d_b_c @ M3 @ Q14 @ Q2 @ Io2 )
            = ( distinguishes_d_b_c @ M3 @ Q14 @ Q2 @ Io2 ) ) ) ) ) ).

% does_distinguish_correctness
thf(fact_133_does__distinguish__correctness,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
       => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
         => ( ( does_d3309555387068894566_a_b_c @ M3 @ Q14 @ Q2 @ Io2 )
            = ( distinguishes_a_b_c @ M3 @ Q14 @ Q2 @ Io2 ) ) ) ) ) ).

% does_distinguish_correctness
thf(fact_134_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Q4: produc2669932201312201782od_c_a,Io2: list_P903359562653991662od_b_c] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( maxima1470962857315526920_a_b_c @ M3 @ Q4 @ Io2 ) @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_135_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Q4: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( maxima8146652644187019584_c_b_c @ M3 @ Q4 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_136_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M3: fsm_a_b_c,Q4: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( maxima1559550560783484624_a_b_c @ M3 @ Q4 @ Io2 ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_137_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M3: fsm_d_b_c,Q4: d,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( maxima9124834369493100883_d_b_c @ M3 @ Q4 @ Io2 ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_138_get__distinguishing__sequence__from__ofsm__tables__distinguishes,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Q2: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( distinguishes_d_b_c @ M3 @ Q14 @ Q2 @ ( get_di622774388077934782_d_b_c @ M3 @ Q14 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_distinguishes
thf(fact_139_get__distinguishing__sequence__from__ofsm__tables__distinguishes,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( distinguishes_a_b_c @ M3 @ Q14 @ Q2 @ ( get_di2280862616223094331_a_b_c @ M3 @ Q14 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_distinguishes
thf(fact_140_single__input_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( single999786218259502647_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ Xa @ ( transi2941759273464634107_a_a_b @ X ) )
               => ( ( ( produc8171714036265584980od_c_a @ X3 )
                    = ( produc8171714036265584980od_c_a @ Xa ) )
                 => ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) ) ) ) ) ).

% single_input.elims(3)
thf(fact_141_single__input_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( single_input_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa @ ( transitions_a_b_c @ X ) )
               => ( ( ( produc4225943634317630866od_c_a @ X3 )
                    = ( produc4225943634317630866od_c_a @ Xa ) )
                 => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) ) ) ) ) ).

% single_input.elims(3)
thf(fact_142_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_143_prod_Ocollapse,axiom,
    ! [Prod: produc4534891796109904283_b_c_e] :
      ( ( produc2511600812177743883_b_c_e @ ( produc1447154562020694007_b_c_e @ Prod ) @ ( produc6779600879576379961_b_c_e @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_144_prod_Ocollapse,axiom,
    ! [Prod: produc2669932201312201782od_c_a] :
      ( ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ Prod ) @ ( produc8088130389382527188od_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_145_prod_Ocollapse,axiom,
    ! [Prod: produc2133359284458116493od_c_a] :
      ( ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ Prod ) @ ( produc5221446324160585515od_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_146_prod_Ocollapse,axiom,
    ! [Prod: product_prod_c_a] :
      ( ( product_Pair_c_a @ ( product_fst_c_a @ Prod ) @ ( product_snd_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_147_fsm__transition__target,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
     => ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M3 ) ) ) ).

% fsm_transition_target
thf(fact_148_fsm__transition__target,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
     => ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M3 ) ) ) ).

% fsm_transition_target
thf(fact_149_reachable__states__next,axiom,
    ! [Q4: product_prod_c_a,M3: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( member5074992350434858958od_c_a @ Q4 @ ( reacha5035603111973943274_a_a_b @ M3 ) )
     => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ( ( ( produc8171714036265584980od_c_a @ T )
            = Q4 )
         => ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( reacha5035603111973943274_a_a_b @ M3 ) ) ) ) ) ).

% reachable_states_next
thf(fact_150_reachable__states__next,axiom,
    ! [Q4: a,M3: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
       => ( ( ( produc4225943634317630866od_c_a @ T )
            = Q4 )
         => ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( reacha1620305530751930115_a_b_c @ M3 ) ) ) ) ) ).

% reachable_states_next
thf(fact_151_reachable__states__initial__or__target,axiom,
    ! [Q4: d,M3: fsm_d_b_c] :
      ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
     => ( ( Q4
          = ( initial_d_b_c @ M3 ) )
        | ? [X3: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X3 @ ( transitions_d_b_c @ M3 ) )
            & ( member_d @ ( produc1508465569166014290od_c_d @ X3 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) )
            & ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
              = Q4 ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_152_reachable__states__initial__or__target,axiom,
    ! [Q4: product_prod_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member5074992350434858958od_c_a @ Q4 @ ( reacha5035603111973943274_a_a_b @ M3 ) )
     => ( ( Q4
          = ( initia681974817753967189_a_a_b @ M3 ) )
        | ? [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ M3 ) )
            & ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ X3 ) @ ( reacha5035603111973943274_a_a_b @ M3 ) )
            & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
              = Q4 ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_153_reachable__states__initial__or__target,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( ( Q4
          = ( initial_a_b_c @ M3 ) )
        | ? [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M3 ) )
            & ( member_a @ ( produc4225943634317630866od_c_a @ X3 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) )
            & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
              = Q4 ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_154_reachable__states__induct,axiom,
    ! [Q4: d,M3: fsm_d_b_c,P: d > $o] :
      ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
     => ( ( P @ ( initial_d_b_c @ M3 ) )
       => ( ! [T2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M3 ) )
             => ( ( member_d @ ( produc1508465569166014290od_c_d @ T2 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) )
               => ( ( P @ ( produc1508465569166014290od_c_d @ T2 ) )
                 => ( P @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_induct
thf(fact_155_reachable__states__induct,axiom,
    ! [Q4: product_prod_c_a,M3: fsm_Pr1886043760914421514_a_a_b,P: product_prod_c_a > $o] :
      ( ( member5074992350434858958od_c_a @ Q4 @ ( reacha5035603111973943274_a_a_b @ M3 ) )
     => ( ( P @ ( initia681974817753967189_a_a_b @ M3 ) )
       => ( ! [T2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ T2 @ ( transi2941759273464634107_a_a_b @ M3 ) )
             => ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T2 ) @ ( reacha5035603111973943274_a_a_b @ M3 ) )
               => ( ( P @ ( produc8171714036265584980od_c_a @ T2 ) )
                 => ( P @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_induct
thf(fact_156_reachable__states__induct,axiom,
    ! [Q4: a,M3: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( ( P @ ( initial_a_b_c @ M3 ) )
       => ( ! [T2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M3 ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T2 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) )
               => ( ( P @ ( produc4225943634317630866od_c_a @ T2 ) )
                 => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_induct
thf(fact_157_reachable__states__cases,axiom,
    ! [Q4: d,M3: fsm_d_b_c,P: d > $o] :
      ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
     => ( ( P @ ( initial_d_b_c @ M3 ) )
       => ( ! [T2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M3 ) )
             => ( ( member_d @ ( produc1508465569166014290od_c_d @ T2 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) )
               => ( P @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_cases
thf(fact_158_reachable__states__cases,axiom,
    ! [Q4: product_prod_c_a,M3: fsm_Pr1886043760914421514_a_a_b,P: product_prod_c_a > $o] :
      ( ( member5074992350434858958od_c_a @ Q4 @ ( reacha5035603111973943274_a_a_b @ M3 ) )
     => ( ( P @ ( initia681974817753967189_a_a_b @ M3 ) )
       => ( ! [T2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ T2 @ ( transi2941759273464634107_a_a_b @ M3 ) )
             => ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T2 ) @ ( reacha5035603111973943274_a_a_b @ M3 ) )
               => ( P @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_cases
thf(fact_159_reachable__states__cases,axiom,
    ! [Q4: a,M3: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( ( P @ ( initial_a_b_c @ M3 ) )
       => ( ! [T2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M3 ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T2 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) )
               => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) )
         => ( P @ Q4 ) ) ) ) ).

% reachable_states_cases
thf(fact_160_after__reachable,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Io2: list_P903359562653991662od_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) )
       => ( ( member5502040268208861279od_c_a @ Q4 @ ( reacha1389639598965321787_a_b_c @ M3 ) )
         => ( member5502040268208861279od_c_a @ ( after_2239399860513592206_a_b_c @ M3 @ Q4 @ Io2 ) @ ( reacha1389639598965321787_a_b_c @ M3 ) ) ) ) ) ).

% after_reachable
thf(fact_161_after__reachable,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Io2: list_P903359562653991662od_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) )
       => ( ( member6330420149250801815od_b_c @ Q4 @ ( reacha8116992257183400179_c_b_c @ M3 ) )
         => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M3 @ Q4 @ Io2 ) @ ( reacha8116992257183400179_c_b_c @ M3 ) ) ) ) ) ).

% after_reachable
thf(fact_162_after__reachable,axiom,
    ! [M3: fsm_d_b_c,Io2: list_P903359562653991662od_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
         => ( member_d @ ( after_d_b_c @ M3 @ Q4 @ Io2 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) ) ) ) ) ).

% after_reachable
thf(fact_163_after__reachable,axiom,
    ! [M3: fsm_a_b_c,Io2: list_P903359562653991662od_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
         => ( member_a @ ( after_a_b_c @ M3 @ Q4 @ Io2 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) ) ) ) ) ).

% after_reachable
thf(fact_164_snd__eqD,axiom,
    ! [X: prefix425356687782099470od_b_c,Y: e,A2: e] :
      ( ( ( produc6779600879576379961_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_165_snd__eqD,axiom,
    ! [X: b,Y: c,A2: c] :
      ( ( ( product_snd_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_166_snd__eqD,axiom,
    ! [X: a,Y: produc2133359284458116493od_c_a,A2: produc2133359284458116493od_c_a] :
      ( ( ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_167_snd__eqD,axiom,
    ! [X: b,Y: product_prod_c_a,A2: product_prod_c_a] :
      ( ( ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_168_snd__eqD,axiom,
    ! [X: c,Y: a,A2: a] :
      ( ( ( product_snd_c_a @ ( product_Pair_c_a @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_169_snd__conv,axiom,
    ! [X1: prefix425356687782099470od_b_c,X22: e] :
      ( ( produc6779600879576379961_b_c_e @ ( produc2511600812177743883_b_c_e @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_170_snd__conv,axiom,
    ! [X1: b,X22: c] :
      ( ( product_snd_b_c @ ( product_Pair_b_c @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_171_snd__conv,axiom,
    ! [X1: a,X22: produc2133359284458116493od_c_a] :
      ( ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_172_snd__conv,axiom,
    ! [X1: b,X22: product_prod_c_a] :
      ( ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_173_snd__conv,axiom,
    ! [X1: c,X22: a] :
      ( ( product_snd_c_a @ ( product_Pair_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_174_sndE,axiom,
    ! [X: produc4534891796109904283_b_c_e,A2: prefix425356687782099470od_b_c,B2: e,P: e > $o] :
      ( ( X
        = ( produc2511600812177743883_b_c_e @ A2 @ B2 ) )
     => ( ( P @ ( produc6779600879576379961_b_c_e @ X ) )
       => ( P @ B2 ) ) ) ).

% sndE
thf(fact_175_sndE,axiom,
    ! [X: product_prod_b_c,A2: b,B2: c,P: c > $o] :
      ( ( X
        = ( product_Pair_b_c @ A2 @ B2 ) )
     => ( ( P @ ( product_snd_b_c @ X ) )
       => ( P @ B2 ) ) ) ).

% sndE
thf(fact_176_sndE,axiom,
    ! [X: produc2669932201312201782od_c_a,A2: a,B2: produc2133359284458116493od_c_a,P: produc2133359284458116493od_c_a > $o] :
      ( ( X
        = ( produc5762801557034676134od_c_a @ A2 @ B2 ) )
     => ( ( P @ ( produc8088130389382527188od_c_a @ X ) )
       => ( P @ B2 ) ) ) ).

% sndE
thf(fact_177_sndE,axiom,
    ! [X: produc2133359284458116493od_c_a,A2: b,B2: product_prod_c_a,P: product_prod_c_a > $o] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ A2 @ B2 ) )
     => ( ( P @ ( produc5221446324160585515od_c_a @ X ) )
       => ( P @ B2 ) ) ) ).

% sndE
thf(fact_178_sndE,axiom,
    ! [X: product_prod_c_a,A2: c,B2: a,P: a > $o] :
      ( ( X
        = ( product_Pair_c_a @ A2 @ B2 ) )
     => ( ( P @ ( product_snd_c_a @ X ) )
       => ( P @ B2 ) ) ) ).

% sndE
thf(fact_179_sndI,axiom,
    ! [X: produc4534891796109904283_b_c_e,Y: prefix425356687782099470od_b_c,Z: e] :
      ( ( X
        = ( produc2511600812177743883_b_c_e @ Y @ Z ) )
     => ( ( produc6779600879576379961_b_c_e @ X )
        = Z ) ) ).

% sndI
thf(fact_180_sndI,axiom,
    ! [X: product_prod_b_c,Y: b,Z: c] :
      ( ( X
        = ( product_Pair_b_c @ Y @ Z ) )
     => ( ( product_snd_b_c @ X )
        = Z ) ) ).

% sndI
thf(fact_181_sndI,axiom,
    ! [X: produc2669932201312201782od_c_a,Y: a,Z: produc2133359284458116493od_c_a] :
      ( ( X
        = ( produc5762801557034676134od_c_a @ Y @ Z ) )
     => ( ( produc8088130389382527188od_c_a @ X )
        = Z ) ) ).

% sndI
thf(fact_182_sndI,axiom,
    ! [X: produc2133359284458116493od_c_a,Y: b,Z: product_prod_c_a] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ Y @ Z ) )
     => ( ( produc5221446324160585515od_c_a @ X )
        = Z ) ) ).

% sndI
thf(fact_183_sndI,axiom,
    ! [X: product_prod_c_a,Y: c,Z: a] :
      ( ( X
        = ( product_Pair_c_a @ Y @ Z ) )
     => ( ( product_snd_c_a @ X )
        = Z ) ) ).

% sndI
thf(fact_184_eq__snd__iff,axiom,
    ! [B2: e,P2: produc4534891796109904283_b_c_e] :
      ( ( B2
        = ( produc6779600879576379961_b_c_e @ P2 ) )
      = ( ? [A3: prefix425356687782099470od_b_c] :
            ( P2
            = ( produc2511600812177743883_b_c_e @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_185_eq__snd__iff,axiom,
    ! [B2: c,P2: product_prod_b_c] :
      ( ( B2
        = ( product_snd_b_c @ P2 ) )
      = ( ? [A3: b] :
            ( P2
            = ( product_Pair_b_c @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_186_eq__snd__iff,axiom,
    ! [B2: produc2133359284458116493od_c_a,P2: produc2669932201312201782od_c_a] :
      ( ( B2
        = ( produc8088130389382527188od_c_a @ P2 ) )
      = ( ? [A3: a] :
            ( P2
            = ( produc5762801557034676134od_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_187_eq__snd__iff,axiom,
    ! [B2: product_prod_c_a,P2: produc2133359284458116493od_c_a] :
      ( ( B2
        = ( produc5221446324160585515od_c_a @ P2 ) )
      = ( ? [A3: b] :
            ( P2
            = ( produc3440865914000881661od_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_188_eq__snd__iff,axiom,
    ! [B2: a,P2: product_prod_c_a] :
      ( ( B2
        = ( product_snd_c_a @ P2 ) )
      = ( ? [A3: c] :
            ( P2
            = ( product_Pair_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_189_reachable__states__initial,axiom,
    ! [M3: fsm_d_b_c] : ( member_d @ ( initial_d_b_c @ M3 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) ) ).

% reachable_states_initial
thf(fact_190_reachable__states__initial,axiom,
    ! [M3: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M3 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) ) ).

% reachable_states_initial
thf(fact_191_prod_Oexpand,axiom,
    ! [Prod: produc4534891796109904283_b_c_e,Prod2: produc4534891796109904283_b_c_e] :
      ( ( ( ( produc1447154562020694007_b_c_e @ Prod )
          = ( produc1447154562020694007_b_c_e @ Prod2 ) )
        & ( ( produc6779600879576379961_b_c_e @ Prod )
          = ( produc6779600879576379961_b_c_e @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_192_prod_Oexpand,axiom,
    ! [Prod: produc2669932201312201782od_c_a,Prod2: produc2669932201312201782od_c_a] :
      ( ( ( ( produc4225943634317630866od_c_a @ Prod )
          = ( produc4225943634317630866od_c_a @ Prod2 ) )
        & ( ( produc8088130389382527188od_c_a @ Prod )
          = ( produc8088130389382527188od_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_193_prod_Oexpand,axiom,
    ! [Prod: produc2133359284458116493od_c_a,Prod2: produc2133359284458116493od_c_a] :
      ( ( ( ( produc301949074746585577od_c_a @ Prod )
          = ( produc301949074746585577od_c_a @ Prod2 ) )
        & ( ( produc5221446324160585515od_c_a @ Prod )
          = ( produc5221446324160585515od_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_194_prod_Oexpand,axiom,
    ! [Prod: product_prod_c_a,Prod2: product_prod_c_a] :
      ( ( ( ( product_fst_c_a @ Prod )
          = ( product_fst_c_a @ Prod2 ) )
        & ( ( product_snd_c_a @ Prod )
          = ( product_snd_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_195_prod__eqI,axiom,
    ! [P2: produc4534891796109904283_b_c_e,Q4: produc4534891796109904283_b_c_e] :
      ( ( ( produc1447154562020694007_b_c_e @ P2 )
        = ( produc1447154562020694007_b_c_e @ Q4 ) )
     => ( ( ( produc6779600879576379961_b_c_e @ P2 )
          = ( produc6779600879576379961_b_c_e @ Q4 ) )
       => ( P2 = Q4 ) ) ) ).

% prod_eqI
thf(fact_196_prod__eqI,axiom,
    ! [P2: produc2669932201312201782od_c_a,Q4: produc2669932201312201782od_c_a] :
      ( ( ( produc4225943634317630866od_c_a @ P2 )
        = ( produc4225943634317630866od_c_a @ Q4 ) )
     => ( ( ( produc8088130389382527188od_c_a @ P2 )
          = ( produc8088130389382527188od_c_a @ Q4 ) )
       => ( P2 = Q4 ) ) ) ).

% prod_eqI
thf(fact_197_prod__eqI,axiom,
    ! [P2: produc2133359284458116493od_c_a,Q4: produc2133359284458116493od_c_a] :
      ( ( ( produc301949074746585577od_c_a @ P2 )
        = ( produc301949074746585577od_c_a @ Q4 ) )
     => ( ( ( produc5221446324160585515od_c_a @ P2 )
          = ( produc5221446324160585515od_c_a @ Q4 ) )
       => ( P2 = Q4 ) ) ) ).

% prod_eqI
thf(fact_198_prod__eqI,axiom,
    ! [P2: product_prod_c_a,Q4: product_prod_c_a] :
      ( ( ( product_fst_c_a @ P2 )
        = ( product_fst_c_a @ Q4 ) )
     => ( ( ( product_snd_c_a @ P2 )
          = ( product_snd_c_a @ Q4 ) )
       => ( P2 = Q4 ) ) ) ).

% prod_eqI
thf(fact_199_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc4534891796109904283_b_c_e,Z2: produc4534891796109904283_b_c_e] : ( Y6 = Z2 ) )
    = ( ^ [S2: produc4534891796109904283_b_c_e,T3: produc4534891796109904283_b_c_e] :
          ( ( ( produc1447154562020694007_b_c_e @ S2 )
            = ( produc1447154562020694007_b_c_e @ T3 ) )
          & ( ( produc6779600879576379961_b_c_e @ S2 )
            = ( produc6779600879576379961_b_c_e @ T3 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_200_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc2669932201312201782od_c_a,Z2: produc2669932201312201782od_c_a] : ( Y6 = Z2 ) )
    = ( ^ [S2: produc2669932201312201782od_c_a,T3: produc2669932201312201782od_c_a] :
          ( ( ( produc4225943634317630866od_c_a @ S2 )
            = ( produc4225943634317630866od_c_a @ T3 ) )
          & ( ( produc8088130389382527188od_c_a @ S2 )
            = ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_201_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc2133359284458116493od_c_a,Z2: produc2133359284458116493od_c_a] : ( Y6 = Z2 ) )
    = ( ^ [S2: produc2133359284458116493od_c_a,T3: produc2133359284458116493od_c_a] :
          ( ( ( produc301949074746585577od_c_a @ S2 )
            = ( produc301949074746585577od_c_a @ T3 ) )
          & ( ( produc5221446324160585515od_c_a @ S2 )
            = ( produc5221446324160585515od_c_a @ T3 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_202_prod__eq__iff,axiom,
    ( ( ^ [Y6: product_prod_c_a,Z2: product_prod_c_a] : ( Y6 = Z2 ) )
    = ( ^ [S2: product_prod_c_a,T3: product_prod_c_a] :
          ( ( ( product_fst_c_a @ S2 )
            = ( product_fst_c_a @ T3 ) )
          & ( ( product_snd_c_a @ S2 )
            = ( product_snd_c_a @ T3 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_203_Ex__prod__contract,axiom,
    ! [P: prefix425356687782099470od_b_c > e > $o] :
      ( ( ? [A3: prefix425356687782099470od_b_c,X6: e] : ( P @ A3 @ X6 ) )
      = ( ? [Z3: produc4534891796109904283_b_c_e] : ( P @ ( produc1447154562020694007_b_c_e @ Z3 ) @ ( produc6779600879576379961_b_c_e @ Z3 ) ) ) ) ).

% Ex_prod_contract
thf(fact_204_Ex__prod__contract,axiom,
    ! [P: a > produc2133359284458116493od_c_a > $o] :
      ( ( ? [A3: a,X6: produc2133359284458116493od_c_a] : ( P @ A3 @ X6 ) )
      = ( ? [Z3: produc2669932201312201782od_c_a] : ( P @ ( produc4225943634317630866od_c_a @ Z3 ) @ ( produc8088130389382527188od_c_a @ Z3 ) ) ) ) ).

% Ex_prod_contract
thf(fact_205_Ex__prod__contract,axiom,
    ! [P: b > product_prod_c_a > $o] :
      ( ( ? [A3: b,X6: product_prod_c_a] : ( P @ A3 @ X6 ) )
      = ( ? [Z3: produc2133359284458116493od_c_a] : ( P @ ( produc301949074746585577od_c_a @ Z3 ) @ ( produc5221446324160585515od_c_a @ Z3 ) ) ) ) ).

% Ex_prod_contract
thf(fact_206_Ex__prod__contract,axiom,
    ! [P: c > a > $o] :
      ( ( ? [A3: c,X6: a] : ( P @ A3 @ X6 ) )
      = ( ? [Z3: product_prod_c_a] : ( P @ ( product_fst_c_a @ Z3 ) @ ( product_snd_c_a @ Z3 ) ) ) ) ).

% Ex_prod_contract
thf(fact_207_All__prod__contract,axiom,
    ! [P: prefix425356687782099470od_b_c > e > $o] :
      ( ( ! [A3: prefix425356687782099470od_b_c,X6: e] : ( P @ A3 @ X6 ) )
      = ( ! [Z3: produc4534891796109904283_b_c_e] : ( P @ ( produc1447154562020694007_b_c_e @ Z3 ) @ ( produc6779600879576379961_b_c_e @ Z3 ) ) ) ) ).

% All_prod_contract
thf(fact_208_All__prod__contract,axiom,
    ! [P: a > produc2133359284458116493od_c_a > $o] :
      ( ( ! [A3: a,X6: produc2133359284458116493od_c_a] : ( P @ A3 @ X6 ) )
      = ( ! [Z3: produc2669932201312201782od_c_a] : ( P @ ( produc4225943634317630866od_c_a @ Z3 ) @ ( produc8088130389382527188od_c_a @ Z3 ) ) ) ) ).

% All_prod_contract
thf(fact_209_All__prod__contract,axiom,
    ! [P: b > product_prod_c_a > $o] :
      ( ( ! [A3: b,X6: product_prod_c_a] : ( P @ A3 @ X6 ) )
      = ( ! [Z3: produc2133359284458116493od_c_a] : ( P @ ( produc301949074746585577od_c_a @ Z3 ) @ ( produc5221446324160585515od_c_a @ Z3 ) ) ) ) ).

% All_prod_contract
thf(fact_210_All__prod__contract,axiom,
    ! [P: c > a > $o] :
      ( ( ! [A3: c,X6: a] : ( P @ A3 @ X6 ) )
      = ( ! [Z3: product_prod_c_a] : ( P @ ( product_fst_c_a @ Z3 ) @ ( product_snd_c_a @ Z3 ) ) ) ) ).

% All_prod_contract
thf(fact_211_reachable__state__is__state,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( member_a @ Q4 @ ( states_a_b_c @ M3 ) ) ) ).

% reachable_state_is_state
thf(fact_212_after__reachable__initial,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ ( initia3341036835946388646_a_b_c @ M3 ) ) )
       => ( member5502040268208861279od_c_a @ ( after_2239399860513592206_a_b_c @ M3 @ ( initia3341036835946388646_a_b_c @ M3 ) @ Io2 ) @ ( reacha1389639598965321787_a_b_c @ M3 ) ) ) ) ).

% after_reachable_initial
thf(fact_213_after__reachable__initial,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ ( initia3567573336347591134_c_b_c @ M3 ) ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M3 @ ( initia3567573336347591134_c_b_c @ M3 ) @ Io2 ) @ ( reacha8116992257183400179_c_b_c @ M3 ) ) ) ) ).

% after_reachable_initial
thf(fact_214_after__reachable__initial,axiom,
    ! [M3: fsm_d_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
       => ( member_d @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Io2 ) @ ( reacha9185589339461546374_d_b_c @ M3 ) ) ) ) ).

% after_reachable_initial
thf(fact_215_after__reachable__initial,axiom,
    ! [M3: fsm_a_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
       => ( member_a @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Io2 ) @ ( reacha1620305530751930115_a_b_c @ M3 ) ) ) ) ).

% after_reachable_initial
thf(fact_216_observable_Osimps,axiom,
    ( observable_d_b_c
    = ( ^ [M: fsm_d_b_c] :
        ! [X2: produc1399170498009216118od_c_d] :
          ( ( member4231278564905875615od_c_d @ X2 @ ( transitions_d_b_c @ M ) )
         => ! [Y2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ Y2 @ ( transitions_d_b_c @ M ) )
             => ( ( ( ( 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_217_observable_Osimps,axiom,
    ( observ2964502264774598958_a_a_b
    = ( ^ [M: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Y2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) )
               => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                  = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_218_observable_Osimps,axiom,
    ( observable_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M ) )
             => ( ( ( ( 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_219_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_220_observable_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( observ2964502264774598958_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ X ) )
                 => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                        = ( produc8171714036265584980od_c_a @ Y2 ) )
                      & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                        = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) )
                   => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                      = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_221_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_222_observable_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c] :
      ( ( observable_d_b_c @ X )
     => ! [X5: produc1399170498009216118od_c_d] :
          ( ( member4231278564905875615od_c_d @ X5 @ ( transitions_d_b_c @ X ) )
         => ! [Xa2: produc1399170498009216118od_c_d] :
              ( ( member4231278564905875615od_c_d @ Xa2 @ ( transitions_d_b_c @ X ) )
             => ( ( ( ( produc1508465569166014290od_c_d @ X5 )
                    = ( produc1508465569166014290od_c_d @ Xa2 ) )
                  & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X5 ) )
                    = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) )
                  & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X5 ) ) )
                    = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X5 ) ) )
                  = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_223_observable_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( observ2964502264774598958_a_a_b @ X )
     => ! [X5: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X5 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Xa2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X5 )
                    = ( produc8171714036265584980od_c_a @ Xa2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) )
               => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) ) )
                  = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_224_observable_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( observable_a_b_c @ X )
     => ! [X5: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X5 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X5 )
                    = ( produc4225943634317630866od_c_a @ Xa2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_225_observable_Oelims_I3_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 ) )
           => ! [Xa: produc1399170498009216118od_c_d] :
                ( ( member4231278564905875615od_c_d @ Xa @ ( transitions_d_b_c @ X ) )
               => ( ( ( ( produc1508465569166014290od_c_d @ X3 )
                      = ( produc1508465569166014290od_c_d @ Xa ) )
                    & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) )
                      = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Xa ) ) )
                    & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
                      = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa ) ) ) ) )
                 => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
                    = ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Xa ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_226_observable_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( observ2964502264774598958_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ Xa @ ( transi2941759273464634107_a_a_b @ X ) )
               => ( ( ( ( produc8171714036265584980od_c_a @ X3 )
                      = ( produc8171714036265584980od_c_a @ Xa ) )
                    & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) ) )
                 => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_227_observable_Oelims_I3_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 ) )
           => ! [Xa: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                      = ( produc4225943634317630866od_c_a @ Xa ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) ) )
                 => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_228_deterministic_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( determ4061018006534944583_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ Xa @ ( transi2941759273464634107_a_a_b @ X ) )
               => ( ( ( ( produc8171714036265584980od_c_a @ X3 )
                      = ( produc8171714036265584980od_c_a @ Xa ) )
                    & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) )
                 => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) )
                    & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(3)
thf(fact_229_deterministic_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( deterministic_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                      = ( produc4225943634317630866od_c_a @ Xa ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) )
                 => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) )
                    & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(3)
thf(fact_230_deterministic_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( determ4061018006534944583_a_a_b @ X )
     => ! [X5: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X5 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Xa2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X5 )
                    = ( produc8171714036265584980od_c_a @ Xa2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) )
                  & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(2)
thf(fact_231_deterministic_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( deterministic_a_b_c @ X )
     => ! [X5: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X5 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X5 )
                    = ( produc4225943634317630866od_c_a @ Xa2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) )
                  & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(2)
thf(fact_232_deterministic_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( determ4061018006534944583_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ X ) )
                 => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                        = ( produc8171714036265584980od_c_a @ Y2 ) )
                      & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                        = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                   => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                      & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(1)
thf(fact_233_deterministic_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( deterministic_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 ) ) ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(1)
thf(fact_234_deterministic_Osimps,axiom,
    ( determ4061018006534944583_a_a_b
    = ( ^ [M: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Y2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                  & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% deterministic.simps
thf(fact_235_deterministic_Osimps,axiom,
    ( deterministic_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M ) )
             => ( ( ( ( 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 ) ) ) ) ) ) ) ) ) ) ).

% deterministic.simps
thf(fact_236_observable__transition__target__language__eq,axiom,
    ! [M3: fsm_d_b_c,T1: produc1399170498009216118od_c_d,T22: produc1399170498009216118od_c_d] :
      ( ( ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T1 ) )
        = ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T22 ) ) )
     => ( ( member4231278564905875615od_c_d @ T1 @ ( transitions_d_b_c @ M3 ) )
       => ( ( member4231278564905875615od_c_d @ T22 @ ( transitions_d_b_c @ M3 ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) ) )
                = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) )
             => ( ( observable_d_b_c @ M3 )
               => ( ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) ) ) )
                  = ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_237_observable__transition__target__language__eq,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,T1: produc3205353004677322104od_c_a,T22: produc3205353004677322104od_c_a] :
      ( ( ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T1 ) )
        = ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T22 ) ) )
     => ( ( member6508725278956418977od_c_a @ T1 @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ( ( member6508725278956418977od_c_a @ T22 @ ( transi2941759273464634107_a_a_b @ M3 ) )
         => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) )
           => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) )
                = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) )
             => ( ( observ2964502264774598958_a_a_b @ M3 )
               => ( ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) ) )
                  = ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_238_observable__transition__target__language__eq,axiom,
    ! [M3: fsm_a_b_c,T1: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T1 ) )
        = ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T1 @ ( transitions_a_b_c @ M3 ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M3 ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M3 )
               => ( ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) ) )
                  = ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_239_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_240_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4534891796109904283_b_c_e] :
      ( Prod
      = ( produc2511600812177743883_b_c_e @ ( produc1447154562020694007_b_c_e @ Prod ) @ ( produc6779600879576379961_b_c_e @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_241_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2669932201312201782od_c_a] :
      ( Prod
      = ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ Prod ) @ ( produc8088130389382527188od_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_242_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2133359284458116493od_c_a] :
      ( Prod
      = ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ Prod ) @ ( produc5221446324160585515od_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_243_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_c_a] :
      ( Prod
      = ( product_Pair_c_a @ ( product_fst_c_a @ Prod ) @ ( product_snd_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_244_surjective__pairing,axiom,
    ! [T: product_prod_b_c] :
      ( T
      = ( product_Pair_b_c @ ( product_fst_b_c @ T ) @ ( product_snd_b_c @ T ) ) ) ).

% surjective_pairing
thf(fact_245_surjective__pairing,axiom,
    ! [T: produc4534891796109904283_b_c_e] :
      ( T
      = ( produc2511600812177743883_b_c_e @ ( produc1447154562020694007_b_c_e @ T ) @ ( produc6779600879576379961_b_c_e @ T ) ) ) ).

% surjective_pairing
thf(fact_246_surjective__pairing,axiom,
    ! [T: produc2669932201312201782od_c_a] :
      ( T
      = ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ T ) @ ( produc8088130389382527188od_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_247_surjective__pairing,axiom,
    ! [T: produc2133359284458116493od_c_a] :
      ( T
      = ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ T ) @ ( produc5221446324160585515od_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_248_surjective__pairing,axiom,
    ! [T: product_prod_c_a] :
      ( T
      = ( product_Pair_c_a @ ( product_fst_c_a @ T ) @ ( product_snd_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_249_observable__transition__unique,axiom,
    ! [M3: fsm_d_b_c,T: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
       => ? [X3: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X3 @ ( transitions_d_b_c @ M3 ) )
            & ( ( produc1508465569166014290od_c_d @ X3 )
              = ( produc1508465569166014290od_c_d @ T ) )
            & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) )
            & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ X3 ) ) )
              = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) )
            & ! [Y7: produc1399170498009216118od_c_d] :
                ( ( ( member4231278564905875615od_c_d @ Y7 @ ( transitions_d_b_c @ M3 ) )
                  & ( ( produc1508465569166014290od_c_d @ Y7 )
                    = ( produc1508465569166014290od_c_d @ T ) )
                  & ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ Y7 ) )
                    = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) )
                  & ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ Y7 ) ) )
                    = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) )
               => ( Y7 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_250_observable__transition__unique,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( observ2964502264774598958_a_a_b @ M3 )
     => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ? [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ M3 ) )
            & ( ( produc8171714036265584980od_c_a @ X3 )
              = ( produc8171714036265584980od_c_a @ T ) )
            & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) )
            & ! [Y7: produc3205353004677322104od_c_a] :
                ( ( ( member6508725278956418977od_c_a @ Y7 @ ( transi2941759273464634107_a_a_b @ M3 ) )
                  & ( ( produc8171714036265584980od_c_a @ Y7 )
                    = ( produc8171714036265584980od_c_a @ T ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y7 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y7 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) )
               => ( Y7 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_251_observable__transition__unique,axiom,
    ! [M3: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
       => ? [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M3 ) )
            & ( ( produc4225943634317630866od_c_a @ X3 )
              = ( produc4225943634317630866od_c_a @ T ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
              = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) )
            & ! [Y7: produc2669932201312201782od_c_a] :
                ( ( ( member5502040268208861279od_c_a @ Y7 @ ( transitions_a_b_c @ M3 ) )
                  & ( ( produc4225943634317630866od_c_a @ Y7 )
                    = ( produc4225943634317630866od_c_a @ T ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y7 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y7 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) )
               => ( Y7 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_252_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: produc2669932201312201782od_c_a > d,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_be5632368444736963777_c_a_d @ F @ ( reacha1389639598965321787_a_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_Pro3731892891411965979_a_b_c @ M12 @ ( initia3341036835946388646_a_b_c @ M12 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_253_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: list_P903359562653991662od_b_c > d,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F @ ( reacha8116992257183400179_c_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_lis2930931384350476499_c_b_c @ M12 @ ( initia3567573336347591134_c_b_c @ M12 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_254_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: d > d,M12: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_d_d @ F @ ( reacha9185589339461546374_d_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_255_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: produc2669932201312201782od_c_a > a,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_be5632368444736963774_c_a_a @ F @ ( reacha1389639598965321787_a_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_Pro3731892891411965979_a_b_c @ M12 @ ( initia3341036835946388646_a_b_c @ M12 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_256_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: list_P903359562653991662od_b_c > a,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F @ ( reacha8116992257183400179_c_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_lis2930931384350476499_c_b_c @ M12 @ ( initia3567573336347591134_c_b_c @ M12 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_257_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: d > a,M12: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_d_a @ F @ ( reacha9185589339461546374_d_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_258_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: a > d,M12: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_a_d @ F @ ( reacha1620305530751930115_a_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) )
            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_259_language__equivalence__from__isomorphism__reachable,axiom,
    ! [F: a > a,M12: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_a_a @ F @ ( reacha1620305530751930115_a_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) )
            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_reachable
thf(fact_260_establish__convergence__static__finite,axiom,
    ! [T4: prefix425356687782099470od_b_c,Dist_fun: nat > a > prefix425356687782099470od_b_c,M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,G2: e,Cg_insert2: e > list_P903359562653991662od_b_c > e,Cg_lookup2: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,M4: nat,T: produc2669932201312201782od_c_a] :
      ( ( prefix6767660319289835678od_b_c @ T4 )
     => ( prefix6767660319289835678od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm821963860068034213_b_c_e @ Dist_fun @ M3 @ V @ T4 @ G2 @ Cg_insert2 @ Cg_lookup2 @ M4 @ T ) ) ) ) ).

% establish_convergence_static_finite
thf(fact_261_after__is__state,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Io2: list_P903359562653991662od_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) )
       => ( member5502040268208861279od_c_a @ ( after_2239399860513592206_a_b_c @ M3 @ Q4 @ Io2 ) @ ( states895637122477222528_a_b_c @ M3 ) ) ) ) ).

% after_is_state
thf(fact_262_after__is__state,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Io2: list_P903359562653991662od_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M3 @ Q4 @ Io2 ) @ ( states7681702920031268536_c_b_c @ M3 ) ) ) ) ).

% after_is_state
thf(fact_263_after__is__state,axiom,
    ! [M3: fsm_a_b_c,Io2: list_P903359562653991662od_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( member_a @ ( after_a_b_c @ M3 @ Q4 @ Io2 ) @ ( states_a_b_c @ M3 ) ) ) ) ).

% after_is_state
thf(fact_264_after__is__state,axiom,
    ! [M3: fsm_d_b_c,Io2: list_P903359562653991662od_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( member_d @ ( after_d_b_c @ M3 @ Q4 @ Io2 ) @ ( states_d_b_c @ M3 ) ) ) ) ).

% after_is_state
thf(fact_265_single__input_Osimps,axiom,
    ( single999786218259502647_a_a_b
    = ( ^ [M: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M ) )
             => ( ( ( produc8171714036265584980od_c_a @ X2 )
                  = ( produc8171714036265584980od_c_a @ Y2 ) )
               => ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                  = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ).

% single_input.simps
thf(fact_266_single__input_Osimps,axiom,
    ( single_input_a_b_c
    = ( ^ [M: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M ) )
             => ( ( ( produc4225943634317630866od_c_a @ X2 )
                  = ( produc4225943634317630866od_c_a @ Y2 ) )
               => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                  = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ).

% single_input.simps
thf(fact_267_single__input_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( single999786218259502647_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ X ) )
                 => ( ( ( produc8171714036265584980od_c_a @ X2 )
                      = ( produc8171714036265584980od_c_a @ Y2 ) )
                   => ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% single_input.elims(1)
thf(fact_268_single__input_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( single_input_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 ) ) ) ) ) ) ) ) ) ).

% single_input.elims(1)
thf(fact_269_single__input_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( single999786218259502647_a_a_b @ X )
     => ! [X5: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X5 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Xa2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ( ( ( produc8171714036265584980od_c_a @ X5 )
                  = ( produc8171714036265584980od_c_a @ Xa2 ) )
               => ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X5 ) )
                  = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) ) ) ) ).

% single_input.elims(2)
thf(fact_270_single__input_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( single_input_a_b_c @ X )
     => ! [X5: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X5 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( produc4225943634317630866od_c_a @ X5 )
                  = ( produc4225943634317630866od_c_a @ Xa2 ) )
               => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X5 ) )
                  = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ).

% single_input.elims(2)
thf(fact_271_retains__outputs__for__states__and__inputs__def,axiom,
    ( retain6283235197096808344_a_a_b
    = ( ^ [M: fsm_Pr1886043760914421514_a_a_b,S3: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ S3 ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Y2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
               => ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ S3 ) ) ) ) ) ) ) ).

% retains_outputs_for_states_and_inputs_def
thf(fact_272_retains__outputs__for__states__and__inputs__def,axiom,
    ( retain2430384024318543025_a_b_c
    = ( ^ [M: fsm_a_b_c,S3: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ S3 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Y2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
               => ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ S3 ) ) ) ) ) ) ) ).

% retains_outputs_for_states_and_inputs_def
thf(fact_273_is__state__cover__assignment__observable__after,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( state_6014242345326633810_d_b_c @ M3 @ V )
       => ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
         => ( ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( V @ Q4 ) )
            = Q4 ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_274_is__state__cover__assignment__observable__after,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( state_7672330573471793359_a_b_c @ M3 @ V )
       => ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
         => ( ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( V @ Q4 ) )
            = Q4 ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_275_state__cover__assignment__after_I1_J,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,V: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( state_1238012481214864903_a_b_c @ M3 @ V )
       => ( ( member5502040268208861279od_c_a @ Q4 @ ( reacha1389639598965321787_a_b_c @ M3 ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ ( initia3341036835946388646_a_b_c @ M3 ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_276_state__cover__assignment__after_I1_J,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( state_2362830510734323903_c_b_c @ M3 @ V )
       => ( ( member6330420149250801815od_b_c @ Q4 @ ( reacha8116992257183400179_c_b_c @ M3 ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_lis2930931384350476499_c_b_c @ M3 @ ( initia3567573336347591134_c_b_c @ M3 ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_277_state__cover__assignment__after_I1_J,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( state_6014242345326633810_d_b_c @ M3 @ V )
       => ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_278_state__cover__assignment__after_I1_J,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( state_7672330573471793359_a_b_c @ M3 @ V )
       => ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_279_is__state__cover__assignment__language,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,V: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( state_1238012481214864903_a_b_c @ M3 @ V )
     => ( ( member5502040268208861279od_c_a @ Q4 @ ( reacha1389639598965321787_a_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ ( initia3341036835946388646_a_b_c @ M3 ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_280_is__state__cover__assignment__language,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( state_2362830510734323903_c_b_c @ M3 @ V )
     => ( ( member6330420149250801815od_b_c @ Q4 @ ( reacha8116992257183400179_c_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_lis2930931384350476499_c_b_c @ M3 @ ( initia3567573336347591134_c_b_c @ M3 ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_281_is__state__cover__assignment__language,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,Q4: d] :
      ( ( state_6014242345326633810_d_b_c @ M3 @ V )
     => ( ( member_d @ Q4 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_282_is__state__cover__assignment__language,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q4: a] :
      ( ( state_7672330573471793359_a_b_c @ M3 @ V )
     => ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q4 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_283_convergence__graph__initial__invar__def,axiom,
    ( conver3708542147478018715_c_d_e
    = ( ^ [M1: fsm_a_b_c,M2: fsm_d_b_c,Cg_lookup: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,Cg_initial: fsm_a_b_c > prefix425356687782099470od_b_c > e] :
        ! [T5: prefix425356687782099470od_b_c] :
          ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T5 ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M2 @ ( initial_d_b_c @ M2 ) ) @ ( prefix9085958534787526401od_b_c @ T5 ) ) )
         => ( ( prefix6767660319289835678od_b_c @ T5 )
           => ( conver7089555221631485245_c_d_e @ M1 @ M2 @ Cg_lookup @ ( Cg_initial @ M1 @ T5 ) ) ) ) ) ) ).

% convergence_graph_initial_invar_def
thf(fact_284_state__cover__assignment__inj,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,Q14: d,Q2: d] :
      ( ( state_6014242345326633810_d_b_c @ M3 @ V )
     => ( ( observable_d_b_c @ M3 )
       => ( ( member_d @ Q14 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( ( V @ Q14 )
               != ( V @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_285_state__cover__assignment__inj,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q14: a,Q2: a] :
      ( ( state_7672330573471793359_a_b_c @ M3 @ V )
     => ( ( observable_a_b_c @ M3 )
       => ( ( member_a @ Q14 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( ( V @ Q14 )
               != ( V @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_286_assms_I11_J,axiom,
    ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ v @ ( reacha1620305530751930115_a_b_c @ m1 ) ) @ ( prefix9085958534787526401od_b_c @ t ) ).

% assms(11)
thf(fact_287_observable__language__transition__target,axiom,
    ! [M3: fsm_d_b_c,T: produc1399170498009216118od_c_d,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) @ Io2 ) @ ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T ) ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_288_observable__language__transition__target,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a,Io2: list_P1467974523212632366od_a_b] :
      ( ( observ2964502264774598958_a_a_b @ M3 )
     => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) @ Io2 ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T ) ) )
         => ( member6895035109809442519od_a_b @ Io2 @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_289_observable__language__transition__target,axiom,
    ! [M3: fsm_a_b_c,T: produc2669932201312201782od_c_a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) @ Io2 ) @ ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T ) ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_290_exI__realizer,axiom,
    ! [P: c > b > $o,Y: c,X: b] :
      ( ( P @ Y @ X )
     => ( P @ ( product_snd_b_c @ ( product_Pair_b_c @ X @ Y ) ) @ ( product_fst_b_c @ ( product_Pair_b_c @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_291_exI__realizer,axiom,
    ! [P: e > prefix425356687782099470od_b_c > $o,Y: e,X: prefix425356687782099470od_b_c] :
      ( ( P @ Y @ X )
     => ( P @ ( produc6779600879576379961_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) ) @ ( produc1447154562020694007_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_292_exI__realizer,axiom,
    ! [P: produc2133359284458116493od_c_a > a > $o,Y: produc2133359284458116493od_c_a,X: a] :
      ( ( P @ Y @ X )
     => ( P @ ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) ) @ ( produc4225943634317630866od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_293_exI__realizer,axiom,
    ! [P: product_prod_c_a > b > $o,Y: product_prod_c_a,X: b] :
      ( ( P @ Y @ X )
     => ( P @ ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) ) @ ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_294_exI__realizer,axiom,
    ! [P: a > c > $o,Y: a,X: c] :
      ( ( P @ Y @ X )
     => ( P @ ( product_snd_c_a @ ( product_Pair_c_a @ X @ Y ) ) @ ( product_fst_c_a @ ( product_Pair_c_a @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_295_image__eqI,axiom,
    ! [B2: produc2669932201312201782od_c_a,F: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a,X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member5502040268208861279od_c_a @ X @ A )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_2169818278710580869od_c_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_296_image__eqI,axiom,
    ! [B2: a,F: produc2669932201312201782od_c_a > a,X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member5502040268208861279od_c_a @ X @ A )
       => ( member_a @ B2 @ ( image_9171994905208062541_c_a_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_297_image__eqI,axiom,
    ! [B2: list_P903359562653991662od_b_c,F: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member5502040268208861279od_c_a @ X @ A )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_826490394676381629od_b_c @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_298_image__eqI,axiom,
    ! [B2: produc2669932201312201782od_c_a,F: a > produc2669932201312201782od_c_a,X: a,A: set_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_a @ X @ A )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_4184489845059386301od_c_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_299_image__eqI,axiom,
    ! [B2: a,F: a > a,X: a,A: set_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_a @ X @ A )
       => ( member_a @ B2 @ ( image_a_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_300_image__eqI,axiom,
    ! [B2: list_P903359562653991662od_b_c,F: a > list_P903359562653991662od_b_c,X: a,A: set_a] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_a @ X @ A )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_8656872703560917237od_b_c @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_301_image__eqI,axiom,
    ! [B2: produc2669932201312201782od_c_a,F: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a,X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member6330420149250801815od_b_c @ X @ A )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_7601443023479506637od_c_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_302_image__eqI,axiom,
    ! [B2: a,F: list_P903359562653991662od_b_c > a,X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member6330420149250801815od_b_c @ X @ A )
       => ( member_a @ B2 @ ( image_3173854338463926933_b_c_a @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_303_image__eqI,axiom,
    ! [B2: list_P903359562653991662od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member6330420149250801815od_b_c @ X @ A )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_2850395784482391045od_b_c @ F @ A ) ) ) ) ).

% image_eqI
thf(fact_304_subset__antisym,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( ord_le282488521294790766od_b_c @ B @ A )
       => ( A = B ) ) ) ).

% subset_antisym
thf(fact_305_subsetI,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ A )
         => ( member5502040268208861279od_c_a @ X3 @ B ) )
     => ( ord_le3226338165915859510od_c_a @ A @ B ) ) ).

% subsetI
thf(fact_306_subsetI,axiom,
    ! [A: set_a,B: set_a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( member_a @ X3 @ B ) )
     => ( ord_less_eq_set_a @ A @ B ) ) ).

% subsetI
thf(fact_307_subsetI,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( member6330420149250801815od_b_c @ X3 @ B ) )
     => ( ord_le282488521294790766od_b_c @ A @ B ) ) ).

% subsetI
thf(fact_308_inf_Obounded__iff,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B2 @ C ) )
      = ( ( ord_le282488521294790766od_b_c @ A2 @ B2 )
        & ( ord_le282488521294790766od_b_c @ A2 @ C ) ) ) ).

% inf.bounded_iff
thf(fact_309_inf_Obounded__iff,axiom,
    ! [A2: nat,B2: nat,C: nat] :
      ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
      = ( ( ord_less_eq_nat @ A2 @ B2 )
        & ( ord_less_eq_nat @ A2 @ C ) ) ) ).

% inf.bounded_iff
thf(fact_310_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_311_le__inf__iff,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
      = ( ( ord_less_eq_nat @ X @ Y )
        & ( ord_less_eq_nat @ X @ Z ) ) ) ).

% le_inf_iff
thf(fact_312_Int__subset__iff,axiom,
    ! [C2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C2 @ ( inf_in4978071631833541052od_b_c @ A @ B ) )
      = ( ( ord_le282488521294790766od_b_c @ C2 @ A )
        & ( ord_le282488521294790766od_b_c @ C2 @ B ) ) ) ).

% Int_subset_iff
thf(fact_313_xy,axiom,
    ( xy
    = ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ t2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ t2 ) ) ) ) ) ).

% xy
thf(fact_314__092_060beta_062,axiom,
    ( beta
    = ( v @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ t2 ) ) ) ) ) ).

% \<beta>
thf(fact_315_assms_I12_J,axiom,
    preser261684820601417592_b_c_d @ m1 @ m2 @ ( image_8656872703560917237od_b_c @ v @ ( reacha1620305530751930115_a_b_c @ m1 ) ) ).

% assms(12)
thf(fact_316_qTarget,axiom,
    ( qTarget
    = ( after_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) @ ( v @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ t2 ) ) ) ) ) ) ).

% qTarget
thf(fact_317_image__Int__subset,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,B: set_a] : ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F @ ( inf_inf_set_a @ A @ B ) ) @ ( inf_in4978071631833541052od_b_c @ ( image_8656872703560917237od_b_c @ F @ A ) @ ( image_8656872703560917237od_b_c @ F @ B ) ) ) ).

% image_Int_subset
thf(fact_318_image__Int__subset,axiom,
    ! [F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) @ ( inf_in4978071631833541052od_b_c @ ( image_2850395784482391045od_b_c @ F @ A ) @ ( image_2850395784482391045od_b_c @ F @ B ) ) ) ).

% image_Int_subset
thf(fact_319_subset__image__iff,axiom,
    ! [B: set_li6436108459499378894od_b_c,F: a > list_P903359562653991662od_b_c,A: set_a] :
      ( ( ord_le282488521294790766od_b_c @ B @ ( image_8656872703560917237od_b_c @ F @ A ) )
      = ( ? [AA: set_a] :
            ( ( ord_less_eq_set_a @ AA @ A )
            & ( B
              = ( image_8656872703560917237od_b_c @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_320_subset__image__iff,axiom,
    ! [B: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ ( image_2850395784482391045od_b_c @ F @ A ) )
      = ( ? [AA: set_li6436108459499378894od_b_c] :
            ( ( ord_le282488521294790766od_b_c @ AA @ A )
            & ( B
              = ( image_2850395784482391045od_b_c @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_321_image__subset__iff,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F @ A ) @ B )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( member6330420149250801815od_b_c @ ( F @ X2 ) @ B ) ) ) ) ).

% image_subset_iff
thf(fact_322_Collect__mono__iff,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Q7: list_P903359562653991662od_b_c > $o] :
      ( ( ord_le282488521294790766od_b_c @ ( collec2280997390073109977od_b_c @ P ) @ ( collec2280997390073109977od_b_c @ Q7 ) )
      = ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( P @ X2 )
           => ( Q7 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_323_subset__imageE,axiom,
    ! [B: set_li6436108459499378894od_b_c,F: a > list_P903359562653991662od_b_c,A: set_a] :
      ( ( ord_le282488521294790766od_b_c @ B @ ( image_8656872703560917237od_b_c @ F @ A ) )
     => ~ ! [C3: set_a] :
            ( ( ord_less_eq_set_a @ C3 @ A )
           => ( B
             != ( image_8656872703560917237od_b_c @ F @ C3 ) ) ) ) ).

% subset_imageE
thf(fact_324_subset__imageE,axiom,
    ! [B: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ ( image_2850395784482391045od_b_c @ F @ A ) )
     => ~ ! [C3: set_li6436108459499378894od_b_c] :
            ( ( ord_le282488521294790766od_b_c @ C3 @ A )
           => ( B
             != ( image_2850395784482391045od_b_c @ F @ C3 ) ) ) ) ).

% subset_imageE
thf(fact_325_set__eq__subset,axiom,
    ( ( ^ [Y6: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] : ( Y6 = Z2 ) )
    = ( ^ [A4: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
          ( ( ord_le282488521294790766od_b_c @ A4 @ B4 )
          & ( ord_le282488521294790766od_b_c @ B4 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_326_rev__image__eqI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B2: produc2669932201312201782od_c_a,F: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_2169818278710580869od_c_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_327_rev__image__eqI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B2: a,F: produc2669932201312201782od_c_a > a] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member_a @ B2 @ ( image_9171994905208062541_c_a_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_328_rev__image__eqI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B2: list_P903359562653991662od_b_c,F: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_826490394676381629od_b_c @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_329_rev__image__eqI,axiom,
    ! [X: a,A: set_a,B2: produc2669932201312201782od_c_a,F: a > produc2669932201312201782od_c_a] :
      ( ( member_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_4184489845059386301od_c_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_330_rev__image__eqI,axiom,
    ! [X: a,A: set_a,B2: a,F: a > a] :
      ( ( member_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member_a @ B2 @ ( image_a_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_331_rev__image__eqI,axiom,
    ! [X: a,A: set_a,B2: list_P903359562653991662od_b_c,F: a > list_P903359562653991662od_b_c] :
      ( ( member_a @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_8656872703560917237od_b_c @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_332_rev__image__eqI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B2: produc2669932201312201782od_c_a,F: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member5502040268208861279od_c_a @ B2 @ ( image_7601443023479506637od_c_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_333_rev__image__eqI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B2: a,F: list_P903359562653991662od_b_c > a] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member_a @ B2 @ ( image_3173854338463926933_b_c_a @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_334_rev__image__eqI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( ( B2
          = ( F @ X ) )
       => ( member6330420149250801815od_b_c @ B2 @ ( image_2850395784482391045od_b_c @ F @ A ) ) ) ) ).

% rev_image_eqI
thf(fact_335_image__subsetI,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ A )
         => ( member5502040268208861279od_c_a @ ( F @ X3 ) @ B ) )
     => ( ord_le3226338165915859510od_c_a @ ( image_2169818278710580869od_c_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_336_image__subsetI,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > a,B: set_a] :
      ( ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ A )
         => ( member_a @ ( F @ X3 ) @ B ) )
     => ( ord_less_eq_set_a @ ( image_9171994905208062541_c_a_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_337_image__subsetI,axiom,
    ! [A: set_a,F: a > produc2669932201312201782od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( member5502040268208861279od_c_a @ ( F @ X3 ) @ B ) )
     => ( ord_le3226338165915859510od_c_a @ ( image_4184489845059386301od_c_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_338_image__subsetI,axiom,
    ! [A: set_a,F: a > a,B: set_a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( member_a @ ( F @ X3 ) @ B ) )
     => ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_339_image__subsetI,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a,B: set_Pr8357624050790843030od_c_a] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( member5502040268208861279od_c_a @ ( F @ X3 ) @ B ) )
     => ( ord_le3226338165915859510od_c_a @ ( image_7601443023479506637od_c_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_340_image__subsetI,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > a,B: set_a] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( member_a @ ( F @ X3 ) @ B ) )
     => ( ord_less_eq_set_a @ ( image_3173854338463926933_b_c_a @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_341_image__subsetI,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ A )
         => ( member6330420149250801815od_b_c @ ( F @ X3 ) @ B ) )
     => ( ord_le282488521294790766od_b_c @ ( image_826490394676381629od_b_c @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_342_image__subsetI,axiom,
    ! [A: set_a,F: a > list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( member6330420149250801815od_b_c @ ( F @ X3 ) @ B ) )
     => ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_343_image__subsetI,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( member6330420149250801815od_b_c @ ( F @ X3 ) @ B ) )
     => ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F @ A ) @ B ) ) ).

% image_subsetI
thf(fact_344_subset__trans,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( ord_le282488521294790766od_b_c @ B @ C2 )
       => ( ord_le282488521294790766od_b_c @ A @ C2 ) ) ) ).

% subset_trans
thf(fact_345_Collect__mono,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Q7: list_P903359562653991662od_b_c > $o] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( P @ X3 )
         => ( Q7 @ X3 ) )
     => ( ord_le282488521294790766od_b_c @ ( collec2280997390073109977od_b_c @ P ) @ ( collec2280997390073109977od_b_c @ Q7 ) ) ) ).

% Collect_mono
thf(fact_346_subset__refl,axiom,
    ! [A: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ A @ A ) ).

% subset_refl
thf(fact_347_ball__imageD,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,P: list_P903359562653991662od_b_c > $o] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( image_8656872703560917237od_b_c @ F @ A ) )
         => ( P @ X3 ) )
     => ! [X5: a] :
          ( ( member_a @ X5 @ A )
         => ( P @ ( F @ X5 ) ) ) ) ).

% ball_imageD
thf(fact_348_subset__iff,axiom,
    ( ord_le3226338165915859510od_c_a
    = ( ^ [A4: set_Pr8357624050790843030od_c_a,B4: set_Pr8357624050790843030od_c_a] :
        ! [T3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ T3 @ A4 )
         => ( member5502040268208861279od_c_a @ T3 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_349_subset__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B4: set_a] :
        ! [T3: a] :
          ( ( member_a @ T3 @ A4 )
         => ( member_a @ T3 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_350_subset__iff,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A4: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
        ! [T3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ T3 @ A4 )
         => ( member6330420149250801815od_b_c @ T3 @ B4 ) ) ) ) ).

% subset_iff
thf(fact_351_image__mono,axiom,
    ! [A: set_a,B: set_a,F: a > list_P903359562653991662od_b_c] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F @ A ) @ ( image_8656872703560917237od_b_c @ F @ B ) ) ) ).

% image_mono
thf(fact_352_image__mono,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F @ A ) @ ( image_2850395784482391045od_b_c @ F @ B ) ) ) ).

% image_mono
thf(fact_353_image__cong,axiom,
    ! [M3: set_a,N: set_a,F: a > list_P903359562653991662od_b_c,G3: a > list_P903359562653991662od_b_c] :
      ( ( M3 = N )
     => ( ! [X3: a] :
            ( ( member_a @ X3 @ N )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( image_8656872703560917237od_b_c @ F @ M3 )
          = ( image_8656872703560917237od_b_c @ G3 @ N ) ) ) ) ).

% image_cong
thf(fact_354_equalityD2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A = B )
     => ( ord_le282488521294790766od_b_c @ B @ A ) ) ).

% equalityD2
thf(fact_355_equalityD1,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A = B )
     => ( ord_le282488521294790766od_b_c @ A @ B ) ) ).

% equalityD1
thf(fact_356_bex__imageD,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,P: list_P903359562653991662od_b_c > $o] :
      ( ? [X5: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X5 @ ( image_8656872703560917237od_b_c @ F @ A ) )
          & ( P @ X5 ) )
     => ? [X3: a] :
          ( ( member_a @ X3 @ A )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_357_subset__eq,axiom,
    ( ord_le3226338165915859510od_c_a
    = ( ^ [A4: set_Pr8357624050790843030od_c_a,B4: set_Pr8357624050790843030od_c_a] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ A4 )
         => ( member5502040268208861279od_c_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_358_subset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B4: set_a] :
        ! [X2: a] :
          ( ( member_a @ X2 @ A4 )
         => ( member_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_359_subset__eq,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A4: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ A4 )
         => ( member6330420149250801815od_b_c @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_360_image__iff,axiom,
    ! [Z: list_P903359562653991662od_b_c,F: a > list_P903359562653991662od_b_c,A: set_a] :
      ( ( member6330420149250801815od_b_c @ Z @ ( image_8656872703560917237od_b_c @ F @ A ) )
      = ( ? [X2: a] :
            ( ( member_a @ X2 @ A )
            & ( Z
              = ( F @ X2 ) ) ) ) ) ).

% image_iff
thf(fact_361_equalityE,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A = B )
     => ~ ( ( ord_le282488521294790766od_b_c @ A @ B )
         => ~ ( ord_le282488521294790766od_b_c @ B @ A ) ) ) ).

% equalityE
thf(fact_362_subsetD,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a,C: produc2669932201312201782od_c_a] :
      ( ( ord_le3226338165915859510od_c_a @ A @ B )
     => ( ( member5502040268208861279od_c_a @ C @ A )
       => ( member5502040268208861279od_c_a @ C @ B ) ) ) ).

% subsetD
thf(fact_363_subsetD,axiom,
    ! [A: set_a,B: set_a,C: a] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ( member_a @ C @ A )
       => ( member_a @ C @ B ) ) ) ).

% subsetD
thf(fact_364_subsetD,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( member6330420149250801815od_b_c @ C @ A )
       => ( member6330420149250801815od_b_c @ C @ B ) ) ) ).

% subsetD
thf(fact_365_in__mono,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a,X: produc2669932201312201782od_c_a] :
      ( ( ord_le3226338165915859510od_c_a @ A @ B )
     => ( ( member5502040268208861279od_c_a @ X @ A )
       => ( member5502040268208861279od_c_a @ X @ B ) ) ) ).

% in_mono
thf(fact_366_in__mono,axiom,
    ! [A: set_a,B: set_a,X: a] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ( member_a @ X @ A )
       => ( member_a @ X @ B ) ) ) ).

% in_mono
thf(fact_367_in__mono,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( member6330420149250801815od_b_c @ X @ A )
       => ( member6330420149250801815od_b_c @ X @ B ) ) ) ).

% in_mono
thf(fact_368_imageI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( member5502040268208861279od_c_a @ ( F @ X ) @ ( image_2169818278710580869od_c_a @ F @ A ) ) ) ).

% imageI
thf(fact_369_imageI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > a] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_9171994905208062541_c_a_a @ F @ A ) ) ) ).

% imageI
thf(fact_370_imageI,axiom,
    ! [X: produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,F: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c] :
      ( ( member5502040268208861279od_c_a @ X @ A )
     => ( member6330420149250801815od_b_c @ ( F @ X ) @ ( image_826490394676381629od_b_c @ F @ A ) ) ) ).

% imageI
thf(fact_371_imageI,axiom,
    ! [X: a,A: set_a,F: a > produc2669932201312201782od_c_a] :
      ( ( member_a @ X @ A )
     => ( member5502040268208861279od_c_a @ ( F @ X ) @ ( image_4184489845059386301od_c_a @ F @ A ) ) ) ).

% imageI
thf(fact_372_imageI,axiom,
    ! [X: a,A: set_a,F: a > a] :
      ( ( member_a @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_a_a @ F @ A ) ) ) ).

% imageI
thf(fact_373_imageI,axiom,
    ! [X: a,A: set_a,F: a > list_P903359562653991662od_b_c] :
      ( ( member_a @ X @ A )
     => ( member6330420149250801815od_b_c @ ( F @ X ) @ ( image_8656872703560917237od_b_c @ F @ A ) ) ) ).

% imageI
thf(fact_374_imageI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( member5502040268208861279od_c_a @ ( F @ X ) @ ( image_7601443023479506637od_c_a @ F @ A ) ) ) ).

% imageI
thf(fact_375_imageI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > a] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( member_a @ ( F @ X ) @ ( image_3173854338463926933_b_c_a @ F @ A ) ) ) ).

% imageI
thf(fact_376_imageI,axiom,
    ! [X: list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ A )
     => ( member6330420149250801815od_b_c @ ( F @ X ) @ ( image_2850395784482391045od_b_c @ F @ A ) ) ) ).

% imageI
thf(fact_377_subset__Collect__conv,axiom,
    ! [S: set_li6436108459499378894od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( ord_le282488521294790766od_b_c @ S @ ( collec2280997390073109977od_b_c @ P ) )
      = ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ S )
           => ( P @ X2 ) ) ) ) ).

% subset_Collect_conv
thf(fact_378_ord__eq__le__eq__trans,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,D: set_li6436108459499378894od_b_c] :
      ( ( A2 = B2 )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C )
       => ( ( C = D )
         => ( ord_le282488521294790766od_b_c @ A2 @ D ) ) ) ) ).

% ord_eq_le_eq_trans
thf(fact_379_ord__eq__le__eq__trans,axiom,
    ! [A2: nat,B2: nat,C: nat,D: nat] :
      ( ( A2 = B2 )
     => ( ( ord_less_eq_nat @ B2 @ C )
       => ( ( C = D )
         => ( ord_less_eq_nat @ A2 @ D ) ) ) ) ).

% ord_eq_le_eq_trans
thf(fact_380_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_381_list__tail__coinc,axiom,
    ! [N1: list_P903359562653991662od_b_c,R1: list_l8907847357763382004od_b_c,N2: list_P903359562653991662od_b_c,R2: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ N1 @ R1 )
        = ( cons_l342771267123639716od_b_c @ N2 @ R2 ) )
     => ( ( N1 = N2 )
        & ( R1 = R2 ) ) ) ).

% list_tail_coinc
thf(fact_382_inf_OcoboundedI2,axiom,
    ! [B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ C )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_383_inf_OcoboundedI2,axiom,
    ! [B2: nat,C: nat,A2: nat] :
      ( ( ord_less_eq_nat @ B2 @ C )
     => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_384_inf_OcoboundedI1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ C )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_385_inf_OcoboundedI1,axiom,
    ! [A2: nat,C: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A2 @ C )
     => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_386_inf_Oabsorb__iff2,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [B3: set_li6436108459499378894od_b_c,A3: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ A3 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_387_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_nat
    = ( ^ [B3: nat,A3: nat] :
          ( ( inf_inf_nat @ A3 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_388_inf_Oabsorb__iff1,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A3: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( ( inf_in4978071631833541052od_b_c @ A3 @ B3 )
          = A3 ) ) ) ).

% inf.absorb_iff1
thf(fact_389_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B3: nat] :
          ( ( inf_inf_nat @ A3 @ B3 )
          = A3 ) ) ) ).

% inf.absorb_iff1
thf(fact_390_inf_Ocobounded2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_391_inf_Ocobounded2,axiom,
    ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_392_inf_Ocobounded1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ A2 ) ).

% inf.cobounded1
thf(fact_393_inf_Ocobounded1,axiom,
    ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ A2 ) ).

% inf.cobounded1
thf(fact_394_inf_Oorder__iff,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A3: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( A3
          = ( inf_in4978071631833541052od_b_c @ A3 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_395_inf_Oorder__iff,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B3: nat] :
          ( A3
          = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_396_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_397_inf__greatest,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ X @ Z )
       => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).

% inf_greatest
thf(fact_398_inf_OboundedI,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ A2 @ C )
       => ( ord_le282488521294790766od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_399_inf_OboundedI,axiom,
    ! [A2: nat,B2: nat,C: nat] :
      ( ( ord_less_eq_nat @ A2 @ B2 )
     => ( ( ord_less_eq_nat @ A2 @ C )
       => ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_400_inf_OboundedE,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ ( inf_in4978071631833541052od_b_c @ B2 @ C ) )
     => ~ ( ( ord_le282488521294790766od_b_c @ A2 @ B2 )
         => ~ ( ord_le282488521294790766od_b_c @ A2 @ C ) ) ) ).

% inf.boundedE
thf(fact_401_inf_OboundedE,axiom,
    ! [A2: nat,B2: nat,C: nat] :
      ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
     => ~ ( ( ord_less_eq_nat @ A2 @ B2 )
         => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).

% inf.boundedE
thf(fact_402_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_403_inf__absorb2,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( inf_inf_nat @ X @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_404_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_405_inf__absorb1,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( inf_inf_nat @ X @ Y )
        = X ) ) ).

% inf_absorb1
thf(fact_406_inf_Oabsorb2,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ A2 )
     => ( ( inf_in4978071631833541052od_b_c @ A2 @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_407_inf_Oabsorb2,axiom,
    ! [B2: nat,A2: nat] :
      ( ( ord_less_eq_nat @ B2 @ A2 )
     => ( ( inf_inf_nat @ A2 @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_408_inf_Oabsorb1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B2 )
     => ( ( inf_in4978071631833541052od_b_c @ A2 @ B2 )
        = A2 ) ) ).

% inf.absorb1
thf(fact_409_inf_Oabsorb1,axiom,
    ! [A2: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A2 @ B2 )
     => ( ( inf_inf_nat @ A2 @ B2 )
        = A2 ) ) ).

% inf.absorb1
thf(fact_410_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_411_le__iff__inf,axiom,
    ( ord_less_eq_nat
    = ( ^ [X2: nat,Y2: nat] :
          ( ( inf_inf_nat @ X2 @ Y2 )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_412_inf__unique,axiom,
    ! [F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ! [X3: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( F @ X3 @ Y3 ) @ X3 )
     => ( ! [X3: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( F @ X3 @ Y3 ) @ Y3 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y3: set_li6436108459499378894od_b_c,Z4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y3 )
             => ( ( ord_le282488521294790766od_b_c @ X3 @ Z4 )
               => ( ord_le282488521294790766od_b_c @ X3 @ ( F @ Y3 @ Z4 ) ) ) )
         => ( ( inf_in4978071631833541052od_b_c @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_413_inf__unique,axiom,
    ! [F: nat > nat > nat,X: nat,Y: nat] :
      ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ X3 )
     => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ Y3 )
       => ( ! [X3: nat,Y3: nat,Z4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y3 )
             => ( ( ord_less_eq_nat @ X3 @ Z4 )
               => ( ord_less_eq_nat @ X3 @ ( F @ Y3 @ Z4 ) ) ) )
         => ( ( inf_inf_nat @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_414_inf_OorderI,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( A2
        = ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) )
     => ( ord_le282488521294790766od_b_c @ A2 @ B2 ) ) ).

% inf.orderI
thf(fact_415_inf_OorderI,axiom,
    ! [A2: nat,B2: nat] :
      ( ( A2
        = ( inf_inf_nat @ A2 @ B2 ) )
     => ( ord_less_eq_nat @ A2 @ B2 ) ) ).

% inf.orderI
thf(fact_416_inf_OorderE,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B2 )
     => ( A2
        = ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) ) ) ).

% inf.orderE
thf(fact_417_inf_OorderE,axiom,
    ! [A2: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A2 @ B2 )
     => ( A2
        = ( inf_inf_nat @ A2 @ B2 ) ) ) ).

% inf.orderE
thf(fact_418_le__infI2,axiom,
    ! [B2: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ X )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ X ) ) ).

% le_infI2
thf(fact_419_le__infI2,axiom,
    ! [B2: nat,X: nat,A2: nat] :
      ( ( ord_less_eq_nat @ B2 @ X )
     => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).

% le_infI2
thf(fact_420_le__infI1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ X )
     => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ X ) ) ).

% le_infI1
thf(fact_421_le__infI1,axiom,
    ! [A2: nat,X: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A2 @ X )
     => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).

% le_infI1
thf(fact_422_inf__mono,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,D: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ C )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ D )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) @ ( inf_in4978071631833541052od_b_c @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_423_inf__mono,axiom,
    ! [A2: nat,C: nat,B2: nat,D: nat] :
      ( ( ord_less_eq_nat @ A2 @ C )
     => ( ( ord_less_eq_nat @ B2 @ D )
       => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ ( inf_inf_nat @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_424_le__infI,axiom,
    ! [X: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ A2 )
     => ( ( ord_le282488521294790766od_b_c @ X @ B2 )
       => ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) ) ) ) ).

% le_infI
thf(fact_425_le__infI,axiom,
    ! [X: nat,A2: nat,B2: nat] :
      ( ( ord_less_eq_nat @ X @ A2 )
     => ( ( ord_less_eq_nat @ X @ B2 )
       => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A2 @ B2 ) ) ) ) ).

% le_infI
thf(fact_426_le__infE,axiom,
    ! [X: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ ( inf_in4978071631833541052od_b_c @ A2 @ B2 ) )
     => ~ ( ( ord_le282488521294790766od_b_c @ X @ A2 )
         => ~ ( ord_le282488521294790766od_b_c @ X @ B2 ) ) ) ).

% le_infE
thf(fact_427_le__infE,axiom,
    ! [X: nat,A2: nat,B2: nat] :
      ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A2 @ B2 ) )
     => ~ ( ( ord_less_eq_nat @ X @ A2 )
         => ~ ( ord_less_eq_nat @ X @ B2 ) ) ) ).

% le_infE
thf(fact_428_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_429_inf__le2,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).

% inf_le2
thf(fact_430_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_431_inf__le1,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).

% inf_le1
thf(fact_432_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_433_inf__sup__ord_I1_J,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).

% inf_sup_ord(1)
thf(fact_434_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_435_inf__sup__ord_I2_J,axiom,
    ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_436_inter__eq__subsetI,axiom,
    ! [S: set_li6436108459499378894od_b_c,S4: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ S @ S4 )
     => ( ( ( inf_in4978071631833541052od_b_c @ A @ S4 )
          = ( inf_in4978071631833541052od_b_c @ B @ S4 ) )
       => ( ( inf_in4978071631833541052od_b_c @ A @ S )
          = ( inf_in4978071631833541052od_b_c @ B @ S ) ) ) ) ).

% inter_eq_subsetI
thf(fact_437_Int__Collect__mono,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a,P: produc2669932201312201782od_c_a > $o,Q7: produc2669932201312201782od_c_a > $o] :
      ( ( ord_le3226338165915859510od_c_a @ A @ B )
     => ( ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ A )
           => ( ( P @ X3 )
             => ( Q7 @ X3 ) ) )
       => ( ord_le3226338165915859510od_c_a @ ( inf_in3815988127369930372od_c_a @ A @ ( collec8405073525749625505od_c_a @ P ) ) @ ( inf_in3815988127369930372od_c_a @ B @ ( collec8405073525749625505od_c_a @ Q7 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_438_Int__Collect__mono,axiom,
    ! [A: set_a,B: set_a,P: a > $o,Q7: a > $o] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ! [X3: a] :
            ( ( member_a @ X3 @ A )
           => ( ( P @ X3 )
             => ( Q7 @ X3 ) ) )
       => ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ ( collect_a @ P ) ) @ ( inf_inf_set_a @ B @ ( collect_a @ Q7 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_439_Int__Collect__mono,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,P: list_P903359562653991662od_b_c > $o,Q7: list_P903359562653991662od_b_c > $o] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ A )
           => ( ( P @ X3 )
             => ( Q7 @ X3 ) ) )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ ( collec2280997390073109977od_b_c @ P ) ) @ ( inf_in4978071631833541052od_b_c @ B @ ( collec2280997390073109977od_b_c @ Q7 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_440_Int__greatest,axiom,
    ! [C2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C2 @ A )
     => ( ( ord_le282488521294790766od_b_c @ C2 @ B )
       => ( ord_le282488521294790766od_b_c @ C2 @ ( inf_in4978071631833541052od_b_c @ A @ B ) ) ) ) ).

% Int_greatest
thf(fact_441_Int__absorb2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = A ) ) ).

% Int_absorb2
thf(fact_442_Int__absorb1,axiom,
    ! [B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ A )
     => ( ( inf_in4978071631833541052od_b_c @ A @ B )
        = B ) ) ).

% Int_absorb1
thf(fact_443_Int__lower2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ B ) ).

% Int_lower2
thf(fact_444_Int__lower1,axiom,
    ! [A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ A ) ).

% Int_lower1
thf(fact_445_Int__mono,axiom,
    ! [A: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,D2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ C2 )
     => ( ( ord_le282488521294790766od_b_c @ B @ D2 )
       => ( ord_le282488521294790766od_b_c @ ( inf_in4978071631833541052od_b_c @ A @ B ) @ ( inf_in4978071631833541052od_b_c @ C2 @ D2 ) ) ) ) ).

% Int_mono
thf(fact_446_state__cover__assignment__language,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c] :
      ( ( state_6014242345326633810_d_b_c @ M3 @ V )
     => ( ord_le282488521294790766od_b_c @ ( image_1329551058250833970od_b_c @ V @ ( reacha9185589339461546374_d_b_c @ M3 ) ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ) ).

% state_cover_assignment_language
thf(fact_447_state__cover__assignment__language,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ M3 @ V )
     => ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ V @ ( reacha1620305530751930115_a_b_c @ M3 ) ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ) ).

% state_cover_assignment_language
thf(fact_448_establish__convergence__static__subset,axiom,
    ! [T4: prefix425356687782099470od_b_c,Dist_fun: nat > a > prefix425356687782099470od_b_c,M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,G2: e,Cg_insert2: e > list_P903359562653991662od_b_c > e,Cg_lookup2: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,M4: nat,T: produc2669932201312201782od_c_a] : ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ T4 ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm821963860068034213_b_c_e @ Dist_fun @ M3 @ V @ T4 @ G2 @ Cg_insert2 @ Cg_lookup2 @ M4 @ T ) ) ) ) ).

% establish_convergence_static_subset
thf(fact_449_exE__realizer_H,axiom,
    ! [P: e > prefix425356687782099470od_b_c > $o,P2: produc4534891796109904283_b_c_e] :
      ( ( P @ ( produc6779600879576379961_b_c_e @ P2 ) @ ( produc1447154562020694007_b_c_e @ P2 ) )
     => ~ ! [X3: prefix425356687782099470od_b_c,Y3: e] :
            ~ ( P @ Y3 @ X3 ) ) ).

% exE_realizer'
thf(fact_450_exE__realizer_H,axiom,
    ! [P: produc2133359284458116493od_c_a > a > $o,P2: produc2669932201312201782od_c_a] :
      ( ( P @ ( produc8088130389382527188od_c_a @ P2 ) @ ( produc4225943634317630866od_c_a @ P2 ) )
     => ~ ! [X3: a,Y3: produc2133359284458116493od_c_a] :
            ~ ( P @ Y3 @ X3 ) ) ).

% exE_realizer'
thf(fact_451_exE__realizer_H,axiom,
    ! [P: product_prod_c_a > b > $o,P2: produc2133359284458116493od_c_a] :
      ( ( P @ ( produc5221446324160585515od_c_a @ P2 ) @ ( produc301949074746585577od_c_a @ P2 ) )
     => ~ ! [X3: b,Y3: product_prod_c_a] :
            ~ ( P @ Y3 @ X3 ) ) ).

% exE_realizer'
thf(fact_452_exE__realizer_H,axiom,
    ! [P: a > c > $o,P2: product_prod_c_a] :
      ( ( P @ ( product_snd_c_a @ P2 ) @ ( product_fst_c_a @ P2 ) )
     => ~ ! [X3: c,Y3: a] :
            ~ ( P @ Y3 @ X3 ) ) ).

% exE_realizer'
thf(fact_453_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: produc2669932201312201782od_c_a > d,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_d_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( bij_be5632368444736963777_c_a_d @ F @ ( states895637122477222528_a_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( states895637122477222528_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( states895637122477222528_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_Pro3731892891411965979_a_b_c @ M12 @ Q4 ) @ ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_454_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: list_P903359562653991662od_b_c > d,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F @ ( states7681702920031268536_c_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( states7681702920031268536_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M12 @ Q4 ) @ ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_455_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: d > d,M12: fsm_d_b_c,M22: fsm_d_b_c,Q4: d] :
      ( ( bij_betw_d_d @ F @ ( states_d_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( states_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q4 @ ( states_d_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M12 @ Q4 ) @ ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_456_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: produc2669932201312201782od_c_a > a,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_a_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ( bij_be5632368444736963774_c_a_a @ F @ ( states895637122477222528_a_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( states895637122477222528_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( states895637122477222528_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_Pro3731892891411965979_a_b_c @ M12 @ Q4 ) @ ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_457_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: list_P903359562653991662od_b_c > a,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F @ ( states7681702920031268536_c_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( states7681702920031268536_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( states7681702920031268536_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M12 @ Q4 ) @ ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_458_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: d > a,M12: fsm_d_b_c,M22: fsm_a_b_c,Q4: d] :
      ( ( bij_betw_d_a @ F @ ( states_d_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( states_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( states_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_d @ Q4 @ ( states_d_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M12 @ Q4 ) @ ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_459_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: a > d,M12: fsm_a_b_c,M22: fsm_d_b_c,Q4: a] :
      ( ( bij_betw_a_d @ F @ ( states_a_b_c @ M12 ) @ ( states_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( states_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q4 @ ( states_a_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M12 @ Q4 ) @ ( lS_d_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_460_language__equivalence__from__isomorphism__helper,axiom,
    ! [F: a > a,M12: fsm_a_b_c,M22: fsm_a_b_c,Q4: a] :
      ( ( bij_betw_a_a @ F @ ( states_a_b_c @ M12 ) @ ( states_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( states_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( states_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ( member_a @ Q4 @ ( states_a_b_c @ M12 ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M12 @ Q4 ) @ ( lS_a_b_c @ M22 @ ( F @ Q4 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_461_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: produc2669932201312201782od_c_a > d,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_be5632368444736963777_c_a_d @ F @ ( reacha1389639598965321787_a_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_Pro3731892891411965979_a_b_c @ M12 @ ( initia3341036835946388646_a_b_c @ M12 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_462_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: list_P903359562653991662od_b_c > d,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_d_b_c] :
      ( ( bij_be3300351249680192137_b_c_d @ F @ ( reacha8116992257183400179_c_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M12 @ ( initia3567573336347591134_c_b_c @ M12 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_463_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: d > d,M12: fsm_d_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_d_d @ F @ ( reacha9185589339461546374_d_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_464_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: produc2669932201312201782od_c_a > a,M12: fsm_Pr6425204305901329755_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_be5632368444736963774_c_a_a @ F @ ( reacha1389639598965321787_a_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3341036835946388646_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: produc2669932201312201782od_c_a,X3: b,Y3: c,Q6: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Q5 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
             => ( ( member5502040268208861279od_c_a @ Q6 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
               => ( ( member6671621370117864543od_c_a @ ( produc6668960782114422694od_c_a @ Q5 @ ( produc727174699211671861od_c_a @ X3 @ ( produc8442212246646489037od_c_a @ Y3 @ Q6 ) ) ) @ ( transi5559090763681538380_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_Pro3731892891411965979_a_b_c @ M12 @ ( initia3341036835946388646_a_b_c @ M12 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_465_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: list_P903359562653991662od_b_c > a,M12: fsm_li6801133765522507155_c_b_c,M22: fsm_a_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F @ ( reacha8116992257183400179_c_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initia3567573336347591134_c_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: list_P903359562653991662od_b_c,X3: b,Y3: c,Q6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q5 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
             => ( ( member6330420149250801815od_b_c @ Q6 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
               => ( ( member8124909232574984543od_b_c @ ( produc1782422034411576486od_b_c @ Q5 @ ( produc5857734884866716141od_b_c @ X3 @ ( produc4268225641733455109od_b_c @ Y3 @ Q6 ) ) ) @ ( transi3161963839906981764_c_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M12 @ ( initia3567573336347591134_c_b_c @ M12 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_466_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: d > a,M12: fsm_d_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_d_a @ F @ ( reacha9185589339461546374_d_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_d_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: d,X3: b,Y3: c,Q6: d] :
              ( ( member_d @ Q5 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
             => ( ( member_d @ Q6 @ ( reacha9185589339461546374_d_b_c @ M12 ) )
               => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q5 @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ Q6 ) ) ) @ ( transitions_d_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_467_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: a > d,M12: fsm_a_b_c,M22: fsm_d_b_c] :
      ( ( bij_betw_a_d @ F @ ( reacha1620305530751930115_a_b_c @ M12 ) @ ( reacha9185589339461546374_d_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_d_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ ( F @ Q5 ) @ ( produc3440865926910568064od_c_d @ X3 @ ( product_Pair_c_d @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_d_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_468_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F: a > a,M12: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( bij_betw_a_a @ F @ ( reacha1620305530751930115_a_b_c @ M12 ) @ ( reacha1620305530751930115_a_b_c @ M22 ) )
     => ( ( ( F @ ( initial_a_b_c @ M12 ) )
          = ( initial_a_b_c @ M22 ) )
       => ( ! [Q5: a,X3: b,Y3: c,Q6: a] :
              ( ( member_a @ Q5 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
             => ( ( member_a @ Q6 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
               => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q5 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q6 ) ) ) @ ( transitions_a_b_c @ M12 ) )
                  = ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ ( F @ Q5 ) @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ ( F @ Q6 ) ) ) ) @ ( transitions_a_b_c @ M22 ) ) ) ) )
         => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_469_LS__prepend__transition,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) @ Io2 ) @ ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_470_LS__prepend__transition,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b,Io2: list_P1467974523212632366od_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
     => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) )
       => ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) @ Io2 ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_471_LS__prepend__transition,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) @ Io2 ) @ ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_472_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios: list_P903359562653991662od_b_c,M3: fsm_d_b_c,Q4: d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios ) @ ( lS_d_b_c @ M3 @ Q4 ) )
     => ~ ! [T2: produc1399170498009216118od_c_d] :
            ( ( ( produc1508465569166014290od_c_d @ T2 )
              = Q4 )
           => ( ( member4231278564905875615od_c_d @ T2 @ ( transitions_d_b_c @ M3 ) )
             => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) )
                  = X )
               => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios @ ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T2 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_473_language__next__transition__ob,axiom,
    ! [X: a,Y: b,Ios: list_P1467974523212632366od_a_b,M3: fsm_Pr1886043760914421514_a_a_b,Q4: product_prod_c_a] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X @ Y ) @ Ios ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ Q4 ) )
     => ~ ! [T2: produc3205353004677322104od_c_a] :
            ( ( ( produc8171714036265584980od_c_a @ T2 )
              = Q4 )
           => ( ( member6508725278956418977od_c_a @ T2 @ ( transi2941759273464634107_a_a_b @ M3 ) )
             => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) )
                  = X )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) ) )
                    = Y )
                 => ~ ( member6895035109809442519od_a_b @ Ios @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_474_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios: list_P903359562653991662od_b_c,M3: fsm_a_b_c,Q4: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios ) @ ( lS_a_b_c @ M3 @ Q4 ) )
     => ~ ! [T2: produc2669932201312201782od_c_a] :
            ( ( ( produc4225943634317630866od_c_a @ T2 )
              = Q4 )
           => ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M3 ) )
             => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) )
                  = X )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios @ ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_475_observable__transition__target__language__subset,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,T1: produc3205353004677322104od_c_a,T22: produc3205353004677322104od_c_a] :
      ( ( ord_le153002609085230766od_a_b @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T1 ) ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T22 ) ) )
     => ( ( member6508725278956418977od_c_a @ T1 @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ( ( member6508725278956418977od_c_a @ T22 @ ( transi2941759273464634107_a_a_b @ M3 ) )
         => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) )
           => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) )
                = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) )
             => ( ( observ2964502264774598958_a_a_b @ M3 )
               => ( ord_le153002609085230766od_a_b @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) ) ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_476_observable__transition__target__language__subset,axiom,
    ! [M3: fsm_d_b_c,T1: produc1399170498009216118od_c_d,T22: produc1399170498009216118od_c_d] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T1 ) ) @ ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T22 ) ) )
     => ( ( member4231278564905875615od_c_d @ T1 @ ( transitions_d_b_c @ M3 ) )
       => ( ( member4231278564905875615od_c_d @ T22 @ ( transitions_d_b_c @ M3 ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) )
              = ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) ) )
                = ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) )
             => ( ( observable_d_b_c @ M3 )
               => ( ord_le282488521294790766od_b_c @ ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T1 ) ) ) ) @ ( lS_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_477_observable__transition__target__language__subset,axiom,
    ! [M3: fsm_a_b_c,T1: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T1 ) ) @ ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T1 @ ( transitions_a_b_c @ M3 ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M3 ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M3 )
               => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) ) ) @ ( lS_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_478_conjI__realizer,axiom,
    ! [P: b > $o,P2: b,Q7: c > $o,Q4: c] :
      ( ( P @ P2 )
     => ( ( Q7 @ Q4 )
       => ( ( P @ ( product_fst_b_c @ ( product_Pair_b_c @ P2 @ Q4 ) ) )
          & ( Q7 @ ( product_snd_b_c @ ( product_Pair_b_c @ P2 @ Q4 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_479_conjI__realizer,axiom,
    ! [P: prefix425356687782099470od_b_c > $o,P2: prefix425356687782099470od_b_c,Q7: e > $o,Q4: e] :
      ( ( P @ P2 )
     => ( ( Q7 @ Q4 )
       => ( ( P @ ( produc1447154562020694007_b_c_e @ ( produc2511600812177743883_b_c_e @ P2 @ Q4 ) ) )
          & ( Q7 @ ( produc6779600879576379961_b_c_e @ ( produc2511600812177743883_b_c_e @ P2 @ Q4 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_480_conjI__realizer,axiom,
    ! [P: a > $o,P2: a,Q7: produc2133359284458116493od_c_a > $o,Q4: produc2133359284458116493od_c_a] :
      ( ( P @ P2 )
     => ( ( Q7 @ Q4 )
       => ( ( P @ ( produc4225943634317630866od_c_a @ ( produc5762801557034676134od_c_a @ P2 @ Q4 ) ) )
          & ( Q7 @ ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ P2 @ Q4 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_481_conjI__realizer,axiom,
    ! [P: b > $o,P2: b,Q7: product_prod_c_a > $o,Q4: product_prod_c_a] :
      ( ( P @ P2 )
     => ( ( Q7 @ Q4 )
       => ( ( P @ ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ P2 @ Q4 ) ) )
          & ( Q7 @ ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ P2 @ Q4 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_482_conjI__realizer,axiom,
    ! [P: c > $o,P2: c,Q7: a > $o,Q4: a] :
      ( ( P @ P2 )
     => ( ( Q7 @ Q4 )
       => ( ( P @ ( product_fst_c_a @ ( product_Pair_c_a @ P2 @ Q4 ) ) )
          & ( Q7 @ ( product_snd_c_a @ ( product_Pair_c_a @ P2 @ Q4 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_483_assms_I10_J,axiom,
    member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( v @ ( 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 ) ) @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) ).

% assms(10)
thf(fact_484_observable__language__next,axiom,
    ! [Io2: product_prod_b_c,Ios: list_P903359562653991662od_b_c,M3: fsm_d_b_c,T: produc1399170498009216118od_c_d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io2 @ Ios ) @ ( lS_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T ) ) )
     => ( ( observable_d_b_c @ M3 )
       => ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
         => ( ( ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) )
              = ( product_fst_b_c @ Io2 ) )
           => ( ( ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) )
                = ( product_snd_b_c @ Io2 ) )
             => ( member6330420149250801815od_b_c @ Ios @ ( lS_d_b_c @ ( from_FSM_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ M3 @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_485_observable__language__next,axiom,
    ! [Io2: product_prod_c_a,Ios: list_P125642481956313003od_c_a,M3: fsm_Pr7461828476839194351_a_c_a,T: produc3729687299602777783od_c_a] :
      ( ( member5552703068553123156od_c_a @ ( cons_P1742027962761213787od_c_a @ Io2 @ Ios ) @ ( lS_Pro1436182445161660463_a_c_a @ M3 @ ( produc1784202036732648467od_c_a @ T ) ) )
     => ( ( observ3736821838051356051_a_c_a @ M3 )
       => ( ( member5500486793640445664od_c_a @ T @ ( transi5448983560151880288_a_c_a @ M3 ) )
         => ( ( ( produc7173261134821384633od_c_a @ ( produc2799690148840255317od_c_a @ T ) )
              = ( product_fst_c_a @ Io2 ) )
           => ( ( ( produc4225943634317630866od_c_a @ ( produc4398916234287704827od_c_a @ ( produc2799690148840255317od_c_a @ T ) ) )
                = ( product_snd_c_a @ Io2 ) )
             => ( member5552703068553123156od_c_a @ Ios @ ( lS_Pro1436182445161660463_a_c_a @ ( from_F8501008907474727400_a_c_a @ M3 @ ( produc8088130389382527188od_c_a @ ( produc4398916234287704827od_c_a @ ( produc2799690148840255317od_c_a @ T ) ) ) ) @ ( initia6168580702928107450_a_c_a @ ( from_F8501008907474727400_a_c_a @ M3 @ ( produc8088130389382527188od_c_a @ ( produc4398916234287704827od_c_a @ ( produc2799690148840255317od_c_a @ T ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_486_observable__language__next,axiom,
    ! [Io2: product_prod_a_b,Ios: list_P1467974523212632366od_a_b,M3: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ Io2 @ Ios ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T ) ) )
     => ( ( observ2964502264774598958_a_a_b @ M3 )
       => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
         => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) )
              = ( product_fst_a_b @ Io2 ) )
           => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
                = ( product_snd_a_b @ Io2 ) )
             => ( member6895035109809442519od_a_b @ Ios @ ( lS_Pro5114676609533226954_a_a_b @ ( from_F6727869081933152899_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) @ ( initia681974817753967189_a_a_b @ ( from_F6727869081933152899_a_a_b @ M3 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_487_observable__language__next,axiom,
    ! [Io2: product_prod_b_c,Ios: list_P903359562653991662od_b_c,M3: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io2 @ Ios ) @ ( lS_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T ) ) )
     => ( ( observable_a_b_c @ M3 )
       => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) )
              = ( product_fst_b_c @ Io2 ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
                = ( product_snd_b_c @ Io2 ) )
             => ( member6330420149250801815od_b_c @ Ios @ ( lS_a_b_c @ ( from_FSM_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M3 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_488_after__transition__exhaust,axiom,
    ! [M3: fsm_d_b_c,T: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
       => ( ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) )
          = ( after_d_b_c @ M3 @ ( produc1508465569166014290od_c_d @ T ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_489_after__transition__exhaust,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( observ2964502264774598958_a_a_b @ M3 )
     => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
       => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
          = ( after_3087770633486430525_a_a_b @ M3 @ ( produc8171714036265584980od_c_a @ T ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) @ nil_Product_prod_a_b ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_490_after__transition__exhaust,axiom,
    ! [M3: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
       => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
          = ( after_a_b_c @ M3 @ ( produc4225943634317630866od_c_a @ T ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_491_assms_I16_J,axiom,
    ! [Q4: a] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ m1 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( dist_fun @ zero_zero_nat @ Q4 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ t @ ( v @ Q4 ) ) ) ) ) ).

% assms(16)
thf(fact_492_bij__betw__byWitness,axiom,
    ! [A: set_li6436108459499378894od_b_c,F2: a > list_P903359562653991662od_b_c,F: list_P903359562653991662od_b_c > a,A7: set_a] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( ( F2 @ ( F @ X3 ) )
            = X3 ) )
     => ( ! [X3: a] :
            ( ( member_a @ X3 @ A7 )
           => ( ( F @ ( F2 @ X3 ) )
              = X3 ) )
       => ( ( ord_less_eq_set_a @ ( image_3173854338463926933_b_c_a @ F @ A ) @ A7 )
         => ( ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F2 @ A7 ) @ A )
           => ( bij_be3300351249680192134_b_c_a @ F @ A @ A7 ) ) ) ) ) ).

% bij_betw_byWitness
thf(fact_493_bij__betw__byWitness,axiom,
    ! [A: set_a,F2: list_P903359562653991662od_b_c > a,F: a > list_P903359562653991662od_b_c,A7: set_li6436108459499378894od_b_c] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A )
         => ( ( F2 @ ( F @ X3 ) )
            = X3 ) )
     => ( ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ A7 )
           => ( ( F @ ( F2 @ X3 ) )
              = X3 ) )
       => ( ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ F @ A ) @ A7 )
         => ( ( ord_less_eq_set_a @ ( image_3173854338463926933_b_c_a @ F2 @ A7 ) @ A )
           => ( bij_be8783369614777182438od_b_c @ F @ A @ A7 ) ) ) ) ) ).

% bij_betw_byWitness
thf(fact_494_bij__betw__byWitness,axiom,
    ! [A: set_li6436108459499378894od_b_c,F2: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A7: set_li6436108459499378894od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A )
         => ( ( F2 @ ( F @ X3 ) )
            = X3 ) )
     => ( ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ A7 )
           => ( ( F @ ( F2 @ X3 ) )
              = X3 ) )
       => ( ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F @ A ) @ A7 )
         => ( ( ord_le282488521294790766od_b_c @ ( image_2850395784482391045od_b_c @ F2 @ A7 ) @ A )
           => ( bij_be8534141360866068086od_b_c @ F @ A @ A7 ) ) ) ) ) ).

% bij_betw_byWitness
thf(fact_495_bij__betw__subset,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,A7: set_li6436108459499378894od_b_c,B: set_a,B7: set_li6436108459499378894od_b_c] :
      ( ( bij_be8783369614777182438od_b_c @ F @ A @ A7 )
     => ( ( ord_less_eq_set_a @ B @ A )
       => ( ( ( image_8656872703560917237od_b_c @ F @ B )
            = B7 )
         => ( bij_be8783369614777182438od_b_c @ F @ B @ B7 ) ) ) ) ).

% bij_betw_subset
thf(fact_496_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: b > c > $o,X: b,Y: c,A2: product_prod_b_c] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( product_Pair_b_c @ X @ Y ) )
       => ( P @ ( product_fst_b_c @ A2 ) @ ( product_snd_b_c @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_497_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: prefix425356687782099470od_b_c > e > $o,X: prefix425356687782099470od_b_c,Y: e,A2: produc4534891796109904283_b_c_e] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc2511600812177743883_b_c_e @ X @ Y ) )
       => ( P @ ( produc1447154562020694007_b_c_e @ A2 ) @ ( produc6779600879576379961_b_c_e @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_498_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: a > produc2133359284458116493od_c_a > $o,X: a,Y: produc2133359284458116493od_c_a,A2: produc2669932201312201782od_c_a] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc5762801557034676134od_c_a @ X @ Y ) )
       => ( P @ ( produc4225943634317630866od_c_a @ A2 ) @ ( produc8088130389382527188od_c_a @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_499_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: b > product_prod_c_a > $o,X: b,Y: product_prod_c_a,A2: produc2133359284458116493od_c_a] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc3440865914000881661od_c_a @ X @ Y ) )
       => ( P @ ( produc301949074746585577od_c_a @ A2 ) @ ( produc5221446324160585515od_c_a @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_500_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: c > a > $o,X: c,Y: a,A2: product_prod_c_a] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( product_Pair_c_a @ X @ Y ) )
       => ( P @ ( product_fst_c_a @ A2 ) @ ( product_snd_c_a @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_501_LS__single__transition,axiom,
    ! [X: b,Y: c,M3: fsm_d_b_c,Q4: d] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_d_b_c @ M3 @ Q4 ) )
      = ( ? [X2: produc1399170498009216118od_c_d] :
            ( ( member4231278564905875615od_c_d @ X2 @ ( transitions_d_b_c @ M3 ) )
            & ( ( produc1508465569166014290od_c_d @ X2 )
              = Q4 )
            & ( ( 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_502_LS__single__transition,axiom,
    ! [X: a,Y: b,M3: fsm_Pr1886043760914421514_a_a_b,Q4: product_prod_c_a] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X @ Y ) @ nil_Product_prod_a_b ) @ ( lS_Pro5114676609533226954_a_a_b @ M3 @ Q4 ) )
      = ( ? [X2: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M3 ) )
            & ( ( produc8171714036265584980od_c_a @ X2 )
              = Q4 )
            & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
              = X )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
              = Y ) ) ) ) ).

% LS_single_transition
thf(fact_503_LS__single__transition,axiom,
    ! [X: b,Y: c,M3: fsm_a_b_c,Q4: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_a_b_c @ M3 @ Q4 ) )
      = ( ? [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M3 ) )
            & ( ( produc4225943634317630866od_c_a @ X2 )
              = Q4 )
            & ( ( 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_504_list_Oinject,axiom,
    ! [X21: product_prod_b_c,X222: list_P903359562653991662od_b_c,Y21: product_prod_b_c,Y222: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X21 @ X222 )
        = ( cons_P4529483553340347422od_b_c @ Y21 @ Y222 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y222 ) ) ) ).

% list.inject
thf(fact_505_list_Oinject,axiom,
    ! [X21: list_P903359562653991662od_b_c,X222: list_l8907847357763382004od_b_c,Y21: list_P903359562653991662od_b_c,Y222: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ X21 @ X222 )
        = ( cons_l342771267123639716od_b_c @ Y21 @ Y222 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y222 ) ) ) ).

% list.inject
thf(fact_506_img__snd,axiom,
    ! [A2: prefix425356687782099470od_b_c,B2: e,S: set_Pr3237851069733663483_b_c_e] :
      ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ A2 @ B2 ) @ S )
     => ( member_e @ B2 @ ( image_2493620005906216236_c_e_e @ produc6779600879576379961_b_c_e @ S ) ) ) ).

% img_snd
thf(fact_507_img__snd,axiom,
    ! [A2: b,B2: c,S: set_Product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A2 @ B2 ) @ S )
     => ( member_c @ B2 @ ( image_7762865866877615261_b_c_c @ product_snd_b_c @ S ) ) ) ).

% img_snd
thf(fact_508_img__snd,axiom,
    ! [A2: a,B2: produc2133359284458116493od_c_a,S: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ A2 @ B2 ) @ S )
     => ( member1160383752307813046od_c_a @ B2 @ ( image_644133890040260316od_c_a @ produc8088130389382527188od_c_a @ S ) ) ) ).

% img_snd
thf(fact_509_img__snd,axiom,
    ! [A2: b,B2: product_prod_c_a,S: set_Pr272002107461315949od_c_a] :
      ( ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ A2 @ B2 ) @ S )
     => ( member5074992350434858958od_c_a @ B2 @ ( image_1453128995064482141od_c_a @ produc5221446324160585515od_c_a @ S ) ) ) ).

% img_snd
thf(fact_510_img__snd,axiom,
    ! [A2: c,B2: a,S: set_Product_prod_c_a] :
      ( ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ A2 @ B2 ) @ S )
     => ( member_a @ B2 @ ( image_5407010446420943518_c_a_a @ product_snd_c_a @ S ) ) ) ).

% img_snd
thf(fact_511_img__fst,axiom,
    ! [A2: b,B2: c,S: set_Product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ A2 @ B2 ) @ S )
     => ( member_b @ A2 @ ( image_7762865866877615260_b_c_b @ product_fst_b_c @ S ) ) ) ).

% img_fst
thf(fact_512_img__fst,axiom,
    ! [A2: prefix425356687782099470od_b_c,B2: e,S: set_Pr3237851069733663483_b_c_e] :
      ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ A2 @ B2 ) @ S )
     => ( member2378525361814473399od_b_c @ A2 @ ( image_3005832862676689720od_b_c @ produc1447154562020694007_b_c_e @ S ) ) ) ).

% img_fst
thf(fact_513_img__fst,axiom,
    ! [A2: a,B2: produc2133359284458116493od_c_a,S: set_Pr8357624050790843030od_c_a] :
      ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ A2 @ B2 ) @ S )
     => ( member_a @ A2 @ ( image_9171994905208062541_c_a_a @ produc4225943634317630866od_c_a @ S ) ) ) ).

% img_fst
thf(fact_514_img__fst,axiom,
    ! [A2: b,B2: product_prod_c_a,S: set_Pr272002107461315949od_c_a] :
      ( ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ A2 @ B2 ) @ S )
     => ( member_b @ A2 @ ( image_8972666397057282743_c_a_b @ produc301949074746585577od_c_a @ S ) ) ) ).

% img_fst
thf(fact_515_img__fst,axiom,
    ! [A2: c,B2: a,S: set_Product_prod_c_a] :
      ( ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ A2 @ B2 ) @ S )
     => ( member_c @ A2 @ ( image_5407010446420943520_c_a_c @ product_fst_c_a @ S ) ) ) ).

% img_fst
thf(fact_516_op__conc__empty__img__id,axiom,
    ! [L: set_li6436108459499378894od_b_c] :
      ( ( image_2850395784482391045od_b_c @ ( append2547753245680614915od_b_c @ nil_Product_prod_b_c ) @ L )
      = L ) ).

% op_conc_empty_img_id
thf(fact_517_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_518_foldl__append,axiom,
    ! [F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e,A2: produc4534891796109904283_b_c_e,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( foldl_2934561762154836916od_b_c @ F @ A2 @ ( append6992831555715836169od_b_c @ Xs @ Ys ) )
      = ( foldl_2934561762154836916od_b_c @ F @ ( foldl_2934561762154836916od_b_c @ F @ A2 @ Xs ) @ Ys ) ) ).

% foldl_append
thf(fact_519_from__FSM__simps_I5_J,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( states_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) )
        = ( states_a_b_c @ M3 ) ) ) ).

% from_FSM_simps(5)
thf(fact_520_from__from,axiom,
    ! [Q14: a,M3: fsm_a_b_c,Q15: a] :
      ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
     => ( ( member_a @ Q15 @ ( states_a_b_c @ M3 ) )
       => ( ( from_FSM_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q14 ) @ Q15 )
          = ( from_FSM_a_b_c @ M3 @ Q15 ) ) ) ) ).

% from_from
thf(fact_521_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_522_append1__eq__conv,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c,Ys: list_l8907847357763382004od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) )
        = ( append6992831555715836169od_b_c @ Ys @ ( cons_l342771267123639716od_b_c @ Y @ nil_li8071162985807626740od_b_c ) ) )
      = ( ( Xs = Ys )
        & ( X = Y ) ) ) ).

% append1_eq_conv
thf(fact_523_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_524_list__ee__eq__leel_I1_J,axiom,
    ! [E1: list_P903359562653991662od_b_c,E2: list_P903359562653991662od_b_c,L1: list_l8907847357763382004od_b_c,E12: list_P903359562653991662od_b_c,E22: list_P903359562653991662od_b_c,L2: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ E1 @ ( cons_l342771267123639716od_b_c @ E2 @ nil_li8071162985807626740od_b_c ) )
        = ( append6992831555715836169od_b_c @ L1 @ ( cons_l342771267123639716od_b_c @ E12 @ ( cons_l342771267123639716od_b_c @ E22 @ L2 ) ) ) )
      = ( ( L1 = nil_li8071162985807626740od_b_c )
        & ( E1 = E12 )
        & ( E2 = E22 )
        & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ).

% list_ee_eq_leel(1)
thf(fact_525_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_526_list__ee__eq__leel_I2_J,axiom,
    ! [L1: list_l8907847357763382004od_b_c,E12: list_P903359562653991662od_b_c,E22: list_P903359562653991662od_b_c,L2: list_l8907847357763382004od_b_c,E1: list_P903359562653991662od_b_c,E2: list_P903359562653991662od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ L1 @ ( cons_l342771267123639716od_b_c @ E12 @ ( cons_l342771267123639716od_b_c @ E22 @ L2 ) ) )
        = ( cons_l342771267123639716od_b_c @ E1 @ ( cons_l342771267123639716od_b_c @ E2 @ nil_li8071162985807626740od_b_c ) ) )
      = ( ( L1 = nil_li8071162985807626740od_b_c )
        & ( E1 = E12 )
        & ( E2 = E22 )
        & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ).

% list_ee_eq_leel(2)
thf(fact_527_list__se__match_I1_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,L2: list_P903359562653991662od_b_c,A2: product_prod_b_c] :
      ( ( L1 != nil_Product_prod_b_c )
     => ( ( ( append2547753245680614915od_b_c @ L1 @ L2 )
          = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) )
        = ( ( L1
            = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) )
          & ( L2 = nil_Product_prod_b_c ) ) ) ) ).

% list_se_match(1)
thf(fact_528_list__se__match_I1_J,axiom,
    ! [L1: list_l8907847357763382004od_b_c,L2: list_l8907847357763382004od_b_c,A2: list_P903359562653991662od_b_c] :
      ( ( L1 != nil_li8071162985807626740od_b_c )
     => ( ( ( append6992831555715836169od_b_c @ L1 @ L2 )
          = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) )
        = ( ( L1
            = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) )
          & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ) ).

% list_se_match(1)
thf(fact_529_list__se__match_I2_J,axiom,
    ! [L2: list_P903359562653991662od_b_c,L1: list_P903359562653991662od_b_c,A2: product_prod_b_c] :
      ( ( L2 != nil_Product_prod_b_c )
     => ( ( ( append2547753245680614915od_b_c @ L1 @ L2 )
          = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) )
        = ( ( L1 = nil_Product_prod_b_c )
          & ( L2
            = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) ) ) ) ) ).

% list_se_match(2)
thf(fact_530_list__se__match_I2_J,axiom,
    ! [L2: list_l8907847357763382004od_b_c,L1: list_l8907847357763382004od_b_c,A2: list_P903359562653991662od_b_c] :
      ( ( L2 != nil_li8071162985807626740od_b_c )
     => ( ( ( append6992831555715836169od_b_c @ L1 @ L2 )
          = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) )
        = ( ( L1 = nil_li8071162985807626740od_b_c )
          & ( L2
            = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) ) ) ) ) ).

% list_se_match(2)
thf(fact_531_list__se__match_I3_J,axiom,
    ! [L1: list_P903359562653991662od_b_c,A2: product_prod_b_c,L2: list_P903359562653991662od_b_c] :
      ( ( L1 != nil_Product_prod_b_c )
     => ( ( ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c )
          = ( append2547753245680614915od_b_c @ L1 @ L2 ) )
        = ( ( L1
            = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) )
          & ( L2 = nil_Product_prod_b_c ) ) ) ) ).

% list_se_match(3)
thf(fact_532_list__se__match_I3_J,axiom,
    ! [L1: list_l8907847357763382004od_b_c,A2: list_P903359562653991662od_b_c,L2: list_l8907847357763382004od_b_c] :
      ( ( L1 != nil_li8071162985807626740od_b_c )
     => ( ( ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c )
          = ( append6992831555715836169od_b_c @ L1 @ L2 ) )
        = ( ( L1
            = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) )
          & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ) ).

% list_se_match(3)
thf(fact_533_list__se__match_I4_J,axiom,
    ! [L2: list_P903359562653991662od_b_c,A2: product_prod_b_c,L1: list_P903359562653991662od_b_c] :
      ( ( L2 != nil_Product_prod_b_c )
     => ( ( ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c )
          = ( append2547753245680614915od_b_c @ L1 @ L2 ) )
        = ( ( L1 = nil_Product_prod_b_c )
          & ( L2
            = ( cons_P4529483553340347422od_b_c @ A2 @ nil_Product_prod_b_c ) ) ) ) ) ).

% list_se_match(4)
thf(fact_534_list__se__match_I4_J,axiom,
    ! [L2: list_l8907847357763382004od_b_c,A2: list_P903359562653991662od_b_c,L1: list_l8907847357763382004od_b_c] :
      ( ( L2 != nil_li8071162985807626740od_b_c )
     => ( ( ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c )
          = ( append6992831555715836169od_b_c @ L1 @ L2 ) )
        = ( ( L1 = nil_li8071162985807626740od_b_c )
          & ( L2
            = ( cons_l342771267123639716od_b_c @ A2 @ nil_li8071162985807626740od_b_c ) ) ) ) ) ).

% list_se_match(4)
thf(fact_535_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_536_list__e__eq__lel_I1_J,axiom,
    ! [E: list_P903359562653991662od_b_c,L1: list_l8907847357763382004od_b_c,E3: list_P903359562653991662od_b_c,L2: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ E @ nil_li8071162985807626740od_b_c )
        = ( append6992831555715836169od_b_c @ L1 @ ( cons_l342771267123639716od_b_c @ E3 @ L2 ) ) )
      = ( ( L1 = nil_li8071162985807626740od_b_c )
        & ( E3 = E )
        & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ).

% list_e_eq_lel(1)
thf(fact_537_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_538_list__e__eq__lel_I2_J,axiom,
    ! [L1: list_l8907847357763382004od_b_c,E3: list_P903359562653991662od_b_c,L2: list_l8907847357763382004od_b_c,E: list_P903359562653991662od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ L1 @ ( cons_l342771267123639716od_b_c @ E3 @ L2 ) )
        = ( cons_l342771267123639716od_b_c @ E @ nil_li8071162985807626740od_b_c ) )
      = ( ( L1 = nil_li8071162985807626740od_b_c )
        & ( E3 = E )
        & ( L2 = nil_li8071162985807626740od_b_c ) ) ) ).

% list_e_eq_lel(2)
thf(fact_539_from__FSM__simps_I1_J,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( initial_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) )
        = Q4 ) ) ).

% from_FSM_simps(1)
thf(fact_540_from__FSM__simps_I1_J,axiom,
    ! [Q4: d,M3: fsm_d_b_c] :
      ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
     => ( ( initial_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) )
        = Q4 ) ) ).

% from_FSM_simps(1)
thf(fact_541_from__FSM__simps_I4_J,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( transitions_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) )
        = ( transitions_a_b_c @ M3 ) ) ) ).

% from_FSM_simps(4)
thf(fact_542_shuffles_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys2 ) )
     => ( ! [Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ Xs2 @ nil_Product_prod_b_c ) )
       => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) ) ) ).

% shuffles.cases
thf(fact_543_shuffles_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ! [Ys2: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ Ys2 ) )
     => ( ! [Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ Xs2 @ nil_li8071162985807626740od_b_c ) )
       => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) ) ) ).

% shuffles.cases
thf(fact_544_sorted__wrt_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P3: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P3 @ nil_Product_prod_b_c ) )
     => ~ ! [P3: product_prod_b_c > product_prod_b_c > $o,X3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X3 @ Ys2 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_545_sorted__wrt_Ocases,axiom,
    ! [X: produc5505233395267183789od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
          ( X
         != ( produc4871614819610250653od_b_c @ P3 @ nil_li8071162985807626740od_b_c ) )
     => ~ ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc4871614819610250653od_b_c @ P3 @ ( cons_l342771267123639716od_b_c @ X3 @ Ys2 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_546_successively_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P3: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P3 @ nil_Product_prod_b_c ) )
     => ( ! [P3: product_prod_b_c > product_prod_b_c > $o,X3: product_prod_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) )
       => ~ ! [P3: product_prod_b_c > product_prod_b_c > $o,X3: product_prod_b_c,Y3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_547_successively_Ocases,axiom,
    ! [X: produc5505233395267183789od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
          ( X
         != ( produc4871614819610250653od_b_c @ P3 @ nil_li8071162985807626740od_b_c ) )
     => ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c] :
            ( X
           != ( produc4871614819610250653od_b_c @ P3 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc4871614819610250653od_b_c @ P3 @ ( cons_l342771267123639716od_b_c @ X3 @ ( cons_l342771267123639716od_b_c @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_548_list_Odistinct_I1_J,axiom,
    ! [X21: product_prod_b_c,X222: list_P903359562653991662od_b_c] :
      ( nil_Product_prod_b_c
     != ( cons_P4529483553340347422od_b_c @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_549_list_Odistinct_I1_J,axiom,
    ! [X21: list_P903359562653991662od_b_c,X222: list_l8907847357763382004od_b_c] :
      ( nil_li8071162985807626740od_b_c
     != ( cons_l342771267123639716od_b_c @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_550_list_OdiscI,axiom,
    ! [List: list_P903359562653991662od_b_c,X21: product_prod_b_c,X222: list_P903359562653991662od_b_c] :
      ( ( List
        = ( cons_P4529483553340347422od_b_c @ X21 @ X222 ) )
     => ( List != nil_Product_prod_b_c ) ) ).

% list.discI
thf(fact_551_list_OdiscI,axiom,
    ! [List: list_l8907847357763382004od_b_c,X21: list_P903359562653991662od_b_c,X222: list_l8907847357763382004od_b_c] :
      ( ( List
        = ( cons_l342771267123639716od_b_c @ X21 @ X222 ) )
     => ( List != nil_li8071162985807626740od_b_c ) ) ).

% list.discI
thf(fact_552_list_Oexhaust,axiom,
    ! [Y: list_P903359562653991662od_b_c] :
      ( ( Y != nil_Product_prod_b_c )
     => ~ ! [X212: product_prod_b_c,X223: list_P903359562653991662od_b_c] :
            ( Y
           != ( cons_P4529483553340347422od_b_c @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_553_list_Oexhaust,axiom,
    ! [Y: list_l8907847357763382004od_b_c] :
      ( ( Y != nil_li8071162985807626740od_b_c )
     => ~ ! [X212: list_P903359562653991662od_b_c,X223: list_l8907847357763382004od_b_c] :
            ( Y
           != ( cons_l342771267123639716od_b_c @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_554_min__list_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
          ( X
         != ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) )
     => ( X = nil_Product_prod_b_c ) ) ).

% min_list.cases
thf(fact_555_min__list_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
          ( X
         != ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) )
     => ( X = nil_li8071162985807626740od_b_c ) ) ).

% min_list.cases
thf(fact_556_transpose_Ocases,axiom,
    ! [X: list_l5832389826979350138od_b_c] :
      ( ( X != nil_li2931525173191110394od_b_c )
     => ( ! [Xss: list_l5832389826979350138od_b_c] :
            ( X
           != ( cons_l4927760930246986410od_b_c @ nil_li8071162985807626740od_b_c @ Xss ) )
       => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Xss: list_l5832389826979350138od_b_c] :
              ( X
             != ( cons_l4927760930246986410od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_557_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 ) )
       => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Xss: list_l8907847357763382004od_b_c] :
              ( X
             != ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_558_remdups__adj_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ( ! [X3: product_prod_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) )
       => ~ ! [X3: product_prod_b_c,Y3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( cons_P4529483553340347422od_b_c @ X3 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_559_remdups__adj_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ( X != nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) )
       => ~ ! [X3: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( X
             != ( cons_l342771267123639716od_b_c @ X3 @ ( cons_l342771267123639716od_b_c @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_560_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_561_append__Cons,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( append6992831555715836169od_b_c @ ( cons_l342771267123639716od_b_c @ X @ Xs ) @ Ys )
      = ( cons_l342771267123639716od_b_c @ X @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) ) ).

% append_Cons
thf(fact_562_rev__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( ( P @ Xs2 )
           => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_563_rev__induct,axiom,
    ! [P: list_l8907847357763382004od_b_c > $o,Xs: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( ( P @ Xs2 )
           => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_564_rev__exhaust,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
     => ~ ! [Ys2: list_P903359562653991662od_b_c,Y3: product_prod_b_c] :
            ( Xs
           != ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) ).

% rev_exhaust
thf(fact_565_rev__exhaust,axiom,
    ! [Xs: list_l8907847357763382004od_b_c] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
     => ~ ! [Ys2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c] :
            ( Xs
           != ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) ) ).

% rev_exhaust
thf(fact_566_neq__Nil__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
      = ( ? [Y2: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
            ( Xs
            = ( cons_P4529483553340347422od_b_c @ Y2 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_567_neq__Nil__conv,axiom,
    ! [Xs: list_l8907847357763382004od_b_c] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
      = ( ? [Y2: list_P903359562653991662od_b_c,Ys3: list_l8907847357763382004od_b_c] :
            ( Xs
            = ( cons_l342771267123639716od_b_c @ Y2 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_568_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 )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_569_list__induct2_H,axiom,
    ! [P: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ nil_li8071162985807626740od_b_c )
       => ( ! [Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] : ( P @ nil_Product_prod_b_c @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_570_list__induct2_H,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_Product_prod_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_571_list__induct2_H,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ nil_li8071162985807626740od_b_c )
       => ( ! [Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_572_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_573_Cons__eq__appendI,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs1: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,Xs: list_l8907847357763382004od_b_c,Zs: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ X @ Xs1 )
        = Ys )
     => ( ( Xs
          = ( append6992831555715836169od_b_c @ Xs1 @ Zs ) )
       => ( ( cons_l342771267123639716od_b_c @ X @ Xs )
          = ( append6992831555715836169od_b_c @ Ys @ Zs ) ) ) ) ).

% Cons_eq_appendI
thf(fact_574_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 ) )
        | ? [Ys4: list_P903359562653991662od_b_c] :
            ( ( ( cons_P4529483553340347422od_b_c @ X @ Ys4 )
              = Ys )
            & ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_575_Cons__eq__append__conv,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,Zs: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ X @ Xs )
        = ( append6992831555715836169od_b_c @ Ys @ Zs ) )
      = ( ( ( Ys = nil_li8071162985807626740od_b_c )
          & ( ( cons_l342771267123639716od_b_c @ X @ Xs )
            = Zs ) )
        | ? [Ys4: list_l8907847357763382004od_b_c] :
            ( ( ( cons_l342771267123639716od_b_c @ X @ Ys4 )
              = Ys )
            & ( Xs
              = ( append6992831555715836169od_b_c @ Ys4 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_576_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 ) ) )
        | ? [Ys4: list_P903359562653991662od_b_c] :
            ( ( Ys
              = ( cons_P4529483553340347422od_b_c @ X @ Ys4 ) )
            & ( ( append2547753245680614915od_b_c @ Ys4 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_577_append__eq__Cons__conv,axiom,
    ! [Ys: list_l8907847357763382004od_b_c,Zs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ Ys @ Zs )
        = ( cons_l342771267123639716od_b_c @ X @ Xs ) )
      = ( ( ( Ys = nil_li8071162985807626740od_b_c )
          & ( Zs
            = ( cons_l342771267123639716od_b_c @ X @ Xs ) ) )
        | ? [Ys4: list_l8907847357763382004od_b_c] :
            ( ( Ys
              = ( cons_l342771267123639716od_b_c @ X @ Ys4 ) )
            & ( ( append6992831555715836169od_b_c @ Ys4 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_578_rev__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X3: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) )
       => ( ! [X3: 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 @ X3 @ nil_Product_prod_b_c ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_579_rev__nonempty__induct,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,P: list_l8907847357763382004od_b_c > $o] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) )
       => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( ( Xs2 != nil_li8071162985807626740od_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_580_list__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X3: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) )
       => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xs2 != nil_Product_prod_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_581_list__nonempty__induct,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,P: list_l8907847357763382004od_b_c > $o] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) )
       => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( ( Xs2 != nil_li8071162985807626740od_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_582_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_583_list__append__eq__Cons__cases,axiom,
    ! [Ys: list_l8907847357763382004od_b_c,Zs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ Ys @ Zs )
        = ( cons_l342771267123639716od_b_c @ X @ Xs ) )
     => ( ( ( Ys = nil_li8071162985807626740od_b_c )
         => ( Zs
           != ( cons_l342771267123639716od_b_c @ X @ Xs ) ) )
       => ~ ! [Ys5: list_l8907847357763382004od_b_c] :
              ( ( Ys
                = ( cons_l342771267123639716od_b_c @ X @ Ys5 ) )
             => ( ( append6992831555715836169od_b_c @ Ys5 @ Zs )
               != Xs ) ) ) ) ).

% list_append_eq_Cons_cases
thf(fact_584_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_585_list__Cons__eq__append__cases,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,Zs: list_l8907847357763382004od_b_c] :
      ( ( ( cons_l342771267123639716od_b_c @ X @ Xs )
        = ( append6992831555715836169od_b_c @ Ys @ Zs ) )
     => ( ( ( Ys = nil_li8071162985807626740od_b_c )
         => ( Zs
           != ( cons_l342771267123639716od_b_c @ X @ Xs ) ) )
       => ~ ! [Ys5: list_l8907847357763382004od_b_c] :
              ( ( Ys
                = ( cons_l342771267123639716od_b_c @ X @ Ys5 ) )
             => ( ( append6992831555715836169od_b_c @ Ys5 @ Zs )
               != Xs ) ) ) ) ).

% list_Cons_eq_append_cases
thf(fact_586_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 )
       => ( ! [X3: product_prod_b_c,Y3: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) )
         => ( ! [X3: 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 @ X3 @ nil_Product_prod_b_c ) ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
           => ( ! [X3: product_prod_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                  ( ( Ys2 != nil_Product_prod_b_c )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
             => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                    ( ( P @ Xs2 @ Ys2 )
                   => ( ( Xs2 != nil_Product_prod_b_c )
                     => ( ( Ys2 != nil_Product_prod_b_c )
                       => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) ) )
               => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).

% rev_nonempty_induct2'
thf(fact_587_rev__nonempty__induct2_H,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_l8907847357763382004od_b_c,P: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ( Ys != nil_li8071162985807626740od_b_c )
       => ( ! [X3: product_prod_b_c,Y3: list_P903359562653991662od_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c] :
                ( ( Xs2 != nil_Product_prod_b_c )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) )
           => ( ! [X3: product_prod_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                  ( ( Ys2 != nil_li8071162985807626740od_b_c )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) )
             => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                    ( ( P @ Xs2 @ Ys2 )
                   => ( ( Xs2 != nil_Product_prod_b_c )
                     => ( ( Ys2 != nil_li8071162985807626740od_b_c )
                       => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) ) ) )
               => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).

% rev_nonempty_induct2'
thf(fact_588_rev__nonempty__induct2_H,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,Ys: list_P903359562653991662od_b_c,P: list_l8907847357763382004od_b_c > list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
     => ( ( Ys != nil_Product_prod_b_c )
       => ( ! [X3: list_P903359562653991662od_b_c,Y3: product_prod_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c] :
                ( ( Xs2 != nil_li8071162985807626740od_b_c )
               => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
           => ( ! [X3: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                  ( ( Ys2 != nil_Product_prod_b_c )
                 => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
             => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                    ( ( P @ Xs2 @ Ys2 )
                   => ( ( Xs2 != nil_li8071162985807626740od_b_c )
                     => ( ( Ys2 != nil_Product_prod_b_c )
                       => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) ) ) )
               => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).

% rev_nonempty_induct2'
thf(fact_589_rev__nonempty__induct2_H,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,P: list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o] :
      ( ( Xs != nil_li8071162985807626740od_b_c )
     => ( ( Ys != nil_li8071162985807626740od_b_c )
       => ( ! [X3: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c] :
                ( ( Xs2 != nil_li8071162985807626740od_b_c )
               => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) )
           => ( ! [X3: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                  ( ( Ys2 != nil_li8071162985807626740od_b_c )
                 => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) )
             => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                    ( ( P @ Xs2 @ Ys2 )
                   => ( ( Xs2 != nil_li8071162985807626740od_b_c )
                     => ( ( Ys2 != nil_li8071162985807626740od_b_c )
                       => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) ) ) )
               => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).

% rev_nonempty_induct2'
thf(fact_590_neq__Nil__rev__conv,axiom,
    ! [L3: list_P903359562653991662od_b_c] :
      ( ( L3 != nil_Product_prod_b_c )
      = ( ? [Xs3: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
            ( L3
            = ( append2547753245680614915od_b_c @ Xs3 @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) ) ) ) ) ).

% neq_Nil_rev_conv
thf(fact_591_neq__Nil__rev__conv,axiom,
    ! [L3: list_l8907847357763382004od_b_c] :
      ( ( L3 != nil_li8071162985807626740od_b_c )
      = ( ? [Xs3: list_l8907847357763382004od_b_c,X2: list_P903359562653991662od_b_c] :
            ( L3
            = ( append6992831555715836169od_b_c @ Xs3 @ ( cons_l342771267123639716od_b_c @ X2 @ nil_li8071162985807626740od_b_c ) ) ) ) ) ).

% neq_Nil_rev_conv
thf(fact_592_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 )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% rev_induct2'
thf(fact_593_rev__induct2_H,axiom,
    ! [P: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ nil_li8071162985807626740od_b_c )
       => ( ! [Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] : ( P @ nil_Product_prod_b_c @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% rev_induct2'
thf(fact_594_rev__induct2_H,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_Product_prod_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] : ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ nil_Product_prod_b_c )
       => ( ! [Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ nil_Product_prod_b_c ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% rev_induct2'
thf(fact_595_rev__induct2_H,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] : ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ nil_li8071162985807626740od_b_c )
       => ( ! [Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( append6992831555715836169od_b_c @ Xs2 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ Y3 @ nil_li8071162985807626740od_b_c ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% rev_induct2'
thf(fact_596_neq__Nil__revE,axiom,
    ! [L3: list_P903359562653991662od_b_c] :
      ( ( L3 != nil_Product_prod_b_c )
     => ~ ! [Ll: list_P903359562653991662od_b_c,E4: product_prod_b_c] :
            ( L3
           != ( append2547753245680614915od_b_c @ Ll @ ( cons_P4529483553340347422od_b_c @ E4 @ nil_Product_prod_b_c ) ) ) ) ).

% neq_Nil_revE
thf(fact_597_neq__Nil__revE,axiom,
    ! [L3: list_l8907847357763382004od_b_c] :
      ( ( L3 != nil_li8071162985807626740od_b_c )
     => ~ ! [Ll: list_l8907847357763382004od_b_c,E4: list_P903359562653991662od_b_c] :
            ( L3
           != ( append6992831555715836169od_b_c @ Ll @ ( cons_l342771267123639716od_b_c @ E4 @ nil_li8071162985807626740od_b_c ) ) ) ) ).

% neq_Nil_revE
thf(fact_598_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_599_foldl__Nil,axiom,
    ! [F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e,A2: produc4534891796109904283_b_c_e] :
      ( ( foldl_2934561762154836916od_b_c @ F @ A2 @ nil_li8071162985807626740od_b_c )
      = A2 ) ).

% foldl_Nil
thf(fact_600_foldl__rule__aux__P,axiom,
    ! [I: produc4534891796109904283_b_c_e > list_l8907847357763382004od_b_c > $o,Sigma_0: produc4534891796109904283_b_c_e,L0: list_l8907847357763382004od_b_c,F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e,P: produc4534891796109904283_b_c_e > $o] :
      ( ( I @ Sigma_0 @ L0 )
     => ( ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Sigma: produc4534891796109904283_b_c_e] :
            ( ( L0
              = ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) ) )
           => ( ( I @ Sigma @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) )
             => ( I @ ( F @ Sigma @ X3 ) @ L22 ) ) )
       => ( ! [Sigma: produc4534891796109904283_b_c_e] :
              ( ( I @ Sigma @ nil_li8071162985807626740od_b_c )
             => ( P @ Sigma ) )
         => ( P @ ( foldl_2934561762154836916od_b_c @ F @ Sigma_0 @ L0 ) ) ) ) ) ).

% foldl_rule_aux_P
thf(fact_601_foldl__rule__aux,axiom,
    ! [I: produc4534891796109904283_b_c_e > list_l8907847357763382004od_b_c > $o,Sigma_0: produc4534891796109904283_b_c_e,L0: list_l8907847357763382004od_b_c,F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e] :
      ( ( I @ Sigma_0 @ L0 )
     => ( ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Sigma: produc4534891796109904283_b_c_e] :
            ( ( L0
              = ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) ) )
           => ( ( I @ Sigma @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) )
             => ( I @ ( F @ Sigma @ X3 ) @ L22 ) ) )
       => ( I @ ( foldl_2934561762154836916od_b_c @ F @ Sigma_0 @ L0 ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% foldl_rule_aux
thf(fact_602_foldl__rule__P,axiom,
    ! [I: produc4534891796109904283_b_c_e > list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,Sigma_0: produc4534891796109904283_b_c_e,L0: list_l8907847357763382004od_b_c,F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e,P: produc4534891796109904283_b_c_e > $o] :
      ( ( I @ Sigma_0 @ nil_li8071162985807626740od_b_c @ L0 )
     => ( ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Sigma: produc4534891796109904283_b_c_e] :
            ( ( L0
              = ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) ) )
           => ( ( I @ Sigma @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) )
             => ( I @ ( F @ Sigma @ X3 ) @ ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ L22 ) ) )
       => ( ! [Sigma: produc4534891796109904283_b_c_e] :
              ( ( I @ Sigma @ L0 @ nil_li8071162985807626740od_b_c )
             => ( P @ Sigma ) )
         => ( P @ ( foldl_2934561762154836916od_b_c @ F @ Sigma_0 @ L0 ) ) ) ) ) ).

% foldl_rule_P
thf(fact_603_foldl__rule,axiom,
    ! [I: produc4534891796109904283_b_c_e > list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,Sigma_0: produc4534891796109904283_b_c_e,L0: list_l8907847357763382004od_b_c,F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e] :
      ( ( I @ Sigma_0 @ nil_li8071162985807626740od_b_c @ L0 )
     => ( ! [L12: list_l8907847357763382004od_b_c,L22: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Sigma: produc4534891796109904283_b_c_e] :
            ( ( L0
              = ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) ) )
           => ( ( I @ Sigma @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ L22 ) )
             => ( I @ ( F @ Sigma @ X3 ) @ ( append6992831555715836169od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) @ L22 ) ) )
       => ( I @ ( foldl_2934561762154836916od_b_c @ F @ Sigma_0 @ L0 ) @ L0 @ nil_li8071162985807626740od_b_c ) ) ) ).

% foldl_rule
thf(fact_604_list__match__lel__lel,axiom,
    ! [C1: list_P903359562653991662od_b_c,Qs: product_prod_b_c,C22: list_P903359562653991662od_b_c,C12: list_P903359562653991662od_b_c,Qs2: product_prod_b_c,C23: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ C1 @ ( cons_P4529483553340347422od_b_c @ Qs @ C22 ) )
        = ( append2547753245680614915od_b_c @ C12 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C23 ) ) )
     => ( ! [C21: list_P903359562653991662od_b_c] :
            ( ( C1
              = ( append2547753245680614915od_b_c @ C12 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C21 ) ) )
           => ( C23
             != ( append2547753245680614915od_b_c @ C21 @ ( cons_P4529483553340347422od_b_c @ Qs @ C22 ) ) ) )
       => ( ( ( C12 = C1 )
           => ( ( Qs2 = Qs )
             => ( C23 != C22 ) ) )
         => ~ ! [C212: list_P903359562653991662od_b_c] :
                ( ( C12
                  = ( append2547753245680614915od_b_c @ C1 @ ( cons_P4529483553340347422od_b_c @ Qs @ C212 ) ) )
               => ( C22
                 != ( append2547753245680614915od_b_c @ C212 @ ( cons_P4529483553340347422od_b_c @ Qs2 @ C23 ) ) ) ) ) ) ) ).

% list_match_lel_lel
thf(fact_605_list__match__lel__lel,axiom,
    ! [C1: list_l8907847357763382004od_b_c,Qs: list_P903359562653991662od_b_c,C22: list_l8907847357763382004od_b_c,C12: list_l8907847357763382004od_b_c,Qs2: list_P903359562653991662od_b_c,C23: list_l8907847357763382004od_b_c] :
      ( ( ( append6992831555715836169od_b_c @ C1 @ ( cons_l342771267123639716od_b_c @ Qs @ C22 ) )
        = ( append6992831555715836169od_b_c @ C12 @ ( cons_l342771267123639716od_b_c @ Qs2 @ C23 ) ) )
     => ( ! [C21: list_l8907847357763382004od_b_c] :
            ( ( C1
              = ( append6992831555715836169od_b_c @ C12 @ ( cons_l342771267123639716od_b_c @ Qs2 @ C21 ) ) )
           => ( C23
             != ( append6992831555715836169od_b_c @ C21 @ ( cons_l342771267123639716od_b_c @ Qs @ C22 ) ) ) )
       => ( ( ( C12 = C1 )
           => ( ( Qs2 = Qs )
             => ( C23 != C22 ) ) )
         => ~ ! [C212: list_l8907847357763382004od_b_c] :
                ( ( C12
                  = ( append6992831555715836169od_b_c @ C1 @ ( cons_l342771267123639716od_b_c @ Qs @ C212 ) ) )
               => ( C22
                 != ( append6992831555715836169od_b_c @ C212 @ ( cons_l342771267123639716od_b_c @ Qs2 @ C23 ) ) ) ) ) ) ) ).

% list_match_lel_lel
thf(fact_606_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,M3: fsm_a_b_c,Q4: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_a_b_c @ M3 @ Q4 ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ).

% language_prefix
thf(fact_607_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,M3: fsm_d_b_c,Q4: d] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_d_b_c @ M3 @ Q4 ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ).

% language_prefix
thf(fact_608_neq__NilE,axiom,
    ! [L3: list_P903359562653991662od_b_c] :
      ( ( L3 != nil_Product_prod_b_c )
     => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( L3
           != ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) ).

% neq_NilE
thf(fact_609_neq__NilE,axiom,
    ! [L3: list_l8907847357763382004od_b_c] :
      ( ( L3 != nil_li8071162985807626740od_b_c )
     => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( L3
           != ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ).

% neq_NilE
thf(fact_610_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_611_list__2pre__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c > $o,W1: list_P903359562653991662od_b_c,W2: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [E4: product_prod_b_c,W12: list_P903359562653991662od_b_c,W22: list_l8907847357763382004od_b_c] :
            ( ( P @ W12 @ W22 )
           => ( P @ ( cons_P4529483553340347422od_b_c @ E4 @ W12 ) @ W22 ) )
       => ( ! [E4: list_P903359562653991662od_b_c,W13: list_P903359562653991662od_b_c,W23: list_l8907847357763382004od_b_c] :
              ( ( P @ W13 @ W23 )
             => ( P @ W13 @ ( cons_l342771267123639716od_b_c @ E4 @ W23 ) ) )
         => ( P @ W1 @ W2 ) ) ) ) ).

% list_2pre_induct
thf(fact_612_list__2pre__induct,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_P903359562653991662od_b_c > $o,W1: list_l8907847357763382004od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_Product_prod_b_c )
     => ( ! [E4: list_P903359562653991662od_b_c,W12: list_l8907847357763382004od_b_c,W22: list_P903359562653991662od_b_c] :
            ( ( P @ W12 @ W22 )
           => ( P @ ( cons_l342771267123639716od_b_c @ E4 @ W12 ) @ W22 ) )
       => ( ! [E4: product_prod_b_c,W13: list_l8907847357763382004od_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_613_list__2pre__induct,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,W1: list_l8907847357763382004od_b_c,W2: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c @ nil_li8071162985807626740od_b_c )
     => ( ! [E4: list_P903359562653991662od_b_c,W12: list_l8907847357763382004od_b_c,W22: list_l8907847357763382004od_b_c] :
            ( ( P @ W12 @ W22 )
           => ( P @ ( cons_l342771267123639716od_b_c @ E4 @ W12 ) @ W22 ) )
       => ( ! [E4: list_P903359562653991662od_b_c,W13: list_l8907847357763382004od_b_c,W23: list_l8907847357763382004od_b_c] :
              ( ( P @ W13 @ W23 )
             => ( P @ W13 @ ( cons_l342771267123639716od_b_c @ E4 @ W23 ) ) )
         => ( P @ W1 @ W2 ) ) ) ) ).

% list_2pre_induct
thf(fact_614_list__induct__first2,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [X3: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) )
       => ( ! [X12: product_prod_b_c,X23: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( P @ Xs2 )
             => ( P @ ( cons_P4529483553340347422od_b_c @ X12 @ ( cons_P4529483553340347422od_b_c @ X23 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_induct_first2
thf(fact_615_list__induct__first2,axiom,
    ! [P: list_l8907847357763382004od_b_c > $o,Xs: list_l8907847357763382004od_b_c] :
      ( ( P @ nil_li8071162985807626740od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c] : ( P @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) )
       => ( ! [X12: list_P903359562653991662od_b_c,X23: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( ( P @ Xs2 )
             => ( P @ ( cons_l342771267123639716od_b_c @ X12 @ ( cons_l342771267123639716od_b_c @ X23 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_induct_first2
thf(fact_616_mergesort__by__rel__merge__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,R: 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 )
       => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( ( R @ X3 @ Y3 )
             => ( ( P @ Xs2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ~ ( R @ X3 @ Y3 )
               => ( ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ Ys2 )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% mergesort_by_rel_merge_induct
thf(fact_617_mergesort__by__rel__merge__induct,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_P903359562653991662od_b_c > $o,R: list_P903359562653991662od_b_c > product_prod_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ! [Xs2: list_l8907847357763382004od_b_c] : ( P @ Xs2 @ nil_Product_prod_b_c )
     => ( ! [X_1: list_P903359562653991662od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ X_1 )
       => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( ( R @ X3 @ Y3 )
             => ( ( P @ Xs2 @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) )
               => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ~ ( R @ X3 @ Y3 )
               => ( ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ Ys2 )
                 => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% mergesort_by_rel_merge_induct
thf(fact_618_mergesort__by__rel__merge__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c > $o,R: product_prod_b_c > list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ! [Xs2: list_P903359562653991662od_b_c] : ( P @ Xs2 @ nil_li8071162985807626740od_b_c )
     => ( ! [X_1: list_l8907847357763382004od_b_c] : ( P @ nil_Product_prod_b_c @ X_1 )
       => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
              ( ( R @ X3 @ Y3 )
             => ( ( P @ Xs2 @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) )
         => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ~ ( R @ X3 @ Y3 )
               => ( ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ Ys2 )
                 => ( P @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% mergesort_by_rel_merge_induct
thf(fact_619_mergesort__by__rel__merge__induct,axiom,
    ! [P: list_l8907847357763382004od_b_c > list_l8907847357763382004od_b_c > $o,R: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ! [Xs2: list_l8907847357763382004od_b_c] : ( P @ Xs2 @ nil_li8071162985807626740od_b_c )
     => ( ! [X_1: list_l8907847357763382004od_b_c] : ( P @ nil_li8071162985807626740od_b_c @ X_1 )
       => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
              ( ( R @ X3 @ Y3 )
             => ( ( P @ Xs2 @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) )
               => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) )
         => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
                ( ~ ( R @ X3 @ Y3 )
               => ( ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ Ys2 )
                 => ( P @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% mergesort_by_rel_merge_induct
thf(fact_620_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,X3: product_prod_b_c] :
            ( X
           != ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Xs12 @ Xs22 ) @ ( cons_P4529483553340347422od_b_c @ X3 @ nil_Product_prod_b_c ) ) )
       => ~ ! [Xs12: list_P903359562653991662od_b_c,Xs22: list_P903359562653991662od_b_c,X12: 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 @ X12 @ ( cons_P4529483553340347422od_b_c @ X23 @ Xs2 ) ) ) ) ) ) ).

% mergesort_by_rel_split.cases
thf(fact_621_mergesort__by__rel__split_Ocases,axiom,
    ! [X: produc8709072580131811508od_b_c] :
      ( ! [Xs12: list_l8907847357763382004od_b_c,Xs22: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc8304045725518759076od_b_c @ ( produc2983116027154973335od_b_c @ Xs12 @ Xs22 ) @ nil_li8071162985807626740od_b_c ) )
     => ( ! [Xs12: list_l8907847357763382004od_b_c,Xs22: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c] :
            ( X
           != ( produc8304045725518759076od_b_c @ ( produc2983116027154973335od_b_c @ Xs12 @ Xs22 ) @ ( cons_l342771267123639716od_b_c @ X3 @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [Xs12: list_l8907847357763382004od_b_c,Xs22: list_l8907847357763382004od_b_c,X12: list_P903359562653991662od_b_c,X23: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc8304045725518759076od_b_c @ ( produc2983116027154973335od_b_c @ Xs12 @ Xs22 ) @ ( cons_l342771267123639716od_b_c @ X12 @ ( cons_l342771267123639716od_b_c @ X23 @ Xs2 ) ) ) ) ) ) ).

% mergesort_by_rel_split.cases
thf(fact_622_mergesort__by__rel__merge_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [R3: product_prod_b_c > product_prod_b_c > $o,X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc7428879202731100112od_b_c @ R3 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) )
     => ( ! [R3: product_prod_b_c > product_prod_b_c > $o,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ R3 @ ( produc3076307724246486423od_b_c @ Xs2 @ nil_Product_prod_b_c ) ) )
       => ~ ! [R3: product_prod_b_c > product_prod_b_c > $o,V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( X
             != ( produc7428879202731100112od_b_c @ R3 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) ) ) ) ) ) ).

% mergesort_by_rel_merge.cases
thf(fact_623_mergesort__by__rel__merge_Ocases,axiom,
    ! [X: produc3826428549763104736od_b_c] :
      ( ! [R3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc3970083798833846608od_b_c @ R3 @ ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) )
     => ( ! [R3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc3970083798833846608od_b_c @ R3 @ ( produc2983116027154973335od_b_c @ Xs2 @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [R3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc3970083798833846608od_b_c @ R3 @ ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) ) ) ) ) ) ).

% mergesort_by_rel_merge.cases
thf(fact_624_quicksort__by__rel_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [R3: product_prod_b_c > product_prod_b_c > $o,Sl: list_P903359562653991662od_b_c] :
          ( X
         != ( produc7428879202731100112od_b_c @ R3 @ ( produc3076307724246486423od_b_c @ Sl @ nil_Product_prod_b_c ) ) )
     => ~ ! [R3: product_prod_b_c > product_prod_b_c > $o,Sl: list_P903359562653991662od_b_c,X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ R3 @ ( produc3076307724246486423od_b_c @ Sl @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) ) ) ).

% quicksort_by_rel.cases
thf(fact_625_quicksort__by__rel_Ocases,axiom,
    ! [X: produc3826428549763104736od_b_c] :
      ( ! [R3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Sl: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc3970083798833846608od_b_c @ R3 @ ( produc2983116027154973335od_b_c @ Sl @ nil_li8071162985807626740od_b_c ) ) )
     => ~ ! [R3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Sl: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc3970083798833846608od_b_c @ R3 @ ( produc2983116027154973335od_b_c @ Sl @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ) ) ).

% quicksort_by_rel.cases
thf(fact_626_partition__rev_Ocases,axiom,
    ! [X: produc6480465915480880334od_b_c] :
      ( ! [P3: product_prod_b_c > $o,Yes: list_P903359562653991662od_b_c,No: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3614263070280852224od_b_c @ P3 @ ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Yes @ No ) @ nil_Product_prod_b_c ) ) )
     => ~ ! [P3: product_prod_b_c > $o,Yes: list_P903359562653991662od_b_c,No: list_P903359562653991662od_b_c,X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3614263070280852224od_b_c @ P3 @ ( produc8805658965386351518od_b_c @ ( produc3076307724246486423od_b_c @ Yes @ No ) @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) ) ) ).

% partition_rev.cases
thf(fact_627_partition__rev_Ocases,axiom,
    ! [X: produc8466275945506343258od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > $o,Yes: list_l8907847357763382004od_b_c,No: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc5355742538196110988od_b_c @ P3 @ ( produc8304045725518759076od_b_c @ ( produc2983116027154973335od_b_c @ Yes @ No ) @ nil_li8071162985807626740od_b_c ) ) )
     => ~ ! [P3: list_P903359562653991662od_b_c > $o,Yes: list_l8907847357763382004od_b_c,No: list_l8907847357763382004od_b_c,X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc5355742538196110988od_b_c @ P3 @ ( produc8304045725518759076od_b_c @ ( produc2983116027154973335od_b_c @ Yes @ No ) @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ) ) ).

% partition_rev.cases
thf(fact_628_list__all__zip_Ocases,axiom,
    ! [X: produc6700159619980657760od_b_c] :
      ( ! [P3: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc7428879202731100112od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ nil_Product_prod_b_c ) ) )
     => ( ! [P3: product_prod_b_c > product_prod_b_c > $o,A6: product_prod_b_c,As: list_P903359562653991662od_b_c,B6: product_prod_b_c,Bs: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7428879202731100112od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ A6 @ As ) @ ( cons_P4529483553340347422od_b_c @ B6 @ Bs ) ) ) )
       => ( ! [P3: product_prod_b_c > product_prod_b_c > $o,V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( X
             != ( produc7428879202731100112od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) @ nil_Product_prod_b_c ) ) )
         => ~ ! [P3: product_prod_b_c > product_prod_b_c > $o,V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
                ( X
               != ( produc7428879202731100112od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) ) ) ) ) ) ) ).

% list_all_zip.cases
thf(fact_629_list__all__zip_Ocases,axiom,
    ! [X: produc1803680567332345068od_b_c] :
      ( ! [P3: product_prod_b_c > list_P903359562653991662od_b_c > $o] :
          ( X
         != ( produc3493468722173126236od_b_c @ P3 @ ( produc169793319869648157od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
     => ( ! [P3: product_prod_b_c > list_P903359562653991662od_b_c > $o,A6: product_prod_b_c,As: list_P903359562653991662od_b_c,B6: list_P903359562653991662od_b_c,Bs: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc3493468722173126236od_b_c @ P3 @ ( produc169793319869648157od_b_c @ ( cons_P4529483553340347422od_b_c @ A6 @ As ) @ ( cons_l342771267123639716od_b_c @ B6 @ Bs ) ) ) )
       => ( ! [P3: product_prod_b_c > list_P903359562653991662od_b_c > $o,V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3493468722173126236od_b_c @ P3 @ ( produc169793319869648157od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) @ nil_li8071162985807626740od_b_c ) ) )
         => ~ ! [P3: product_prod_b_c > list_P903359562653991662od_b_c > $o,V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
                ( X
               != ( produc3493468722173126236od_b_c @ P3 @ ( produc169793319869648157od_b_c @ nil_Product_prod_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) ) ) ) ) ) ) ).

% list_all_zip.cases
thf(fact_630_list__all__zip_Ocases,axiom,
    ! [X: produc8528282105297090900od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc8387532175233844420od_b_c @ P3 @ ( produc4100501727608129553od_b_c @ nil_li8071162985807626740od_b_c @ nil_Product_prod_b_c ) ) )
     => ( ! [P3: list_P903359562653991662od_b_c > product_prod_b_c > $o,A6: list_P903359562653991662od_b_c,As: list_l8907847357763382004od_b_c,B6: product_prod_b_c,Bs: list_P903359562653991662od_b_c] :
            ( X
           != ( produc8387532175233844420od_b_c @ P3 @ ( produc4100501727608129553od_b_c @ ( cons_l342771267123639716od_b_c @ A6 @ As ) @ ( cons_P4529483553340347422od_b_c @ B6 @ Bs ) ) ) )
       => ( ! [P3: list_P903359562653991662od_b_c > product_prod_b_c > $o,V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc8387532175233844420od_b_c @ P3 @ ( produc4100501727608129553od_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) @ nil_Product_prod_b_c ) ) )
         => ~ ! [P3: list_P903359562653991662od_b_c > product_prod_b_c > $o,V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
                ( X
               != ( produc8387532175233844420od_b_c @ P3 @ ( produc4100501727608129553od_b_c @ nil_li8071162985807626740od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) ) ) ) ) ) ) ).

% list_all_zip.cases
thf(fact_631_list__all__zip_Ocases,axiom,
    ! [X: produc3826428549763104736od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o] :
          ( X
         != ( produc3970083798833846608od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ nil_li8071162985807626740od_b_c ) ) )
     => ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,A6: list_P903359562653991662od_b_c,As: list_l8907847357763382004od_b_c,B6: list_P903359562653991662od_b_c,Bs: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc3970083798833846608od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ A6 @ As ) @ ( cons_l342771267123639716od_b_c @ B6 @ Bs ) ) ) )
       => ( ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc3970083798833846608od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) @ nil_li8071162985807626740od_b_c ) ) )
         => ~ ! [P3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
                ( X
               != ( produc3970083798833846608od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) ) ) ) ) ) ) ).

% list_all_zip.cases
thf(fact_632_merge_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [L22: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ L22 ) )
     => ( ! [V2: product_prod_b_c,Va: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ V2 @ Va ) @ nil_Product_prod_b_c ) )
       => ~ ! [X12: 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 @ X12 @ L12 ) @ ( cons_P4529483553340347422od_b_c @ X23 @ L22 ) ) ) ) ) ).

% merge.cases
thf(fact_633_merge_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ! [L22: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ L22 ) )
     => ( ! [V2: list_P903359562653991662od_b_c,Va: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ V2 @ Va ) @ nil_li8071162985807626740od_b_c ) )
       => ~ ! [X12: list_P903359562653991662od_b_c,L12: list_l8907847357763382004od_b_c,X23: list_P903359562653991662od_b_c,L22: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X12 @ L12 ) @ ( cons_l342771267123639716od_b_c @ X23 @ L22 ) ) ) ) ) ).

% merge.cases
thf(fact_634_FSM_Oafter_Osimps_I1_J,axiom,
    ! [M3: fsm_a_b_c,Q4: a] :
      ( ( after_a_b_c @ M3 @ Q4 @ nil_Product_prod_b_c )
      = Q4 ) ).

% FSM.after.simps(1)
thf(fact_635_from__FSM__observable,axiom,
    ! [M3: fsm_a_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( observable_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) ) ) ).

% from_FSM_observable
thf(fact_636_from__FSM__observable,axiom,
    ! [M3: fsm_d_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( observable_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) ) ) ).

% from_FSM_observable
thf(fact_637_in__snd__imageE,axiom,
    ! [Y: e,S: set_Pr3237851069733663483_b_c_e] :
      ( ( member_e @ Y @ ( image_2493620005906216236_c_e_e @ produc6779600879576379961_b_c_e @ S ) )
     => ~ ! [X3: prefix425356687782099470od_b_c] :
            ~ ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_638_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 ) )
     => ~ ! [X3: b] :
            ~ ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X3 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_639_in__snd__imageE,axiom,
    ! [Y: produc2133359284458116493od_c_a,S: set_Pr8357624050790843030od_c_a] :
      ( ( member1160383752307813046od_c_a @ Y @ ( image_644133890040260316od_c_a @ produc8088130389382527188od_c_a @ S ) )
     => ~ ! [X3: a] :
            ~ ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X3 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_640_in__snd__imageE,axiom,
    ! [Y: product_prod_c_a,S: set_Pr272002107461315949od_c_a] :
      ( ( member5074992350434858958od_c_a @ Y @ ( image_1453128995064482141od_c_a @ produc5221446324160585515od_c_a @ S ) )
     => ~ ! [X3: b] :
            ~ ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ X3 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_641_in__snd__imageE,axiom,
    ! [Y: a,S: set_Product_prod_c_a] :
      ( ( member_a @ Y @ ( image_5407010446420943518_c_a_a @ product_snd_c_a @ S ) )
     => ~ ! [X3: c] :
            ~ ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ X3 @ Y ) @ S ) ) ).

% in_snd_imageE
thf(fact_642_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_643_in__fst__imageE,axiom,
    ! [X: prefix425356687782099470od_b_c,S: set_Pr3237851069733663483_b_c_e] :
      ( ( member2378525361814473399od_b_c @ X @ ( image_3005832862676689720od_b_c @ produc1447154562020694007_b_c_e @ S ) )
     => ~ ! [Y3: e] :
            ~ ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_644_in__fst__imageE,axiom,
    ! [X: a,S: set_Pr8357624050790843030od_c_a] :
      ( ( member_a @ X @ ( image_9171994905208062541_c_a_a @ produc4225943634317630866od_c_a @ S ) )
     => ~ ! [Y3: produc2133359284458116493od_c_a] :
            ~ ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_645_in__fst__imageE,axiom,
    ! [X: b,S: set_Pr272002107461315949od_c_a] :
      ( ( member_b @ X @ ( image_8972666397057282743_c_a_b @ produc301949074746585577od_c_a @ S ) )
     => ~ ! [Y3: product_prod_c_a] :
            ~ ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_646_in__fst__imageE,axiom,
    ! [X: c,S: set_Product_prod_c_a] :
      ( ( member_c @ X @ ( image_5407010446420943520_c_a_c @ product_fst_c_a @ S ) )
     => ~ ! [Y3: a] :
            ~ ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ X @ Y3 ) @ S ) ) ).

% in_fst_imageE
thf(fact_647_language__contains__empty__sequence,axiom,
    ! [M3: fsm_a_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ).

% language_contains_empty_sequence
thf(fact_648_language__contains__empty__sequence,axiom,
    ! [M3: fsm_d_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ).

% language_contains_empty_sequence
thf(fact_649_distinguishes__not__Nil,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Q14: produc2669932201312201782od_c_a,Q2: produc2669932201312201782od_c_a,Io2: list_P903359562653991662od_b_c] :
      ( ( distin4657727790478416823_a_b_c @ M3 @ Q14 @ Q2 @ Io2 )
     => ( ( member5502040268208861279od_c_a @ Q14 @ ( states895637122477222528_a_b_c @ M3 ) )
       => ( ( member5502040268208861279od_c_a @ Q2 @ ( states895637122477222528_a_b_c @ M3 ) )
         => ( Io2 != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_650_distinguishes__not__Nil,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Q14: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( distin2804555989863659119_c_b_c @ M3 @ Q14 @ Q2 @ Io2 )
     => ( ( member6330420149250801815od_b_c @ Q14 @ ( states7681702920031268536_c_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M3 ) )
         => ( Io2 != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_651_distinguishes__not__Nil,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a,Io2: list_P903359562653991662od_b_c] :
      ( ( distinguishes_a_b_c @ M3 @ Q14 @ Q2 @ Io2 )
     => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
       => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
         => ( Io2 != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_652_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P268689088907702561_b_c_e,M3: fsm_Pr379724744552003854_b_c_e,Q4: produc2669932201312201782od_c_a] :
      ( ~ ( member8329588800322848842_b_c_e @ Io2 @ ( lS_Pro6032960129543757646_b_c_e @ M3 @ Q4 ) )
     => ( ( member5502040268208861279od_c_a @ Q4 @ ( states3043464935519986995_b_c_e @ M3 ) )
       => ( ( observ3091655274719039154_b_c_e @ M3 )
         => ~ ! [Io3: list_P268689088907702561_b_c_e,X3: prefix425356687782099470od_b_c,Y3: e] :
                ( ? [Io4: list_P268689088907702561_b_c_e] :
                    ( Io2
                    = ( append3015380627477509558_b_c_e @ Io3 @ ( append3015380627477509558_b_c_e @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) @ Io4 ) ) )
               => ( ( member8329588800322848842_b_c_e @ Io3 @ ( lS_Pro6032960129543757646_b_c_e @ M3 @ Q4 ) )
                 => ( member8329588800322848842_b_c_e @ ( append3015380627477509558_b_c_e @ Io3 @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( lS_Pro6032960129543757646_b_c_e @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_653_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P268689088907702561_b_c_e,M3: fsm_a_8518373703003225814_b_c_e,Q4: a] :
      ( ~ ( member8329588800322848842_b_c_e @ Io2 @ ( lS_a_P1558670498994022934_b_c_e @ M3 @ Q4 ) )
     => ( ( member_a @ Q4 @ ( states7743438715959359227_b_c_e @ M3 ) )
       => ( ( observ7286853435796284794_b_c_e @ M3 )
         => ~ ! [Io3: list_P268689088907702561_b_c_e,X3: prefix425356687782099470od_b_c,Y3: e] :
                ( ? [Io4: list_P268689088907702561_b_c_e] :
                    ( Io2
                    = ( append3015380627477509558_b_c_e @ Io3 @ ( append3015380627477509558_b_c_e @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) @ Io4 ) ) )
               => ( ( member8329588800322848842_b_c_e @ Io3 @ ( lS_a_P1558670498994022934_b_c_e @ M3 @ Q4 ) )
                 => ( member8329588800322848842_b_c_e @ ( append3015380627477509558_b_c_e @ Io3 @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( lS_a_P1558670498994022934_b_c_e @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_654_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P268689088907702561_b_c_e,M3: fsm_li553205354899133766_b_c_e,Q4: list_P903359562653991662od_b_c] :
      ( ~ ( member8329588800322848842_b_c_e @ Io2 @ ( lS_lis2888767557860045830_b_c_e @ M3 @ Q4 ) )
     => ( ( member6330420149250801815od_b_c @ Q4 @ ( states8947519511248575851_b_c_e @ M3 ) )
       => ( ( observ3923965058616338794_b_c_e @ M3 )
         => ~ ! [Io3: list_P268689088907702561_b_c_e,X3: prefix425356687782099470od_b_c,Y3: e] :
                ( ? [Io4: list_P268689088907702561_b_c_e] :
                    ( Io2
                    = ( append3015380627477509558_b_c_e @ Io3 @ ( append3015380627477509558_b_c_e @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) @ Io4 ) ) )
               => ( ( member8329588800322848842_b_c_e @ Io3 @ ( lS_lis2888767557860045830_b_c_e @ M3 @ Q4 ) )
                 => ( member8329588800322848842_b_c_e @ ( append3015380627477509558_b_c_e @ Io3 @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ X3 @ Y3 ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( lS_lis2888767557860045830_b_c_e @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_655_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P903359562653991662od_b_c,M3: fsm_Pr6425204305901329755_a_b_c,Q4: produc2669932201312201782od_c_a] :
      ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) )
     => ( ( member5502040268208861279od_c_a @ Q4 @ ( states895637122477222528_a_b_c @ M3 ) )
       => ( ( observ6303369326153519487_a_b_c @ M3 )
         => ~ ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
                ( ? [Io4: list_P903359562653991662od_b_c] :
                    ( Io2
                    = ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io3 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_656_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P903359562653991662od_b_c,M3: fsm_li6801133765522507155_c_b_c,Q4: list_P903359562653991662od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) )
     => ( ( member6330420149250801815od_b_c @ Q4 @ ( states7681702920031268536_c_b_c @ M3 ) )
       => ( ( observ6293852833591064631_c_b_c @ M3 )
         => ~ ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
                ( ? [Io4: list_P903359562653991662od_b_c] :
                    ( Io2
                    = ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io3 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_657_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P903359562653991662od_b_c,M3: fsm_a_b_c,Q4: a] :
      ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ Q4 ) )
     => ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
       => ( ( observable_a_b_c @ M3 )
         => ~ ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
                ( ? [Io4: list_P903359562653991662od_b_c] :
                    ( Io2
                    = ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io3 @ ( lS_a_b_c @ M3 @ Q4 ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_658_language__maximal__contained__prefix__ob,axiom,
    ! [Io2: list_P903359562653991662od_b_c,M3: fsm_d_b_c,Q4: d] :
      ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ Q4 ) )
     => ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
       => ( ( observable_d_b_c @ M3 )
         => ~ ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
                ( ? [Io4: list_P903359562653991662od_b_c] :
                    ( Io2
                    = ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io3 @ ( lS_d_b_c @ M3 @ Q4 ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_659_from__FSM__reachable__states,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
     => ( ord_less_eq_set_a @ ( reacha1620305530751930115_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) ) @ ( reacha1620305530751930115_a_b_c @ M3 ) ) ) ).

% from_FSM_reachable_states
thf(fact_660_snd__image__mp,axiom,
    ! [A: set_Pr3237851069733663483_b_c_e,B: set_e,X: prefix425356687782099470od_b_c,Y: e] :
      ( ( ord_less_eq_set_e @ ( image_2493620005906216236_c_e_e @ produc6779600879576379961_b_c_e @ A ) @ B )
     => ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) @ A )
       => ( member_e @ Y @ B ) ) ) ).

% snd_image_mp
thf(fact_661_snd__image__mp,axiom,
    ! [A: set_Product_prod_b_c,B: set_c,X: b,Y: c] :
      ( ( ord_less_eq_set_c @ ( image_7762865866877615261_b_c_c @ product_snd_b_c @ A ) @ B )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ A )
       => ( member_c @ Y @ B ) ) ) ).

% snd_image_mp
thf(fact_662_snd__image__mp,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_Pr272002107461315949od_c_a,X: a,Y: produc2133359284458116493od_c_a] :
      ( ( ord_le4080174072498570509od_c_a @ ( image_644133890040260316od_c_a @ produc8088130389382527188od_c_a @ A ) @ B )
     => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) @ A )
       => ( member1160383752307813046od_c_a @ Y @ B ) ) ) ).

% snd_image_mp
thf(fact_663_snd__image__mp,axiom,
    ! [A: set_Pr272002107461315949od_c_a,B: set_Product_prod_c_a,X: b,Y: product_prod_c_a] :
      ( ( ord_le8698776994054418981od_c_a @ ( image_1453128995064482141od_c_a @ produc5221446324160585515od_c_a @ A ) @ B )
     => ( ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) @ A )
       => ( member5074992350434858958od_c_a @ Y @ B ) ) ) ).

% snd_image_mp
thf(fact_664_snd__image__mp,axiom,
    ! [A: set_Product_prod_c_a,B: set_a,X: c,Y: a] :
      ( ( ord_less_eq_set_a @ ( image_5407010446420943518_c_a_a @ product_snd_c_a @ A ) @ B )
     => ( ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ X @ Y ) @ A )
       => ( member_a @ Y @ B ) ) ) ).

% snd_image_mp
thf(fact_665_fst__image__mp,axiom,
    ! [A: set_Product_prod_b_c,B: set_b,X: b,Y: c] :
      ( ( ord_less_eq_set_b @ ( image_7762865866877615260_b_c_b @ product_fst_b_c @ A ) @ B )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ A )
       => ( member_b @ X @ B ) ) ) ).

% fst_image_mp
thf(fact_666_fst__image__mp,axiom,
    ! [A: set_Pr3237851069733663483_b_c_e,B: set_Pr4395803880006080238od_b_c,X: prefix425356687782099470od_b_c,Y: e] :
      ( ( ord_le5387926975545319054od_b_c @ ( image_3005832862676689720od_b_c @ produc1447154562020694007_b_c_e @ A ) @ B )
     => ( ( member323891770073680196_b_c_e @ ( produc2511600812177743883_b_c_e @ X @ Y ) @ A )
       => ( member2378525361814473399od_b_c @ X @ B ) ) ) ).

% fst_image_mp
thf(fact_667_fst__image__mp,axiom,
    ! [A: set_Pr8357624050790843030od_c_a,B: set_a,X: a,Y: produc2133359284458116493od_c_a] :
      ( ( ord_less_eq_set_a @ ( image_9171994905208062541_c_a_a @ produc4225943634317630866od_c_a @ A ) @ B )
     => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) @ A )
       => ( member_a @ X @ B ) ) ) ).

% fst_image_mp
thf(fact_668_fst__image__mp,axiom,
    ! [A: set_Pr272002107461315949od_c_a,B: set_b,X: b,Y: product_prod_c_a] :
      ( ( ord_less_eq_set_b @ ( image_8972666397057282743_c_a_b @ produc301949074746585577od_c_a @ A ) @ B )
     => ( ( member1160383752307813046od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) @ A )
       => ( member_b @ X @ B ) ) ) ).

% fst_image_mp
thf(fact_669_fst__image__mp,axiom,
    ! [A: set_Product_prod_c_a,B: set_c,X: c,Y: a] :
      ( ( ord_less_eq_set_c @ ( image_5407010446420943520_c_a_c @ product_fst_c_a @ A ) @ B )
     => ( ( member5074992350434858958od_c_a @ ( product_Pair_c_a @ X @ Y ) @ A )
       => ( member_c @ X @ B ) ) ) ).

% fst_image_mp
thf(fact_670_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_671_not__Cons__self2,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( cons_l342771267123639716od_b_c @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_672_observable__after__language__append,axiom,
    ! [M3: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q4: a,Io22: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( ( member6330420149250801815od_b_c @ Io22 @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q4 @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ) ).

% observable_after_language_append
thf(fact_673_observable__after__language__append,axiom,
    ! [M3: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q4: d,Io22: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( ( member6330420149250801815od_b_c @ Io22 @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q4 @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ) ).

% observable_after_language_append
thf(fact_674_observable__after__language__none,axiom,
    ! [M3: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q4: a,Io22: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io22 @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q4 @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ) ).

% observable_after_language_none
thf(fact_675_observable__after__language__none,axiom,
    ! [M3: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Q4: d,Io22: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io22 @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q4 @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io22 ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ) ).

% observable_after_language_none
thf(fact_676_observable__after__eq,axiom,
    ! [M3: fsm_a_b_c,Q4: a,Io1: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( ( after_a_b_c @ M3 @ Q4 @ Io1 )
          = ( after_a_b_c @ M3 @ Q4 @ Io22 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M3 @ Q4 ) )
         => ( ( member6330420149250801815od_b_c @ Io22 @ ( lS_a_b_c @ M3 @ Q4 ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M3 @ Q4 ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_677_observable__after__eq,axiom,
    ! [M3: fsm_d_b_c,Q4: d,Io1: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( ( after_d_b_c @ M3 @ Q4 @ Io1 )
          = ( after_d_b_c @ M3 @ Q4 @ Io22 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_d_b_c @ M3 @ Q4 ) )
         => ( ( member6330420149250801815od_b_c @ Io22 @ ( lS_d_b_c @ M3 @ Q4 ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M3 @ Q4 ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_678_after__language__iff,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Q4: a,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q4 @ Alpha ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ Q4 ) ) ) ) ) ).

% after_language_iff
thf(fact_679_after__language__iff,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Q4: d,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q4 @ Alpha ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ Q4 ) ) ) ) ) ).

% after_language_iff
thf(fact_680_after__split,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Q4: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ Q4 ) )
       => ( ( after_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q4 @ Alpha ) @ Gamma2 )
          = ( after_a_b_c @ M3 @ Q4 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) ) ) ).

% after_split
thf(fact_681_after__split,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Q4: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ Q4 ) )
       => ( ( after_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q4 @ Alpha ) @ Gamma2 )
          = ( after_d_b_c @ M3 @ Q4 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) ) ) ).

% after_split
thf(fact_682_bij__betw__iff__bijections,axiom,
    ( bij_be1058065580227481078od_c_a
    = ( ^ [F3: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a,A4: set_Pr8357624050790843030od_c_a,B4: set_Pr8357624050790843030od_c_a] :
        ? [G4: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a] :
          ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ A4 )
             => ( ( member5502040268208861279od_c_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ B4 )
             => ( ( member5502040268208861279od_c_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_683_bij__betw__iff__bijections,axiom,
    ( bij_be644863384588287534od_c_a
    = ( ^ [F3: a > produc2669932201312201782od_c_a,A4: set_a,B4: set_Pr8357624050790843030od_c_a] :
        ? [G4: produc2669932201312201782od_c_a > a] :
          ( ! [X2: a] :
              ( ( member_a @ X2 @ A4 )
             => ( ( member5502040268208861279od_c_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ B4 )
             => ( ( member_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_684_bij__betw__iff__bijections,axiom,
    ( bij_be5411586866304353214od_c_a
    = ( ^ [F3: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a,A4: set_li6436108459499378894od_b_c,B4: set_Pr8357624050790843030od_c_a] :
        ? [G4: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c] :
          ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A4 )
             => ( ( member5502040268208861279od_c_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ B4 )
             => ( ( member6330420149250801815od_b_c @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_685_bij__betw__iff__bijections,axiom,
    ( bij_be5632368444736963774_c_a_a
    = ( ^ [F3: produc2669932201312201782od_c_a > a,A4: set_Pr8357624050790843030od_c_a,B4: set_a] :
        ? [G4: a > produc2669932201312201782od_c_a] :
          ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ A4 )
             => ( ( member_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: a] :
              ( ( member_a @ X2 @ B4 )
             => ( ( member5502040268208861279od_c_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_686_bij__betw__iff__bijections,axiom,
    ( bij_betw_a_a
    = ( ^ [F3: a > a,A4: set_a,B4: set_a] :
        ? [G4: a > a] :
          ( ! [X2: a] :
              ( ( member_a @ X2 @ A4 )
             => ( ( member_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: a] :
              ( ( member_a @ X2 @ B4 )
             => ( ( member_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_687_bij__betw__iff__bijections,axiom,
    ( bij_be3300351249680192134_b_c_a
    = ( ^ [F3: list_P903359562653991662od_b_c > a,A4: set_li6436108459499378894od_b_c,B4: set_a] :
        ? [G4: a > list_P903359562653991662od_b_c] :
          ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A4 )
             => ( ( member_a @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: a] :
              ( ( member_a @ X2 @ B4 )
             => ( ( member6330420149250801815od_b_c @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_688_bij__betw__iff__bijections,axiom,
    ( bij_be7860006274356004014od_b_c
    = ( ^ [F3: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,A4: set_Pr8357624050790843030od_c_a,B4: set_li6436108459499378894od_b_c] :
        ? [G4: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a] :
          ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ A4 )
             => ( ( member6330420149250801815od_b_c @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ B4 )
             => ( ( member5502040268208861279od_c_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_689_bij__betw__iff__bijections,axiom,
    ( bij_be8783369614777182438od_b_c
    = ( ^ [F3: a > list_P903359562653991662od_b_c,A4: set_a,B4: set_li6436108459499378894od_b_c] :
        ? [G4: list_P903359562653991662od_b_c > a] :
          ( ! [X2: a] :
              ( ( member_a @ X2 @ A4 )
             => ( ( member6330420149250801815od_b_c @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ B4 )
             => ( ( member_a @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_690_bij__betw__iff__bijections,axiom,
    ( bij_be8534141360866068086od_b_c
    = ( ^ [F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A4: set_li6436108459499378894od_b_c,B4: set_li6436108459499378894od_b_c] :
        ? [G4: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
          ( ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A4 )
             => ( ( member6330420149250801815od_b_c @ ( F3 @ X2 ) @ B4 )
                & ( ( G4 @ ( F3 @ X2 ) )
                  = X2 ) ) )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ B4 )
             => ( ( member6330420149250801815od_b_c @ ( G4 @ X2 ) @ A4 )
                & ( ( F3 @ ( G4 @ X2 ) )
                  = X2 ) ) ) ) ) ) ).

% bij_betw_iff_bijections
thf(fact_691_bij__betw__apply,axiom,
    ! [F: produc2669932201312201782od_c_a > produc2669932201312201782od_c_a,A: set_Pr8357624050790843030od_c_a,B: set_Pr8357624050790843030od_c_a,A2: produc2669932201312201782od_c_a] :
      ( ( bij_be1058065580227481078od_c_a @ F @ A @ B )
     => ( ( member5502040268208861279od_c_a @ A2 @ A )
       => ( member5502040268208861279od_c_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_692_bij__betw__apply,axiom,
    ! [F: produc2669932201312201782od_c_a > a,A: set_Pr8357624050790843030od_c_a,B: set_a,A2: produc2669932201312201782od_c_a] :
      ( ( bij_be5632368444736963774_c_a_a @ F @ A @ B )
     => ( ( member5502040268208861279od_c_a @ A2 @ A )
       => ( member_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_693_bij__betw__apply,axiom,
    ! [F: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,A: set_Pr8357624050790843030od_c_a,B: set_li6436108459499378894od_b_c,A2: produc2669932201312201782od_c_a] :
      ( ( bij_be7860006274356004014od_b_c @ F @ A @ B )
     => ( ( member5502040268208861279od_c_a @ A2 @ A )
       => ( member6330420149250801815od_b_c @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_694_bij__betw__apply,axiom,
    ! [F: a > produc2669932201312201782od_c_a,A: set_a,B: set_Pr8357624050790843030od_c_a,A2: a] :
      ( ( bij_be644863384588287534od_c_a @ F @ A @ B )
     => ( ( member_a @ A2 @ A )
       => ( member5502040268208861279od_c_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_695_bij__betw__apply,axiom,
    ! [F: a > a,A: set_a,B: set_a,A2: a] :
      ( ( bij_betw_a_a @ F @ A @ B )
     => ( ( member_a @ A2 @ A )
       => ( member_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_696_bij__betw__apply,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,B: set_li6436108459499378894od_b_c,A2: a] :
      ( ( bij_be8783369614777182438od_b_c @ F @ A @ B )
     => ( ( member_a @ A2 @ A )
       => ( member6330420149250801815od_b_c @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_697_bij__betw__apply,axiom,
    ! [F: list_P903359562653991662od_b_c > produc2669932201312201782od_c_a,A: set_li6436108459499378894od_b_c,B: set_Pr8357624050790843030od_c_a,A2: list_P903359562653991662od_b_c] :
      ( ( bij_be5411586866304353214od_c_a @ F @ A @ B )
     => ( ( member6330420149250801815od_b_c @ A2 @ A )
       => ( member5502040268208861279od_c_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_698_bij__betw__apply,axiom,
    ! [F: list_P903359562653991662od_b_c > a,A: set_li6436108459499378894od_b_c,B: set_a,A2: list_P903359562653991662od_b_c] :
      ( ( bij_be3300351249680192134_b_c_a @ F @ A @ B )
     => ( ( member6330420149250801815od_b_c @ A2 @ A )
       => ( member_a @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_699_bij__betw__apply,axiom,
    ! [F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,A: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,A2: list_P903359562653991662od_b_c] :
      ( ( bij_be8534141360866068086od_b_c @ F @ A @ B )
     => ( ( member6330420149250801815od_b_c @ A2 @ A )
       => ( member6330420149250801815od_b_c @ ( F @ A2 ) @ B ) ) ) ).

% bij_betw_apply
thf(fact_700_from__FSM__language,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( lS_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) ) )
        = ( lS_a_b_c @ M3 @ Q4 ) ) ) ).

% from_FSM_language
thf(fact_701_from__FSM__language,axiom,
    ! [Q4: d,M3: fsm_d_b_c] :
      ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
     => ( ( lS_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) @ ( initial_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) ) )
        = ( lS_d_b_c @ M3 @ Q4 ) ) ) ).

% from_FSM_language
thf(fact_702_after__language__subset,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma2 @ Beta ) @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_703_after__language__subset,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma2 @ Beta ) @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_704_after__language__append__iff,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma2 @ Beta ) @ ( lS_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_705_after__language__append__iff,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma2 @ Beta ) @ ( lS_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_706_distinguish__prepend__initial,axiom,
    ! [M3: fsm_d_b_c,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( distinguishes_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
           => ( distinguishes_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Io1 ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Io22 ) @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_707_distinguish__prepend__initial,axiom,
    ! [M3: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io22: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( distinguishes_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io22 @ Io2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
           => ( distinguishes_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Io1 ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Io22 ) @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_708_distinguish__prepend,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Q14: produc2669932201312201782od_c_a,Io2: list_P903359562653991662od_b_c,Q2: produc2669932201312201782od_c_a,W: list_P903359562653991662od_b_c] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( distin4657727790478416823_a_b_c @ M3 @ ( after_2239399860513592206_a_b_c @ M3 @ Q14 @ Io2 ) @ ( after_2239399860513592206_a_b_c @ M3 @ Q2 @ Io2 ) @ W )
       => ( ( member5502040268208861279od_c_a @ Q14 @ ( states895637122477222528_a_b_c @ M3 ) )
         => ( ( member5502040268208861279od_c_a @ Q2 @ ( states895637122477222528_a_b_c @ M3 ) )
           => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q14 ) )
             => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_Pro3731892891411965979_a_b_c @ M3 @ Q2 ) )
               => ( distin4657727790478416823_a_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_709_distinguish__prepend,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Q14: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( distin2804555989863659119_c_b_c @ M3 @ ( after_4052058690717316294_c_b_c @ M3 @ Q14 @ Io2 ) @ ( after_4052058690717316294_c_b_c @ M3 @ Q2 @ Io2 ) @ W )
       => ( ( member6330420149250801815od_b_c @ Q14 @ ( states7681702920031268536_c_b_c @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M3 ) )
           => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q14 ) )
             => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M3 @ Q2 ) )
               => ( distin2804555989863659119_c_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_710_distinguish__prepend,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Io2: list_P903359562653991662od_b_c,Q2: d,W: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( distinguishes_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q14 @ Io2 ) @ ( after_d_b_c @ M3 @ Q2 @ Io2 ) @ W )
       => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
           => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ Q14 ) )
             => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_d_b_c @ M3 @ Q2 ) )
               => ( distinguishes_d_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_711_distinguish__prepend,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Io2: list_P903359562653991662od_b_c,Q2: a,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( distinguishes_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q14 @ Io2 ) @ ( after_a_b_c @ M3 @ Q2 @ Io2 ) @ W )
       => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
           => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ Q14 ) )
             => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M3 @ Q2 ) )
               => ( distinguishes_a_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ Io2 @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_712_bij__betw__imp__surj__on,axiom,
    ! [F: a > list_P903359562653991662od_b_c,A: set_a,B: set_li6436108459499378894od_b_c] :
      ( ( bij_be8783369614777182438od_b_c @ F @ A @ B )
     => ( ( image_8656872703560917237od_b_c @ F @ A )
        = B ) ) ).

% bij_betw_imp_surj_on
thf(fact_713_foldl__Cons,axiom,
    ! [F: produc4534891796109904283_b_c_e > list_P903359562653991662od_b_c > produc4534891796109904283_b_c_e,A2: produc4534891796109904283_b_c_e,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( foldl_2934561762154836916od_b_c @ F @ A2 @ ( cons_l342771267123639716od_b_c @ X @ Xs ) )
      = ( foldl_2934561762154836916od_b_c @ F @ ( F @ A2 @ X ) @ Xs ) ) ).

% foldl_Cons
thf(fact_714_after__transition,axiom,
    ! [M3: fsm_d_b_c,Q4: d,X: b,Y: c,Q8: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member4231278564905875615od_c_d @ ( produc3045323491883059558od_c_d @ Q4 @ ( produc3440865926910568064od_c_d @ X @ ( product_Pair_c_d @ Y @ Q8 ) ) ) @ ( transitions_d_b_c @ M3 ) )
       => ( ( after_d_b_c @ M3 @ Q4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q8 ) ) ) ).

% after_transition
thf(fact_715_after__transition,axiom,
    ! [M3: fsm_a_b_c,Q4: a,X: b,Y: c,Q8: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q4 @ ( produc3440865914000881661od_c_a @ X @ ( product_Pair_c_a @ Y @ Q8 ) ) ) @ ( transitions_a_b_c @ M3 ) )
       => ( ( after_a_b_c @ M3 @ Q4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q8 ) ) ) ).

% after_transition
thf(fact_716_ttc,axiom,
    ( ttc
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ ( interm26832183538952475_a_b_c @ m1 @ qTarget @ k ) ) ) ).

% ttc
thf(fact_717_after__distinguishes__language,axiom,
    ! [M12: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
         => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Alpha ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Beta ) @ Gamma2 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_718_after__distinguishes__language,axiom,
    ! [M12: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
         => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Alpha ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Beta ) @ Gamma2 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_719_pass__io__set__def,axiom,
    ( pass_io_set_a_b_c
    = ( ^ [M: fsm_a_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io5: list_P903359562653991662od_b_c,X2: b,Y2: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ Ios2 )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_720_pass__io__set__def,axiom,
    ( pass_io_set_d_b_c
    = ( ^ [M: fsm_d_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io5: list_P903359562653991662od_b_c,X2: b,Y2: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ Ios2 )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_721_pass__io__set__maximal__def,axiom,
    ( pass_i5868551379204665570_a_b_c
    = ( ^ [M: fsm_a_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io5: list_P903359562653991662od_b_c,X2: b,Y2: c,Io6: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io6 ) ) @ Ios2 )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
             => ? [Io7: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) @ Io7 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_722_pass__io__set__maximal__def,axiom,
    ( pass_i4210463151059506021_d_b_c
    = ( ^ [M: fsm_d_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io5: list_P903359562653991662od_b_c,X2: b,Y2: c,Io6: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io6 ) ) @ Ios2 )
         => ! [Y4: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) ) @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
             => ? [Io7: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y4 ) @ nil_Product_prod_b_c ) @ Io7 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_723_le__zero__eq,axiom,
    ! [N3: nat] :
      ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
      = ( N3 = zero_zero_nat ) ) ).

% le_zero_eq
thf(fact_724_handle__state__cover__static__applies__dist__sets,axiom,
    ! [Q4: produc2669932201312201782od_c_a,M12: fsm_Pr6425204305901329755_a_b_c,Dist_fun: nat > produc2669932201312201782od_c_a > prefix425356687782099470od_b_c,V: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,Cg_initial2: fsm_Pr6425204305901329755_a_b_c > prefix425356687782099470od_b_c > e,Cg_insert2: e > list_P903359562653991662od_b_c > e,Cg_lookup2: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c] :
      ( ( member5502040268208861279od_c_a @ Q4 @ ( reacha1389639598965321787_a_b_c @ M12 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( Dist_fun @ zero_zero_nat @ Q4 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm1749484760467432131_b_c_e @ Dist_fun @ M12 @ V @ Cg_initial2 @ Cg_insert2 @ Cg_lookup2 ) ) @ ( V @ Q4 ) ) ) ) ) ).

% handle_state_cover_static_applies_dist_sets
thf(fact_725_handle__state__cover__static__applies__dist__sets,axiom,
    ! [Q4: list_P903359562653991662od_b_c,M12: fsm_li6801133765522507155_c_b_c,Dist_fun: nat > list_P903359562653991662od_b_c > prefix425356687782099470od_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Cg_initial2: fsm_li6801133765522507155_c_b_c > prefix425356687782099470od_b_c > e,Cg_insert2: e > list_P903359562653991662od_b_c > e,Cg_lookup2: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q4 @ ( reacha8116992257183400179_c_b_c @ M12 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( Dist_fun @ zero_zero_nat @ Q4 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm3817193849425987467_b_c_e @ Dist_fun @ M12 @ V @ Cg_initial2 @ Cg_insert2 @ Cg_lookup2 ) ) @ ( V @ Q4 ) ) ) ) ) ).

% handle_state_cover_static_applies_dist_sets
thf(fact_726_handle__state__cover__static__applies__dist__sets,axiom,
    ! [Q4: a,M12: fsm_a_b_c,Dist_fun: nat > a > prefix425356687782099470od_b_c,V: a > list_P903359562653991662od_b_c,Cg_initial2: fsm_a_b_c > prefix425356687782099470od_b_c > e,Cg_insert2: e > list_P903359562653991662od_b_c > e,Cg_lookup2: e > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c] :
      ( ( member_a @ Q4 @ ( reacha1620305530751930115_a_b_c @ M12 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( Dist_fun @ zero_zero_nat @ Q4 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ ( produc1447154562020694007_b_c_e @ ( interm1055298885954647291_b_c_e @ Dist_fun @ M12 @ V @ Cg_initial2 @ Cg_insert2 @ Cg_lookup2 ) ) @ ( V @ Q4 ) ) ) ) ) ).

% handle_state_cover_static_applies_dist_sets
thf(fact_727_merge__list_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ( X
       != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ nil_li8071162985807626740od_b_c ) )
     => ( ! [L4: list_P903359562653991662od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ ( cons_l342771267123639716od_b_c @ L4 @ nil_li8071162985807626740od_b_c ) ) )
       => ( ! [La: list_P903359562653991662od_b_c,Acc2: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ La @ Acc2 ) @ nil_li8071162985807626740od_b_c ) )
         => ( ! [La: list_P903359562653991662od_b_c,Acc2: list_l8907847357763382004od_b_c,L4: list_P903359562653991662od_b_c] :
                ( X
               != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ La @ Acc2 ) @ ( cons_l342771267123639716od_b_c @ L4 @ nil_li8071162985807626740od_b_c ) ) )
           => ~ ! [Acc2: list_l8907847357763382004od_b_c,L12: list_P903359562653991662od_b_c,L22: list_P903359562653991662od_b_c,Ls: list_l8907847357763382004od_b_c] :
                  ( X
                 != ( produc2983116027154973335od_b_c @ Acc2 @ ( cons_l342771267123639716od_b_c @ L12 @ ( cons_l342771267123639716od_b_c @ L22 @ Ls ) ) ) ) ) ) ) ) ).

% merge_list.cases
thf(fact_728_shortest__list_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ( X != nil_li8071162985807626740od_b_c )
     => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ).

% shortest_list.cases
thf(fact_729_traces__to__check_Osimps_I1_J,axiom,
    ! [M3: fsm_a_b_c,Q4: a] :
      ( ( interm26832183538952475_a_b_c @ M3 @ Q4 @ zero_zero_nat )
      = nil_li8071162985807626740od_b_c ) ).

% traces_to_check.simps(1)
thf(fact_730_zero__le,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_le
thf(fact_731_preserves__divergence__subset,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_d_b_c,B: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( preser261684820601417592_b_c_d @ M12 @ M22 @ B )
     => ( ( ord_le282488521294790766od_b_c @ A @ B )
       => ( preser261684820601417592_b_c_d @ M12 @ M22 @ A ) ) ) ).

% preserves_divergence_subset
thf(fact_732_equivalence__preserves__divergence,axiom,
    ! [M3: fsm_a_b_c,I: fsm_a_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( observable_a_b_c @ I )
       => ( ( ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) )
            = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
         => ( preser261684820601417589_b_c_a @ M3 @ I @ A ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_733_equivalence__preserves__divergence,axiom,
    ! [M3: fsm_d_b_c,I: fsm_a_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( observable_a_b_c @ I )
       => ( ( ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) )
            = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
         => ( preser4725570932485813170_b_c_a @ M3 @ I @ A ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_734_equivalence__preserves__divergence,axiom,
    ! [M3: fsm_d_b_c,I: fsm_d_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( observable_d_b_c @ I )
       => ( ( ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) )
            = ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
         => ( preser4725570932485813173_b_c_d @ M3 @ I @ A ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_735_equivalence__preserves__divergence,axiom,
    ! [M3: fsm_a_b_c,I: fsm_d_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( observable_d_b_c @ I )
       => ( ( ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) )
            = ( lS_d_b_c @ I @ ( initial_d_b_c @ I ) ) )
         => ( preser261684820601417592_b_c_d @ M3 @ I @ A ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_736_delete__aux_Ocases,axiom,
    ! [X: produc4983050515642857530_b_c_e] :
      ( ! [K3: prefix425356687782099470od_b_c] :
          ( X
         != ( produc3397272950601485866_b_c_e @ K3 @ nil_Pr3869772438633755809_b_c_e ) )
     => ~ ! [K3: prefix425356687782099470od_b_c,K4: prefix425356687782099470od_b_c,V2: e,Xs2: list_P268689088907702561_b_c_e] :
            ( X
           != ( produc3397272950601485866_b_c_e @ K3 @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ K4 @ V2 ) @ Xs2 ) ) ) ) ).

% delete_aux.cases
thf(fact_737_delete__aux_Ocases,axiom,
    ! [X: produc6475121930738208726od_b_c] :
      ( ! [K3: b] :
          ( X
         != ( produc561751498933632326od_b_c @ K3 @ nil_Product_prod_b_c ) )
     => ~ ! [K3: b,K4: b,V2: c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc561751498933632326od_b_c @ K3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K4 @ V2 ) @ Xs2 ) ) ) ) ).

% delete_aux.cases
thf(fact_738_state__cover__transition__converges,axiom,
    ! [M3: fsm_Pr379724744552003854_b_c_e,V: produc2669932201312201782od_c_a > list_P268689088907702561_b_c_e,T: produc5653889938759785317od_c_a] :
      ( ( observ3091655274719039154_b_c_e @ M3 )
     => ( ( state_785075175243941690_b_c_e @ M3 @ V )
       => ( ( member7595321081310302990od_c_a @ T @ ( transi1688854557942799871_b_c_e @ M3 ) )
         => ( ( member5502040268208861279od_c_a @ ( produc2492963354056456385od_c_a @ T ) @ ( reacha6670210832477656942_b_c_e @ M3 ) )
           => ( conver2286499056624411077_b_c_e @ M3 @ ( append3015380627477509558_b_c_e @ ( V @ ( produc2492963354056456385od_c_a @ T ) ) @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ ( produc6205223780958520912od_c_a @ ( produc662025799001735939od_c_a @ T ) ) @ ( produc1981699559789616183od_c_a @ ( produc2682516862346696850od_c_a @ ( produc662025799001735939od_c_a @ T ) ) ) ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( V @ ( produc8430726696110712185od_c_a @ ( produc2682516862346696850od_c_a @ ( produc662025799001735939od_c_a @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_739_state__cover__transition__converges,axiom,
    ! [M3: fsm_a_8518373703003225814_b_c_e,V: a > list_P268689088907702561_b_c_e,T: produc8570131207859728997od_e_a] :
      ( ( observ7286853435796284794_b_c_e @ M3 )
     => ( ( state_8320733454665479682_b_c_e @ M3 @ V )
       => ( ( member8958573442437681166od_e_a @ T @ ( transi8235709246594610119_b_c_e @ M3 ) )
         => ( ( member_a @ ( produc141068547207231937od_e_a @ T ) @ ( reacha4051624011855102518_b_c_e @ M3 ) )
           => ( conver3658120378338990477_b_c_e @ M3 @ ( append3015380627477509558_b_c_e @ ( V @ ( produc141068547207231937od_e_a @ T ) ) @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ ( produc2488811074921770520od_e_a @ ( produc7077781598552879107od_e_a @ T ) ) @ ( product_fst_e_a @ ( produc3877390521829078618od_e_a @ ( produc7077781598552879107od_e_a @ T ) ) ) ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( V @ ( product_snd_e_a @ ( produc3877390521829078618od_e_a @ ( produc7077781598552879107od_e_a @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_740_state__cover__transition__converges,axiom,
    ! [M3: fsm_li553205354899133766_b_c_e,V: list_P903359562653991662od_b_c > list_P268689088907702561_b_c_e,T: produc4773341515281486821od_b_c] :
      ( ( observ3923965058616338794_b_c_e @ M3 )
     => ( ( state_500947992327884274_b_c_e @ M3 @ V )
       => ( ( member106767767543922318od_b_c @ T @ ( transi8805280651617622071_b_c_e @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc6587623637658611777od_b_c @ T ) @ ( reacha9056568326447799334_b_c_e @ M3 ) )
           => ( conver2126987151776935165_b_c_e @ M3 @ ( append3015380627477509558_b_c_e @ ( V @ ( produc6587623637658611777od_b_c @ T ) ) @ ( cons_P1373155238876956753_b_c_e @ ( produc2511600812177743883_b_c_e @ ( produc3845056220139801480od_b_c @ ( produc4469056017158303875od_b_c @ T ) ) @ ( produc3578049712875638895od_b_c @ ( produc539319079932770506od_b_c @ ( produc4469056017158303875od_b_c @ T ) ) ) ) @ nil_Pr3869772438633755809_b_c_e ) ) @ ( V @ ( produc6665304927307347121od_b_c @ ( produc539319079932770506od_b_c @ ( produc4469056017158303875od_b_c @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_741_state__cover__transition__converges,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,V: produc2669932201312201782od_c_a > list_P903359562653991662od_b_c,T: produc1415087868921929270od_c_a] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( state_1238012481214864903_a_b_c @ M3 @ V )
       => ( ( member6671621370117864543od_c_a @ T @ ( transi5559090763681538380_a_b_c @ M3 ) )
         => ( ( member5502040268208861279od_c_a @ ( produc9128270418056373650od_c_a @ T ) @ ( reacha1389639598965321787_a_b_c @ M3 ) )
           => ( conver5325162639162954770_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ ( V @ ( produc9128270418056373650od_c_a @ T ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc987535659865005857od_c_a @ ( produc717598727938249940od_c_a @ T ) ) @ ( produc7173261134821384633od_c_a @ ( produc6682828060051002979od_c_a @ ( produc717598727938249940od_c_a @ T ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( produc4398916234287704827od_c_a @ ( produc6682828060051002979od_c_a @ ( produc717598727938249940od_c_a @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_742_state__cover__transition__converges,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,T: produc596031391177498678od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( state_2362830510734323903_c_b_c @ M3 @ V )
       => ( ( member8124909232574984543od_b_c @ T @ ( transi3161963839906981764_c_b_c @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc5084291339869529746od_b_c @ T ) @ ( reacha8116992257183400179_c_b_c @ M3 ) )
           => ( conver6852411701971397450_c_b_c @ M3 @ ( append2547753245680614915od_b_c @ ( V @ ( produc5084291339869529746od_b_c @ T ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc4488652850390612441od_b_c @ ( produc829356566976367572od_b_c @ T ) ) @ ( produc5388473464130769137od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( produc8475728678562477363od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_743_state__cover__transition__converges,axiom,
    ! [M3: fsm_d_b_c,V: d > list_P903359562653991662od_b_c,T: produc1399170498009216118od_c_d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( state_6014242345326633810_d_b_c @ M3 @ V )
       => ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
         => ( ( member_d @ ( produc1508465569166014290od_c_d @ T ) @ ( reacha9185589339461546374_d_b_c @ M3 ) )
           => ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ ( V @ ( produc1508465569166014290od_c_d @ T ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_744_state__cover__transition__converges,axiom,
    ! [M3: fsm_Pr1886043760914421514_a_a_b,V: product_prod_c_a > list_P1467974523212632366od_a_b,T: produc3205353004677322104od_c_a] :
      ( ( observ2964502264774598958_a_a_b @ M3 )
     => ( ( state_7248828479493717430_a_a_b @ M3 @ V )
       => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
         => ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( reacha5035603111973943274_a_a_b @ M3 ) )
           => ( conver1569733173216426433_a_a_b @ M3 @ ( append5335208823350062147od_a_b @ ( V @ ( produc8171714036265584980od_c_a @ T ) ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) @ nil_Product_prod_a_b ) ) @ ( V @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_745_state__cover__transition__converges,axiom,
    ! [M3: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,T: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( state_7672330573471793359_a_b_c @ M3 @ V )
       => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
         => ( ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( reacha1620305530751930115_a_b_c @ M3 ) )
           => ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ ( V @ ( produc4225943634317630866od_c_a @ T ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_746_minimally__distinguishes__no__prefix,axiom,
    ! [M3: fsm_d_b_c,U: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ W ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ W ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( minima7808819671940975144_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ U ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_747_minimally__distinguishes__no__prefix,axiom,
    ! [M3: fsm_a_b_c,U: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ W ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ W ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( minima243535863231358885_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ U ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_748_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M3: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
     => ( converge_a_b_c @ M3 @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_749_converge__refl,axiom,
    ! [Alpha: list_P903359562653991662od_b_c,M3: fsm_d_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
     => ( converge_d_b_c @ M3 @ Alpha @ Alpha ) ) ).

% converge_refl
thf(fact_750_converge__append__iff,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( converge_a_b_c @ M3 @ Alpha @ Beta )
       => ( ( converge_a_b_c @ M3 @ Gamma2 @ ( append2547753245680614915od_b_c @ Alpha @ Omega ) )
          = ( converge_a_b_c @ M3 @ Gamma2 @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_751_converge__append__iff,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( converge_d_b_c @ M3 @ Alpha @ Beta )
       => ( ( converge_d_b_c @ M3 @ Gamma2 @ ( append2547753245680614915od_b_c @ Alpha @ Omega ) )
          = ( converge_d_b_c @ M3 @ Gamma2 @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_752_converge_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_a_b_c @ X @ Xa3 @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_753_converge_Oelims_I3_J,axiom,
    ! [X: fsm_d_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_d_b_c @ X @ Xa3 @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
            = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_754_converge_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ X @ Xa3 @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
          = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_755_converge_Oelims_I2_J,axiom,
    ! [X: fsm_d_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_d_b_c @ X @ Xa3 @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
          = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_756_converge_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_a_b_c @ X @ Xa3 @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_757_converge_Oelims_I1_J,axiom,
    ! [X: fsm_d_b_c,Xa3: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_d_b_c @ X @ Xa3 @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa3 @ ( 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 ) @ Xa3 ) )
            = ( lS_d_b_c @ X @ ( after_d_b_c @ X @ ( initial_d_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_758_converge_Osimps,axiom,
    ( converge_a_b_c
    = ( ^ [M: fsm_a_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
          & ( ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Pi ) )
            = ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_759_converge_Osimps,axiom,
    ( converge_d_b_c
    = ( ^ [M: fsm_d_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
          & ( ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Pi ) )
            = ( lS_d_b_c @ M @ ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_760_converge__trans__2_I1_J,axiom,
    ! [M3: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( converge_a_b_c @ M3 @ U @ V3 )
         => ( ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_761_converge__trans__2_I1_J,axiom,
    ! [M3: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( converge_d_b_c @ M3 @ U @ V3 )
         => ( ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_762_converge__trans__2_I2_J,axiom,
    ! [M3: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( converge_a_b_c @ M3 @ U @ V3 )
         => ( ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_763_converge__trans__2_I2_J,axiom,
    ! [M3: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( converge_d_b_c @ M3 @ U @ V3 )
         => ( ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_764_converge__trans__2_I3_J,axiom,
    ! [M3: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( converge_a_b_c @ M3 @ U @ V3 )
         => ( ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_765_converge__trans__2_I3_J,axiom,
    ! [M3: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( converge_d_b_c @ M3 @ U @ V3 )
         => ( ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_766_minimally__distinguishes__ex,axiom,
    ! [Q14: d,M3: fsm_d_b_c,Q2: d] :
      ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
     => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
       => ( ( ( lS_d_b_c @ M3 @ Q14 )
           != ( lS_d_b_c @ M3 @ Q2 ) )
         => ~ ! [V2: list_P903359562653991662od_b_c] :
                ~ ( minima7808819671940975144_d_b_c @ M3 @ Q14 @ Q2 @ V2 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_767_minimally__distinguishes__ex,axiom,
    ! [Q14: a,M3: fsm_a_b_c,Q2: a] :
      ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
     => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
       => ( ( ( lS_a_b_c @ M3 @ Q14 )
           != ( lS_a_b_c @ M3 @ Q2 ) )
         => ~ ! [V2: list_P903359562653991662od_b_c] :
                ~ ( minima243535863231358885_a_b_c @ M3 @ Q14 @ Q2 @ V2 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_768_diverge__prefix,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ~ ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) )
           => ~ ( converge_a_b_c @ M3 @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_769_diverge__prefix,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ~ ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) )
           => ~ ( converge_d_b_c @ M3 @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_770_converge__append,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( converge_a_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
           => ( converge_a_b_c @ M3 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) ) ) ) ) ) ).

% converge_append
thf(fact_771_converge__append,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( converge_d_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
           => ( converge_d_b_c @ M3 @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) ) ) ) ) ) ).

% converge_append
thf(fact_772_converge__extend,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( converge_a_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_773_converge__extend,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( converge_d_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_774_converge__append__language__iff,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( converge_a_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_775_converge__append__language__iff,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( converge_d_b_c @ M3 @ Alpha @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma2 ) @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_776_preserves__divergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa3: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser261684820601417592_b_c_d @ X @ Xa3 @ 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 ) )
           => ! [Xa: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ~ ( converge_a_b_c @ X @ X3 @ Xa )
                 => ~ ( converge_d_b_c @ Xa3 @ X3 @ Xa ) ) ) ) ) ).

% preserves_divergence.elims(3)
thf(fact_777_preserves__divergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa3: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser261684820601417592_b_c_d @ X @ Xa3 @ Xb )
     => ! [X5: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X5 @ ( 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 @ X5 @ Xa2 )
               => ~ ( converge_d_b_c @ Xa3 @ X5 @ Xa2 ) ) ) ) ) ).

% preserves_divergence.elims(2)
thf(fact_778_preserves__divergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa3: fsm_d_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser261684820601417592_b_c_d @ X @ Xa3 @ 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 @ Xa3 @ X2 @ Y2 ) ) ) ) ) ) ) ).

% preserves_divergence.elims(1)
thf(fact_779_preserves__divergence_Osimps,axiom,
    ( preser261684820601417592_b_c_d
    = ( ^ [M1: fsm_a_b_c,M2: fsm_d_b_c,A4: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ A4 ) )
         => ! [Y2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ A4 ) )
             => ( ~ ( converge_a_b_c @ M1 @ X2 @ Y2 )
               => ~ ( converge_d_b_c @ M2 @ X2 @ Y2 ) ) ) ) ) ) ).

% preserves_divergence.simps
thf(fact_780_state__cover__assignment__diverges,axiom,
    ! [M3: fsm_d_b_c,F: d > list_P903359562653991662od_b_c,Q14: d,Q2: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( state_6014242345326633810_d_b_c @ M3 @ F )
         => ( ( member_d @ Q14 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
           => ( ( member_d @ Q2 @ ( reacha9185589339461546374_d_b_c @ M3 ) )
             => ( ( Q14 != Q2 )
               => ~ ( converge_d_b_c @ M3 @ ( F @ Q14 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_781_state__cover__assignment__diverges,axiom,
    ! [M3: fsm_a_b_c,F: a > list_P903359562653991662od_b_c,Q14: a,Q2: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( state_7672330573471793359_a_b_c @ M3 @ F )
         => ( ( member_a @ Q14 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
           => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M3 ) )
             => ( ( Q14 != Q2 )
               => ~ ( converge_a_b_c @ M3 @ ( F @ Q14 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_782_convergence__minimal,axiom,
    ! [M3: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_a_b_c @ M3 )
     => ( ( observable_a_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
           => ( ( converge_a_b_c @ M3 @ Alpha @ Beta )
              = ( ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Alpha )
                = ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_783_convergence__minimal,axiom,
    ! [M3: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_d_b_c @ M3 )
     => ( ( observable_d_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
           => ( ( converge_d_b_c @ M3 @ Alpha @ Beta )
              = ( ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Alpha )
                = ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_784_distinguish__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ U ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ V3 ) @ Gamma2 )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma2 ) @ T4 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma2 ) @ T4 )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                   => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_785_distinguish__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ U ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ V3 ) @ Gamma2 )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma2 ) @ T4 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma2 ) @ T4 )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                   => ~ ( converge_d_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_786_distinguish__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ U ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ V3 ) @ Gamma2 )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma2 ) @ T4 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma2 ) @ T4 )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                   => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_787_distinguish__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ U ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ V3 ) @ Gamma2 )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma2 ) @ T4 )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma2 ) @ T4 )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                   => ~ ( converge_d_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_788_clearjunk_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [P4: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ P4 @ Ps ) ) ) ).

% clearjunk.cases
thf(fact_789_map__default_Ocases,axiom,
    ! [X: produc2009451851958091931od_b_c] :
      ( ! [K3: b,V2: c,F4: c > c] :
          ( X
         != ( produc1384939585547926677od_b_c @ K3 @ ( produc3590379597927054951od_b_c @ V2 @ ( produc1101678828523717360od_b_c @ F4 @ nil_Product_prod_b_c ) ) ) )
     => ~ ! [K3: b,V2: c,F4: c > c,P4: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1384939585547926677od_b_c @ K3 @ ( produc3590379597927054951od_b_c @ V2 @ ( produc1101678828523717360od_b_c @ F4 @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps ) ) ) ) ) ) ).

% map_default.cases
thf(fact_790_map__entry_Ocases,axiom,
    ! [X: produc6452300523622238572od_b_c] :
      ( ! [K3: b,F4: c > c] :
          ( X
         != ( produc7015427828931889894od_b_c @ K3 @ ( produc1101678828523717360od_b_c @ F4 @ nil_Product_prod_b_c ) ) )
     => ~ ! [K3: b,F4: c > c,P4: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7015427828931889894od_b_c @ K3 @ ( produc1101678828523717360od_b_c @ F4 @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps ) ) ) ) ) ).

% map_entry.cases
thf(fact_791_get__distinguishing__sequence__from__ofsm__tables__is__minimally__distinguishing,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( minima243535863231358885_a_b_c @ M3 @ Q14 @ Q2 @ ( get_di2280862616223094331_a_b_c @ M3 @ Q14 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_minimally_distinguishing
thf(fact_792_get__distinguishing__sequence__from__ofsm__tables__is__minimally__distinguishing,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Q2: d] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
           => ( ( Q14 != Q2 )
             => ( minima7808819671940975144_d_b_c @ M3 @ Q14 @ Q2 @ ( get_di622774388077934782_d_b_c @ M3 @ Q14 @ Q2 ) ) ) ) ) ) ) ).

% get_distinguishing_sequence_from_ofsm_tables_is_minimally_distinguishing
thf(fact_793_distinguish__converge__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
           => ( ( member6330420149250801815od_b_c @ V4 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
             => ( ( converge_d_b_c @ M12 @ U @ U2 )
               => ( ( converge_d_b_c @ M12 @ V3 @ V4 )
                 => ( ( converge_a_b_c @ M22 @ U @ U2 )
                   => ( ( converge_a_b_c @ M22 @ V3 @ V4 )
                     => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ U ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ V3 ) @ Gamma2 )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma2 ) @ T4 )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V4 @ Gamma2 ) @ T4 )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                             => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_794_distinguish__converge__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
           => ( ( member6330420149250801815od_b_c @ V4 @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
             => ( ( converge_d_b_c @ M12 @ U @ U2 )
               => ( ( converge_d_b_c @ M12 @ V3 @ V4 )
                 => ( ( converge_d_b_c @ M22 @ U @ U2 )
                   => ( ( converge_d_b_c @ M22 @ V3 @ V4 )
                     => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ U ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ V3 ) @ Gamma2 )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma2 ) @ T4 )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V4 @ Gamma2 ) @ T4 )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                             => ~ ( converge_d_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_795_distinguish__converge__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
           => ( ( member6330420149250801815od_b_c @ V4 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
             => ( ( converge_a_b_c @ M12 @ U @ U2 )
               => ( ( converge_a_b_c @ M12 @ V3 @ V4 )
                 => ( ( converge_a_b_c @ M22 @ U @ U2 )
                   => ( ( converge_a_b_c @ M22 @ V3 @ V4 )
                     => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ U ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ V3 ) @ Gamma2 )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma2 ) @ T4 )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V4 @ Gamma2 ) @ T4 )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                             => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_796_distinguish__converge__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_d_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T4: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( member6330420149250801815od_b_c @ U2 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
           => ( ( member6330420149250801815od_b_c @ V4 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
             => ( ( converge_a_b_c @ M12 @ U @ U2 )
               => ( ( converge_a_b_c @ M12 @ V3 @ V4 )
                 => ( ( converge_d_b_c @ M22 @ U @ U2 )
                   => ( ( converge_d_b_c @ M22 @ V3 @ V4 )
                     => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ U ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ V3 ) @ Gamma2 )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U2 @ Gamma2 ) @ T4 )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V4 @ Gamma2 ) @ T4 )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                             => ~ ( converge_d_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_797_after__distinguishes__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Alpha ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Beta ) @ Gamma2 )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_798_after__distinguishes__diverge,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_d_b_c @ M12 @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Alpha ) @ ( after_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) @ Beta ) @ Gamma2 )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_d_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_799_after__distinguishes__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_a_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Alpha ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Beta ) @ Gamma2 )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_800_after__distinguishes__diverge,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_d_b_c,Alpha: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma2: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M12 @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Alpha ) @ ( after_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) @ Beta ) @ Gamma2 )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_d_b_c @ M22 @ Alpha @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_801_minimally__distinguishes__after__append,axiom,
    ! [M3: fsm_Pr6425204305901329755_a_b_c,Q14: produc2669932201312201782od_c_a,Q2: produc2669932201312201782od_c_a,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observ6303369326153519487_a_b_c @ M3 )
     => ( ( minima5859589491558189769_a_b_c @ M3 )
       => ( ( member5502040268208861279od_c_a @ Q14 @ ( states895637122477222528_a_b_c @ M3 ) )
         => ( ( member5502040268208861279od_c_a @ Q2 @ ( states895637122477222528_a_b_c @ M3 ) )
           => ( ( minima2249419514473181917_a_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima2249419514473181917_a_b_c @ M3 @ ( after_2239399860513592206_a_b_c @ M3 @ Q14 @ W ) @ ( after_2239399860513592206_a_b_c @ M3 @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_802_minimally__distinguishes__after__append,axiom,
    ! [M3: fsm_li6801133765522507155_c_b_c,Q14: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M3 )
     => ( ( minima1987601567150520449_c_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ Q14 @ ( states7681702920031268536_c_b_c @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M3 ) )
           => ( ( minima9089413714839006869_c_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima9089413714839006869_c_b_c @ M3 @ ( after_4052058690717316294_c_b_c @ M3 @ Q14 @ W ) @ ( after_4052058690717316294_c_b_c @ M3 @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_803_minimally__distinguishes__after__append,axiom,
    ! [M3: fsm_a_b_c,Q14: a,Q2: a,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( member_a @ Q14 @ ( states_a_b_c @ M3 ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M3 ) )
           => ( ( minima243535863231358885_a_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M3 @ ( after_a_b_c @ M3 @ Q14 @ W ) @ ( after_a_b_c @ M3 @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_804_minimally__distinguishes__after__append,axiom,
    ! [M3: fsm_d_b_c,Q14: d,Q2: d,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( member_d @ Q14 @ ( states_d_b_c @ M3 ) )
         => ( ( member_d @ Q2 @ ( states_d_b_c @ M3 ) )
           => ( ( minima7808819671940975144_d_b_c @ M3 @ Q14 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima7808819671940975144_d_b_c @ M3 @ ( after_d_b_c @ M3 @ Q14 @ W ) @ ( after_d_b_c @ M3 @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_805_minimally__distinguishes__after__append__initial,axiom,
    ! [M3: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M3 )
     => ( ( minimal_a_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) ) )
           => ( ( minima243535863231358885_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ U ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M3 @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_a_b_c @ M3 @ ( initial_a_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_806_minimally__distinguishes__after__append__initial,axiom,
    ! [M3: fsm_d_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_d_b_c @ M3 )
     => ( ( minimal_d_b_c @ M3 )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) ) )
           => ( ( minima7808819671940975144_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ U ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima7808819671940975144_d_b_c @ M3 @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_d_b_c @ M3 @ ( initial_d_b_c @ M3 ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_807_subset__after__subset,axiom,
    ! [T23: prefix425356687782099470od_b_c,T12: prefix425356687782099470od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ T23 ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T23 @ Xs ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Xs ) ) ) ) ).

% subset_after_subset
thf(fact_808_n__lists__Nil,axiom,
    ! [N3: nat] :
      ( ( ( N3 = zero_zero_nat )
       => ( ( n_list5224936925692304502od_b_c @ N3 @ nil_Product_prod_b_c )
          = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
      & ( ( N3 != zero_zero_nat )
       => ( ( n_list5224936925692304502od_b_c @ N3 @ nil_Product_prod_b_c )
          = nil_li8071162985807626740od_b_c ) ) ) ).

% n_lists_Nil
thf(fact_809_after__set__Cons,axiom,
    ! [Gamma2: list_P903359562653991662od_b_c,T4: prefix425356687782099470od_b_c,Alpha: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Gamma2 @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T4 @ Alpha ) ) )
     => ( ( Gamma2 != nil_Product_prod_b_c )
       => ( member6330420149250801815od_b_c @ Alpha @ ( prefix9085958534787526401od_b_c @ T4 ) ) ) ) ).

% after_set_Cons
thf(fact_810_is__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) )
     => ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ nil_Product_prod_b_c ) )
       => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) ) ) ) ).

% is_prefix.cases
thf(fact_811_is__prefix_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ! [Uu: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ Uu ) )
     => ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ nil_li8071162985807626740od_b_c ) )
       => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) ) ) ) ).

% is_prefix.cases
thf(fact_812_linear__order__from__list__position_H_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_813_linear__order__from__list__position_H_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ( X != nil_li8071162985807626740od_b_c )
     => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_814_find__index_Ocases,axiom,
    ! [X: produc7816210539016439438od_b_c] :
      ( ! [F4: product_prod_b_c > $o] :
          ( X
         != ( produc7392021306980666816od_b_c @ F4 @ nil_Product_prod_b_c ) )
     => ~ ! [F4: product_prod_b_c > $o,X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7392021306980666816od_b_c @ F4 @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) ) ) ) ).

% find_index.cases
thf(fact_815_find__index_Ocases,axiom,
    ! [X: produc6759551401623590298od_b_c] :
      ( ! [F4: list_P903359562653991662od_b_c > $o] :
          ( X
         != ( produc2445333656321382604od_b_c @ F4 @ nil_li8071162985807626740od_b_c ) )
     => ~ ! [F4: list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2445333656321382604od_b_c @ F4 @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) ) ) ) ).

% find_index.cases
thf(fact_816_set__Nil,axiom,
    ! [T: prefix425356687782099470od_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( prefix9085958534787526401od_b_c @ T ) ) ).

% set_Nil
thf(fact_817_set__prefix,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,T4: prefix425356687782099470od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) @ ( prefix9085958534787526401od_b_c @ T4 ) )
     => ( member6330420149250801815od_b_c @ Xs @ ( prefix9085958534787526401od_b_c @ T4 ) ) ) ).

% set_prefix
thf(fact_818_finite__tree__set__eq,axiom,
    ! [T1: prefix425356687782099470od_b_c,T22: prefix425356687782099470od_b_c] :
      ( ( ( prefix9085958534787526401od_b_c @ T1 )
        = ( prefix9085958534787526401od_b_c @ T22 ) )
     => ( ( prefix6767660319289835678od_b_c @ T1 )
       => ( T1 = T22 ) ) ) ).

% finite_tree_set_eq
thf(fact_819_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_820_find__remove_H_Ocases,axiom,
    ! [X: produc5559707038353031495od_b_c] :
      ( ! [P3: product_prod_b_c > $o,Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc1005531610559690873od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) ) )
     => ~ ! [P3: product_prod_b_c > $o,X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Prev: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1005531610559690873od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_821_find__remove_H_Ocases,axiom,
    ! [X: produc3649958337673990605od_b_c] :
      ( ! [P3: list_P903359562653991662od_b_c > $o,Uu: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc7261280145910222719od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ Uu ) ) )
     => ~ ! [P3: list_P903359562653991662od_b_c > $o,X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Prev: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc7261280145910222719od_b_c @ P3 @ ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_822_longest__common__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y3: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y3 @ Ys2 ) ) )
     => ( ! [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_823_longest__common__prefix_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Y3: list_P903359562653991662od_b_c,Ys2: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ Y3 @ Ys2 ) ) )
     => ( ! [Uv: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ Uv ) )
       => ~ ! [Uu: list_l8907847357763382004od_b_c] :
              ( X
             != ( produc2983116027154973335od_b_c @ Uu @ nil_li8071162985807626740od_b_c ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_824_subset__eq__mset__impl_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys2 ) )
     => ~ ! [X3: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Ys2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X3 @ Xs2 ) @ Ys2 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_825_subset__eq__mset__impl_Ocases,axiom,
    ! [X: produc464288617779538343od_b_c] :
      ( ! [Ys2: list_l8907847357763382004od_b_c] :
          ( X
         != ( produc2983116027154973335od_b_c @ nil_li8071162985807626740od_b_c @ Ys2 ) )
     => ~ ! [X3: list_P903359562653991662od_b_c,Xs2: list_l8907847357763382004od_b_c,Ys2: list_l8907847357763382004od_b_c] :
            ( X
           != ( produc2983116027154973335od_b_c @ ( cons_l342771267123639716od_b_c @ X3 @ Xs2 ) @ Ys2 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_826_le0,axiom,
    ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N3 ) ).

% le0
thf(fact_827_assms_I6_J,axiom,
    ( ( outputs_d_b_c @ m2 )
    = ( outputs_a_b_c @ m1 ) ) ).

% assms(6)
thf(fact_828_assms_I5_J,axiom,
    ( ( inputs_d_b_c @ m2 )
    = ( inputs_a_b_c @ m1 ) ) ).

% assms(5)
thf(fact_829_bot__nat__0_Oextremum,axiom,
    ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) ).

% bot_nat_0.extremum
thf(fact_830_from__FSM__simps_I2_J,axiom,
    ! [Q4: d,M3: fsm_d_b_c] :
      ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
     => ( ( inputs_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) )
        = ( inputs_d_b_c @ M3 ) ) ) ).

% from_FSM_simps(2)
thf(fact_831_from__FSM__simps_I2_J,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( inputs_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) )
        = ( inputs_a_b_c @ M3 ) ) ) ).

% from_FSM_simps(2)
thf(fact_832_from__FSM__simps_I3_J,axiom,
    ! [Q4: d,M3: fsm_d_b_c] :
      ( ( member_d @ Q4 @ ( states_d_b_c @ M3 ) )
     => ( ( outputs_d_b_c @ ( from_FSM_d_b_c @ M3 @ Q4 ) )
        = ( outputs_d_b_c @ M3 ) ) ) ).

% from_FSM_simps(3)
thf(fact_833_from__FSM__simps_I3_J,axiom,
    ! [Q4: a,M3: fsm_a_b_c] :
      ( ( member_a @ Q4 @ ( states_a_b_c @ M3 ) )
     => ( ( outputs_a_b_c @ ( from_FSM_a_b_c @ M3 @ Q4 ) )
        = ( outputs_a_b_c @ M3 ) ) ) ).

% from_FSM_simps(3)
thf(fact_834_fsm__transition__input,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
     => ( member_b @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( inputs_d_b_c @ M3 ) ) ) ).

% fsm_transition_input
thf(fact_835_fsm__transition__input,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
     => ( member_a @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( inputs8636541066849307272_a_a_b @ M3 ) ) ) ).

% fsm_transition_input
thf(fact_836_fsm__transition__input,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
     => ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M3 ) ) ) ).

% fsm_transition_input
thf(fact_837_fsm__transition__output,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member4231278564905875615od_c_d @ T @ ( transitions_d_b_c @ M3 ) )
     => ( member_c @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( outputs_d_b_c @ M3 ) ) ) ).

% fsm_transition_output
thf(fact_838_fsm__transition__output,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M3 ) )
     => ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M3 ) ) ) ).

% fsm_transition_output
thf(fact_839_fsm__transition__output,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M3 ) )
     => ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M3 ) ) ) ).

% fsm_transition_output
thf(fact_840_le__refl,axiom,
    ! [N3: nat] : ( ord_less_eq_nat @ N3 @ N3 ) ).

% le_refl
thf(fact_841_le__trans,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ( ord_less_eq_nat @ J @ K )
       => ( ord_less_eq_nat @ I2 @ K ) ) ) ).

% le_trans
thf(fact_842_eq__imp__le,axiom,
    ! [M4: nat,N3: nat] :
      ( ( M4 = N3 )
     => ( ord_less_eq_nat @ M4 @ N3 ) ) ).

% eq_imp_le
thf(fact_843_le__antisym,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
     => ( ( ord_less_eq_nat @ N3 @ M4 )
       => ( M4 = N3 ) ) ) ).

% le_antisym
thf(fact_844_nat__le__linear,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
      | ( ord_less_eq_nat @ N3 @ M4 ) ) ).

% nat_le_linear
thf(fact_845_Nat_Oex__has__greatest__nat,axiom,
    ! [P: nat > $o,K: nat,B2: nat] :
      ( ( P @ K )
     => ( ! [Y3: nat] :
            ( ( P @ Y3 )
           => ( ord_less_eq_nat @ Y3 @ B2 ) )
       => ? [X3: nat] :
            ( ( P @ X3 )
            & ! [Y7: nat] :
                ( ( P @ Y7 )
               => ( ord_less_eq_nat @ Y7 @ X3 ) ) ) ) ) ).

% Nat.ex_has_greatest_nat
thf(fact_846_less__eq__nat_Osimps_I1_J,axiom,
    ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N3 ) ).

% less_eq_nat.simps(1)
thf(fact_847_bot__nat__0_Oextremum__unique,axiom,
    ! [A2: nat] :
      ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
      = ( A2 = zero_zero_nat ) ) ).

% bot_nat_0.extremum_unique
thf(fact_848_bot__nat__0_Oextremum__uniqueI,axiom,
    ! [A2: nat] :
      ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
     => ( A2 = zero_zero_nat ) ) ).

% bot_nat_0.extremum_uniqueI
thf(fact_849_le__0__eq,axiom,
    ! [N3: nat] :
      ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
      = ( N3 = zero_zero_nat ) ) ).

% le_0_eq
thf(fact_850_transition__cover__def,axiom,
    ( transi4707692219127933252_d_b_c
    = ( ^ [M: fsm_d_b_c,A4: set_li6436108459499378894od_b_c] :
        ! [X2: d] :
          ( ( member_d @ X2 @ ( reacha9185589339461546374_d_b_c @ M ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_d_b_c @ M ) )
             => ! [Z3: c] :
                  ( ( member_c @ Z3 @ ( outputs_d_b_c @ M ) )
                 => ? [Alpha2: list_P903359562653991662od_b_c] :
                      ( ( member6330420149250801815od_b_c @ Alpha2 @ A4 )
                      & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ Y2 @ Z3 ) @ nil_Product_prod_b_c ) ) @ A4 )
                      & ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_d_b_c @ M @ ( initial_d_b_c @ M ) ) )
                      & ( ( after_d_b_c @ M @ ( initial_d_b_c @ M ) @ Alpha2 )
                        = X2 ) ) ) ) ) ) ) ).

% transition_cover_def
thf(fact_851_transition__cover__def,axiom,
    ( transi6365780447273092801_a_b_c
    = ( ^ [M: fsm_a_b_c,A4: set_li6436108459499378894od_b_c] :
        ! [X2: a] :
          ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_a_b_c @ M ) )
             => ! [Z3: c] :
                  ( ( member_c @ Z3 @ ( outputs_a_b_c @ M ) )
                 => ? [Alpha2: list_P903359562653991662od_b_c] :
                      ( ( member6330420149250801815od_b_c @ Alpha2 @ A4 )
                      & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ Y2 @ Z3 ) @ nil_Product_prod_b_c ) ) @ A4 )
                      & ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
                      & ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha2 )
                        = X2 ) ) ) ) ) ) ) ).

% transition_cover_def
thf(fact_852_add__transition__simps_I1_J,axiom,
    ! [T: produc7928013997122480633od_a_a,M3: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T ) @ ( states_a_a_a @ M3 ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T ) ) @ ( inputs_a_a_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( outputs_a_a_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( states_a_a_a @ M3 ) )
           => ( ( initial_a_a_a @ ( add_transition_a_a_a @ M3 @ T ) )
              = ( initial_a_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_853_add__transition__simps_I1_J,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member_d @ ( produc1508465569166014290od_c_d @ T ) @ ( states_d_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( inputs_d_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( outputs_d_b_c @ M3 ) )
         => ( ( member_d @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( states_d_b_c @ M3 ) )
           => ( ( initial_d_b_c @ ( add_transition_d_b_c @ M3 @ T ) )
              = ( initial_d_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_854_add__transition__simps_I1_J,axiom,
    ! [T: produc4005982821264896119od_c_a,M3: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T ) @ ( states_a_a_c @ M3 ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) @ ( inputs_a_a_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( outputs_a_a_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( states_a_a_c @ M3 ) )
           => ( ( initial_a_a_c @ ( add_transition_a_a_c @ M3 @ T ) )
              = ( initial_a_a_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_855_add__transition__simps_I1_J,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M3 ) )
           => ( ( initial_a_b_c @ ( add_transition_a_b_c @ M3 @ T ) )
              = ( initial_a_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_856_add__transition__simps_I1_J,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( states367398909958982703_a_a_b @ M3 ) )
     => ( ( member_a @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( inputs8636541066849307272_a_a_b @ M3 ) )
       => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M3 ) )
         => ( ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M3 ) )
           => ( ( initia681974817753967189_a_a_b @ ( add_tr9092525862940605347_a_a_b @ M3 @ T ) )
              = ( initia681974817753967189_a_a_b @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_857_add__transition__simps_I1_J,axiom,
    ! [T: produc2087948699193236105_b_c_a,M3: fsm_a_7552132522915400786od_b_c] :
      ( ( member_a @ ( produc3102587841397929701_b_c_a @ T ) @ ( states4320773439939871863od_b_c @ M3 ) )
     => ( ( member_a @ ( produc4234511675236055356_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) @ ( inputs9062306232769921616od_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( produc1715878850288909075_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( output1637060935040647823od_b_c @ M3 ) )
         => ( ( member_a @ ( produc4803134064720617301_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( states4320773439939871863od_b_c @ M3 ) )
           => ( ( initia206643856256194461od_b_c @ ( add_tr4215521083985406443od_b_c @ M3 @ T ) )
              = ( initia206643856256194461od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_858_add__transition__simps_I1_J,axiom,
    ! [T: produc7762444076724098953od_a_a,M3: fsm_a_7051172154634843122_b_c_a] :
      ( ( member_a @ ( produc2807411494350320613od_a_a @ T ) @ ( states8061127111697657367_b_c_a @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc1524795514040166460od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) @ ( inputs3579287867672931312_b_c_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( output5377414606798433327_b_c_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( states8061127111697657367_b_c_a @ M3 ) )
           => ( ( initia3946997528013979965_b_c_a @ ( add_tr7955874755743191947_b_c_a @ M3 @ T ) )
              = ( initia3946997528013979965_b_c_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_859_add__transition__simps_I1_J,axiom,
    ! [T: produc188457162657408377od_b_c,M3: fsm_li365217302033949778_c_a_a] :
      ( ( member6330420149250801815od_b_c @ ( produc1529007608618196309od_b_c @ T ) @ ( states1245786465149168759_c_a_a @ M3 ) )
     => ( ( member_a @ ( produc4735472043516613020od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) @ ( inputs5987319257979218512_c_a_a @ M3 ) )
       => ( ( member_a @ ( produc7198897215385899379od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( output7785445997104720527_c_a_a @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc1062780392962831797od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( states1245786465149168759_c_a_a @ M3 ) )
           => ( ( initia6355028918320267165_c_a_a @ ( add_tr1140534109194703339_c_a_a @ M3 @ T ) )
              = ( initia6355028918320267165_c_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_860_add__transition__simps_I1_J,axiom,
    ! [T: produc1184151105221883753_b_c_e,M3: fsm_e_4732773946761272438od_b_c] :
      ( ( member_e @ ( produc34240595722896069_b_c_e @ T ) @ ( states3636361102570918555od_b_c @ M3 ) )
     => ( ( member_a @ ( produc7207886088560661024_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) @ ( inputs5582678414982214516od_b_c @ M3 ) )
       => ( ( member2378525361814473399od_b_c @ ( produc1447154562020694007_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( output1721242166954907827od_b_c @ M3 ) )
         => ( ( member_e @ ( produc6779600879576379961_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( states3636361102570918555od_b_c @ M3 ) )
           => ( ( initia6004613875839854529od_b_c @ ( add_tr8133270723906991119od_b_c @ M3 @ T ) )
              = ( initia6004613875839854529od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_861_add__transition__simps_I1_J,axiom,
    ! [T: produc3840412900866514439od_c_a,M3: fsm_a_7051172163241300724_b_c_c] :
      ( ( member_a @ ( produc1536113493140347235od_c_a @ T ) @ ( states8061127111697657369_b_c_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc5173256386949590202od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) @ ( inputs3579287867672931314_b_c_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( output5377414606798433329_b_c_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( states8061127111697657369_b_c_c @ M3 ) )
           => ( ( initia3946997528013979967_b_c_c @ ( add_tr7955874755743191949_b_c_c @ M3 @ T ) )
              = ( initia3946997528013979967_b_c_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_862_add__transition__simps_I5_J,axiom,
    ! [T: produc7928013997122480633od_a_a,M3: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T ) @ ( states_a_a_a @ M3 ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T ) ) @ ( inputs_a_a_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( outputs_a_a_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( states_a_a_a @ M3 ) )
           => ( ( states_a_a_a @ ( add_transition_a_a_a @ M3 @ T ) )
              = ( states_a_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_863_add__transition__simps_I5_J,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member_d @ ( produc1508465569166014290od_c_d @ T ) @ ( states_d_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( inputs_d_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( outputs_d_b_c @ M3 ) )
         => ( ( member_d @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( states_d_b_c @ M3 ) )
           => ( ( states_d_b_c @ ( add_transition_d_b_c @ M3 @ T ) )
              = ( states_d_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_864_add__transition__simps_I5_J,axiom,
    ! [T: produc4005982821264896119od_c_a,M3: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T ) @ ( states_a_a_c @ M3 ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) @ ( inputs_a_a_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( outputs_a_a_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( states_a_a_c @ M3 ) )
           => ( ( states_a_a_c @ ( add_transition_a_a_c @ M3 @ T ) )
              = ( states_a_a_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_865_add__transition__simps_I5_J,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M3 ) )
           => ( ( states_a_b_c @ ( add_transition_a_b_c @ M3 @ T ) )
              = ( states_a_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_866_add__transition__simps_I5_J,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( states367398909958982703_a_a_b @ M3 ) )
     => ( ( member_a @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( inputs8636541066849307272_a_a_b @ M3 ) )
       => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M3 ) )
         => ( ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M3 ) )
           => ( ( states367398909958982703_a_a_b @ ( add_tr9092525862940605347_a_a_b @ M3 @ T ) )
              = ( states367398909958982703_a_a_b @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_867_add__transition__simps_I5_J,axiom,
    ! [T: produc2087948699193236105_b_c_a,M3: fsm_a_7552132522915400786od_b_c] :
      ( ( member_a @ ( produc3102587841397929701_b_c_a @ T ) @ ( states4320773439939871863od_b_c @ M3 ) )
     => ( ( member_a @ ( produc4234511675236055356_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) @ ( inputs9062306232769921616od_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( produc1715878850288909075_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( output1637060935040647823od_b_c @ M3 ) )
         => ( ( member_a @ ( produc4803134064720617301_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( states4320773439939871863od_b_c @ M3 ) )
           => ( ( states4320773439939871863od_b_c @ ( add_tr4215521083985406443od_b_c @ M3 @ T ) )
              = ( states4320773439939871863od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_868_add__transition__simps_I5_J,axiom,
    ! [T: produc7762444076724098953od_a_a,M3: fsm_a_7051172154634843122_b_c_a] :
      ( ( member_a @ ( produc2807411494350320613od_a_a @ T ) @ ( states8061127111697657367_b_c_a @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc1524795514040166460od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) @ ( inputs3579287867672931312_b_c_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( output5377414606798433327_b_c_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( states8061127111697657367_b_c_a @ M3 ) )
           => ( ( states8061127111697657367_b_c_a @ ( add_tr7955874755743191947_b_c_a @ M3 @ T ) )
              = ( states8061127111697657367_b_c_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_869_add__transition__simps_I5_J,axiom,
    ! [T: produc188457162657408377od_b_c,M3: fsm_li365217302033949778_c_a_a] :
      ( ( member6330420149250801815od_b_c @ ( produc1529007608618196309od_b_c @ T ) @ ( states1245786465149168759_c_a_a @ M3 ) )
     => ( ( member_a @ ( produc4735472043516613020od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) @ ( inputs5987319257979218512_c_a_a @ M3 ) )
       => ( ( member_a @ ( produc7198897215385899379od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( output7785445997104720527_c_a_a @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc1062780392962831797od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( states1245786465149168759_c_a_a @ M3 ) )
           => ( ( states1245786465149168759_c_a_a @ ( add_tr1140534109194703339_c_a_a @ M3 @ T ) )
              = ( states1245786465149168759_c_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_870_add__transition__simps_I5_J,axiom,
    ! [T: produc1184151105221883753_b_c_e,M3: fsm_e_4732773946761272438od_b_c] :
      ( ( member_e @ ( produc34240595722896069_b_c_e @ T ) @ ( states3636361102570918555od_b_c @ M3 ) )
     => ( ( member_a @ ( produc7207886088560661024_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) @ ( inputs5582678414982214516od_b_c @ M3 ) )
       => ( ( member2378525361814473399od_b_c @ ( produc1447154562020694007_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( output1721242166954907827od_b_c @ M3 ) )
         => ( ( member_e @ ( produc6779600879576379961_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( states3636361102570918555od_b_c @ M3 ) )
           => ( ( states3636361102570918555od_b_c @ ( add_tr8133270723906991119od_b_c @ M3 @ T ) )
              = ( states3636361102570918555od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_871_add__transition__simps_I5_J,axiom,
    ! [T: produc3840412900866514439od_c_a,M3: fsm_a_7051172163241300724_b_c_c] :
      ( ( member_a @ ( produc1536113493140347235od_c_a @ T ) @ ( states8061127111697657369_b_c_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc5173256386949590202od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) @ ( inputs3579287867672931314_b_c_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( output5377414606798433329_b_c_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( states8061127111697657369_b_c_c @ M3 ) )
           => ( ( states8061127111697657369_b_c_c @ ( add_tr7955874755743191949_b_c_c @ M3 @ T ) )
              = ( states8061127111697657369_b_c_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_872_add__transition__simps_I3_J,axiom,
    ! [T: produc7928013997122480633od_a_a,M3: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T ) @ ( states_a_a_a @ M3 ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T ) ) @ ( inputs_a_a_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( outputs_a_a_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( states_a_a_a @ M3 ) )
           => ( ( outputs_a_a_a @ ( add_transition_a_a_a @ M3 @ T ) )
              = ( outputs_a_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_873_add__transition__simps_I3_J,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member_d @ ( produc1508465569166014290od_c_d @ T ) @ ( states_d_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( inputs_d_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( outputs_d_b_c @ M3 ) )
         => ( ( member_d @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( states_d_b_c @ M3 ) )
           => ( ( outputs_d_b_c @ ( add_transition_d_b_c @ M3 @ T ) )
              = ( outputs_d_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_874_add__transition__simps_I3_J,axiom,
    ! [T: produc4005982821264896119od_c_a,M3: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T ) @ ( states_a_a_c @ M3 ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) @ ( inputs_a_a_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( outputs_a_a_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( states_a_a_c @ M3 ) )
           => ( ( outputs_a_a_c @ ( add_transition_a_a_c @ M3 @ T ) )
              = ( outputs_a_a_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_875_add__transition__simps_I3_J,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M3 ) )
           => ( ( outputs_a_b_c @ ( add_transition_a_b_c @ M3 @ T ) )
              = ( outputs_a_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_876_add__transition__simps_I3_J,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( states367398909958982703_a_a_b @ M3 ) )
     => ( ( member_a @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( inputs8636541066849307272_a_a_b @ M3 ) )
       => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M3 ) )
         => ( ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M3 ) )
           => ( ( output2371653660386375239_a_a_b @ ( add_tr9092525862940605347_a_a_b @ M3 @ T ) )
              = ( output2371653660386375239_a_a_b @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_877_add__transition__simps_I3_J,axiom,
    ! [T: produc2087948699193236105_b_c_a,M3: fsm_a_7552132522915400786od_b_c] :
      ( ( member_a @ ( produc3102587841397929701_b_c_a @ T ) @ ( states4320773439939871863od_b_c @ M3 ) )
     => ( ( member_a @ ( produc4234511675236055356_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) @ ( inputs9062306232769921616od_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( produc1715878850288909075_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( output1637060935040647823od_b_c @ M3 ) )
         => ( ( member_a @ ( produc4803134064720617301_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( states4320773439939871863od_b_c @ M3 ) )
           => ( ( output1637060935040647823od_b_c @ ( add_tr4215521083985406443od_b_c @ M3 @ T ) )
              = ( output1637060935040647823od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_878_add__transition__simps_I3_J,axiom,
    ! [T: produc7762444076724098953od_a_a,M3: fsm_a_7051172154634843122_b_c_a] :
      ( ( member_a @ ( produc2807411494350320613od_a_a @ T ) @ ( states8061127111697657367_b_c_a @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc1524795514040166460od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) @ ( inputs3579287867672931312_b_c_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( output5377414606798433327_b_c_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( states8061127111697657367_b_c_a @ M3 ) )
           => ( ( output5377414606798433327_b_c_a @ ( add_tr7955874755743191947_b_c_a @ M3 @ T ) )
              = ( output5377414606798433327_b_c_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_879_add__transition__simps_I3_J,axiom,
    ! [T: produc188457162657408377od_b_c,M3: fsm_li365217302033949778_c_a_a] :
      ( ( member6330420149250801815od_b_c @ ( produc1529007608618196309od_b_c @ T ) @ ( states1245786465149168759_c_a_a @ M3 ) )
     => ( ( member_a @ ( produc4735472043516613020od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) @ ( inputs5987319257979218512_c_a_a @ M3 ) )
       => ( ( member_a @ ( produc7198897215385899379od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( output7785445997104720527_c_a_a @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc1062780392962831797od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( states1245786465149168759_c_a_a @ M3 ) )
           => ( ( output7785445997104720527_c_a_a @ ( add_tr1140534109194703339_c_a_a @ M3 @ T ) )
              = ( output7785445997104720527_c_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_880_add__transition__simps_I3_J,axiom,
    ! [T: produc1184151105221883753_b_c_e,M3: fsm_e_4732773946761272438od_b_c] :
      ( ( member_e @ ( produc34240595722896069_b_c_e @ T ) @ ( states3636361102570918555od_b_c @ M3 ) )
     => ( ( member_a @ ( produc7207886088560661024_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) @ ( inputs5582678414982214516od_b_c @ M3 ) )
       => ( ( member2378525361814473399od_b_c @ ( produc1447154562020694007_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( output1721242166954907827od_b_c @ M3 ) )
         => ( ( member_e @ ( produc6779600879576379961_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( states3636361102570918555od_b_c @ M3 ) )
           => ( ( output1721242166954907827od_b_c @ ( add_tr8133270723906991119od_b_c @ M3 @ T ) )
              = ( output1721242166954907827od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_881_add__transition__simps_I3_J,axiom,
    ! [T: produc3840412900866514439od_c_a,M3: fsm_a_7051172163241300724_b_c_c] :
      ( ( member_a @ ( produc1536113493140347235od_c_a @ T ) @ ( states8061127111697657369_b_c_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc5173256386949590202od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) @ ( inputs3579287867672931314_b_c_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( output5377414606798433329_b_c_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( states8061127111697657369_b_c_c @ M3 ) )
           => ( ( output5377414606798433329_b_c_c @ ( add_tr7955874755743191949_b_c_c @ M3 @ T ) )
              = ( output5377414606798433329_b_c_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_882_add__transition__simps_I2_J,axiom,
    ! [T: produc7928013997122480633od_a_a,M3: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T ) @ ( states_a_a_a @ M3 ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T ) ) @ ( inputs_a_a_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( outputs_a_a_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T ) ) ) @ ( states_a_a_a @ M3 ) )
           => ( ( inputs_a_a_a @ ( add_transition_a_a_a @ M3 @ T ) )
              = ( inputs_a_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_883_add__transition__simps_I2_J,axiom,
    ! [T: produc1399170498009216118od_c_d,M3: fsm_d_b_c] :
      ( ( member_d @ ( produc1508465569166014290od_c_d @ T ) @ ( states_d_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949087656271980od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) @ ( inputs_d_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( outputs_d_b_c @ M3 ) )
         => ( ( member_d @ ( product_snd_c_d @ ( produc5221446337070271918od_c_d @ ( produc5370652324230910612od_c_d @ T ) ) ) @ ( states_d_b_c @ M3 ) )
           => ( ( inputs_d_b_c @ ( add_transition_d_b_c @ M3 @ T ) )
              = ( inputs_d_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_884_add__transition__simps_I2_J,axiom,
    ! [T: produc4005982821264896119od_c_a,M3: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T ) @ ( states_a_a_c @ M3 ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) @ ( inputs_a_a_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( outputs_a_a_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T ) ) ) @ ( states_a_a_c @ M3 ) )
           => ( ( inputs_a_a_c @ ( add_transition_a_a_c @ M3 @ T ) )
              = ( inputs_a_a_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_885_add__transition__simps_I2_J,axiom,
    ! [T: produc2669932201312201782od_c_a,M3: fsm_a_b_c] :
      ( ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M3 ) )
     => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M3 ) )
           => ( ( inputs_a_b_c @ ( add_transition_a_b_c @ M3 @ T ) )
              = ( inputs_a_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_886_add__transition__simps_I2_J,axiom,
    ! [T: produc3205353004677322104od_c_a,M3: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member5074992350434858958od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( states367398909958982703_a_a_b @ M3 ) )
     => ( ( member_a @ ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) @ ( inputs8636541066849307272_a_a_b @ M3 ) )
       => ( ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M3 ) )
         => ( ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M3 ) )
           => ( ( inputs8636541066849307272_a_a_b @ ( add_tr9092525862940605347_a_a_b @ M3 @ T ) )
              = ( inputs8636541066849307272_a_a_b @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_887_add__transition__simps_I2_J,axiom,
    ! [T: produc2087948699193236105_b_c_a,M3: fsm_a_7552132522915400786od_b_c] :
      ( ( member_a @ ( produc3102587841397929701_b_c_a @ T ) @ ( states4320773439939871863od_b_c @ M3 ) )
     => ( ( member_a @ ( produc4234511675236055356_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) @ ( inputs9062306232769921616od_b_c @ M3 ) )
       => ( ( member6330420149250801815od_b_c @ ( produc1715878850288909075_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( output1637060935040647823od_b_c @ M3 ) )
         => ( ( member_a @ ( produc4803134064720617301_b_c_a @ ( produc2928457758587325310_b_c_a @ ( produc3992262032349443879_b_c_a @ T ) ) ) @ ( states4320773439939871863od_b_c @ M3 ) )
           => ( ( inputs9062306232769921616od_b_c @ ( add_tr4215521083985406443od_b_c @ M3 @ T ) )
              = ( inputs9062306232769921616od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_888_add__transition__simps_I2_J,axiom,
    ! [T: produc7762444076724098953od_a_a,M3: fsm_a_7051172154634843122_b_c_a] :
      ( ( member_a @ ( produc2807411494350320613od_a_a @ T ) @ ( states8061127111697657367_b_c_a @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc1524795514040166460od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) @ ( inputs3579287867672931312_b_c_a @ M3 ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( output5377414606798433327_b_c_a @ M3 ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc218741597391436414od_a_a @ ( produc3697085685301834791od_a_a @ T ) ) ) @ ( states8061127111697657367_b_c_a @ M3 ) )
           => ( ( inputs3579287867672931312_b_c_a @ ( add_tr7955874755743191947_b_c_a @ M3 @ T ) )
              = ( inputs3579287867672931312_b_c_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_889_add__transition__simps_I2_J,axiom,
    ! [T: produc188457162657408377od_b_c,M3: fsm_li365217302033949778_c_a_a] :
      ( ( member6330420149250801815od_b_c @ ( produc1529007608618196309od_b_c @ T ) @ ( states1245786465149168759_c_a_a @ M3 ) )
     => ( ( member_a @ ( produc4735472043516613020od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) @ ( inputs5987319257979218512_c_a_a @ M3 ) )
       => ( ( member_a @ ( produc7198897215385899379od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( output7785445997104720527_c_a_a @ M3 ) )
         => ( ( member6330420149250801815od_b_c @ ( produc1062780392962831797od_b_c @ ( produc3429418126867882974od_b_c @ ( produc6497444872579809943od_b_c @ T ) ) ) @ ( states1245786465149168759_c_a_a @ M3 ) )
           => ( ( inputs5987319257979218512_c_a_a @ ( add_tr1140534109194703339_c_a_a @ M3 @ T ) )
              = ( inputs5987319257979218512_c_a_a @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_890_add__transition__simps_I2_J,axiom,
    ! [T: produc1184151105221883753_b_c_e,M3: fsm_e_4732773946761272438od_b_c] :
      ( ( member_e @ ( produc34240595722896069_b_c_e @ T ) @ ( states3636361102570918555od_b_c @ M3 ) )
     => ( ( member_a @ ( produc7207886088560661024_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) @ ( inputs5582678414982214516od_b_c @ M3 ) )
       => ( ( member2378525361814473399od_b_c @ ( produc1447154562020694007_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( output1721242166954907827od_b_c @ M3 ) )
         => ( ( member_e @ ( produc6779600879576379961_b_c_e @ ( produc8596465535467969122_b_c_e @ ( produc6970953647068543239_b_c_e @ T ) ) ) @ ( states3636361102570918555od_b_c @ M3 ) )
           => ( ( inputs5582678414982214516od_b_c @ ( add_tr8133270723906991119od_b_c @ M3 @ T ) )
              = ( inputs5582678414982214516od_b_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_891_add__transition__simps_I2_J,axiom,
    ! [T: produc3840412900866514439od_c_a,M3: fsm_a_7051172163241300724_b_c_c] :
      ( ( member_a @ ( produc1536113493140347235od_c_a @ T ) @ ( states8061127111697657369_b_c_c @ M3 ) )
     => ( ( member6330420149250801815od_b_c @ ( produc5173256386949590202od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) @ ( inputs3579287867672931314_b_c_c @ M3 ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( output5377414606798433329_b_c_c @ M3 ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc3867202470300860156od_c_a @ ( produc2425787684091861413od_c_a @ T ) ) ) @ ( states8061127111697657369_b_c_c @ M3 ) )
           => ( ( inputs3579287867672931314_b_c_c @ ( add_tr7955874755743191949_b_c_c @ M3 @ T ) )
              = ( inputs3579287867672931314_b_c_c @ M3 ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_892_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_a_b_c,T4: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( ( inputs_a_b_c @ M22 )
                = ( inputs_a_b_c @ M12 ) )
             => ( ( ( outputs_a_b_c @ M22 )
                  = ( outputs_a_b_c @ M12 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                 => ( ( ord_le282488521294790766od_b_c @ A @ T4 )
                   => ( ( transi6365780447273092801_a_b_c @ M12 @ A )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A )
                       => ( ( preser1543909642583041678_b_c_a @ M12 @ M22 @ A )
                         => ( ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) )
                            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_893_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M12: fsm_a_b_c,M22: fsm_d_b_c,T4: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_a_b_c @ M12 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( ( inputs_d_b_c @ M22 )
                = ( inputs_a_b_c @ M12 ) )
             => ( ( ( outputs_d_b_c @ M22 )
                  = ( outputs_a_b_c @ M12 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ T4 )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                 => ( ( ord_le282488521294790766od_b_c @ A @ T4 )
                   => ( ( transi6365780447273092801_a_b_c @ M12 @ A )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A )
                       => ( ( preser1543909642583041681_b_c_d @ M12 @ M22 @ A )
                         => ( ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) )
                            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_894_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_a_b_c,T4: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( ( inputs_a_b_c @ M22 )
                = ( inputs_d_b_c @ M12 ) )
             => ( ( ( outputs_a_b_c @ M22 )
                  = ( outputs_d_b_c @ M12 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T4 ) )
                 => ( ( ord_le282488521294790766od_b_c @ A @ T4 )
                   => ( ( transi4707692219127933252_d_b_c @ M12 @ A )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A )
                       => ( ( preser6007795754467437259_b_c_a @ M12 @ M22 @ A )
                         => ( ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) )
                            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_895_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M12: fsm_d_b_c,M22: fsm_d_b_c,T4: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( observable_d_b_c @ M12 )
     => ( ( observable_d_b_c @ M22 )
       => ( ( minimal_d_b_c @ M12 )
         => ( ( minimal_d_b_c @ M22 )
           => ( ( ( inputs_d_b_c @ M22 )
                = ( inputs_d_b_c @ M12 ) )
             => ( ( ( outputs_d_b_c @ M22 )
                  = ( outputs_d_b_c @ M12 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) ) @ T4 )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) @ T4 ) )
                 => ( ( ord_le282488521294790766od_b_c @ A @ T4 )
                   => ( ( transi4707692219127933252_d_b_c @ M12 @ A )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A )
                       => ( ( preser6007795754467437262_b_c_d @ M12 @ M22 @ A )
                         => ( ( lS_d_b_c @ M12 @ ( initial_d_b_c @ M12 ) )
                            = ( lS_d_b_c @ M22 @ ( initial_d_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_896_k,axiom,
    ( k
    = ( minus_minus_nat @ m @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ m1 ) ) ) ) ).

% k
thf(fact_897_diff__diff__cancel,axiom,
    ! [I2: nat,N3: nat] :
      ( ( ord_less_eq_nat @ I2 @ N3 )
     => ( ( minus_minus_nat @ N3 @ ( minus_minus_nat @ N3 @ I2 ) )
        = I2 ) ) ).

% diff_diff_cancel
thf(fact_898_diff__is__0__eq_H,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
     => ( ( minus_minus_nat @ M4 @ N3 )
        = zero_zero_nat ) ) ).

% diff_is_0_eq'
thf(fact_899_diff__is__0__eq,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ( minus_minus_nat @ M4 @ N3 )
        = zero_zero_nat )
      = ( ord_less_eq_nat @ M4 @ N3 ) ) ).

% diff_is_0_eq
thf(fact_900_diff__le__mono2,axiom,
    ! [M4: nat,N3: nat,L3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ L3 @ N3 ) @ ( minus_minus_nat @ L3 @ M4 ) ) ) ).

% diff_le_mono2
thf(fact_901_le__diff__iff_H,axiom,
    ! [A2: nat,C: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A2 @ C )
     => ( ( ord_less_eq_nat @ B2 @ C )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A2 ) @ ( minus_minus_nat @ C @ B2 ) )
          = ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).

% le_diff_iff'
thf(fact_902_diff__le__self,axiom,
    ! [M4: nat,N3: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M4 @ N3 ) @ M4 ) ).

% diff_le_self
thf(fact_903_diff__le__mono,axiom,
    ! [M4: nat,N3: nat,L3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ M4 @ L3 ) @ ( minus_minus_nat @ N3 @ L3 ) ) ) ).

% diff_le_mono
thf(fact_904_Nat_Odiff__diff__eq,axiom,
    ! [K: nat,M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ K @ M4 )
     => ( ( ord_less_eq_nat @ K @ N3 )
       => ( ( minus_minus_nat @ ( minus_minus_nat @ M4 @ K ) @ ( minus_minus_nat @ N3 @ K ) )
          = ( minus_minus_nat @ M4 @ N3 ) ) ) ) ).

% Nat.diff_diff_eq
thf(fact_905_le__diff__iff,axiom,
    ! [K: nat,M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ K @ M4 )
     => ( ( ord_less_eq_nat @ K @ N3 )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M4 @ K ) @ ( minus_minus_nat @ N3 @ K ) )
          = ( ord_less_eq_nat @ M4 @ N3 ) ) ) ) ).

% le_diff_iff
thf(fact_906_eq__diff__iff,axiom,
    ! [K: nat,M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ K @ M4 )
     => ( ( ord_less_eq_nat @ K @ N3 )
       => ( ( ( minus_minus_nat @ M4 @ K )
            = ( minus_minus_nat @ N3 @ K ) )
          = ( M4 = N3 ) ) ) ) ).

% eq_diff_iff
thf(fact_907_exists__leI,axiom,
    ! [N3: nat,P: nat > $o] :
      ( ( ! [N4: nat] :
            ( ( ord_less_nat @ N4 @ N3 )
           => ~ ( P @ N4 ) )
       => ( P @ N3 ) )
     => ? [N5: nat] :
          ( ( ord_less_eq_nat @ N5 @ N3 )
          & ( P @ N5 ) ) ) ).

% exists_leI
thf(fact_908_less__mono__imp__le__mono,axiom,
    ! [F: nat > nat,I2: nat,J: nat] :
      ( ! [I3: nat,J2: nat] :
          ( ( ord_less_nat @ I3 @ J2 )
         => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
     => ( ( ord_less_eq_nat @ I2 @ J )
       => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).

% less_mono_imp_le_mono
thf(fact_909_le__neq__implies__less,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ M4 @ N3 )
     => ( ( M4 != N3 )
       => ( ord_less_nat @ M4 @ N3 ) ) ) ).

% le_neq_implies_less
thf(fact_910_less__or__eq__imp__le,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ( ord_less_nat @ M4 @ N3 )
        | ( M4 = N3 ) )
     => ( ord_less_eq_nat @ M4 @ N3 ) ) ).

% less_or_eq_imp_le
thf(fact_911_le__eq__less__or__eq,axiom,
    ( ord_less_eq_nat
    = ( ^ [M5: nat,N6: nat] :
          ( ( ord_less_nat @ M5 @ N6 )
          | ( M5 = N6 ) ) ) ) ).

% le_eq_less_or_eq
thf(fact_912_less__imp__le__nat,axiom,
    ! [M4: nat,N3: nat] :
      ( ( ord_less_nat @ M4 @ N3 )
     => ( ord_less_eq_nat @ M4 @ N3 ) ) ).

% less_imp_le_nat
thf(fact_913_nat__less__le,axiom,
    ( ord_less_nat
    = ( ^ [M5: nat,N6: nat] :
          ( ( ord_less_eq_nat @ M5 @ N6 )
          & ( M5 != N6 ) ) ) ) ).

% nat_less_le
thf(fact_914_ex__least__nat__le,axiom,
    ! [P: nat > $o,N3: nat] :
      ( ( P @ N3 )
     => ( ~ ( P @ zero_zero_nat )
       => ? [K3: nat] :
            ( ( ord_less_eq_nat @ K3 @ N3 )
            & ! [I4: nat] :
                ( ( ord_less_nat @ I4 @ K3 )
               => ~ ( P @ I4 ) )
            & ( P @ K3 ) ) ) ) ).

% ex_least_nat_le
thf(fact_915_diff__less__mono,axiom,
    ! [A2: nat,B2: nat,C: nat] :
      ( ( ord_less_nat @ A2 @ B2 )
     => ( ( ord_less_eq_nat @ C @ A2 )
       => ( ord_less_nat @ ( minus_minus_nat @ A2 @ C ) @ ( minus_minus_nat @ B2 @ C ) ) ) ) ).

% diff_less_mono
thf(fact_916_less__diff__iff,axiom,
    ! [K: nat,M4: nat,N3: nat] :
      ( ( ord_less_eq_nat @ K @ M4 )
     => ( ( ord_less_eq_nat @ K @ N3 )
       => ( ( ord_less_nat @ ( minus_minus_nat @ M4 @ K ) @ ( minus_minus_nat @ N3 @ K ) )
          = ( ord_less_nat @ M4 @ N3 ) ) ) ) ).

% less_diff_iff
thf(fact_917_nat__geq__1__eq__neqz,axiom,
    ! [X: nat] :
      ( ( ord_less_eq_nat @ one_one_nat @ X )
      = ( X != zero_zero_nat ) ) ).

% nat_geq_1_eq_neqz
thf(fact_918_bounded__Max__nat,axiom,
    ! [P: nat > $o,X: nat,M3: nat] :
      ( ( P @ X )
     => ( ! [X3: nat] :
            ( ( P @ X3 )
           => ( ord_less_eq_nat @ X3 @ M3 ) )
       => ~ ! [M6: nat] :
              ( ( P @ M6 )
             => ~ ! [X5: nat] :
                    ( ( P @ X5 )
                   => ( ord_less_eq_nat @ X5 @ M6 ) ) ) ) ) ).

% bounded_Max_nat
thf(fact_919_finite__nat__set__iff__bounded__le,axiom,
    ( finite_finite_nat
    = ( ^ [N7: set_nat] :
        ? [M5: nat] :
        ! [X2: nat] :
          ( ( member_nat @ X2 @ N7 )
         => ( ord_less_eq_nat @ X2 @ M5 ) ) ) ) ).

% finite_nat_set_iff_bounded_le

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694007_b_c_e @ ( foldl_2934561762154836916od_b_c @ handleTrace @ ( produc2511600812177743883_b_c_e @ t @ g ) @ ttc ) ) ) )
    = ( inf_in4978071631833541052od_b_c @ ( lS_d_b_c @ m2 @ ( initial_d_b_c @ m2 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694007_b_c_e @ ( foldl_2934561762154836916od_b_c @ handleTrace @ ( produc2511600812177743883_b_c_e @ t @ g ) @ ttc ) ) ) ) ) ).

%------------------------------------------------------------------------------