TPTP Problem File: SLH0991^1.p

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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : FSM_Tests/0059_Simple_Convergence_Graph/prob_01012_044404__20623654_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2206 ( 489 unt; 919 typ;   0 def)
%            Number of atoms       : 4728 (1957 equ;   0 cnn)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives : 20607 ( 934   ~;  71   |; 369   &;16730   @)
%                                         (   0 <=>;2503  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   8 avg)
%            Number of types       :  212 ( 211 usr)
%            Number of type conns  : 1654 (1654   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  711 ( 708 usr;  57 con; 0-4 aty)
%            Number of variables   : 4997 (  96   ^;4673   !; 228   ?;4997   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:29:42.658
%------------------------------------------------------------------------------
% Could-be-implicit typings (211)
thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J_J,type,
    produc6892749230674326005od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc6599362722213357102od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc4201866467197088793od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc136864206262228050od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc5436143990428185615od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc8905949819191209269od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc4155545519608197068od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc246785466268114886od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc6013625613799016975od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc3622972877636639297od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc1801560611250510664od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSM____Impl__Ofsm____impl_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6510285022982376705od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc8660020554386975555od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc4550864312075981571od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6285210691406119693od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc6483782000891358638od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc7489520080164906694od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc6844535102171174857od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6250212354305936633od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc3298291110960068788od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    list_P5370328139307421263od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    set_Pr6133615449426215977od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6416010238344180095od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6133449566840171033od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc3626440574470744009od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc941565555952692937od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc4084954254102156249od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc3345434161935928879od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_Pr5812197030978132777od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc8278318776394211699od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc4267876118020951450od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc3633803565885464646od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc388879027768430262od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc3935921425066410441od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc4368844512119319232od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr731044129912021033od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6935835972710448245od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7003135847223052371od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    fsm_fs8047552373904900237od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc8235995322212035239od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc5998163534577424309od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc8701494430851074505od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc2095529977478686646od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    set_Pr7954061446304757788od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc8178655232312819025od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc8043380187910098957od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    fsm_li467911846419323815od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc5620510707799782816od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_Pr4210316172971897624od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc5482552087341567164od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    set_li104036716953425826od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    fsm_fs3444354198583051774od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2793283351794386037od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6680082661646774695od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6744346567773647288od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_Pr4286734062635796237od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc1153669656519933622od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc8522616430465603254od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    list_P5302045529885307074od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_M_Eo_J_J,type,
    set_Pr1979380953684217522_a_b_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_Pr5622538825374275996od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc8331063474073164274od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    fsm_li9174950046736424472od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J_J,type,
    produc2175610488484699543st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc9134726091994374893od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc3893167590797037997od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr4832031994198807704od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr803608928346326407od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_li2133032475778560915od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_M_Eo_J,type,
    produc7103389596696383826_a_b_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc8937288731615916348od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc6303315885879197575od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7071465670189454904od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc6292233528018597543od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc4243862795798826663od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    list_P5488608094462411443od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr3384986265503004545od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr1051027220935592077od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc8956912041617273782od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc3232039666172969398od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2073128436939348198od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J_J,type,
    produc4872601182145619129list_o: $tType ).

thf(ty_n_t__FSM____Impl__Ofsm____impl_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    fSM_fs4935216794212288482od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J_J,type,
    produc19496163836001069st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc4803344270401830612od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8628745980099788577od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2518759752815613485od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_P1164858718851775149od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr3498424749146541447od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr2242436922956002695od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3899447382255381072od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3334210663054469735od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fsm_li3816064051032718074od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    fsm_fs4691611325187074810od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J,type,
    produc2533616784052650198st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc263801385964556654od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc1688629678973589927od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8767915422032708007od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_Pr4856876843892373641od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc4943249325152908478od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3357997149271159322od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J_J,type,
    produc7154445628944892357list_o: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    fsm_li6929239050930586644od_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fsm_fs4038567970311364852od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc9101336024286631233od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    list_P2891578699137632811od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_P8601282865932132013od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr3015088788472578951od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc1075984531370556585od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc724608359110776885od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    set_li7888096385779382799od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J,type,
    produc4796846013342594440st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J,type,
    produc245062040767252272list_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__d_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    produc2109192171533205685od_b_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__c_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    produc1033877881492090229od_b_c: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fsm_li2173814106350063374od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7169317207952727333od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7397007428618769063od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_P2373415021271773893od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J_J,type,
    set_li7469257630003736542od_b_d: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J_J,type,
    set_li839162645350771998od_b_c: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc7877445111886203567od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    produc1950156742809263241st_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    list_P3574414722980446895od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_J,type,
    set_Pr2549634154452313093_a_b_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr121319624013539721od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_li7076890251784626569od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc9068417245363831566od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J,type,
    produc1237961142284713782list_o: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_P3068083765560563145od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr8907832335669617775od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc9005793448470268223od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J,type,
    produc6268931404698553153od_b_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    produc6427713924023405888od_b_c: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J,type,
    list_P8454989104189725694od_b_d: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    list_P5017272815184427326od_b_c: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    list_l378912295992385958od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J,type,
    set_Pr1262082100177054424od_b_d: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    set_Pr7047737848026531864od_b_c: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J,type,
    produc2087898033365526821_a_b_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc4356081027818849609od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2313482920965681321od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_P5169789268404693161od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    produc4326814125627636033st_nat: $tType ).

thf(ty_n_t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fSM_fs17440223606942999od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc6829992310584780345od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_I_Eo_M_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_I_Eo_J_J_J,type,
    produc1709182781532539895list_o: $tType ).

thf(ty_n_t__Option__Ooption_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    option4548628174090016992od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    produc84550687463314808od_b_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    produc6657052613134160568od_b_c: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3520053589329427452od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_l6099054058445139744od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_li7540826859550765818od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8908614768156765891od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3910515788072733219od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    list_s7922523924679432314od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_se1014227543623231828od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J,type,
    produc4690905340047322919list_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc254973753779126261st_nat: $tType ).

thf(ty_n_t__FSM__Ofsm_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mtf__a_Mtf__b_J,type,
    fsm_fs1840479945969036537_b_a_b: $tType ).

thf(ty_n_t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    fSM_fs4309808098908436657od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc6345636018528648726od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2639161875728825943od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    list_P6112925938187837720od_b_d: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    list_P8634110456476873367od_b_c: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_l6443893005374362810od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_f1445794025290330138od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_li948167846089608596od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_fs5173440902860351732od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc1828647624359046049st_nat: $tType ).

thf(ty_n_t__FSM__Ofsm_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mtf__a_Mtf__b_J,type,
    fsm_li1655959576902402579_b_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_Eo_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc4226810134323546766st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    produc7974263126369132087st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_I_Eo_M_062_I_Eo_M_Eo_J_J_Mt__List__Olist_I_Eo_J_J,type,
    produc8642409424279824599list_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    produc3621550705533957266od_b_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    produc3550516665487611281od_b_c: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_l8778361445553822004od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    fset_l1334069825099621524od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    set_li6306622547289818894od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_I_Eo_J_J,type,
    produc7102631898165422375list_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J,type,
    produc796964778762255539list_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_I_Eo_M_Eo_J_Mt__List__Olist_I_Eo_J_J,type,
    produc4895375484934168814list_o: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    list_P1467974523212632366od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    set_Product_prod_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    product_prod_nat_nat: $tType ).

thf(ty_n_t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__d_J,type,
    fSM_fsm_impl_a_b_d: $tType ).

thf(ty_n_t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__c_J,type,
    fSM_fsm_impl_a_b_c: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    list_list_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__d_J,type,
    product_prod_b_d: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    product_prod_b_c: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    product_prod_a_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_I_Eo_J_J,type,
    list_list_o: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__d_Mtf__a_Mtf__b_J,type,
    fsm_d_a_b: $tType ).

thf(ty_n_t__FSM__Ofsm_Itf__c_Mtf__a_Mtf__b_J,type,
    fsm_c_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
    list_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__Option__Ooption_Itf__d_J,type,
    option_d: $tType ).

thf(ty_n_t__Option__Ooption_Itf__c_J,type,
    option_c: $tType ).

thf(ty_n_t__List__Olist_Itf__d_J,type,
    list_d: $tType ).

thf(ty_n_t__List__Olist_Itf__c_J,type,
    list_c: $tType ).

thf(ty_n_t__List__Olist_Itf__a_J,type,
    list_a: $tType ).

thf(ty_n_t__Set__Oset_Itf__d_J,type,
    set_d: $tType ).

thf(ty_n_t__Set__Oset_Itf__c_J,type,
    set_c: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

thf(ty_n_t__List__Olist_I_Eo_J,type,
    list_o: $tType ).

thf(ty_n_t__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

thf(ty_n_tf__d,type,
    d: $tType ).

thf(ty_n_tf__c,type,
    c: $tType ).

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (708)
thf(sy_c_AList_Odelete__aux_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    delete6197099393584013480od_a_b: $o > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Odelete__aux_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    delete3629537940609567931od_a_b: $o > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Odelete__aux_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    delete3925988326758032172od_a_b: fset_l1334069825099621524od_a_b > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Odelete__aux__rel_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    delete8919263077593111253od_a_b: produc4943249325152908478od_a_b > produc4943249325152908478od_a_b > $o ).

thf(sy_c_AList_Odelete__aux__rel_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    delete2995761608754898920od_a_b: produc8178655232312819025od_a_b > produc8178655232312819025od_a_b > $o ).

thf(sy_c_AList_Odelete__aux__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    delete7018282185866685657od_a_b: produc3633803565885464646od_a_b > produc3633803565885464646od_a_b > $o ).

thf(sy_c_AList_Omap__default_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_de6169289306397452762od_a_b: $o > list_f1445794025290330138od_a_b > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Omap__default_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_de5747135492376268781od_a_b: $o > produc2518759752815613485od_a_b > ( produc2518759752815613485od_a_b > produc2518759752815613485od_a_b ) > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Omap__default_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_de5790008637807865694od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Omap__default__rel_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_de1802405036153999395od_a_b: produc6013625613799016975od_a_b > produc6013625613799016975od_a_b > $o ).

thf(sy_c_AList_Omap__default__rel_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_de8168527554739364662od_a_b: produc6892749230674326005od_a_b > produc6892749230674326005od_a_b > $o ).

thf(sy_c_AList_Omap__default__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_de8082232421929852711od_a_b: produc5436143990428185615od_a_b > produc5436143990428185615od_a_b > $o ).

thf(sy_c_AList_Omap__entry_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_en6964498282550363979od_a_b: $o > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Omap__entry_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_en6063826221664084574od_a_b: $o > ( produc2518759752815613485od_a_b > produc2518759752815613485od_a_b ) > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Omap__entry_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_en3197194780112073295od_a_b: fset_l1334069825099621524od_a_b > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Omap__entry__rel_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_en6339584017969766386od_a_b: produc7489520080164906694od_a_b > produc7489520080164906694od_a_b > $o ).

thf(sy_c_AList_Omap__entry__rel_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_en7425035617249803781od_a_b: produc4201866467197088793od_a_b > produc4201866467197088793od_a_b > $o ).

thf(sy_c_AList_Omap__entry__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_en202605468252318070od_a_b: produc246785466268114886od_a_b > produc246785466268114886od_a_b > $o ).

thf(sy_c_AList_Omap__ran_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_ra7768207298033780897od_a_b: ( $o > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Omap__ran_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_ra2300569569700106676od_a_b: ( $o > list_f1445794025290330138od_a_b > produc2518759752815613485od_a_b ) > list_P3574414722980446895od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Omap__ran_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_ra7039145154704061134od_a_b: ( $o > produc2518759752815613485od_a_b > list_f1445794025290330138od_a_b ) > list_P5302045529885307074od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Omap__ran_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_ra8397445362931850465od_a_b: ( $o > produc2518759752815613485od_a_b > produc2518759752815613485od_a_b ) > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Omap__ran_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_ra104177868202533149od_a_b: ( fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Omerge_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    merge_9196116298519041767od_a_b: list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Oupdate_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    update8681303028256525566od_a_b: $o > list_f1445794025290330138od_a_b > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Oupdate_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    update3607110547477456657od_a_b: $o > produc2518759752815613485od_a_b > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Oupdate_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    update1532413134665826556od_a_b: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > list_P1164858718851775149od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_AList_Oupdate_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    update9221375438537324674od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Oupdate__with__aux_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo,type,
    update7744615274700815744_a_b_o: list_f1445794025290330138od_a_b > $o > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_AList_Oupdate__with__aux_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    update1355849682342953596od_a_b: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b > ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_AList_Oupdate__with__aux_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    update2008830506971281325_a_b_o: produc2518759752815613485od_a_b > $o > ( produc2518759752815613485od_a_b > produc2518759752815613485od_a_b ) > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_AList_Oupdates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    update696951664350256759od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    bNF_Gr9187693764577137459od_a_b: set_li7540826859550765818od_a_b > fset_l1334069825099621524od_a_b > set_li7540826859550765818od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    bNF_Gr1899121854005402445od_a_b: set_li948167846089608596od_a_b > list_P1467974523212632366od_a_b > set_li948167846089608596od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_Gr6004602585737257543od_a_b: set_li6306622547289818894od_a_b > product_prod_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    bNF_Gr6941718835010197679od_a_b: set_li7540826859550765818od_a_b > list_f1445794025290330138od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    bNF_Gr5295578694846582473od_a_b: set_li948167846089608596od_a_b > list_l8778361445553822004od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bNF_Gr1699325108002784195od_a_b: set_li6306622547289818894od_a_b > list_P1467974523212632366od_a_b > set_Product_prod_a_b ).

thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    basic_8042737028673046454od_a_b: ( $o > nat ) > ( list_f1445794025290330138od_a_b > nat ) > produc2313482920965681321od_a_b > nat ).

thf(sy_c_Convergence_Oconverge_001tf__c_001tf__a_001tf__b,type,
    converge_c_a_b: fsm_c_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_Convergence_Oconverge_001tf__d_001tf__a_001tf__b,type,
    converge_d_a_b: fsm_d_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_OLS_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lS_fse3523897189346949940od_a_b: fsm_fs4038567970311364852od_a_b > fset_l1334069825099621524od_a_b > set_li7076890251784626569od_a_b ).

thf(sy_c_FSM_OLS_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    lS_fse7711909652459976378od_a_b: fsm_fs4691611325187074810od_a_b > fset_l1334069825099621524od_a_b > set_li7888096385779382799od_a_b ).

thf(sy_c_FSM_OLS_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    lS_fse7190820750362262733od_a_b: fsm_fs8047552373904900237od_a_b > fset_l1334069825099621524od_a_b > set_li104036716953425826od_a_b ).

thf(sy_c_FSM_OLS_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    lS_fse8932539686287297598od_a_b: fsm_fs3444354198583051774od_a_b > fset_l1334069825099621524od_a_b > set_li2133032475778560915od_a_b ).

thf(sy_c_FSM_OLS_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    lS_fse7452106412789865273_b_a_b: fsm_fs1840479945969036537_b_a_b > fset_l1334069825099621524od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lS_lis3357525008826253498od_a_b: fsm_li3816064051032718074od_a_b > list_f1445794025290330138od_a_b > set_li7076890251784626569od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lS_lis6227585698039082446od_a_b: fsm_li2173814106350063374od_a_b > list_P1467974523212632366od_a_b > set_li7076890251784626569od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    lS_lis5520868105703117908od_a_b: fsm_li6929239050930586644od_a_b > list_P1467974523212632366od_a_b > set_li7888096385779382799od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    lS_lis7345120860424838247od_a_b: fsm_li467911846419323815od_a_b > list_P1467974523212632366od_a_b > set_li104036716953425826od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    lS_lis5005023478512920792od_a_b: fsm_li9174950046736424472od_a_b > list_P1467974523212632366od_a_b > set_li2133032475778560915od_a_b ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    lS_lis474700916027962579_b_a_b: fsm_li1655959576902402579_b_a_b > list_P1467974523212632366od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_OLS_001tf__c_001tf__a_001tf__b,type,
    lS_c_a_b: fsm_c_a_b > c > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_OLS_001tf__d_001tf__a_001tf__b,type,
    lS_d_a_b: fsm_d_a_b > d > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_OLS__acyclic_001tf__c_001tf__a_001tf__b,type,
    lS_acyclic_c_a_b: fsm_c_a_b > c > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_OLS__acyclic_001tf__d_001tf__a_001tf__b,type,
    lS_acyclic_d_a_b: fsm_d_a_b > d > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Oacyclic_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    acycli2500287621552212143od_a_b: fsm_li3816064051032718074od_a_b > $o ).

thf(sy_c_FSM_Oacyclic_001tf__c_001tf__a_001tf__b,type,
    acyclic_c_a_b: fsm_c_a_b > $o ).

thf(sy_c_FSM_Oacyclic_001tf__d_001tf__a_001tf__b,type,
    acyclic_d_a_b: fsm_d_a_b > $o ).

thf(sy_c_FSM_Oacyclic__paths__up__to__length_001tf__c_001tf__a_001tf__b,type,
    acycli8734752832686661692_c_a_b: fsm_c_a_b > c > nat > set_li839162645350771998od_b_c ).

thf(sy_c_FSM_Oacyclic__paths__up__to__length_001tf__d_001tf__a_001tf__b,type,
    acycli5107599411020016573_d_a_b: fsm_d_a_b > d > nat > set_li7469257630003736542od_b_d ).

thf(sy_c_FSM_Oadd__transition__with__components_001tf__c_001tf__a_001tf__b,type,
    add_tr3757721147379511618_c_a_b: fsm_c_a_b > produc6657052613134160568od_b_c > fsm_c_a_b ).

thf(sy_c_FSM_Oadd__transition__with__components_001tf__d_001tf__a_001tf__b,type,
    add_tr130567725712866499_d_a_b: fsm_d_a_b > produc84550687463314808od_b_d > fsm_d_a_b ).

thf(sy_c_FSM_Oafter_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    after_5198964185542980012_b_a_b: fsm_fs1840479945969036537_b_a_b > fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_FSM_Oafter_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    after_6635595617298838829od_a_b: fsm_li3816064051032718074od_a_b > list_f1445794025290330138od_a_b > list_P5169789268404693161od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_FSM_Oafter_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    after_1595828222394802374_b_a_b: fsm_li1655959576902402579_b_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Oafter_001tf__c_001tf__a_001tf__b,type,
    after_c_a_b: fsm_c_a_b > c > list_P1467974523212632366od_a_b > c ).

thf(sy_c_FSM_Oafter_001tf__d_001tf__a_001tf__b,type,
    after_d_a_b: fsm_d_a_b > d > list_P1467974523212632366od_a_b > d ).

thf(sy_c_FSM_Odeadlock__state_001tf__c_001tf__a_001tf__b,type,
    deadlock_state_c_a_b: fsm_c_a_b > c > $o ).

thf(sy_c_FSM_Odeadlock__state_001tf__d_001tf__a_001tf__b,type,
    deadlock_state_d_a_b: fsm_d_a_b > d > $o ).

thf(sy_c_FSM_Odefined__inputs_001tf__c_001tf__a_001tf__b,type,
    defined_inputs_c_a_b: fsm_c_a_b > c > set_a ).

thf(sy_c_FSM_Odefined__inputs_001tf__d_001tf__a_001tf__b,type,
    defined_inputs_d_a_b: fsm_d_a_b > d > set_a ).

thf(sy_c_FSM_Odeterministic_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    determ8637524772085499191od_a_b: fsm_li3816064051032718074od_a_b > $o ).

thf(sy_c_FSM_Odistinguishes_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    distin4693659209764571861_b_a_b: fsm_fs1840479945969036537_b_a_b > fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Odistinguishes_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    distin348325521541145199_b_a_b: fsm_li1655959576902402579_b_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Odistinguishes_001tf__c_001tf__a_001tf__b,type,
    distinguishes_c_a_b: fsm_c_a_b > c > c > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Odistinguishes_001tf__d_001tf__a_001tf__b,type,
    distinguishes_d_a_b: fsm_d_a_b > d > d > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Ofrom__FSM_001tf__c_001tf__a_001tf__b,type,
    from_FSM_c_a_b: fsm_c_a_b > c > fsm_c_a_b ).

thf(sy_c_FSM_Ofrom__FSM_001tf__d_001tf__a_001tf__b,type,
    from_FSM_d_a_b: fsm_d_a_b > d > fsm_d_a_b ).

thf(sy_c_FSM_Oh__obs_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    h_obs_1937385545949026089od_a_b: fsm_li3816064051032718074od_a_b > list_f1445794025290330138od_a_b > $o > fset_l1334069825099621524od_a_b > option4548628174090016992od_a_b ).

thf(sy_c_FSM_Oh__obs_001tf__c_001tf__a_001tf__b,type,
    h_obs_c_a_b: fsm_c_a_b > c > a > b > option_c ).

thf(sy_c_FSM_Oh__obs_001tf__d_001tf__a_001tf__b,type,
    h_obs_d_a_b: fsm_d_a_b > d > a > b > option_d ).

thf(sy_c_FSM_Oinitial_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    initia5383324526419690047od_a_b: fsm_fs4038567970311364852od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_FSM_Oinitial_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    initia2961132633701536452_b_a_b: fsm_fs1840479945969036537_b_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_FSM_Oinitial_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    initia3208193535625315909od_a_b: fsm_li3816064051032718074od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_FSM_Oinitial_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    initia8636230792963847769od_a_b: fsm_li2173814106350063374od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Oinitial_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    initia1111342868025077214_b_a_b: fsm_li1655959576902402579_b_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Oinitial_001tf__c_001tf__a_001tf__b,type,
    initial_c_a_b: fsm_c_a_b > c ).

thf(sy_c_FSM_Oinitial_001tf__d_001tf__a_001tf__b,type,
    initial_d_a_b: fsm_d_a_b > d ).

thf(sy_c_FSM_Omaximal__prefix__in__language_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    maxima3855660599394504998_b_a_b: fsm_fs1840479945969036537_b_a_b > fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Omaximal__prefix__in__language_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    maxima5690422175864505664_b_a_b: fsm_li1655959576902402579_b_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Omaximal__prefix__in__language_001tf__c_001tf__a_001tf__b,type,
    maxima6316071336277646226_c_a_b: fsm_c_a_b > c > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Omaximal__prefix__in__language_001tf__d_001tf__a_001tf__b,type,
    maxima2688917914611001107_d_a_b: fsm_d_a_b > d > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_FSM_Ominimal_001tf__c_001tf__a_001tf__b,type,
    minimal_c_a_b: fsm_c_a_b > $o ).

thf(sy_c_FSM_Ominimal_001tf__d_001tf__a_001tf__b,type,
    minimal_d_a_b: fsm_d_a_b > $o ).

thf(sy_c_FSM_Ominimally__distinguishes_001tf__c_001tf__a_001tf__b,type,
    minima5000056638725520487_c_a_b: fsm_c_a_b > c > c > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Ominimally__distinguishes_001tf__d_001tf__a_001tf__b,type,
    minima1372903217058875368_d_a_b: fsm_d_a_b > d > d > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    observ3669562468644736030od_a_b: fsm_fs4691611325187074810od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    observ1325349641595455025od_a_b: fsm_fs8047552373904900237od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    observ4317395130350675874od_a_b: fsm_fs3444354198583051774od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    observ529373768824785053_b_a_b: fsm_fs1840479945969036537_b_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    observ8538549861865788958od_a_b: fsm_li3816064051032718074od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    observ5961674566362278840od_a_b: fsm_li6929239050930586644od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    observ9193399924451010507od_a_b: fsm_li467911846419323815od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    observ227875004139865660od_a_b: fsm_li9174950046736424472od_a_b > $o ).

thf(sy_c_FSM_Oobservable_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    observ3837622365268550711_b_a_b: fsm_li1655959576902402579_b_a_b > $o ).

thf(sy_c_FSM_Oobservable_001tf__c_001tf__a_001tf__b,type,
    observable_c_a_b: fsm_c_a_b > $o ).

thf(sy_c_FSM_Oobservable_001tf__d_001tf__a_001tf__b,type,
    observable_d_a_b: fsm_d_a_b > $o ).

thf(sy_c_FSM_Opass__io__set_001tf__c_001tf__a_001tf__b,type,
    pass_io_set_c_a_b: fsm_c_a_b > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_FSM_Opass__io__set_001tf__d_001tf__a_001tf__b,type,
    pass_io_set_d_a_b: fsm_d_a_b > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_FSM_Opass__io__set__maximal_001tf__c_001tf__a_001tf__b,type,
    pass_i1401700117844051364_c_a_b: fsm_c_a_b > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_FSM_Opass__io__set__maximal_001tf__d_001tf__a_001tf__b,type,
    pass_i6997918733032182053_d_a_b: fsm_d_a_b > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_FSM_Opath_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    path_l4848144068100360156od_a_b: fsm_li3816064051032718074od_a_b > list_f1445794025290330138od_a_b > list_P5370328139307421263od_a_b > $o ).

thf(sy_c_FSM_Opath_001tf__c_001tf__a_001tf__b,type,
    path_c_a_b: fsm_c_a_b > c > list_P5017272815184427326od_b_c > $o ).

thf(sy_c_FSM_Opath_001tf__d_001tf__a_001tf__b,type,
    path_d_a_b: fsm_d_a_b > d > list_P8454989104189725694od_b_d > $o ).

thf(sy_c_FSM_Oreachable_001tf__c_001tf__a_001tf__b,type,
    reachable_c_a_b: fsm_c_a_b > c > $o ).

thf(sy_c_FSM_Oreachable_001tf__d_001tf__a_001tf__b,type,
    reachable_d_a_b: fsm_d_a_b > d > $o ).

thf(sy_c_FSM_Oreachable__k_001tf__c_001tf__a_001tf__b,type,
    reachable_k_c_a_b: fsm_c_a_b > c > nat > set_c ).

thf(sy_c_FSM_Oreachable__k_001tf__d_001tf__a_001tf__b,type,
    reachable_k_d_a_b: fsm_d_a_b > d > nat > set_d ).

thf(sy_c_FSM_Oreachable__states_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    reacha3719139522904929108od_a_b: fsm_fs4038567970311364852od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Oreachable__states_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    reacha2755017045781758809_b_a_b: fsm_fs1840479945969036537_b_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Oreachable__states_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    reacha7494367349399693530od_a_b: fsm_li3816064051032718074od_a_b > set_li7540826859550765818od_a_b ).

thf(sy_c_FSM_Oreachable__states_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    reacha4791805987247240686od_a_b: fsm_li2173814106350063374od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Oreachable__states_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    reacha5660761788860886259_b_a_b: fsm_li1655959576902402579_b_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Oreachable__states_001tf__c_001tf__a_001tf__b,type,
    reacha6376826306246091717_c_a_b: fsm_c_a_b > set_c ).

thf(sy_c_FSM_Oreachable__states_001tf__d_001tf__a_001tf__b,type,
    reacha2749672884579446598_d_a_b: fsm_d_a_b > set_d ).

thf(sy_c_FSM_Orename__states_001tf__c_001tf__a_001tf__b_001tf__c,type,
    rename4723348732125710963_a_b_c: fsm_c_a_b > ( c > c ) > fsm_c_a_b ).

thf(sy_c_FSM_Orename__states_001tf__c_001tf__a_001tf__b_001tf__d,type,
    rename4723348732125710964_a_b_d: fsm_c_a_b > ( c > d ) > fsm_d_a_b ).

thf(sy_c_FSM_Orename__states_001tf__d_001tf__a_001tf__b_001tf__c,type,
    rename6211310769420509490_a_b_c: fsm_d_a_b > ( d > c ) > fsm_c_a_b ).

thf(sy_c_FSM_Orename__states_001tf__d_001tf__a_001tf__b_001tf__d,type,
    rename6211310769420509491_a_b_d: fsm_d_a_b > ( d > d ) > fsm_d_a_b ).

thf(sy_c_FSM_Osingle__input_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    single8793350731111814183od_a_b: fsm_li3816064051032718074od_a_b > $o ).

thf(sy_c_FSM_Osize_001tf__c_001tf__a_001tf__b,type,
    size_c_a_b: fsm_c_a_b > nat ).

thf(sy_c_FSM_Osize_001tf__d_001tf__a_001tf__b,type,
    size_d_a_b: fsm_d_a_b > nat ).

thf(sy_c_FSM_Ostates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    states8298490222144566041od_a_b: fsm_fs4038567970311364852od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Ostates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    states817862702784690207od_a_b: fsm_fs4691611325187074810od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Ostates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    states5841465829182338866od_a_b: fsm_fs8047552373904900237od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Ostates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    states7817400623188889891od_a_b: fsm_fs3444354198583051774od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Ostates_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    states760346292458343070_b_a_b: fsm_fs1840479945969036537_b_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    states5686850096005743135od_a_b: fsm_li3816064051032718074od_a_b > set_li7540826859550765818od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    states7671667289678552115od_a_b: fsm_li2173814106350063374od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    states1072089101645958201od_a_b: fsm_li6929239050930586644od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    states535247141084106060od_a_b: fsm_li467911846419323815od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    states61340070856860733od_a_b: fsm_li9174950046736424472od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Ostates_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    states5225472451708754616_b_a_b: fsm_li1655959576902402579_b_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_FSM_Ostates_001tf__c_001tf__a_001tf__b,type,
    states_c_a_b: fsm_c_a_b > set_c ).

thf(sy_c_FSM_Ostates_001tf__d_001tf__a_001tf__b,type,
    states_d_a_b: fsm_d_a_b > set_d ).

thf(sy_c_FSM_Otarget_001tf__c_001tf__a_001tf__b,type,
    target_c_a_b: c > list_P5017272815184427326od_b_c > c ).

thf(sy_c_FSM_Otarget_001tf__d_001tf__a_001tf__b,type,
    target_d_a_b: d > list_P8454989104189725694od_b_d > d ).

thf(sy_c_FSM_Otransitions_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    transi413513904105055205od_a_b: fsm_fs4038567970311364852od_a_b > set_Pr5812197030978132777od_a_b ).

thf(sy_c_FSM_Otransitions_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__a_001tf__b,type,
    transi2241535490925309290_b_a_b: fsm_fs1840479945969036537_b_a_b > set_Pr4210316172971897624od_a_b ).

thf(sy_c_FSM_Otransitions_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    transi2698755513253879019od_a_b: fsm_li3816064051032718074od_a_b > set_Pr6133615449426215977od_a_b ).

thf(sy_c_FSM_Otransitions_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    transi1383219260676973311od_a_b: fsm_li2173814106350063374od_a_b > set_Pr731044129912021033od_a_b ).

thf(sy_c_FSM_Otransitions_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__a_001tf__b,type,
    transi705733371584467844_b_a_b: fsm_li1655959576902402579_b_a_b > set_Pr4832031994198807704od_a_b ).

thf(sy_c_FSM_Otransitions_001tf__c_001tf__a_001tf__b,type,
    transitions_c_a_b: fsm_c_a_b > set_Pr7047737848026531864od_b_c ).

thf(sy_c_FSM_Otransitions_001tf__d_001tf__a_001tf__b,type,
    transitions_d_a_b: fsm_d_a_b > set_Pr1262082100177054424od_b_d ).

thf(sy_c_FSM_Ovisited__states_001tf__c_001tf__a_001tf__b,type,
    visited_states_c_a_b: c > list_P5017272815184427326od_b_c > list_c ).

thf(sy_c_FSM_Ovisited__states_001tf__d_001tf__a_001tf__b,type,
    visited_states_d_a_b: d > list_P8454989104189725694od_b_d > list_d ).

thf(sy_c_FSet_Ofmember_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    fmembe7722352836199763061od_a_b: list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b > $o ).

thf(sy_c_Fun_Obij__betw_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bij_be1705665232800849660od_a_b: ( fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b ) > set_fs5173440902860351732od_a_b > set_li7540826859550765818od_a_b > $o ).

thf(sy_c_Fun_Obij__betw_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__c,type,
    bij_be6008341014587936482_a_b_c: ( fset_l1334069825099621524od_a_b > c ) > set_fs5173440902860351732od_a_b > set_c > $o ).

thf(sy_c_Fun_Obij__betw_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001tf__d,type,
    bij_be6008341014587936483_a_b_d: ( fset_l1334069825099621524od_a_b > d ) > set_fs5173440902860351732od_a_b > set_d > $o ).

thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bij_be5509875313758850402od_a_b: ( list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b ) > set_li6306622547289818894od_a_b > set_li7540826859550765818od_a_b > $o ).

thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__c,type,
    bij_be3428385127041619016_a_b_c: ( list_P1467974523212632366od_a_b > c ) > set_li6306622547289818894od_a_b > set_c > $o ).

thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001tf__d,type,
    bij_be3428385127041619017_a_b_d: ( list_P1467974523212632366od_a_b > d ) > set_li6306622547289818894od_a_b > set_d > $o ).

thf(sy_c_Fun_Obij__betw_001tf__c_001tf__c,type,
    bij_betw_c_c: ( c > c ) > set_c > set_c > $o ).

thf(sy_c_Fun_Obij__betw_001tf__c_001tf__d,type,
    bij_betw_c_d: ( c > d ) > set_c > set_d > $o ).

thf(sy_c_Fun_Obij__betw_001tf__d_001tf__c,type,
    bij_betw_d_c: ( d > c ) > set_d > set_c > $o ).

thf(sy_c_Fun_Obij__betw_001tf__d_001tf__d,type,
    bij_betw_d_d: ( d > d ) > set_d > set_d > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
    minus_minus_nat: nat > nat > nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    minus_8847328276483105883od_a_b: set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    minus_5246360636435702261od_a_b: set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
    plus_plus_nat: nat > nat > nat ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

thf(sy_c_If_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    if_fse2516390947016424794od_a_b: $o > fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_If_001t__List__Olist_I_Eo_J,type,
    if_list_o: $o > list_o > list_o > list_o ).

thf(sy_c_If_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    if_lis3379674621698944480od_a_b: $o > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_If_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    if_lis8377773601782977152od_a_b: $o > list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_If_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    if_lis737310530615849466od_a_b: $o > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(sy_c_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    if_lis1002476807507936500od_a_b: $o > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_If_001t__List__Olist_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    if_lis6932009802700144192od_a_b: $o > list_s7922523924679432314od_a_b > list_s7922523924679432314od_a_b > list_s7922523924679432314od_a_b ).

thf(sy_c_If_001t__List__Olist_Itf__a_J,type,
    if_list_a: $o > list_a > list_a > list_a ).

thf(sy_c_If_001t__List__Olist_Itf__c_J,type,
    if_list_c: $o > list_c > list_c > list_c ).

thf(sy_c_If_001t__List__Olist_Itf__d_J,type,
    if_list_d: $o > list_d > list_d > list_d ).

thf(sy_c_If_001t__Nat__Onat,type,
    if_nat: $o > nat > nat > nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    inf_in6210868181720738530od_a_b: set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    inf_in4848585719623981052od_a_b: set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    inf_in8976041639890736118od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > set_Product_prod_a_b ).

thf(sy_c_List_Oappend_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    append2015155619842375983od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Oappend_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    append1675525773727384373od_a_b: list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Oappend_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    append7557446516274476873od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    append2579811284360515140od_a_b: list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    append4988338609183987159od_a_b: list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    append5873922736804373826od_a_b: list_P1164858718851775149od_a_b > list_P1164858718851775149od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    append5072337359724802120od_a_b: list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    append7576980629738617822od_a_b: list_P3068083765560563145od_a_b > list_P3068083765560563145od_a_b > list_P3068083765560563145od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    append5335208823350062147od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    append7871285015701691475od_b_c: list_P5017272815184427326od_b_c > list_P5017272815184427326od_b_c > list_P5017272815184427326od_b_c ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    append1298783090030845715od_b_d: list_P8454989104189725694od_b_d > list_P8454989104189725694od_b_d > list_P8454989104189725694od_b_d ).

thf(sy_c_List_Obutlast_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    butlas6970048242682811878od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Obutlast_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    butlas2591555278381536128od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    butlas8142365734376493050od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Ocan__select_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    can_se1502477684658679057od_a_b: ( fset_l1334069825099621524od_a_b > $o ) > set_fs5173440902860351732od_a_b > $o ).

thf(sy_c_List_Ocan__select_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    can_se3446867761079811115od_a_b: ( list_P1467974523212632366od_a_b > $o ) > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_List_Oconcat_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    concat3179126272939696085od_a_b: list_l6099054058445139744od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Oconcat_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    concat8700631635091661039od_a_b: list_l6443893005374362810od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    concat6071998534011412713od_a_b: list_l8778361445553822004od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Odistinct_001_Eo,type,
    distinct_o: list_o > $o ).

thf(sy_c_List_Odistinct_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    distin1329390416381046541od_a_b: list_f1445794025290330138od_a_b > $o ).

thf(sy_c_List_Odistinct_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    distin5173564018569636371od_a_b: list_l6099054058445139744od_a_b > $o ).

thf(sy_c_List_Odistinct_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    distin3617893958516599847od_a_b: list_l8778361445553822004od_a_b > $o ).

thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
    distinct_nat: list_nat > $o ).

thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    distin132333874345289761od_a_b: list_P1467974523212632366od_a_b > $o ).

thf(sy_c_List_Odistinct_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    distin6974803764735332205od_a_b: list_s7922523924679432314od_a_b > $o ).

thf(sy_c_List_Odistinct_001tf__c,type,
    distinct_c: list_c > $o ).

thf(sy_c_List_Odistinct_001tf__d,type,
    distinct_d: list_d > $o ).

thf(sy_c_List_Odrop_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    drop_f570763960254934490od_a_b: nat > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Odrop_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    drop_l4132970615840781684od_a_b: nat > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Oenumerate_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    enumer6431117045728783481od_a_b: nat > list_f1445794025290330138od_a_b > list_P3068083765560563145od_a_b ).

thf(sy_c_List_Oinsert_001_Eo,type,
    insert_o: $o > list_o > list_o ).

thf(sy_c_List_Oinsert_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    insert2610919176168914352od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Oinsert_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    insert8509595773599419190od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Oinsert_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    insert831838759768339024od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Oinsert_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    insert4925036576401664074od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Oinsert_001t__Nat__Onat,type,
    insert_nat: nat > list_nat > list_nat ).

thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    insert7736115125267272132od_a_b: product_prod_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Oinsert_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    insert4427174617854087696od_a_b: set_fs5173440902860351732od_a_b > list_s7922523924679432314od_a_b > list_s7922523924679432314od_a_b ).

thf(sy_c_List_Oinsert_001tf__a,type,
    insert_a: a > list_a > list_a ).

thf(sy_c_List_Oinsert_001tf__c,type,
    insert_c: c > list_c > list_c ).

thf(sy_c_List_Oinsert_001tf__d,type,
    insert_d: d > list_d > list_d ).

thf(sy_c_List_Olast_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    last_f4009646753867174963od_a_b: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_List_Olast_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    last_l1496300474439883853od_a_b: list_l8778361445553822004od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olenlex_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lenlex8762485181240705951od_a_b: set_Pr2242436922956002695od_a_b > set_Pr803608928346326407od_a_b ).

thf(sy_c_List_Olex_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lex_fs1791213440591458046od_a_b: set_Pr2242436922956002695od_a_b > set_Pr803608928346326407od_a_b ).

thf(sy_c_List_Olexord_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lexord9144254948259057799od_a_b: set_Pr2242436922956002695od_a_b > set_Pr803608928346326407od_a_b ).

thf(sy_c_List_Olexord_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    lexord2488576207029785249od_a_b: set_Pr3015088788472578951od_a_b > set_Pr3498424749146541447od_a_b ).

thf(sy_c_List_Olist_OCons_001_Eo,type,
    cons_o: $o > list_o > list_o ).

thf(sy_c_List_Olist_OCons_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_f6577355434438001738od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_I_Eo_J,type,
    cons_list_o: list_o > list_list_o > list_list_o ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_l7290444712290925776od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    cons_l2865286841204467926od_a_b: list_l6099054058445139744od_a_b > list_l378912295992385958od_a_b > list_l378912295992385958od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_l4798275018037426410od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
    cons_list_nat: list_nat > list_list_nat > list_list_nat ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    cons_l907386227682280420od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
    cons_nat: nat > list_nat > list_nat ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_P2465205493254962905od_a_b: produc3910515788072733219od_a_b > list_P5169789268404693161od_a_b > list_P5169789268404693161od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    cons_P2672142353023029855od_a_b: produc2313482920965681321od_a_b > list_P3574414722980446895od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    cons_P7065065391077662962od_a_b: produc8937288731615916348od_a_b > list_P5302045529885307074od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_P1864978001919373149od_a_b: produc8767915422032708007od_a_b > list_P1164858718851775149od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    cons_P7745750895690215651od_a_b: produc2518759752815613485od_a_b > list_P5488608094462411443od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    cons_P383312003685503615od_a_b: produc3626440574470744009od_a_b > list_P5370328139307421263od_a_b > list_P5370328139307421263od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_P1524207422287465219od_a_b: produc6829992310584780345od_a_b > list_P3068083765560563145od_a_b > list_P3068083765560563145od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    cons_P1301695370724503771od_a_b: produc7169317207952727333od_a_b > list_P2891578699137632811od_a_b > list_P2891578699137632811od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_P1362141854008209397od_a_b: produc9005793448470268223od_a_b > list_P2373415021271773893od_a_b > list_P2373415021271773893od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    cons_P8793802274825991495od_b_c: produc3550516665487611281od_b_c > list_P8634110456476873367od_b_c > list_P8634110456476873367od_b_c ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    cons_P8864836314872337480od_b_d: produc3621550705533957266od_b_d > list_P6112925938187837720od_b_d > list_P6112925938187837720od_b_d ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    cons_P7316939131009794654od_a_b: product_prod_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    cons_s5741212700939514026od_a_b: set_fs5173440902860351732od_a_b > list_s7922523924679432314od_a_b > list_s7922523924679432314od_a_b ).

thf(sy_c_List_Olist_OCons_001tf__a,type,
    cons_a: a > list_a > list_a ).

thf(sy_c_List_Olist_OCons_001tf__c,type,
    cons_c: c > list_c > list_c ).

thf(sy_c_List_Olist_OCons_001tf__d,type,
    cons_d: d > list_d > list_d ).

thf(sy_c_List_Olist_ONil_001_Eo,type,
    nil_o: list_o ).

thf(sy_c_List_Olist_ONil_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_fs4581119677382125722od_a_b: list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_I_Eo_J,type,
    nil_list_o: list_list_o ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nil_li6050065983854590240od_a_b: list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    nil_li4771897614291402022od_a_b: list_l378912295992385958od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_li2802039260981550394od_a_b: list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
    nil_list_nat: list_list_nat ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    nil_li8635777946366267444od_a_b: list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
    nil_nat: list_nat ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nil_Pr7172365244936649513od_a_b: list_P5169789268404693161od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    nil_Pr7302809325368845999od_a_b: list_P3574414722980446895od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    nil_Pr3614377049866306882od_a_b: list_P5302045529885307074od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nil_Pr4252210933832115117od_a_b: list_P1164858718851775149od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    nil_Pr1838250474468212019od_a_b: list_P5488608094462411443od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    nil_Pr2185010156820804907od_a_b: list_P2891578699137632811od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nil_Pr5469403351896759365od_a_b: list_P2373415021271773893od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    nil_Pr6797566517770115479od_b_c: list_P8634110456476873367od_b_c ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    nil_Pr6868600557816461464od_b_d: list_P6112925938187837720od_b_d ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    nil_Product_prod_a_b: list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    nil_Pr5329896168980422846od_b_c: list_P5017272815184427326od_b_c ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    nil_Pr7980766280164352894od_b_d: list_P8454989104189725694od_b_d ).

thf(sy_c_List_Olist_Ohd_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    hd_fse7826183927675143039od_a_b: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    hd_lis2958756505300214169od_a_b: list_l8778361445553822004od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olist_Omap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    map_fs8651439882968028996od_a_b: ( fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b ) > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_Omap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_fs7724969689208736458od_a_b: ( fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b ) > list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_Omap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    map_fs6872359466567453668od_a_b: ( fset_l1334069825099621524od_a_b > list_l8778361445553822004od_a_b ) > list_f1445794025290330138od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_Omap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    map_fs2600689390591810526od_a_b: ( fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b ) > list_f1445794025290330138od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_Omap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_fs8417695273700992087od_a_b: ( fset_l1334069825099621524od_a_b > produc8767915422032708007od_a_b ) > list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_li2254913030204620100od_a_b: ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_li3123090900592589011od_a_b: ( list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b ) > list_l6099054058445139744od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    map_li4307878677677536599od_a_b: ( list_f1445794025290330138od_a_b > produc2518759752815613485od_a_b ) > list_l6099054058445139744od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_li1742795277881387806od_a_b: ( list_f1445794025290330138od_a_b > set_fs5173440902860351732od_a_b ) > list_l6099054058445139744od_a_b > list_s7922523924679432314od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    map_li7547266996134490026od_a_b: ( list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b ) > list_l8778361445553822004od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_li1484870096797251632od_a_b: ( list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b ) > list_l8778361445553822004od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    map_li5768186579733914698od_a_b: ( list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ) > list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    map_li1070312879311380292od_a_b: ( list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ) > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    map_Pr8806166102037958131_a_b_o: ( produc2313482920965681321od_a_b > $o ) > list_P3574414722980446895od_a_b > list_o ).

thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    map_Pr9157305129235354997od_a_b: ( produc2313482920965681321od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_001_Eo,type,
    map_Pr56420267031402400_a_b_o: ( produc8937288731615916348od_a_b > $o ) > list_P5302045529885307074od_a_b > list_o ).

thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    map_Pr4898593741463396971od_a_b: ( produc2518759752815613485od_a_b > fset_l1334069825099621524od_a_b ) > list_P5488608094462411443od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    map_Pr4429666502407624467od_a_b: ( produc2518759752815613485od_a_b > produc8937288731615916348od_a_b ) > list_P5488608094462411443od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_List_Olist_Oset_001_Eo,type,
    set_o2: list_o > set_o ).

thf(sy_c_List_Olist_Oset_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    set_fs4298891544546585641od_a_b: list_f1445794025290330138od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_li8217014873844115759od_a_b: list_l6099054058445139744od_a_b > set_li7540826859550765818od_a_b ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    set_li2519811128146010313od_a_b: list_l6443893005374362810od_a_b > set_li948167846089608596od_a_b ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    set_li5045283583078295363od_a_b: list_l8778361445553822004od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
    set_nat2: list_nat > set_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr6076554551450486590od_a_b: list_P3574414722980446895od_a_b > set_Pr121319624013539721od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    set_Pr3486397488485167313od_a_b: list_P5302045529885307074od_a_b > set_Pr5622538825374275996od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr3326995048199123516od_a_b: list_P1164858718851775149od_a_b > set_Pr2242436922956002695od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr6825554078267013186od_a_b: list_P5488608094462411443od_a_b > set_Pr1051027220935592077od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    set_Pr1811016573229031484od_a_b: list_P8601282865932132013od_a_b > set_Pr3015088788472578951od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr3993988432441487460od_a_b: list_P3068083765560563145od_a_b > set_Pr8907832335669617775od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    set_Product_prod_a_b2: list_P1467974523212632366od_a_b > set_Product_prod_a_b ).

thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_se4205765813130927241od_a_b: list_s7922523924679432314od_a_b > set_se1014227543623231828od_a_b ).

thf(sy_c_List_Olist_Oset_001tf__a,type,
    set_a2: list_a > set_a ).

thf(sy_c_List_Olist_Oset_001tf__c,type,
    set_c2: list_c > set_c ).

thf(sy_c_List_Olist_Oset_001tf__d,type,
    set_d2: list_d > set_d ).

thf(sy_c_List_Olist_Osize__list_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    size_l2153056584847331996od_a_b: ( fset_l1334069825099621524od_a_b > nat ) > list_f1445794025290330138od_a_b > nat ).

thf(sy_c_List_Olist_Osize__list_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    size_l6337794300503450422od_a_b: ( list_P1467974523212632366od_a_b > nat ) > list_l8778361445553822004od_a_b > nat ).

thf(sy_c_List_Olist_Otl_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    tl_fse1540917908967337859od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist_Otl_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    tl_lis3067933314816597917od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist__ex1_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_e7381079376597858269od_a_b: ( fset_l1334069825099621524od_a_b > $o ) > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_List_Olist__ex1_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    list_e3621433171152788727od_a_b: ( list_P1467974523212632366od_a_b > $o ) > list_l8778361445553822004od_a_b > $o ).

thf(sy_c_List_Olist__update_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_u7851604859245713154od_a_b: list_f1445794025290330138od_a_b > nat > fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Olist__update_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    list_u6451611954593206940od_a_b: list_l8778361445553822004od_a_b > nat > list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olistrel1_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    listre757946421397414515od_a_b: set_Pr2242436922956002695od_a_b > set_Pr803608928346326407od_a_b ).

thf(sy_c_List_Olistrel_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    listre8201142255725533427od_a_b: set_Pr121319624013539721od_a_b > set_Pr4856876843892373641od_a_b ).

thf(sy_c_List_Olistrel_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    listre3706061411988323334od_a_b: set_Pr5622538825374275996od_a_b > set_Pr7954061446304757788od_a_b ).

thf(sy_c_List_Olistrel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    listre6775573709112125169od_a_b: set_Pr2242436922956002695od_a_b > set_Pr803608928346326407od_a_b ).

thf(sy_c_List_Olistrel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    listre5187687223414087671od_a_b: set_Pr1051027220935592077od_a_b > set_Pr4286734062635796237od_a_b ).

thf(sy_c_List_Omember_001_Eo,type,
    member_o: list_o > $o > $o ).

thf(sy_c_List_Omember_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member4364926001285900847od_a_b: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b > $o ).

thf(sy_c_List_Omember_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member8444533430530386997od_a_b: list_l6099054058445139744od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_List_Omember_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member2585845584885325519od_a_b: list_l6443893005374362810od_a_b > list_l8778361445553822004od_a_b > $o ).

thf(sy_c_List_Omember_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member8280676862674542665od_a_b: list_l8778361445553822004od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_List_Omember_001t__Nat__Onat,type,
    member_nat: list_nat > nat > $o ).

thf(sy_c_List_Omember_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    member851666194574169411od_a_b: list_P1467974523212632366od_a_b > product_prod_a_b > $o ).

thf(sy_c_List_Omember_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member8348088493781385871od_a_b: list_s7922523924679432314od_a_b > set_fs5173440902860351732od_a_b > $o ).

thf(sy_c_List_Omember_001tf__a,type,
    member_a: list_a > a > $o ).

thf(sy_c_List_Omember_001tf__c,type,
    member_c: list_c > c > $o ).

thf(sy_c_List_Omember_001tf__d,type,
    member_d: list_d > d > $o ).

thf(sy_c_List_On__lists_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    n_list7006363026360775842od_a_b: nat > list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_On__lists_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    n_list8012392503361751734od_a_b: nat > list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Onth_001_Eo,type,
    nth_o: list_o > nat > $o ).

thf(sy_c_List_Onth_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nth_fs7310631729605226779od_a_b: list_f1445794025290330138od_a_b > nat > fset_l1334069825099621524od_a_b ).

thf(sy_c_List_Onth_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nth_li3998004317099707681od_a_b: list_l6099054058445139744od_a_b > nat > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Onth_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    nth_li6535284973015076149od_a_b: list_l8778361445553822004od_a_b > nat > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Onth_001t__Nat__Onat,type,
    nth_nat: list_nat > nat > nat ).

thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    nth_Pr7741617482765506100od_a_b: list_P5488608094462411443od_a_b > nat > produc2518759752815613485od_a_b ).

thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    nth_Pr5342818094514074866od_a_b: list_P3068083765560563145od_a_b > nat > produc6829992310584780345od_a_b ).

thf(sy_c_List_Oproduct_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc2134592012631421511od_a_b: list_o > list_l6099054058445139744od_a_b > list_P3574414722980446895od_a_b ).

thf(sy_c_List_Oproduct_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7959357592531908954od_a_b: list_o > list_P5488608094462411443od_a_b > list_P5302045529885307074od_a_b ).

thf(sy_c_List_Oproduct_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8535066297417230155od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b > list_P5488608094462411443od_a_b ).

thf(sy_c_List_Oproduct__lists_001_Eo,type,
    product_lists_o: list_list_o > list_list_o ).

thf(sy_c_List_Oproduct__lists_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2086904765359242883od_a_b: list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Oproduct__lists_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc5179936861586982537od_a_b: list_l378912295992385958od_a_b > list_l378912295992385958od_a_b ).

thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    produc5891818806577749399od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_OremoveAll_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    remove7132956074442862240od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_OremoveAll_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    remove6452524568127849510od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_OremoveAll_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    remove7800354776472834362od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Orotate1_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    rotate1032322621218768487od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Osubseqs_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    subseq8423821483446685161od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    subseq3159716953272533757od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Otake_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    take_f8758302346742390914od_a_b: nat > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_List_Otake_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    take_l2578627034827611164od_a_b: nat > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Otake_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    take_P1986783999826777750od_a_b: nat > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_Nat_OSuc,type,
    suc: nat > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
    size_size_list_o: list_o > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    size_s6068669265016274566od_a_b: list_f1445794025290330138od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    size_s3205160614079436684od_a_b: list_l6099054058445139744od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    size_s4021047160419372448od_a_b: list_l8778361445553822004od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
    size_size_list_nat: list_nat > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    size_s5774146080724371231od_a_b: list_P5488608094462411443od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    size_s1491918145416384605od_a_b: list_P3068083765560563145od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    size_s3956712670882376602od_a_b: list_P1467974523212632366od_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    size_s2076481953422752682od_b_c: list_P5017272815184427326od_b_c > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J,type,
    size_s5514198242428051050od_b_d: list_P8454989104189725694od_b_d > nat ).

thf(sy_c_Option_Ooption_ONone_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    none_l1130124498050917115od_a_b: option4548628174090016992od_a_b ).

thf(sy_c_Option_Ooption_ONone_001tf__c,type,
    none_c: option_c ).

thf(sy_c_Option_Ooption_ONone_001tf__d,type,
    none_d: option_d ).

thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
    bot_bot_o: $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    bot_bo5063621712161242880od_a_b: fset_l1334069825099621524od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo8701990416999507078od_a_b: list_f1445794025290330138od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    bot_bo3446722378476343061od_a_b: produc2313482920965681321od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    bot_bo1834714299575479208od_a_b: produc8937288731615916348od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    bot_bo4510604746321438361od_a_b: produc2518759752815613485od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo4080195304570884960od_a_b: set_fs5173440902860351732od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    bot_bo5012769492311455590od_a_b: set_li7540826859550765818od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    bot_bo4036995510831765370od_a_b: set_li6306622547289818894od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    bot_bo3428410327501040244od_a_b: set_Product_prod_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__c_J,type,
    bot_bot_set_c: set_c ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__d_J,type,
    bot_bot_set_d: set_d ).

thf(sy_c_Orderings_Oord__class_Oless_001_Eo,type,
    ord_less_o: $o > $o > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    ord_le98927018796173120od_a_b: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    ord_le7150648013565725894od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__List__Olist_It__Nat__Onat_J,type,
    ord_less_list_nat: list_nat > list_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    ord_le4629424078442911573od_a_b: produc2313482920965681321od_a_b > produc2313482920965681321od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    ord_le5639095759471244264od_a_b: produc8937288731615916348od_a_b > produc8937288731615916348od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    ord_le1232572551315295961od_a_b: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    ord_le1203424502768444845at_nat: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
    ord_less_eq_o: $o > $o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    ord_le5177564485156961332od_a_b: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    ord_le2437917120829568954od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__List__Olist_It__Nat__Onat_J,type,
    ord_less_eq_list_nat: list_nat > list_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    ord_le6405569072945473609od_a_b: produc2313482920965681321od_a_b > produc2313482920965681321od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    ord_le117511869695297756od_a_b: produc8937288731615916348od_a_b > produc8937288731615916348od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    ord_le1997768708718029od_a_b: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    ord_le8460144461188290721at_nat: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    ord_le8981612867897606292od_a_b: set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    ord_le5510395190108133673od_a_b: set_li7076890251784626569od_a_b > set_li7076890251784626569od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    ord_le153002609085230766od_a_b: set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    ord_le7778196599191822633od_a_b: set_Pr121319624013539721od_a_b > set_Pr121319624013539721od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    ord_le4232407541035512124od_a_b: set_Pr5622538825374275996od_a_b > set_Pr5622538825374275996od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    ord_le8991869396981723181od_a_b: set_Pr1051027220935592077od_a_b > set_Pr1051027220935592077od_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    ord_le817736998455962536od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
    ord_min_nat: nat > nat > nat ).

thf(sy_c_Product__Type_OPair_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001t__List__Olist_I_Eo_J,type,
    produc8744836578217649351list_o: ( $o > $o > $o ) > list_o > produc8642409424279824599list_o ).

thf(sy_c_Product__Type_OPair_001_062_I_Eo_M_Eo_J_001t__List__Olist_I_Eo_J,type,
    produc1450004214998940960list_o: ( $o > $o ) > list_o > produc4895375484934168814list_o ).

thf(sy_c_Product__Type_OPair_001_062_I_Eo_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_I_Eo_J_J,type,
    produc8772671931130610601list_o: ( $o > $o ) > produc7102631898165422375list_o > produc1709182781532539895list_o ).

thf(sy_c_Product__Type_OPair_001_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7711833712884794307od_a_b: ( fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o ) > list_f1445794025290330138od_a_b > produc7003135847223052371od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8550268191463221272od_a_b: ( fset_l1334069825099621524od_a_b > $o ) > list_f1445794025290330138od_a_b > produc2073128436939348198od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc3242218216111629733od_a_b: ( fset_l1334069825099621524od_a_b > $o ) > produc4243862795798826663od_a_b > produc8278318776394211699od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_J_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc3708935670247084489od_a_b: ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ) > list_l6099054058445139744od_a_b > produc4084954254102156249od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2726560669223232804od_a_b: ( list_f1445794025290330138od_a_b > $o ) > list_l6099054058445139744od_a_b > produc8331063474073164274od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc7142155960364849067od_a_b: ( list_f1445794025290330138od_a_b > $o ) > produc6680082661646774695od_a_b > produc6250212354305936633od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc2586240828387333809od_a_b: ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P3574414722980446895od_a_b > produc6416010238344180095od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6795408122287886773od_a_b: ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b ) > list_P5488608094462411443od_a_b > produc4550864312075981571od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7760118425732869085od_a_b: ( list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ) > list_l8778361445553822004od_a_b > produc9134726091994374893od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7526162350219154764od_a_b: ( list_P1467974523212632366od_a_b > $o ) > list_l8778361445553822004od_a_b > produc3357997149271159322od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc953458198655700415od_a_b: ( list_P1467974523212632366od_a_b > $o ) > produc1688629678973589927od_a_b > produc8043380187910098957od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc4727192421694094319st_nat: ( nat > nat > $o ) > list_nat > produc254973753779126261st_nat ).

thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_Eo_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc8587622027977423880st_nat: ( nat > $o ) > list_nat > produc4226810134323546766st_nat ).

thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc1851982983375519865st_nat: ( nat > $o ) > produc1828647624359046049st_nat > produc1950156742809263241st_nat ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc5077058152184573444od_a_b: ( produc2518759752815613485od_a_b > produc2518759752815613485od_a_b ) > list_P5302045529885307074od_a_b > produc136864206262228050od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc7704224619955794135od_a_b: ( product_prod_a_b > product_prod_a_b > $o ) > list_P1467974523212632366od_a_b > produc3334210663054469735od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc114956849241483840od_a_b: ( product_prod_a_b > $o ) > list_P1467974523212632366od_a_b > produc9068417245363831566od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc4095041172746057401od_a_b: ( product_prod_a_b > $o ) > produc7397007428618769063od_a_b > produc6303315885879197575od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc6339891136650604691od_a_b: $o > fset_l1334069825099621524od_a_b > produc3910515788072733219od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7489420772309856409od_a_b: $o > list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc1238543672593294367od_a_b: $o > list_l6099054058445139744od_a_b > produc7877445111886203567od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc336006402058072110od_a_b: $o > list_P3574414722980446895od_a_b > produc4943249325152908478od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc7187370450469132609od_a_b: $o > list_P5302045529885307074od_a_b > produc8178655232312819025od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6096372360267053632od_a_b: $o > produc6416010238344180095od_a_b > produc7489520080164906694od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc1988051149204433939od_a_b: $o > produc136864206262228050od_a_b > produc4201866467197088793od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc4815424570203850918od_a_b: $o > produc8767915422032708007od_a_b > produc3232039666172969398od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc1286801380576301484od_a_b: $o > produc2518759752815613485od_a_b > produc8937288731615916348od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3433936959961524160od_a_b: $o > produc9101336024286631233od_a_b > produc3899447382255381072od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc4003124953861756041od_a_b: $o > produc1801560611250510664od_a_b > produc6013625613799016975od_a_b ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J,type,
    produc7533889540795632565list_o: $o > produc1237961142284713782list_o > produc7154445628944892357list_o ).

thf(sy_c_Product__Type_OPair_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    produc854895907051729775od_a_b: $o > produc6599362722213357102od_a_b > produc6892749230674326005od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSM____Impl__Ofsm____impl_I_Eo_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc7559269575785153393od_a_b: fSM_fs4935216794212288482od_a_b > produc8937288731615916348od_a_b > produc6510285022982376705od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc3259603531422225253od_a_b: fSM_fs17440223606942999od_a_b > produc7169317207952727333od_a_b > produc6935835972710448245od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3248700932781776229od_a_b: fSM_fs4309808098908436657od_a_b > produc9005793448470268223od_a_b > produc2793283351794386037od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__c_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    produc3687021008881684069od_b_c: fSM_fsm_impl_a_b_c > produc3550516665487611281od_b_c > produc1033877881492090229od_b_c ).

thf(sy_c_Product__Type_OPair_001t__FSM____Impl__Ofsm____impl_Itf__a_Mtf__b_Mtf__d_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    produc7354553857258181157od_b_d: fSM_fsm_impl_a_b_d > produc3621550705533957266od_b_d > produc2109192171533205685od_b_d ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc8099561100433402519od_a_b: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > produc8767915422032708007od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc6212510018049267869od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > produc2518759752815613485od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc5841801390880218294od_a_b: fset_l1334069825099621524od_a_b > list_P5488608094462411443od_a_b > produc3633803565885464646od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc5291915255311561905od_a_b: fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b > produc9101336024286631233od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc1429321633257256512od_a_b: fset_l1334069825099621524od_a_b > produc4550864312075981571od_a_b > produc246785466268114886od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc6645316577686334777od_a_b: fset_l1334069825099621524od_a_b > produc3232039666172969398od_a_b > produc3935921425066410441od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc567650837873266096od_a_b: fset_l1334069825099621524od_a_b > produc2518759752815613485od_a_b > produc4368844512119319232od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc3504098642911543689od_a_b: fset_l1334069825099621524od_a_b > produc4155545519608197068od_a_b > produc5436143990428185615od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc4086412101881284409od_a_b: fset_l1334069825099621524od_a_b > produc8522616430465603254od_a_b > produc941565555952692937od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6699211207839096121od_a_b: fset_l1334069825099621524od_a_b > produc2095529977478686646od_a_b > produc6844535102171174857od_a_b ).

thf(sy_c_Product__Type_OPair_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc4314678409971068200od_a_b: fset_l1334069825099621524od_a_b > produc7169317207952727333od_a_b > produc6744346567773647288od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__List__Olist_I_Eo_J,type,
    produc8435520187683070743list_o: list_o > list_o > produc7102631898165422375list_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc8240772320746637977od_a_b: list_o > list_l6099054058445139744od_a_b > produc1075984531370556585od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc6961711982280244012od_a_b: list_o > list_P5488608094462411443od_a_b > produc5482552087341567164od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J_J,type,
    produc2209229713021908649list_o: list_o > produc245062040767252272list_o > produc4872601182145619129list_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_I_Eo_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_I_Eo_J_J_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J,type,
    produc9135509632870949792list_o: list_o > produc4690905340047322919list_o > produc245062040767252272list_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo,type,
    produc4366446772417547285_a_b_o: list_f1445794025290330138od_a_b > $o > produc2087898033365526821_a_b_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7350191566654282897od_a_b: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b > produc8628745980099788577od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc4047984609689601431od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > produc4243862795798826663od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc8565745453924327965od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b > produc3893167590797037997od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc302915861673359298od_a_b: list_f1445794025290330138od_a_b > produc6416010238344180095od_a_b > produc1801560611250510664od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc7490164133858390470od_a_b: list_f1445794025290330138od_a_b > produc4550864312075981571od_a_b > produc4155545519608197068od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc5559962869320249254od_a_b: list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b > produc8522616430465603254od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc5205648118086869305od_a_b: list_f1445794025290330138od_a_b > produc8937288731615916348od_a_b > produc3626440574470744009od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc2822848259085985329od_a_b: list_f1445794025290330138od_a_b > produc3298291110960068788od_a_b > produc3622972877636639297od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc4801787804591476900od_a_b: list_f1445794025290330138od_a_b > produc6680082661646774695od_a_b > produc3298291110960068788od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc8193211044935635507od_a_b: list_f1445794025290330138od_a_b > produc388879027768430262od_a_b > produc8660020554386975555od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_I_Eo_J_J_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
    produc2957346356364703511list_o: list_list_o > list_list_o > produc4690905340047322919list_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_I_Eo_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_I_Eo_J_J_J,type,
    produc1191279492341360934list_o: list_list_o > produc796964778762255539list_o > produc1237961142284713782list_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc9191391066883749527od_a_b: list_l6099054058445139744od_a_b > list_l6099054058445139744od_a_b > produc6680082661646774695od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc883383490548289190od_a_b: list_l6099054058445139744od_a_b > produc7877445111886203567od_a_b > produc2095529977478686646od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc1348991824872107557od_a_b: list_l6099054058445139744od_a_b > produc6483782000891358638od_a_b > produc8905949819191209269od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc4034718099474179870od_a_b: list_l6099054058445139744od_a_b > produc8235995322212035239od_a_b > produc6483782000891358638od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_001t__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc8378414639643377047od_a_b: list_l378912295992385958od_a_b > list_l378912295992385958od_a_b > produc8235995322212035239od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    produc6710758018942698406od_a_b: list_l378912295992385958od_a_b > produc724608359110776885od_a_b > produc388879027768430262od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc9051856215140236695od_a_b: list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b > produc6292233528018597543od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc683816545860151206od_a_b: list_l6443893005374362810od_a_b > produc4356081027818849609od_a_b > produc1153669656519933622od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    produc7129799990162260089st_nat: list_list_nat > list_list_nat > produc4326814125627636033st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    produc3419769971367040704st_nat: list_list_nat > produc7974263126369132087st_nat > produc4796846013342594440st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3466467997744452247od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > produc1688629678973589927od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc3700279395275165350od_a_b: list_l8778361445553822004od_a_b > produc8908614768156765891od_a_b > produc8956912041617273782od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc1849413230003979274od_a_b: list_l8778361445553822004od_a_b > produc6292233528018597543od_a_b > produc4267876118020951450od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc5805445161374616061od_a_b: list_l8778361445553822004od_a_b > produc4267876118020951450od_a_b > produc6285210691406119693od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    produc8807741811528022664st_nat: list_nat > produc4326814125627636033st_nat > produc2533616784052650198st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J,type,
    produc4774092089535011407st_nat: list_nat > produc2533616784052650198st_nat > produc2175610488484699543st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc5288560138351607191od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > produc7397007428618769063od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc4061792103530149689od_a_b: list_P1467974523212632366od_a_b > produc3899447382255381072od_a_b > produc8701494430851074505od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc5554862205985698335od_a_b: list_P1467974523212632366od_a_b > produc1153669656519933622od_a_b > produc3345434161935928879od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8500600352266341008od_a_b: list_P1467974523212632366od_a_b > produc1688629678973589927od_a_b > produc5620510707799782816od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc5762985261779254281od_a_b: list_P1467974523212632366od_a_b > produc5620510707799782816od_a_b > produc6133449566840171033od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8932199587862418344od_a_b: list_P1467974523212632366od_a_b > produc9005793448470268223od_a_b > produc7071465670189454904od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc8653188414478805099od_a_b: nat > fset_l1334069825099621524od_a_b > produc6829992310584780345od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J_J,type,
    produc3115374921362880095st_nat: nat > produc4796846013342594440st_nat > produc19496163836001069st_nat ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    produc5238447047330606914_a_b_o: produc2518759752815613485od_a_b > $o > produc7103389596696383826_a_b_o ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    produc6486408844037598248od_a_b: produc2518759752815613485od_a_b > produc136864206262228050od_a_b > produc6599362722213357102od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7167387503278561829od_a_b: product_prod_a_b > produc8956912041617273782od_a_b > produc5998163534577424309od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc2488690576206217668od_a_b: a > list_P2891578699137632811od_a_b > produc4803344270401830612od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc769044295738804958od_a_b: a > list_P2373415021271773893od_a_b > produc263801385964556654od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    produc2746644709676428336od_b_c: a > list_P8634110456476873367od_b_c > produc6427713924023405888od_b_c ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    produc225460191387392689od_b_d: a > list_P6112925938187837720od_b_d > produc6268931404698553153od_b_d ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc6643264353547226055od_a_b: a > list_P1467974523212632366od_a_b > produc2639161875728825943od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc5260523172840707349od_a_b: a > produc3520053589329427452od_a_b > produc7169317207952727333od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc458170271728203695od_a_b: a > produc6345636018528648726od_a_b > produc9005793448470268223od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    produc6867761804911831425od_b_c: a > product_prod_b_c > produc3550516665487611281od_b_c ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__d_J,type,
    produc6867761809215060226od_b_d: a > product_prod_b_d > produc3621550705533957266od_b_d ).

thf(sy_c_Product__Type_OPair_001tf__a_001tf__b,type,
    product_Pair_a_b: a > b > product_prod_a_b ).

thf(sy_c_Product__Type_OPair_001tf__b_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc912194690294371052od_a_b: b > fset_l1334069825099621524od_a_b > produc3520053589329427452od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__b_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc1126366459492273030od_a_b: b > list_P1467974523212632366od_a_b > produc6345636018528648726od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__b_001tf__c,type,
    product_Pair_b_c: b > c > product_prod_b_c ).

thf(sy_c_Product__Type_OPair_001tf__b_001tf__d,type,
    product_Pair_b_d: b > d > product_prod_b_d ).

thf(sy_c_Product__Type_OPair_001tf__c_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    produc8300696160155326504od_b_c: c > produc3550516665487611281od_b_c > produc6657052613134160568od_b_c ).

thf(sy_c_Product__Type_OPair_001tf__d_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    produc4320412792819862376od_b_d: d > produc3621550705533957266od_b_d > produc84550687463314808od_b_d ).

thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc5358503411717041797od_a_b: produc2313482920965681321od_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc4967132223111445515od_a_b: produc7877445111886203567od_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc8768225620527925535od_a_b: produc8908614768156765891od_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2316053142268291992od_a_b: produc8937288731615916348od_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc5739577146777995401od_a_b: produc2518759752815613485od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo,type,
    produc2235529411824732673_a_b_o: produc2087898033365526821_a_b_o > list_f1445794025290330138od_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc6877258695383010429od_a_b: produc8628745980099788577od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3138289943185643391od_a_b: produc6829992310584780345od_a_b > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    produc6267698809022597422_a_b_o: produc7103389596696383826_a_b_o > produc2518759752815613485od_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    produc3728844965657535341od_b_c: produc3550516665487611281od_b_c > a ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__d_J,type,
    produc3728844969960764142od_b_d: produc3621550705533957266od_b_d > a ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001tf__b,type,
    product_fst_a_b: product_prod_a_b > a ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b_001tf__c,type,
    product_fst_b_c: product_prod_b_c > b ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b_001tf__d,type,
    product_fst_b_d: product_prod_b_d > b ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__c_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    produc6763838237438281236od_b_c: produc6657052613134160568od_b_c > c ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__d_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    produc2783554870102817108od_b_d: produc84550687463314808od_b_d > d ).

thf(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc2954343059184910791od_a_b: produc2313482920965681321od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc909441938071963213od_a_b: produc7877445111886203567od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc5480430458100320474od_a_b: produc8937288731615916348od_a_b > produc2518759752815613485od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc396176279405262539od_a_b: produc2518759752815613485od_a_b > list_f1445794025290330138od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo,type,
    produc9054741096147377475_a_b_o: produc2087898033365526821_a_b_o > $o ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc1533857828010277567od_a_b: produc8628745980099788577od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2570711435215982525od_a_b: produc6829992310584780345od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    produc208704087999850096_a_b_o: produc7103389596696383826_a_b_o > $o ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc1217227160481923139od_a_b: produc7169317207952727333od_a_b > produc3520053589329427452od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7006406357458145757od_a_b: produc9005793448470268223od_a_b > produc6345636018528648726od_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__c_J,type,
    produc8648342215071535279od_b_c: produc3550516665487611281od_b_c > product_prod_b_c ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Product____Type__Oprod_Itf__b_Mtf__d_J,type,
    produc8648342219374764080od_b_d: produc3621550705533957266od_b_d > product_prod_b_d ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001tf__b,type,
    product_snd_a_b: product_prod_a_b > b ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b_001tf__c,type,
    product_snd_b_c: product_prod_b_c > c ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b_001tf__d,type,
    product_snd_b_d: product_prod_b_d > d ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__c_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
    produc1402652955648401750od_b_c: produc6657052613134160568od_b_c > produc3550516665487611281od_b_c ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__d_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J,type,
    produc6645741625167713430od_b_d: produc84550687463314808od_b_d > produc3621550705533957266od_b_d ).

thf(sy_c_Product__Type_Oprod_Oswap_001_Eo_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7780892788990209593od_a_b: produc2313482920965681321od_a_b > produc2087898033365526821_a_b_o ).

thf(sy_c_Product__Type_Oprod_Oswap_001_Eo_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc205082526707003212od_a_b: produc8937288731615916348od_a_b > produc7103389596696383826_a_b_o ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc1322645004498421309od_a_b: produc2518759752815613485od_a_b > produc8628745980099788577od_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001_Eo,type,
    produc4657918789097900469_a_b_o: produc2087898033365526821_a_b_o > produc2313482920965681321od_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2460326553103436337od_a_b: produc8628745980099788577od_a_b > produc2518759752815613485od_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001_Eo,type,
    produc4156728193461308642_a_b_o: produc7103389596696383826_a_b_o > produc8937288731615916348od_a_b ).

thf(sy_c_Set_OCollect_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    collec2335753234515135999od_a_b: ( fset_l1334069825099621524od_a_b > $o ) > set_fs5173440902860351732od_a_b ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    collec6680873810700003333od_a_b: ( list_f1445794025290330138od_a_b > $o ) > set_li7540826859550765818od_a_b ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    collec2845612350631750681od_a_b: ( list_P1467974523212632366od_a_b > $o ) > set_li6306622547289818894od_a_b ).

thf(sy_c_Set_OCollect_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    collec4999808032329279071od_a_b: ( set_fs5173440902860351732od_a_b > $o ) > set_se1014227543623231828od_a_b ).

thf(sy_c_Set_OCollect_001tf__a,type,
    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_OCollect_001tf__c,type,
    collect_c: ( c > $o ) > set_c ).

thf(sy_c_Set_OCollect_001tf__d,type,
    collect_d: ( d > $o ) > set_d ).

thf(sy_c_Set_Oimage_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    image_3633131638523200261od_a_b: ( fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b ) > set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_Set_Oimage_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    image_885551376138370655od_a_b: ( list_f1445794025290330138od_a_b > set_fs5173440902860351732od_a_b ) > set_li7540826859550765818od_a_b > set_se1014227543623231828od_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J,type,
    image_3217611746473200321_a_b_o: ( produc2313482920965681321od_a_b > produc2087898033365526821_a_b_o ) > set_Pr121319624013539721od_a_b > set_Pr2549634154452313093_a_b_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_M_Eo_J,type,
    image_5311508624785544475_a_b_o: ( produc8937288731615916348od_a_b > produc7103389596696383826_a_b_o ) > set_Pr5622538825374275996od_a_b > set_Pr1979380953684217522_a_b_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    image_4146237622769870137od_a_b: ( produc2518759752815613485od_a_b > produc8628745980099788577od_a_b ) > set_Pr1051027220935592077od_a_b > set_Pr3384986265503004545od_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    image_8940756588869874889od_a_b: ( produc2087898033365526821_a_b_o > produc2313482920965681321od_a_b ) > set_Pr2549634154452313093_a_b_o > set_Pr121319624013539721od_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    image_3785288736868017745od_a_b: ( produc8628745980099788577od_a_b > produc2518759752815613485od_a_b ) > set_Pr3384986265503004545od_a_b > set_Pr1051027220935592077od_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_M_Eo_J_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    image_6895954947936813679od_a_b: ( produc7103389596696383826_a_b_o > produc8937288731615916348od_a_b ) > set_Pr1979380953684217522_a_b_o > set_Pr5622538825374275996od_a_b ).

thf(sy_c_Set_Oimage_001tf__c_001tf__c,type,
    image_c_c: ( c > c ) > set_c > set_c ).

thf(sy_c_Set_Oimage_001tf__c_001tf__d,type,
    image_c_d: ( c > d ) > set_c > set_d ).

thf(sy_c_Set_Oimage_001tf__d_001tf__c,type,
    image_d_c: ( d > c ) > set_d > set_c ).

thf(sy_c_Set_Oimage_001tf__d_001tf__d,type,
    image_d_d: ( d > d ) > set_d > set_d ).

thf(sy_c_Set_Oinsert_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    insert3249498615411298916od_a_b: fset_l1334069825099621524od_a_b > set_fs5173440902860351732od_a_b > set_fs5173440902860351732od_a_b ).

thf(sy_c_Set_Oinsert_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    insert38576201109616106od_a_b: list_f1445794025290330138od_a_b > set_li7540826859550765818od_a_b > set_li7540826859550765818od_a_b ).

thf(sy_c_Set_Oinsert_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    insert6792547294658701054od_a_b: list_P1467974523212632366od_a_b > set_li6306622547289818894od_a_b > set_li6306622547289818894od_a_b ).

thf(sy_c_Set_Oinsert_001tf__c,type,
    insert_c2: c > set_c > set_c ).

thf(sy_c_Set_Oinsert_001tf__d,type,
    insert_d2: d > set_d > set_d ).

thf(sy_c_Set_Othe__elem_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    the_el4387542105688296585od_a_b: set_fs5173440902860351732od_a_b > fset_l1334069825099621524od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Oprefixes__in__list__helper_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    simple4255713849812333767od_a_b: fset_l1334069825099621524od_a_b > list_l6099054058445139744od_a_b > produc7877445111886203567od_a_b > produc7877445111886203567od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Oprefixes__in__list__helper_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple3641185509419956187od_a_b: product_prod_a_b > list_l8778361445553822004od_a_b > produc8908614768156765891od_a_b > produc8908614768156765891od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Oprefixes__in__list__helper__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    simple5858505605421243878od_a_b: produc6844535102171174857od_a_b > produc6844535102171174857od_a_b > $o ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__1_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple7196191000754466375od_a_b: list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__1__helper_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple257211598216488121od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b > produc2313482920965681321od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__1__helper_H_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple8292391143910244688od_a_b: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > produc8937288731615916348od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__2_H_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple891077427139469213od_a_b: list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b > produc2313482920965681321od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__2_H__rel_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple6863691286768149176od_a_b: produc8522616430465603254od_a_b > produc8522616430465603254od_a_b > $o ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__closure__phase__2__helper_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple4112306255986741752od_a_b: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > produc8937288731615916348od_a_b ).

thf(sy_c_Simple__Convergence__Graph_Osimple__cg__empty_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    simple1082100951563891851od_a_b: list_f1445794025290330138od_a_b ).

thf(sy_c_Sublist_Oprefix_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    prefix7449001915862371055od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Sublist_Oprefix_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    prefix3118977441345254915od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_Sublist_Oprefixes_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    prefix4612422245637881633od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Sublist_Oprefixes_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    prefix3919435433362254901od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_Sublist_Osublists_001_Eo,type,
    sublists_o: list_o > list_list_o ).

thf(sy_c_Sublist_Osublists_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    sublis7484350909052568364od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Sublist_Osublists_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    sublis4548404825810117298od_a_b: list_l6099054058445139744od_a_b > list_l378912295992385958od_a_b ).

thf(sy_c_Sublist_Osublists_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    sublis5610707822503107526od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_Sublist_Osublists_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    sublis2270850047155729216od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_Sublist_Osuffixes_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    suffix888123080290511074od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Util_Olinear__order__from__list__position_H_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    linear8767015901316240446od_a_b: list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_Util_Olinear__order__from__list__position_H__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    linear273309371191718703od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Util_Olist__ordered__pairs_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_o5553444344251545051od_a_b: list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_Util_Olist__ordered__pairs_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    list_o8928240460966572533od_a_b: list_l8778361445553822004od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_Util_Olist__ordered__pairs__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_o2651293876426356178od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Util_Olists__of__length_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    lists_98629209091004527od_a_b: list_f1445794025290330138od_a_b > nat > list_l6099054058445139744od_a_b ).

thf(sy_c_Util_Olists__of__length_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    lists_5148932666697663363od_a_b: list_P1467974523212632366od_a_b > nat > list_l8778361445553822004od_a_b ).

thf(sy_c_Util_Onon__sym__dist__pairs_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    non_sy5167582269473054216od_a_b: list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_Util_Onon__sym__dist__pairs_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    non_sy3462148336120157346od_a_b: list_l8778361445553822004od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_Util_Onon__sym__dist__pairs_H_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    non_sy1352304633095342623od_a_b: list_f1445794025290330138od_a_b > list_P1164858718851775149od_a_b ).

thf(sy_c_Util_Onon__sym__dist__pairs_H_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    non_sy4621517932026394681od_a_b: list_l8778361445553822004od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_Util_Onon__sym__dist__pairs_H__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    non_sy4348299424481621646od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Util_Opow__list_001_Eo,type,
    pow_list_o: list_o > list_list_o ).

thf(sy_c_Util_Opow__list_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    pow_li5660269712609304331od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Util_Opow__list_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    pow_li8436028492934955793od_a_b: list_l6099054058445139744od_a_b > list_l378912295992385958od_a_b ).

thf(sy_c_Util_Opow__list_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    pow_li6114394920801268517od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_Util_Opow__list_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    pow_li7128575976297350687od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_Util_Osuffixes_001_Eo,type,
    suffixes_o: list_o > list_list_o ).

thf(sy_c_Util_Osuffixes_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    suffix4455840324713621126od_a_b: list_f1445794025290330138od_a_b > list_l6099054058445139744od_a_b ).

thf(sy_c_Util_Osuffixes_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    suffix6313696937464205580od_a_b: list_l6099054058445139744od_a_b > list_l378912295992385958od_a_b ).

thf(sy_c_Util_Osuffixes_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    suffix1498375871760299040od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_Util_Osuffixes_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    suffix4939239918433288346od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_Util_Osuffixes__rel_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    suffix2477028357949749991od_a_b: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    accp_l5651743518013118883od_a_b: ( list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o ) > list_f1445794025290330138od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    accp_P7875516549118069959od_a_b: ( produc4943249325152908478od_a_b > produc4943249325152908478od_a_b > $o ) > produc4943249325152908478od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    accp_P4593430778603979354od_a_b: ( produc8178655232312819025od_a_b > produc8178655232312819025od_a_b > $o ) > produc8178655232312819025od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    accp_P1594159262757799549od_a_b: ( produc7489520080164906694od_a_b > produc7489520080164906694od_a_b > $o ) > produc7489520080164906694od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    accp_P8597022368939085008od_a_b: ( produc4201866467197088793od_a_b > produc4201866467197088793od_a_b > $o ) > produc4201866467197088793od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    accp_P6900864555062981958od_a_b: ( produc6013625613799016975od_a_b > produc6013625613799016975od_a_b > $o ) > produc6013625613799016975od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J_J,type,
    accp_P3721793906898479404od_a_b: ( produc6892749230674326005od_a_b > produc6892749230674326005od_a_b > $o ) > produc6892749230674326005od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    accp_P8600931742201088847od_a_b: ( produc3633803565885464646od_a_b > produc3633803565885464646od_a_b > $o ) > produc3633803565885464646od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    accp_P5581439537166740605od_a_b: ( produc246785466268114886od_a_b > produc246785466268114886od_a_b > $o ) > produc246785466268114886od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J_J,type,
    accp_P3807179030927346758od_a_b: ( produc5436143990428185615od_a_b > produc5436143990428185615od_a_b > $o ) > produc5436143990428185615od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J_J,type,
    accp_P5339454666067580242od_a_b: ( produc6844535102171174857od_a_b > produc6844535102171174857od_a_b > $o ) > produc6844535102171174857od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    accp_P8702517312824989759od_a_b: ( produc8522616430465603254od_a_b > produc8522616430465603254od_a_b > $o ) > produc8522616430465603254od_a_b > $o ).

thf(sy_c_member_001_Eo,type,
    member_o2: $o > set_o > $o ).

thf(sy_c_member_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member361094292949318077od_a_b: fset_l1334069825099621524od_a_b > set_fs5173440902860351732od_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member7551773913232940227od_a_b: list_f1445794025290330138od_a_b > set_li7540826859550765818od_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member7805385913403518557od_a_b: list_l8778361445553822004od_a_b > set_li948167846089608596od_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member380949161941006936od_a_b: list_P3574414722980446895od_a_b > set_li7888096385779382799od_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    member33161170550207851od_a_b: list_P5302045529885307074od_a_b > set_li104036716953425826od_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member3794113899005121500od_a_b: list_P5488608094462411443od_a_b > set_li2133032475778560915od_a_b > $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__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J_J,type,
    member6100718384056554727od_b_c: list_P5017272815184427326od_b_c > set_li839162645350771998od_b_c > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J_J,type,
    member315062636207077287od_b_d: list_P8454989104189725694od_b_d > set_li7469257630003736542od_b_d > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat2: nat > set_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    member3029431943403884754od_a_b: produc2313482920965681321od_a_b > set_Pr121319624013539721od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member6983108301751770725od_a_b: produc8937288731615916348od_a_b > set_Pr5622538825374275996od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member2847915659457029072od_a_b: produc8767915422032708007od_a_b > set_Pr2242436922956002695od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    member7205742373938401238od_a_b: produc2518759752815613485od_a_b > set_Pr1051027220935592077od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member7151811798220465266od_a_b: produc3935921425066410441od_a_b > set_Pr5812197030978132777od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member8515146061811315169od_a_b: produc6744346567773647288od_a_b > set_Pr4210316172971897624od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member6201332024754097106od_a_b: produc1075984531370556585od_a_b > set_Pr4856876843892373641od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    member7237066067024242917od_a_b: produc5482552087341567164od_a_b > set_Pr7954061446304757788od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_M_Eo_J,type,
    member2803847055803730254_a_b_o: produc2087898033365526821_a_b_o > set_Pr2549634154452313093_a_b_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member4092356564367800522od_a_b: produc8628745980099788577od_a_b > set_Pr3384986265503004545od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    member2549368600341536720od_a_b: produc4243862795798826663od_a_b > set_Pr803608928346326407od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    member6680126217112042070od_a_b: produc3893167590797037997od_a_b > set_Pr4286734062635796237od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J_J,type,
    member9099908583776647538od_a_b: produc3626440574470744009od_a_b > set_Pr6133615449426215977od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member4992001953252686800od_a_b: produc1688629678973589927od_a_b > set_Pr3498424749146541447od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member3051990972100052432od_a_b: produc7397007428618769063od_a_b > set_Pr3015088788472578951od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    member6531131955963215218od_a_b: produc8701494430851074505od_a_b > set_Pr731044129912021033od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    member5376971474732164961od_a_b: produc7071465670189454904od_a_b > set_Pr4832031994198807704od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member3914385324806363600od_a_b: produc6829992310584780345od_a_b > set_Pr8907832335669617775od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_M_Eo_J,type,
    member5149209166832238203_a_b_o: produc7103389596696383826_a_b_o > set_Pr1979380953684217522_a_b_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    member1426531481828664017od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__c_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__c_J_J_J,type,
    member265788643176044257od_b_c: produc6657052613134160568od_b_c > set_Pr7047737848026531864od_b_c > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mt__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mtf__d_J_J_J,type,
    member2916658754359974305od_b_d: produc84550687463314808od_b_d > set_Pr1262082100177054424od_b_d > $o ).

thf(sy_c_member_001t__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    member3854304715014625821od_a_b: set_fs5173440902860351732od_a_b > set_se1014227543623231828od_a_b > $o ).

thf(sy_c_member_001tf__a,type,
    member_a2: a > set_a > $o ).

thf(sy_c_member_001tf__c,type,
    member_c2: c > set_c > $o ).

thf(sy_c_member_001tf__d,type,
    member_d2: d > set_d > $o ).

thf(sy_v_M1,type,
    m1: fsm_c_a_b ).

thf(sy_v_M2,type,
    m2: fsm_d_a_b ).

thf(sy_v_b,type,
    b2: $o ).

thf(sy_v_ba____,type,
    ba: $o ).

thf(sy_v_don,type,
    don: list_f1445794025290330138od_a_b ).

thf(sy_v_dona____,type,
    dona: list_f1445794025290330138od_a_b ).

thf(sy_v_hasChanged____,type,
    hasChanged: $o ).

thf(sy_v_u,type,
    u: list_P1467974523212632366od_a_b ).

thf(sy_v_v,type,
    v: list_P1467974523212632366od_a_b ).

thf(sy_v_x2,type,
    x2: fset_l1334069825099621524od_a_b ).

thf(sy_v_x_H____,type,
    x: fset_l1334069825099621524od_a_b ).

thf(sy_v_x____,type,
    x3: fset_l1334069825099621524od_a_b ).

thf(sy_v_xs_H____,type,
    xs: list_f1445794025290330138od_a_b ).

thf(sy_v_xs____,type,
    xs2: list_f1445794025290330138od_a_b ).

thf(sy_v_xss,type,
    xss: list_f1445794025290330138od_a_b ).

thf(sy_v_xssa____,type,
    xssa: list_f1445794025290330138od_a_b ).

% Relevant facts (1261)
thf(fact_0_local_OCons,axiom,
    ( xssa
    = ( cons_f6577355434438001738od_a_b @ x3 @ xs2 ) ) ).

% local.Cons
thf(fact_1__092_060open_062simple__cg__closure__phase__2__helper_Ax_Axs_A_061_A_IhasChanged_M_Ax_H_M_Axs_H_J_092_060close_062,axiom,
    ( ( simple4112306255986741752od_a_b @ x3 @ xs2 )
    = ( produc1286801380576301484od_a_b @ hasChanged @ ( produc6212510018049267869od_a_b @ x @ xs ) ) ) ).

% \<open>simple_cg_closure_phase_2_helper x xs = (hasChanged, x', xs')\<close>
thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062hasChanged_Ax_H_Axs_H_O_Asimple__cg__closure__phase__2__helper_Ax_Axs_A_061_A_IhasChanged_M_Ax_H_M_Axs_H_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [HasChanged: $o,X: fset_l1334069825099621524od_a_b,Xs: list_f1445794025290330138od_a_b] :
        ( ( simple4112306255986741752od_a_b @ x3 @ xs2 )
       != ( produc1286801380576301484od_a_b @ HasChanged @ ( produc6212510018049267869od_a_b @ X @ Xs ) ) ) ).

% \<open>\<And>thesis. (\<And>hasChanged x' xs'. simple_cg_closure_phase_2_helper x xs = (hasChanged, x', xs') \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_3_list_Oinject,axiom,
    ! [X21: product_prod_a_b,X22: list_P1467974523212632366od_a_b,Y21: product_prod_a_b,Y22: list_P1467974523212632366od_a_b] :
      ( ( ( cons_P7316939131009794654od_a_b @ X21 @ X22 )
        = ( cons_P7316939131009794654od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_4_list_Oinject,axiom,
    ! [X21: list_P1467974523212632366od_a_b,X22: list_l8778361445553822004od_a_b,Y21: list_P1467974523212632366od_a_b,Y22: list_l8778361445553822004od_a_b] :
      ( ( ( cons_l907386227682280420od_a_b @ X21 @ X22 )
        = ( cons_l907386227682280420od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_5_list_Oinject,axiom,
    ! [X21: list_f1445794025290330138od_a_b,X22: list_l6099054058445139744od_a_b,Y21: list_f1445794025290330138od_a_b,Y22: list_l6099054058445139744od_a_b] :
      ( ( ( cons_l7290444712290925776od_a_b @ X21 @ X22 )
        = ( cons_l7290444712290925776od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_6_list_Oinject,axiom,
    ! [X21: $o,X22: list_o,Y21: $o,Y22: list_o] :
      ( ( ( cons_o @ X21 @ X22 )
        = ( cons_o @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_7_list_Oinject,axiom,
    ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
      ( ( ( cons_nat @ X21 @ X22 )
        = ( cons_nat @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_8_list_Oinject,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b,Y21: fset_l1334069825099621524od_a_b,Y22: list_f1445794025290330138od_a_b] :
      ( ( ( cons_f6577355434438001738od_a_b @ X21 @ X22 )
        = ( cons_f6577355434438001738od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_9_prod_Oinject,axiom,
    ! [X1: a,X2: produc6345636018528648726od_a_b,Y1: a,Y2: produc6345636018528648726od_a_b] :
      ( ( ( produc458170271728203695od_a_b @ X1 @ X2 )
        = ( produc458170271728203695od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_10_prod_Oinject,axiom,
    ! [X1: a,X2: produc3520053589329427452od_a_b,Y1: a,Y2: produc3520053589329427452od_a_b] :
      ( ( ( produc5260523172840707349od_a_b @ X1 @ X2 )
        = ( produc5260523172840707349od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_11_prod_Oinject,axiom,
    ! [X1: a,X2: product_prod_b_d,Y1: a,Y2: product_prod_b_d] :
      ( ( ( produc6867761809215060226od_b_d @ X1 @ X2 )
        = ( produc6867761809215060226od_b_d @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_12_prod_Oinject,axiom,
    ! [X1: a,X2: product_prod_b_c,Y1: a,Y2: product_prod_b_c] :
      ( ( ( produc6867761804911831425od_b_c @ X1 @ X2 )
        = ( produc6867761804911831425od_b_c @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_13_prod_Oinject,axiom,
    ! [X1: a,X2: b,Y1: a,Y2: b] :
      ( ( ( product_Pair_a_b @ X1 @ X2 )
        = ( product_Pair_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_14_prod_Oinject,axiom,
    ! [X1: $o,X2: list_f1445794025290330138od_a_b,Y1: $o,Y2: list_f1445794025290330138od_a_b] :
      ( ( ( produc7489420772309856409od_a_b @ X1 @ X2 )
        = ( produc7489420772309856409od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_15_prod_Oinject,axiom,
    ! [X1: $o,X2: produc2518759752815613485od_a_b,Y1: $o,Y2: produc2518759752815613485od_a_b] :
      ( ( ( produc1286801380576301484od_a_b @ X1 @ X2 )
        = ( produc1286801380576301484od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_16_prod_Oinject,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,X2: list_f1445794025290330138od_a_b,Y1: fset_l1334069825099621524od_a_b,Y2: list_f1445794025290330138od_a_b] :
      ( ( ( produc6212510018049267869od_a_b @ X1 @ X2 )
        = ( produc6212510018049267869od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_17_old_Oprod_Oinject,axiom,
    ! [A: a,B: produc6345636018528648726od_a_b,A2: a,B2: produc6345636018528648726od_a_b] :
      ( ( ( produc458170271728203695od_a_b @ A @ B )
        = ( produc458170271728203695od_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_18_old_Oprod_Oinject,axiom,
    ! [A: a,B: produc3520053589329427452od_a_b,A2: a,B2: produc3520053589329427452od_a_b] :
      ( ( ( produc5260523172840707349od_a_b @ A @ B )
        = ( produc5260523172840707349od_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_19_old_Oprod_Oinject,axiom,
    ! [A: a,B: product_prod_b_d,A2: a,B2: product_prod_b_d] :
      ( ( ( produc6867761809215060226od_b_d @ A @ B )
        = ( produc6867761809215060226od_b_d @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_20_old_Oprod_Oinject,axiom,
    ! [A: a,B: product_prod_b_c,A2: a,B2: product_prod_b_c] :
      ( ( ( produc6867761804911831425od_b_c @ A @ B )
        = ( produc6867761804911831425od_b_c @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_21_old_Oprod_Oinject,axiom,
    ! [A: a,B: b,A2: a,B2: b] :
      ( ( ( product_Pair_a_b @ A @ B )
        = ( product_Pair_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_22_old_Oprod_Oinject,axiom,
    ! [A: $o,B: list_f1445794025290330138od_a_b,A2: $o,B2: list_f1445794025290330138od_a_b] :
      ( ( ( produc7489420772309856409od_a_b @ A @ B )
        = ( produc7489420772309856409od_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_23_old_Oprod_Oinject,axiom,
    ! [A: $o,B: produc2518759752815613485od_a_b,A2: $o,B2: produc2518759752815613485od_a_b] :
      ( ( ( produc1286801380576301484od_a_b @ A @ B )
        = ( produc1286801380576301484od_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_24_old_Oprod_Oinject,axiom,
    ! [A: fset_l1334069825099621524od_a_b,B: list_f1445794025290330138od_a_b,A2: fset_l1334069825099621524od_a_b,B2: list_f1445794025290330138od_a_b] :
      ( ( ( produc6212510018049267869od_a_b @ A @ B )
        = ( produc6212510018049267869od_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_25_less_Oprems_I3_J,axiom,
    member361094292949318077od_a_b @ x2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple891077427139469213od_a_b @ xssa @ ( produc7489420772309856409od_a_b @ ba @ dona ) ) ) ) ).

% less.prems(3)
thf(fact_26_not__Cons__self2,axiom,
    ! [X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
      ( ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_27_not__Cons__self2,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( cons_l907386227682280420od_a_b @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_28_not__Cons__self2,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b] :
      ( ( cons_l7290444712290925776od_a_b @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_29_not__Cons__self2,axiom,
    ! [X3: $o,Xs2: list_o] :
      ( ( cons_o @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_30_not__Cons__self2,axiom,
    ! [X3: nat,Xs2: list_nat] :
      ( ( cons_nat @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_31_not__Cons__self2,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_32_h__obs_Ocases,axiom,
    ! [X3: produc2793283351794386037od_a_b] :
      ~ ! [M: fSM_fs4309808098908436657od_a_b,Q: a,X4: b,Y: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc3248700932781776229od_a_b @ M @ ( produc458170271728203695od_a_b @ Q @ ( produc1126366459492273030od_a_b @ X4 @ Y ) ) ) ) ).

% h_obs.cases
thf(fact_33_h__obs_Ocases,axiom,
    ! [X3: produc6935835972710448245od_a_b] :
      ~ ! [M: fSM_fs17440223606942999od_a_b,Q: a,X4: b,Y: fset_l1334069825099621524od_a_b] :
          ( X3
         != ( produc3259603531422225253od_a_b @ M @ ( produc5260523172840707349od_a_b @ Q @ ( produc912194690294371052od_a_b @ X4 @ Y ) ) ) ) ).

% h_obs.cases
thf(fact_34_h__obs_Ocases,axiom,
    ! [X3: produc2109192171533205685od_b_d] :
      ~ ! [M: fSM_fsm_impl_a_b_d,Q: a,X4: b,Y: d] :
          ( X3
         != ( produc7354553857258181157od_b_d @ M @ ( produc6867761809215060226od_b_d @ Q @ ( product_Pair_b_d @ X4 @ Y ) ) ) ) ).

% h_obs.cases
thf(fact_35_h__obs_Ocases,axiom,
    ! [X3: produc1033877881492090229od_b_c] :
      ~ ! [M: fSM_fsm_impl_a_b_c,Q: a,X4: b,Y: c] :
          ( X3
         != ( produc3687021008881684069od_b_c @ M @ ( produc6867761804911831425od_b_c @ Q @ ( product_Pair_b_c @ X4 @ Y ) ) ) ) ).

% h_obs.cases
thf(fact_36_h__obs_Ocases,axiom,
    ! [X3: produc6510285022982376705od_a_b] :
      ~ ! [M: fSM_fs4935216794212288482od_a_b,Q: $o,X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc7559269575785153393od_a_b @ M @ ( produc1286801380576301484od_a_b @ Q @ ( produc6212510018049267869od_a_b @ X4 @ Y ) ) ) ) ).

% h_obs.cases
thf(fact_37_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc9005793448470268223od_a_b] :
      ~ ! [A3: a,B3: produc6345636018528648726od_a_b] :
          ( Y3
         != ( produc458170271728203695od_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc7169317207952727333od_a_b] :
      ~ ! [A3: a,B3: produc3520053589329427452od_a_b] :
          ( Y3
         != ( produc5260523172840707349od_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc3621550705533957266od_b_d] :
      ~ ! [A3: a,B3: product_prod_b_d] :
          ( Y3
         != ( produc6867761809215060226od_b_d @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc3550516665487611281od_b_c] :
      ~ ! [A3: a,B3: product_prod_b_c] :
          ( Y3
         != ( produc6867761804911831425od_b_c @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_41_old_Oprod_Oexhaust,axiom,
    ! [Y3: product_prod_a_b] :
      ~ ! [A3: a,B3: b] :
          ( Y3
         != ( product_Pair_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_42_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc2313482920965681321od_a_b] :
      ~ ! [A3: $o,B3: list_f1445794025290330138od_a_b] :
          ( Y3
         != ( produc7489420772309856409od_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_43_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc8937288731615916348od_a_b] :
      ~ ! [A3: $o,B3: produc2518759752815613485od_a_b] :
          ( Y3
         != ( produc1286801380576301484od_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_44_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc2518759752815613485od_a_b] :
      ~ ! [A3: fset_l1334069825099621524od_a_b,B3: list_f1445794025290330138od_a_b] :
          ( Y3
         != ( produc6212510018049267869od_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_45_True,axiom,
    hasChanged ).

% True
thf(fact_46_assms_I3_J,axiom,
    member361094292949318077od_a_b @ x2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple891077427139469213od_a_b @ xss @ ( produc7489420772309856409od_a_b @ b2 @ don ) ) ) ) ).

% assms(3)
thf(fact_47_simple__cg__closure__phase__1__helper_H_Ocases,axiom,
    ! [X3: produc4368844512119319232od_a_b] :
      ~ ! [X4: fset_l1334069825099621524od_a_b,X12: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc567650837873266096od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ X12 @ Xs3 ) ) ) ).

% simple_cg_closure_phase_1_helper'.cases
thf(fact_48_snd__conv,axiom,
    ! [X1: a,X2: produc6345636018528648726od_a_b] :
      ( ( produc7006406357458145757od_a_b @ ( produc458170271728203695od_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_49_snd__conv,axiom,
    ! [X1: a,X2: produc3520053589329427452od_a_b] :
      ( ( produc1217227160481923139od_a_b @ ( produc5260523172840707349od_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_50_snd__conv,axiom,
    ! [X1: b,X2: d] :
      ( ( product_snd_b_d @ ( product_Pair_b_d @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_51_snd__conv,axiom,
    ! [X1: b,X2: c] :
      ( ( product_snd_b_c @ ( product_Pair_b_c @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_52_snd__conv,axiom,
    ! [X1: a,X2: product_prod_b_d] :
      ( ( produc8648342219374764080od_b_d @ ( produc6867761809215060226od_b_d @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_53_snd__conv,axiom,
    ! [X1: a,X2: product_prod_b_c] :
      ( ( produc8648342215071535279od_b_c @ ( produc6867761804911831425od_b_c @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_54_snd__conv,axiom,
    ! [X1: a,X2: b] :
      ( ( product_snd_a_b @ ( product_Pair_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_55_snd__conv,axiom,
    ! [X1: $o,X2: produc2518759752815613485od_a_b] :
      ( ( produc5480430458100320474od_a_b @ ( produc1286801380576301484od_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_56_snd__conv,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,X2: list_f1445794025290330138od_a_b] :
      ( ( produc396176279405262539od_a_b @ ( produc6212510018049267869od_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_57_snd__conv,axiom,
    ! [X1: $o,X2: list_f1445794025290330138od_a_b] :
      ( ( produc2954343059184910791od_a_b @ ( produc7489420772309856409od_a_b @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_58_snd__eqD,axiom,
    ! [X3: a,Y3: produc6345636018528648726od_a_b,A: produc6345636018528648726od_a_b] :
      ( ( ( produc7006406357458145757od_a_b @ ( produc458170271728203695od_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_59_snd__eqD,axiom,
    ! [X3: a,Y3: produc3520053589329427452od_a_b,A: produc3520053589329427452od_a_b] :
      ( ( ( produc1217227160481923139od_a_b @ ( produc5260523172840707349od_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_60_snd__eqD,axiom,
    ! [X3: b,Y3: d,A: d] :
      ( ( ( product_snd_b_d @ ( product_Pair_b_d @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_61_snd__eqD,axiom,
    ! [X3: b,Y3: c,A: c] :
      ( ( ( product_snd_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_62_snd__eqD,axiom,
    ! [X3: a,Y3: product_prod_b_d,A: product_prod_b_d] :
      ( ( ( produc8648342219374764080od_b_d @ ( produc6867761809215060226od_b_d @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_63_snd__eqD,axiom,
    ! [X3: a,Y3: product_prod_b_c,A: product_prod_b_c] :
      ( ( ( produc8648342215071535279od_b_c @ ( produc6867761804911831425od_b_c @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_64_snd__eqD,axiom,
    ! [X3: a,Y3: b,A: b] :
      ( ( ( product_snd_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_65_snd__eqD,axiom,
    ! [X3: $o,Y3: produc2518759752815613485od_a_b,A: produc2518759752815613485od_a_b] :
      ( ( ( produc5480430458100320474od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_66_snd__eqD,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b,A: list_f1445794025290330138od_a_b] :
      ( ( ( produc396176279405262539od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_67_snd__eqD,axiom,
    ! [X3: $o,Y3: list_f1445794025290330138od_a_b,A: list_f1445794025290330138od_a_b] :
      ( ( ( produc2954343059184910791od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_68_set__ConsD,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_69_set__ConsD,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_70_set__ConsD,axiom,
    ! [Y3: a,X3: a,Xs2: list_a] :
      ( ( member_a2 @ Y3 @ ( set_a2 @ ( cons_a @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member_a2 @ Y3 @ ( set_a2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_71_set__ConsD,axiom,
    ! [Y3: d,X3: d,Xs2: list_d] :
      ( ( member_d2 @ Y3 @ ( set_d2 @ ( cons_d @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member_d2 @ Y3 @ ( set_d2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_72_set__ConsD,axiom,
    ! [Y3: c,X3: c,Xs2: list_c] :
      ( ( member_c2 @ Y3 @ ( set_c2 @ ( cons_c @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member_c2 @ Y3 @ ( set_c2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_73_set__ConsD,axiom,
    ! [Y3: $o,X3: $o,Xs2: list_o] :
      ( ( member_o2 @ Y3 @ ( set_o2 @ ( cons_o @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member_o2 @ Y3 @ ( set_o2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_74_set__ConsD,axiom,
    ! [Y3: nat,X3: nat,Xs2: list_nat] :
      ( ( member_nat2 @ Y3 @ ( set_nat2 @ ( cons_nat @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member_nat2 @ Y3 @ ( set_nat2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_75_set__ConsD,axiom,
    ! [Y3: product_prod_a_b,X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ Y3 @ ( set_Product_prod_a_b2 @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member1426531481828664017od_a_b @ Y3 @ ( set_Product_prod_a_b2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_76_set__ConsD,axiom,
    ! [Y3: list_l8778361445553822004od_a_b,X3: list_l8778361445553822004od_a_b,Xs2: list_l6443893005374362810od_a_b] :
      ( ( member7805385913403518557od_a_b @ Y3 @ ( set_li2519811128146010313od_a_b @ ( cons_l4798275018037426410od_a_b @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member7805385913403518557od_a_b @ Y3 @ ( set_li2519811128146010313od_a_b @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_77_set__ConsD,axiom,
    ! [Y3: set_fs5173440902860351732od_a_b,X3: set_fs5173440902860351732od_a_b,Xs2: list_s7922523924679432314od_a_b] :
      ( ( member3854304715014625821od_a_b @ Y3 @ ( set_se4205765813130927241od_a_b @ ( cons_s5741212700939514026od_a_b @ X3 @ Xs2 ) ) )
     => ( ( Y3 = X3 )
        | ( member3854304715014625821od_a_b @ Y3 @ ( set_se4205765813130927241od_a_b @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_78_list_Oset__cases,axiom,
    ! [E: list_P1467974523212632366od_a_b,A: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ E @ ( set_li5045283583078295363od_a_b @ A ) )
     => ( ! [Z2: list_l8778361445553822004od_a_b] :
            ( A
           != ( cons_l907386227682280420od_a_b @ E @ Z2 ) )
       => ~ ! [Z1: list_P1467974523212632366od_a_b,Z2: list_l8778361445553822004od_a_b] :
              ( ( A
                = ( cons_l907386227682280420od_a_b @ Z1 @ Z2 ) )
             => ~ ( member6895035109809442519od_a_b @ E @ ( set_li5045283583078295363od_a_b @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_79_list_Oset__cases,axiom,
    ! [E: fset_l1334069825099621524od_a_b,A: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ E @ ( set_fs4298891544546585641od_a_b @ A ) )
     => ( ! [Z2: list_f1445794025290330138od_a_b] :
            ( A
           != ( cons_f6577355434438001738od_a_b @ E @ Z2 ) )
       => ~ ! [Z1: fset_l1334069825099621524od_a_b,Z2: list_f1445794025290330138od_a_b] :
              ( ( A
                = ( cons_f6577355434438001738od_a_b @ Z1 @ Z2 ) )
             => ~ ( member361094292949318077od_a_b @ E @ ( set_fs4298891544546585641od_a_b @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_80_list_Oset__cases,axiom,
    ! [E: a,A: list_a] :
      ( ( member_a2 @ E @ ( set_a2 @ A ) )
     => ( ! [Z2: list_a] :
            ( A
           != ( cons_a @ E @ Z2 ) )
       => ~ ! [Z1: a,Z2: list_a] :
              ( ( A
                = ( cons_a @ Z1 @ Z2 ) )
             => ~ ( member_a2 @ E @ ( set_a2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_81_list_Oset__cases,axiom,
    ! [E: d,A: list_d] :
      ( ( member_d2 @ E @ ( set_d2 @ A ) )
     => ( ! [Z2: list_d] :
            ( A
           != ( cons_d @ E @ Z2 ) )
       => ~ ! [Z1: d,Z2: list_d] :
              ( ( A
                = ( cons_d @ Z1 @ Z2 ) )
             => ~ ( member_d2 @ E @ ( set_d2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_82_list_Oset__cases,axiom,
    ! [E: c,A: list_c] :
      ( ( member_c2 @ E @ ( set_c2 @ A ) )
     => ( ! [Z2: list_c] :
            ( A
           != ( cons_c @ E @ Z2 ) )
       => ~ ! [Z1: c,Z2: list_c] :
              ( ( A
                = ( cons_c @ Z1 @ Z2 ) )
             => ~ ( member_c2 @ E @ ( set_c2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_83_list_Oset__cases,axiom,
    ! [E: $o,A: list_o] :
      ( ( member_o2 @ E @ ( set_o2 @ A ) )
     => ( ! [Z2: list_o] :
            ( A
           != ( cons_o @ E @ Z2 ) )
       => ~ ! [Z1: $o,Z2: list_o] :
              ( ( A
                = ( cons_o @ Z1 @ Z2 ) )
             => ~ ( member_o2 @ E @ ( set_o2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_84_list_Oset__cases,axiom,
    ! [E: nat,A: list_nat] :
      ( ( member_nat2 @ E @ ( set_nat2 @ A ) )
     => ( ! [Z2: list_nat] :
            ( A
           != ( cons_nat @ E @ Z2 ) )
       => ~ ! [Z1: nat,Z2: list_nat] :
              ( ( A
                = ( cons_nat @ Z1 @ Z2 ) )
             => ~ ( member_nat2 @ E @ ( set_nat2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_85_list_Oset__cases,axiom,
    ! [E: product_prod_a_b,A: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ E @ ( set_Product_prod_a_b2 @ A ) )
     => ( ! [Z2: list_P1467974523212632366od_a_b] :
            ( A
           != ( cons_P7316939131009794654od_a_b @ E @ Z2 ) )
       => ~ ! [Z1: product_prod_a_b,Z2: list_P1467974523212632366od_a_b] :
              ( ( A
                = ( cons_P7316939131009794654od_a_b @ Z1 @ Z2 ) )
             => ~ ( member1426531481828664017od_a_b @ E @ ( set_Product_prod_a_b2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_86_list_Oset__cases,axiom,
    ! [E: list_l8778361445553822004od_a_b,A: list_l6443893005374362810od_a_b] :
      ( ( member7805385913403518557od_a_b @ E @ ( set_li2519811128146010313od_a_b @ A ) )
     => ( ! [Z2: list_l6443893005374362810od_a_b] :
            ( A
           != ( cons_l4798275018037426410od_a_b @ E @ Z2 ) )
       => ~ ! [Z1: list_l8778361445553822004od_a_b,Z2: list_l6443893005374362810od_a_b] :
              ( ( A
                = ( cons_l4798275018037426410od_a_b @ Z1 @ Z2 ) )
             => ~ ( member7805385913403518557od_a_b @ E @ ( set_li2519811128146010313od_a_b @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_87_list_Oset__cases,axiom,
    ! [E: set_fs5173440902860351732od_a_b,A: list_s7922523924679432314od_a_b] :
      ( ( member3854304715014625821od_a_b @ E @ ( set_se4205765813130927241od_a_b @ A ) )
     => ( ! [Z2: list_s7922523924679432314od_a_b] :
            ( A
           != ( cons_s5741212700939514026od_a_b @ E @ Z2 ) )
       => ~ ! [Z1: set_fs5173440902860351732od_a_b,Z2: list_s7922523924679432314od_a_b] :
              ( ( A
                = ( cons_s5741212700939514026od_a_b @ Z1 @ Z2 ) )
             => ~ ( member3854304715014625821od_a_b @ E @ ( set_se4205765813130927241od_a_b @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_88_list_Oset__intros_I1_J,axiom,
    ! [X21: list_P1467974523212632366od_a_b,X22: list_l8778361445553822004od_a_b] : ( member6895035109809442519od_a_b @ X21 @ ( set_li5045283583078295363od_a_b @ ( cons_l907386227682280420od_a_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_89_list_Oset__intros_I1_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] : ( member361094292949318077od_a_b @ X21 @ ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_90_list_Oset__intros_I1_J,axiom,
    ! [X21: a,X22: list_a] : ( member_a2 @ X21 @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_91_list_Oset__intros_I1_J,axiom,
    ! [X21: d,X22: list_d] : ( member_d2 @ X21 @ ( set_d2 @ ( cons_d @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_92_list_Oset__intros_I1_J,axiom,
    ! [X21: c,X22: list_c] : ( member_c2 @ X21 @ ( set_c2 @ ( cons_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_93_list_Oset__intros_I1_J,axiom,
    ! [X21: $o,X22: list_o] : ( member_o2 @ X21 @ ( set_o2 @ ( cons_o @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_94_list_Oset__intros_I1_J,axiom,
    ! [X21: nat,X22: list_nat] : ( member_nat2 @ X21 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_95_list_Oset__intros_I1_J,axiom,
    ! [X21: product_prod_a_b,X22: list_P1467974523212632366od_a_b] : ( member1426531481828664017od_a_b @ X21 @ ( set_Product_prod_a_b2 @ ( cons_P7316939131009794654od_a_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_96_list_Oset__intros_I1_J,axiom,
    ! [X21: list_l8778361445553822004od_a_b,X22: list_l6443893005374362810od_a_b] : ( member7805385913403518557od_a_b @ X21 @ ( set_li2519811128146010313od_a_b @ ( cons_l4798275018037426410od_a_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_97_list_Oset__intros_I1_J,axiom,
    ! [X21: set_fs5173440902860351732od_a_b,X22: list_s7922523924679432314od_a_b] : ( member3854304715014625821od_a_b @ X21 @ ( set_se4205765813130927241od_a_b @ ( cons_s5741212700939514026od_a_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_98_list_Oset__intros_I2_J,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,X22: list_l8778361445553822004od_a_b,X21: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ X22 ) )
     => ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( cons_l907386227682280420od_a_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_99_list_Oset__intros_I2_J,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b,X21: fset_l1334069825099621524od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ X22 ) )
     => ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_100_list_Oset__intros_I2_J,axiom,
    ! [Y3: a,X22: list_a,X21: a] :
      ( ( member_a2 @ Y3 @ ( set_a2 @ X22 ) )
     => ( member_a2 @ Y3 @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_101_list_Oset__intros_I2_J,axiom,
    ! [Y3: d,X22: list_d,X21: d] :
      ( ( member_d2 @ Y3 @ ( set_d2 @ X22 ) )
     => ( member_d2 @ Y3 @ ( set_d2 @ ( cons_d @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_102_list_Oset__intros_I2_J,axiom,
    ! [Y3: c,X22: list_c,X21: c] :
      ( ( member_c2 @ Y3 @ ( set_c2 @ X22 ) )
     => ( member_c2 @ Y3 @ ( set_c2 @ ( cons_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_103_list_Oset__intros_I2_J,axiom,
    ! [Y3: $o,X22: list_o,X21: $o] :
      ( ( member_o2 @ Y3 @ ( set_o2 @ X22 ) )
     => ( member_o2 @ Y3 @ ( set_o2 @ ( cons_o @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_104_list_Oset__intros_I2_J,axiom,
    ! [Y3: nat,X22: list_nat,X21: nat] :
      ( ( member_nat2 @ Y3 @ ( set_nat2 @ X22 ) )
     => ( member_nat2 @ Y3 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_105_list_Oset__intros_I2_J,axiom,
    ! [Y3: product_prod_a_b,X22: list_P1467974523212632366od_a_b,X21: product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ Y3 @ ( set_Product_prod_a_b2 @ X22 ) )
     => ( member1426531481828664017od_a_b @ Y3 @ ( set_Product_prod_a_b2 @ ( cons_P7316939131009794654od_a_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_106_list_Oset__intros_I2_J,axiom,
    ! [Y3: list_l8778361445553822004od_a_b,X22: list_l6443893005374362810od_a_b,X21: list_l8778361445553822004od_a_b] :
      ( ( member7805385913403518557od_a_b @ Y3 @ ( set_li2519811128146010313od_a_b @ X22 ) )
     => ( member7805385913403518557od_a_b @ Y3 @ ( set_li2519811128146010313od_a_b @ ( cons_l4798275018037426410od_a_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_107_list_Oset__intros_I2_J,axiom,
    ! [Y3: set_fs5173440902860351732od_a_b,X22: list_s7922523924679432314od_a_b,X21: set_fs5173440902860351732od_a_b] :
      ( ( member3854304715014625821od_a_b @ Y3 @ ( set_se4205765813130927241od_a_b @ X22 ) )
     => ( member3854304715014625821od_a_b @ Y3 @ ( set_se4205765813130927241od_a_b @ ( cons_s5741212700939514026od_a_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_108_simple__cg__closure__phase__2__helper_Ocases,axiom,
    ! [X3: produc2518759752815613485od_a_b] :
      ~ ! [X12: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc6212510018049267869od_a_b @ X12 @ Xs3 ) ) ).

% simple_cg_closure_phase_2_helper.cases
thf(fact_109_prod__induct3,axiom,
    ! [P: produc9005793448470268223od_a_b > $o,X3: produc9005793448470268223od_a_b] :
      ( ! [A3: a,B3: b,C: list_P1467974523212632366od_a_b] : ( P @ ( produc458170271728203695od_a_b @ A3 @ ( produc1126366459492273030od_a_b @ B3 @ C ) ) )
     => ( P @ X3 ) ) ).

% prod_induct3
thf(fact_110_prod__induct3,axiom,
    ! [P: produc7169317207952727333od_a_b > $o,X3: produc7169317207952727333od_a_b] :
      ( ! [A3: a,B3: b,C: fset_l1334069825099621524od_a_b] : ( P @ ( produc5260523172840707349od_a_b @ A3 @ ( produc912194690294371052od_a_b @ B3 @ C ) ) )
     => ( P @ X3 ) ) ).

% prod_induct3
thf(fact_111_prod__induct3,axiom,
    ! [P: produc3621550705533957266od_b_d > $o,X3: produc3621550705533957266od_b_d] :
      ( ! [A3: a,B3: b,C: d] : ( P @ ( produc6867761809215060226od_b_d @ A3 @ ( product_Pair_b_d @ B3 @ C ) ) )
     => ( P @ X3 ) ) ).

% prod_induct3
thf(fact_112_prod__induct3,axiom,
    ! [P: produc3550516665487611281od_b_c > $o,X3: produc3550516665487611281od_b_c] :
      ( ! [A3: a,B3: b,C: c] : ( P @ ( produc6867761804911831425od_b_c @ A3 @ ( product_Pair_b_c @ B3 @ C ) ) )
     => ( P @ X3 ) ) ).

% prod_induct3
thf(fact_113_prod__induct3,axiom,
    ! [P: produc8937288731615916348od_a_b > $o,X3: produc8937288731615916348od_a_b] :
      ( ! [A3: $o,B3: fset_l1334069825099621524od_a_b,C: list_f1445794025290330138od_a_b] : ( P @ ( produc1286801380576301484od_a_b @ A3 @ ( produc6212510018049267869od_a_b @ B3 @ C ) ) )
     => ( P @ X3 ) ) ).

% prod_induct3
thf(fact_114_prod__cases3,axiom,
    ! [Y3: produc9005793448470268223od_a_b] :
      ~ ! [A3: a,B3: b,C: list_P1467974523212632366od_a_b] :
          ( Y3
         != ( produc458170271728203695od_a_b @ A3 @ ( produc1126366459492273030od_a_b @ B3 @ C ) ) ) ).

% prod_cases3
thf(fact_115_prod__cases3,axiom,
    ! [Y3: produc7169317207952727333od_a_b] :
      ~ ! [A3: a,B3: b,C: fset_l1334069825099621524od_a_b] :
          ( Y3
         != ( produc5260523172840707349od_a_b @ A3 @ ( produc912194690294371052od_a_b @ B3 @ C ) ) ) ).

% prod_cases3
thf(fact_116_prod__cases3,axiom,
    ! [Y3: produc3621550705533957266od_b_d] :
      ~ ! [A3: a,B3: b,C: d] :
          ( Y3
         != ( produc6867761809215060226od_b_d @ A3 @ ( product_Pair_b_d @ B3 @ C ) ) ) ).

% prod_cases3
thf(fact_117_prod__cases3,axiom,
    ! [Y3: produc3550516665487611281od_b_c] :
      ~ ! [A3: a,B3: b,C: c] :
          ( Y3
         != ( produc6867761804911831425od_b_c @ A3 @ ( product_Pair_b_c @ B3 @ C ) ) ) ).

% prod_cases3
thf(fact_118_prod__cases3,axiom,
    ! [Y3: produc8937288731615916348od_a_b] :
      ~ ! [A3: $o,B3: fset_l1334069825099621524od_a_b,C: list_f1445794025290330138od_a_b] :
          ( Y3
         != ( produc1286801380576301484od_a_b @ A3 @ ( produc6212510018049267869od_a_b @ B3 @ C ) ) ) ).

% prod_cases3
thf(fact_119_Pair__inject,axiom,
    ! [A: a,B: produc6345636018528648726od_a_b,A2: a,B2: produc6345636018528648726od_a_b] :
      ( ( ( produc458170271728203695od_a_b @ A @ B )
        = ( produc458170271728203695od_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_120_Pair__inject,axiom,
    ! [A: a,B: produc3520053589329427452od_a_b,A2: a,B2: produc3520053589329427452od_a_b] :
      ( ( ( produc5260523172840707349od_a_b @ A @ B )
        = ( produc5260523172840707349od_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_121_Pair__inject,axiom,
    ! [A: a,B: product_prod_b_d,A2: a,B2: product_prod_b_d] :
      ( ( ( produc6867761809215060226od_b_d @ A @ B )
        = ( produc6867761809215060226od_b_d @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_122_Pair__inject,axiom,
    ! [A: a,B: product_prod_b_c,A2: a,B2: product_prod_b_c] :
      ( ( ( produc6867761804911831425od_b_c @ A @ B )
        = ( produc6867761804911831425od_b_c @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_123_Pair__inject,axiom,
    ! [A: a,B: b,A2: a,B2: b] :
      ( ( ( product_Pair_a_b @ A @ B )
        = ( product_Pair_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_124_Pair__inject,axiom,
    ! [A: $o,B: list_f1445794025290330138od_a_b,A2: $o,B2: list_f1445794025290330138od_a_b] :
      ( ( ( produc7489420772309856409od_a_b @ A @ B )
        = ( produc7489420772309856409od_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_125_Pair__inject,axiom,
    ! [A: $o,B: produc2518759752815613485od_a_b,A2: $o,B2: produc2518759752815613485od_a_b] :
      ( ( ( produc1286801380576301484od_a_b @ A @ B )
        = ( produc1286801380576301484od_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_126_Pair__inject,axiom,
    ! [A: fset_l1334069825099621524od_a_b,B: list_f1445794025290330138od_a_b,A2: fset_l1334069825099621524od_a_b,B2: list_f1445794025290330138od_a_b] :
      ( ( ( produc6212510018049267869od_a_b @ A @ B )
        = ( produc6212510018049267869od_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_127_prod__cases,axiom,
    ! [P: produc9005793448470268223od_a_b > $o,P2: produc9005793448470268223od_a_b] :
      ( ! [A3: a,B3: produc6345636018528648726od_a_b] : ( P @ ( produc458170271728203695od_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_128_prod__cases,axiom,
    ! [P: produc7169317207952727333od_a_b > $o,P2: produc7169317207952727333od_a_b] :
      ( ! [A3: a,B3: produc3520053589329427452od_a_b] : ( P @ ( produc5260523172840707349od_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_129_prod__cases,axiom,
    ! [P: produc3621550705533957266od_b_d > $o,P2: produc3621550705533957266od_b_d] :
      ( ! [A3: a,B3: product_prod_b_d] : ( P @ ( produc6867761809215060226od_b_d @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_130_prod__cases,axiom,
    ! [P: produc3550516665487611281od_b_c > $o,P2: produc3550516665487611281od_b_c] :
      ( ! [A3: a,B3: product_prod_b_c] : ( P @ ( produc6867761804911831425od_b_c @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_131_prod__cases,axiom,
    ! [P: product_prod_a_b > $o,P2: product_prod_a_b] :
      ( ! [A3: a,B3: b] : ( P @ ( product_Pair_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_132_prod__cases,axiom,
    ! [P: produc2313482920965681321od_a_b > $o,P2: produc2313482920965681321od_a_b] :
      ( ! [A3: $o,B3: list_f1445794025290330138od_a_b] : ( P @ ( produc7489420772309856409od_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_133_prod__cases,axiom,
    ! [P: produc8937288731615916348od_a_b > $o,P2: produc8937288731615916348od_a_b] :
      ( ! [A3: $o,B3: produc2518759752815613485od_a_b] : ( P @ ( produc1286801380576301484od_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_134_prod__cases,axiom,
    ! [P: produc2518759752815613485od_a_b > $o,P2: produc2518759752815613485od_a_b] :
      ( ! [A3: fset_l1334069825099621524od_a_b,B3: list_f1445794025290330138od_a_b] : ( P @ ( produc6212510018049267869od_a_b @ A3 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_135_surj__pair,axiom,
    ! [P2: produc9005793448470268223od_a_b] :
    ? [X4: a,Y: produc6345636018528648726od_a_b] :
      ( P2
      = ( produc458170271728203695od_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_136_surj__pair,axiom,
    ! [P2: produc7169317207952727333od_a_b] :
    ? [X4: a,Y: produc3520053589329427452od_a_b] :
      ( P2
      = ( produc5260523172840707349od_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_137_surj__pair,axiom,
    ! [P2: produc3621550705533957266od_b_d] :
    ? [X4: a,Y: product_prod_b_d] :
      ( P2
      = ( produc6867761809215060226od_b_d @ X4 @ Y ) ) ).

% surj_pair
thf(fact_138_surj__pair,axiom,
    ! [P2: produc3550516665487611281od_b_c] :
    ? [X4: a,Y: product_prod_b_c] :
      ( P2
      = ( produc6867761804911831425od_b_c @ X4 @ Y ) ) ).

% surj_pair
thf(fact_139_surj__pair,axiom,
    ! [P2: product_prod_a_b] :
    ? [X4: a,Y: b] :
      ( P2
      = ( product_Pair_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_140_surj__pair,axiom,
    ! [P2: produc2313482920965681321od_a_b] :
    ? [X4: $o,Y: list_f1445794025290330138od_a_b] :
      ( P2
      = ( produc7489420772309856409od_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_141_surj__pair,axiom,
    ! [P2: produc8937288731615916348od_a_b] :
    ? [X4: $o,Y: produc2518759752815613485od_a_b] :
      ( P2
      = ( produc1286801380576301484od_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_142_surj__pair,axiom,
    ! [P2: produc2518759752815613485od_a_b] :
    ? [X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b] :
      ( P2
      = ( produc6212510018049267869od_a_b @ X4 @ Y ) ) ).

% surj_pair
thf(fact_143_mem__Collect__eq,axiom,
    ! [A: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > $o] :
      ( ( member7551773913232940227od_a_b @ A @ ( collec6680873810700003333od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_144_mem__Collect__eq,axiom,
    ! [A: set_fs5173440902860351732od_a_b,P: set_fs5173440902860351732od_a_b > $o] :
      ( ( member3854304715014625821od_a_b @ A @ ( collec4999808032329279071od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_145_mem__Collect__eq,axiom,
    ! [A: d,P: d > $o] :
      ( ( member_d2 @ A @ ( collect_d @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_146_mem__Collect__eq,axiom,
    ! [A: c,P: c > $o] :
      ( ( member_c2 @ A @ ( collect_c @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_147_mem__Collect__eq,axiom,
    ! [A: a,P: a > $o] :
      ( ( member_a2 @ A @ ( collect_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_148_mem__Collect__eq,axiom,
    ! [A: fset_l1334069825099621524od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ( member361094292949318077od_a_b @ A @ ( collec2335753234515135999od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_149_mem__Collect__eq,axiom,
    ! [A: list_P1467974523212632366od_a_b,P: list_P1467974523212632366od_a_b > $o] :
      ( ( member6895035109809442519od_a_b @ A @ ( collec2845612350631750681od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_150_Collect__mem__eq,axiom,
    ! [A4: set_li7540826859550765818od_a_b] :
      ( ( collec6680873810700003333od_a_b
        @ ^ [X5: list_f1445794025290330138od_a_b] : ( member7551773913232940227od_a_b @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_151_Collect__mem__eq,axiom,
    ! [A4: set_se1014227543623231828od_a_b] :
      ( ( collec4999808032329279071od_a_b
        @ ^ [X5: set_fs5173440902860351732od_a_b] : ( member3854304715014625821od_a_b @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_152_Collect__mem__eq,axiom,
    ! [A4: set_d] :
      ( ( collect_d
        @ ^ [X5: d] : ( member_d2 @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_153_Collect__mem__eq,axiom,
    ! [A4: set_c] :
      ( ( collect_c
        @ ^ [X5: c] : ( member_c2 @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_154_Collect__mem__eq,axiom,
    ! [A4: set_a] :
      ( ( collect_a
        @ ^ [X5: a] : ( member_a2 @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_155_Collect__mem__eq,axiom,
    ! [A4: set_fs5173440902860351732od_a_b] :
      ( ( collec2335753234515135999od_a_b
        @ ^ [X5: fset_l1334069825099621524od_a_b] : ( member361094292949318077od_a_b @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_156_Collect__mem__eq,axiom,
    ! [A4: set_li6306622547289818894od_a_b] :
      ( ( collec2845612350631750681od_a_b
        @ ^ [X5: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ X5 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_157_Collect__cong,axiom,
    ! [P: list_P1467974523212632366od_a_b > $o,Q2: list_P1467974523212632366od_a_b > $o] :
      ( ! [X4: list_P1467974523212632366od_a_b] :
          ( ( P @ X4 )
          = ( Q2 @ X4 ) )
     => ( ( collec2845612350631750681od_a_b @ P )
        = ( collec2845612350631750681od_a_b @ Q2 ) ) ) ).

% Collect_cong
thf(fact_158_Collect__cong,axiom,
    ! [P: fset_l1334069825099621524od_a_b > $o,Q2: fset_l1334069825099621524od_a_b > $o] :
      ( ! [X4: fset_l1334069825099621524od_a_b] :
          ( ( P @ X4 )
          = ( Q2 @ X4 ) )
     => ( ( collec2335753234515135999od_a_b @ P )
        = ( collec2335753234515135999od_a_b @ Q2 ) ) ) ).

% Collect_cong
thf(fact_159_assms_I5_J,axiom,
    fmembe7722352836199763061od_a_b @ v @ x2 ).

% assms(5)
thf(fact_160_eq__snd__iff,axiom,
    ! [B: produc6345636018528648726od_a_b,P2: produc9005793448470268223od_a_b] :
      ( ( B
        = ( produc7006406357458145757od_a_b @ P2 ) )
      = ( ? [A5: a] :
            ( P2
            = ( produc458170271728203695od_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_161_eq__snd__iff,axiom,
    ! [B: produc3520053589329427452od_a_b,P2: produc7169317207952727333od_a_b] :
      ( ( B
        = ( produc1217227160481923139od_a_b @ P2 ) )
      = ( ? [A5: a] :
            ( P2
            = ( produc5260523172840707349od_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_162_eq__snd__iff,axiom,
    ! [B: d,P2: product_prod_b_d] :
      ( ( B
        = ( product_snd_b_d @ P2 ) )
      = ( ? [A5: b] :
            ( P2
            = ( product_Pair_b_d @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_163_eq__snd__iff,axiom,
    ! [B: c,P2: product_prod_b_c] :
      ( ( B
        = ( product_snd_b_c @ P2 ) )
      = ( ? [A5: b] :
            ( P2
            = ( product_Pair_b_c @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_164_eq__snd__iff,axiom,
    ! [B: product_prod_b_d,P2: produc3621550705533957266od_b_d] :
      ( ( B
        = ( produc8648342219374764080od_b_d @ P2 ) )
      = ( ? [A5: a] :
            ( P2
            = ( produc6867761809215060226od_b_d @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_165_eq__snd__iff,axiom,
    ! [B: product_prod_b_c,P2: produc3550516665487611281od_b_c] :
      ( ( B
        = ( produc8648342215071535279od_b_c @ P2 ) )
      = ( ? [A5: a] :
            ( P2
            = ( produc6867761804911831425od_b_c @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_166_eq__snd__iff,axiom,
    ! [B: b,P2: product_prod_a_b] :
      ( ( B
        = ( product_snd_a_b @ P2 ) )
      = ( ? [A5: a] :
            ( P2
            = ( product_Pair_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_167_eq__snd__iff,axiom,
    ! [B: produc2518759752815613485od_a_b,P2: produc8937288731615916348od_a_b] :
      ( ( B
        = ( produc5480430458100320474od_a_b @ P2 ) )
      = ( ? [A5: $o] :
            ( P2
            = ( produc1286801380576301484od_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_168_eq__snd__iff,axiom,
    ! [B: list_f1445794025290330138od_a_b,P2: produc2518759752815613485od_a_b] :
      ( ( B
        = ( produc396176279405262539od_a_b @ P2 ) )
      = ( ? [A5: fset_l1334069825099621524od_a_b] :
            ( P2
            = ( produc6212510018049267869od_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_169_eq__snd__iff,axiom,
    ! [B: list_f1445794025290330138od_a_b,P2: produc2313482920965681321od_a_b] :
      ( ( B
        = ( produc2954343059184910791od_a_b @ P2 ) )
      = ( ? [A5: $o] :
            ( P2
            = ( produc7489420772309856409od_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_170_sndI,axiom,
    ! [X3: produc9005793448470268223od_a_b,Y3: a,Z: produc6345636018528648726od_a_b] :
      ( ( X3
        = ( produc458170271728203695od_a_b @ Y3 @ Z ) )
     => ( ( produc7006406357458145757od_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_171_sndI,axiom,
    ! [X3: produc7169317207952727333od_a_b,Y3: a,Z: produc3520053589329427452od_a_b] :
      ( ( X3
        = ( produc5260523172840707349od_a_b @ Y3 @ Z ) )
     => ( ( produc1217227160481923139od_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_172_sndI,axiom,
    ! [X3: product_prod_b_d,Y3: b,Z: d] :
      ( ( X3
        = ( product_Pair_b_d @ Y3 @ Z ) )
     => ( ( product_snd_b_d @ X3 )
        = Z ) ) ).

% sndI
thf(fact_173_sndI,axiom,
    ! [X3: product_prod_b_c,Y3: b,Z: c] :
      ( ( X3
        = ( product_Pair_b_c @ Y3 @ Z ) )
     => ( ( product_snd_b_c @ X3 )
        = Z ) ) ).

% sndI
thf(fact_174_sndI,axiom,
    ! [X3: produc3621550705533957266od_b_d,Y3: a,Z: product_prod_b_d] :
      ( ( X3
        = ( produc6867761809215060226od_b_d @ Y3 @ Z ) )
     => ( ( produc8648342219374764080od_b_d @ X3 )
        = Z ) ) ).

% sndI
thf(fact_175_sndI,axiom,
    ! [X3: produc3550516665487611281od_b_c,Y3: a,Z: product_prod_b_c] :
      ( ( X3
        = ( produc6867761804911831425od_b_c @ Y3 @ Z ) )
     => ( ( produc8648342215071535279od_b_c @ X3 )
        = Z ) ) ).

% sndI
thf(fact_176_sndI,axiom,
    ! [X3: product_prod_a_b,Y3: a,Z: b] :
      ( ( X3
        = ( product_Pair_a_b @ Y3 @ Z ) )
     => ( ( product_snd_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_177_sndI,axiom,
    ! [X3: produc8937288731615916348od_a_b,Y3: $o,Z: produc2518759752815613485od_a_b] :
      ( ( X3
        = ( produc1286801380576301484od_a_b @ Y3 @ Z ) )
     => ( ( produc5480430458100320474od_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_178_sndI,axiom,
    ! [X3: produc2518759752815613485od_a_b,Y3: fset_l1334069825099621524od_a_b,Z: list_f1445794025290330138od_a_b] :
      ( ( X3
        = ( produc6212510018049267869od_a_b @ Y3 @ Z ) )
     => ( ( produc396176279405262539od_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_179_sndI,axiom,
    ! [X3: produc2313482920965681321od_a_b,Y3: $o,Z: list_f1445794025290330138od_a_b] :
      ( ( X3
        = ( produc7489420772309856409od_a_b @ Y3 @ Z ) )
     => ( ( produc2954343059184910791od_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_180_assms_I4_J,axiom,
    fmembe7722352836199763061od_a_b @ u @ x2 ).

% assms(4)
thf(fact_181_not__in__set__insert,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( insert4925036576401664074od_a_b @ X3 @ Xs2 )
        = ( cons_l907386227682280420od_a_b @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_182_not__in__set__insert,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( insert2610919176168914352od_a_b @ X3 @ Xs2 )
        = ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_183_not__in__set__insert,axiom,
    ! [X3: a,Xs2: list_a] :
      ( ~ ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
     => ( ( insert_a @ X3 @ Xs2 )
        = ( cons_a @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_184_not__in__set__insert,axiom,
    ! [X3: d,Xs2: list_d] :
      ( ~ ( member_d2 @ X3 @ ( set_d2 @ Xs2 ) )
     => ( ( insert_d @ X3 @ Xs2 )
        = ( cons_d @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_185_not__in__set__insert,axiom,
    ! [X3: c,Xs2: list_c] :
      ( ~ ( member_c2 @ X3 @ ( set_c2 @ Xs2 ) )
     => ( ( insert_c @ X3 @ Xs2 )
        = ( cons_c @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_186_not__in__set__insert,axiom,
    ! [X3: $o,Xs2: list_o] :
      ( ~ ( member_o2 @ X3 @ ( set_o2 @ Xs2 ) )
     => ( ( insert_o @ X3 @ Xs2 )
        = ( cons_o @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_187_not__in__set__insert,axiom,
    ! [X3: nat,Xs2: list_nat] :
      ( ~ ( member_nat2 @ X3 @ ( set_nat2 @ Xs2 ) )
     => ( ( insert_nat @ X3 @ Xs2 )
        = ( cons_nat @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_188_not__in__set__insert,axiom,
    ! [X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
      ( ~ ( member1426531481828664017od_a_b @ X3 @ ( set_Product_prod_a_b2 @ Xs2 ) )
     => ( ( insert7736115125267272132od_a_b @ X3 @ Xs2 )
        = ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_189_not__in__set__insert,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Xs2: list_l6443893005374362810od_a_b] :
      ( ~ ( member7805385913403518557od_a_b @ X3 @ ( set_li2519811128146010313od_a_b @ Xs2 ) )
     => ( ( insert831838759768339024od_a_b @ X3 @ Xs2 )
        = ( cons_l4798275018037426410od_a_b @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_190_not__in__set__insert,axiom,
    ! [X3: set_fs5173440902860351732od_a_b,Xs2: list_s7922523924679432314od_a_b] :
      ( ~ ( member3854304715014625821od_a_b @ X3 @ ( set_se4205765813130927241od_a_b @ Xs2 ) )
     => ( ( insert4427174617854087696od_a_b @ X3 @ Xs2 )
        = ( cons_s5741212700939514026od_a_b @ X3 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_191_List_Oinsert__def,axiom,
    ( insert4925036576401664074od_a_b
    = ( ^ [X5: list_P1467974523212632366od_a_b,Xs4: list_l8778361445553822004od_a_b] : ( if_lis737310530615849466od_a_b @ ( member6895035109809442519od_a_b @ X5 @ ( set_li5045283583078295363od_a_b @ Xs4 ) ) @ Xs4 @ ( cons_l907386227682280420od_a_b @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_192_List_Oinsert__def,axiom,
    ( insert2610919176168914352od_a_b
    = ( ^ [X5: fset_l1334069825099621524od_a_b,Xs4: list_f1445794025290330138od_a_b] : ( if_lis3379674621698944480od_a_b @ ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs4 ) ) @ Xs4 @ ( cons_f6577355434438001738od_a_b @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_193_List_Oinsert__def,axiom,
    ( insert_a
    = ( ^ [X5: a,Xs4: list_a] : ( if_list_a @ ( member_a2 @ X5 @ ( set_a2 @ Xs4 ) ) @ Xs4 @ ( cons_a @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_194_List_Oinsert__def,axiom,
    ( insert_d
    = ( ^ [X5: d,Xs4: list_d] : ( if_list_d @ ( member_d2 @ X5 @ ( set_d2 @ Xs4 ) ) @ Xs4 @ ( cons_d @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_195_List_Oinsert__def,axiom,
    ( insert_c
    = ( ^ [X5: c,Xs4: list_c] : ( if_list_c @ ( member_c2 @ X5 @ ( set_c2 @ Xs4 ) ) @ Xs4 @ ( cons_c @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_196_List_Oinsert__def,axiom,
    ( insert_o
    = ( ^ [X5: $o,Xs4: list_o] : ( if_list_o @ ( member_o2 @ X5 @ ( set_o2 @ Xs4 ) ) @ Xs4 @ ( cons_o @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_197_List_Oinsert__def,axiom,
    ( insert_nat
    = ( ^ [X5: nat,Xs4: list_nat] : ( if_list_nat @ ( member_nat2 @ X5 @ ( set_nat2 @ Xs4 ) ) @ Xs4 @ ( cons_nat @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_198_List_Oinsert__def,axiom,
    ( insert7736115125267272132od_a_b
    = ( ^ [X5: product_prod_a_b,Xs4: list_P1467974523212632366od_a_b] : ( if_lis1002476807507936500od_a_b @ ( member1426531481828664017od_a_b @ X5 @ ( set_Product_prod_a_b2 @ Xs4 ) ) @ Xs4 @ ( cons_P7316939131009794654od_a_b @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_199_List_Oinsert__def,axiom,
    ( insert831838759768339024od_a_b
    = ( ^ [X5: list_l8778361445553822004od_a_b,Xs4: list_l6443893005374362810od_a_b] : ( if_lis8377773601782977152od_a_b @ ( member7805385913403518557od_a_b @ X5 @ ( set_li2519811128146010313od_a_b @ Xs4 ) ) @ Xs4 @ ( cons_l4798275018037426410od_a_b @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_200_List_Oinsert__def,axiom,
    ( insert4427174617854087696od_a_b
    = ( ^ [X5: set_fs5173440902860351732od_a_b,Xs4: list_s7922523924679432314od_a_b] : ( if_lis6932009802700144192od_a_b @ ( member3854304715014625821od_a_b @ X5 @ ( set_se4205765813130927241od_a_b @ Xs4 ) ) @ Xs4 @ ( cons_s5741212700939514026od_a_b @ X5 @ Xs4 ) ) ) ) ).

% List.insert_def
thf(fact_201_in__set__member,axiom,
    ! [X3: set_fs5173440902860351732od_a_b,Xs2: list_s7922523924679432314od_a_b] :
      ( ( member3854304715014625821od_a_b @ X3 @ ( set_se4205765813130927241od_a_b @ Xs2 ) )
      = ( member8348088493781385871od_a_b @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_202_in__set__member,axiom,
    ! [X3: a,Xs2: list_a] :
      ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
      = ( member_a @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_203_in__set__member,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Xs2: list_l6443893005374362810od_a_b] :
      ( ( member7805385913403518557od_a_b @ X3 @ ( set_li2519811128146010313od_a_b @ Xs2 ) )
      = ( member2585845584885325519od_a_b @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_204_in__set__member,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b] :
      ( ( member7551773913232940227od_a_b @ X3 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
      = ( member8444533430530386997od_a_b @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_205_in__set__member,axiom,
    ! [X3: d,Xs2: list_d] :
      ( ( member_d2 @ X3 @ ( set_d2 @ Xs2 ) )
      = ( member_d @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_206_in__set__member,axiom,
    ! [X3: c,Xs2: list_c] :
      ( ( member_c2 @ X3 @ ( set_c2 @ Xs2 ) )
      = ( member_c @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_207_in__set__member,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
      = ( member8280676862674542665od_a_b @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_208_in__set__member,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( member4364926001285900847od_a_b @ Xs2 @ X3 ) ) ).

% in_set_member
thf(fact_209_member__rec_I1_J,axiom,
    ! [X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: product_prod_a_b] :
      ( ( member851666194574169411od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member851666194574169411od_a_b @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_210_member__rec_I1_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( member8280676862674542665od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member8280676862674542665od_a_b @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_211_member__rec_I1_J,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( member8444533430530386997od_a_b @ ( cons_l7290444712290925776od_a_b @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member8444533430530386997od_a_b @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_212_member__rec_I1_J,axiom,
    ! [X3: $o,Xs2: list_o,Y3: $o] :
      ( ( member_o @ ( cons_o @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member_o @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_213_member__rec_I1_J,axiom,
    ! [X3: nat,Xs2: list_nat,Y3: nat] :
      ( ( member_nat @ ( cons_nat @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member_nat @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_214_member__rec_I1_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( member4364926001285900847od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ Y3 )
      = ( ( X3 = Y3 )
        | ( member4364926001285900847od_a_b @ Xs2 @ Y3 ) ) ) ).

% member_rec(1)
thf(fact_215_in__set__insert,axiom,
    ! [X3: set_fs5173440902860351732od_a_b,Xs2: list_s7922523924679432314od_a_b] :
      ( ( member3854304715014625821od_a_b @ X3 @ ( set_se4205765813130927241od_a_b @ Xs2 ) )
     => ( ( insert4427174617854087696od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_216_in__set__insert,axiom,
    ! [X3: a,Xs2: list_a] :
      ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
     => ( ( insert_a @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_217_in__set__insert,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Xs2: list_l6443893005374362810od_a_b] :
      ( ( member7805385913403518557od_a_b @ X3 @ ( set_li2519811128146010313od_a_b @ Xs2 ) )
     => ( ( insert831838759768339024od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_218_in__set__insert,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b] :
      ( ( member7551773913232940227od_a_b @ X3 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
     => ( ( insert8509595773599419190od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_219_in__set__insert,axiom,
    ! [X3: d,Xs2: list_d] :
      ( ( member_d2 @ X3 @ ( set_d2 @ Xs2 ) )
     => ( ( insert_d @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_220_in__set__insert,axiom,
    ! [X3: c,Xs2: list_c] :
      ( ( member_c2 @ X3 @ ( set_c2 @ Xs2 ) )
     => ( ( insert_c @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_221_in__set__insert,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( insert4925036576401664074od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_222_in__set__insert,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( insert2610919176168914352od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_223_insert__Nil,axiom,
    ! [X3: product_prod_a_b] :
      ( ( insert7736115125267272132od_a_b @ X3 @ nil_Product_prod_a_b )
      = ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) ).

% insert_Nil
thf(fact_224_insert__Nil,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( insert4925036576401664074od_a_b @ X3 @ nil_li8635777946366267444od_a_b )
      = ( cons_l907386227682280420od_a_b @ X3 @ nil_li8635777946366267444od_a_b ) ) ).

% insert_Nil
thf(fact_225_insert__Nil,axiom,
    ! [X3: list_f1445794025290330138od_a_b] :
      ( ( insert8509595773599419190od_a_b @ X3 @ nil_li6050065983854590240od_a_b )
      = ( cons_l7290444712290925776od_a_b @ X3 @ nil_li6050065983854590240od_a_b ) ) ).

% insert_Nil
thf(fact_226_insert__Nil,axiom,
    ! [X3: $o] :
      ( ( insert_o @ X3 @ nil_o )
      = ( cons_o @ X3 @ nil_o ) ) ).

% insert_Nil
thf(fact_227_insert__Nil,axiom,
    ! [X3: nat] :
      ( ( insert_nat @ X3 @ nil_nat )
      = ( cons_nat @ X3 @ nil_nat ) ) ).

% insert_Nil
thf(fact_228_insert__Nil,axiom,
    ! [X3: fset_l1334069825099621524od_a_b] :
      ( ( insert2610919176168914352od_a_b @ X3 @ nil_fs4581119677382125722od_a_b )
      = ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) ).

% insert_Nil
thf(fact_229_member__rec_I2_J,axiom,
    ! [Y3: product_prod_a_b] :
      ~ ( member851666194574169411od_a_b @ nil_Product_prod_a_b @ Y3 ) ).

% member_rec(2)
thf(fact_230_member__rec_I2_J,axiom,
    ! [Y3: list_P1467974523212632366od_a_b] :
      ~ ( member8280676862674542665od_a_b @ nil_li8635777946366267444od_a_b @ Y3 ) ).

% member_rec(2)
thf(fact_231_member__rec_I2_J,axiom,
    ! [Y3: list_f1445794025290330138od_a_b] :
      ~ ( member8444533430530386997od_a_b @ nil_li6050065983854590240od_a_b @ Y3 ) ).

% member_rec(2)
thf(fact_232_member__rec_I2_J,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b] :
      ~ ( member4364926001285900847od_a_b @ nil_fs4581119677382125722od_a_b @ Y3 ) ).

% member_rec(2)
thf(fact_233_member__rec_I2_J,axiom,
    ! [Y3: $o] :
      ~ ( member_o @ nil_o @ Y3 ) ).

% member_rec(2)
thf(fact_234_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc3345434161935928879od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b,Res: produc4356081027818849609od_a_b] :
          ( X3
         != ( produc5554862205985698335od_a_b @ X4 @ ( produc683816545860151206od_a_b @ nil_li2802039260981550394od_a_b @ Res ) ) )
     => ( ! [X4: list_P1467974523212632366od_a_b,Yss: list_l6443893005374362810od_a_b,Res: produc4356081027818849609od_a_b] :
            ( X3
           != ( produc5554862205985698335od_a_b @ X4 @ ( produc683816545860151206od_a_b @ ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ Yss ) @ Res ) ) )
       => ~ ! [X4: list_P1467974523212632366od_a_b,Y: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b,Yss: list_l6443893005374362810od_a_b,Res: produc4356081027818849609od_a_b] :
              ( X3
             != ( produc5554862205985698335od_a_b @ X4 @ ( produc683816545860151206od_a_b @ ( cons_l4798275018037426410od_a_b @ ( cons_l907386227682280420od_a_b @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_235_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc8660020554386975555od_a_b] :
      ( ! [X4: list_f1445794025290330138od_a_b,Res: produc724608359110776885od_a_b] :
          ( X3
         != ( produc8193211044935635507od_a_b @ X4 @ ( produc6710758018942698406od_a_b @ nil_li4771897614291402022od_a_b @ Res ) ) )
     => ( ! [X4: list_f1445794025290330138od_a_b,Yss: list_l378912295992385958od_a_b,Res: produc724608359110776885od_a_b] :
            ( X3
           != ( produc8193211044935635507od_a_b @ X4 @ ( produc6710758018942698406od_a_b @ ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ Yss ) @ Res ) ) )
       => ~ ! [X4: list_f1445794025290330138od_a_b,Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b,Yss: list_l378912295992385958od_a_b,Res: produc724608359110776885od_a_b] :
              ( X3
             != ( produc8193211044935635507od_a_b @ X4 @ ( produc6710758018942698406od_a_b @ ( cons_l2865286841204467926od_a_b @ ( cons_l7290444712290925776od_a_b @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_236_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc7154445628944892357list_o] :
      ( ! [X4: $o,Res: produc796964778762255539list_o] :
          ( X3
         != ( produc7533889540795632565list_o @ X4 @ ( produc1191279492341360934list_o @ nil_list_o @ Res ) ) )
     => ( ! [X4: $o,Yss: list_list_o,Res: produc796964778762255539list_o] :
            ( X3
           != ( produc7533889540795632565list_o @ X4 @ ( produc1191279492341360934list_o @ ( cons_list_o @ nil_o @ Yss ) @ Res ) ) )
       => ~ ! [X4: $o,Y: $o,Ys: list_o,Yss: list_list_o,Res: produc796964778762255539list_o] :
              ( X3
             != ( produc7533889540795632565list_o @ X4 @ ( produc1191279492341360934list_o @ ( cons_list_o @ ( cons_o @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_237_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc19496163836001069st_nat] :
      ( ! [X4: nat,Res: produc7974263126369132087st_nat] :
          ( X3
         != ( produc3115374921362880095st_nat @ X4 @ ( produc3419769971367040704st_nat @ nil_list_nat @ Res ) ) )
     => ( ! [X4: nat,Yss: list_list_nat,Res: produc7974263126369132087st_nat] :
            ( X3
           != ( produc3115374921362880095st_nat @ X4 @ ( produc3419769971367040704st_nat @ ( cons_list_nat @ nil_nat @ Yss ) @ Res ) ) )
       => ~ ! [X4: nat,Y: nat,Ys: list_nat,Yss: list_list_nat,Res: produc7974263126369132087st_nat] :
              ( X3
             != ( produc3115374921362880095st_nat @ X4 @ ( produc3419769971367040704st_nat @ ( cons_list_nat @ ( cons_nat @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_238_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc5998163534577424309od_a_b] :
      ( ! [X4: product_prod_a_b,Res: produc8908614768156765891od_a_b] :
          ( X3
         != ( produc7167387503278561829od_a_b @ X4 @ ( produc3700279395275165350od_a_b @ nil_li8635777946366267444od_a_b @ Res ) ) )
     => ( ! [X4: product_prod_a_b,Yss: list_l8778361445553822004od_a_b,Res: produc8908614768156765891od_a_b] :
            ( X3
           != ( produc7167387503278561829od_a_b @ X4 @ ( produc3700279395275165350od_a_b @ ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ Yss ) @ Res ) ) )
       => ~ ! [X4: product_prod_a_b,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b,Yss: list_l8778361445553822004od_a_b,Res: produc8908614768156765891od_a_b] :
              ( X3
             != ( produc7167387503278561829od_a_b @ X4 @ ( produc3700279395275165350od_a_b @ ( cons_l907386227682280420od_a_b @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_239_prefixes__in__list__helper_Ocases,axiom,
    ! [X3: produc6844535102171174857od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,Res: produc7877445111886203567od_a_b] :
          ( X3
         != ( produc6699211207839096121od_a_b @ X4 @ ( produc883383490548289190od_a_b @ nil_li6050065983854590240od_a_b @ Res ) ) )
     => ( ! [X4: fset_l1334069825099621524od_a_b,Yss: list_l6099054058445139744od_a_b,Res: produc7877445111886203567od_a_b] :
            ( X3
           != ( produc6699211207839096121od_a_b @ X4 @ ( produc883383490548289190od_a_b @ ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ Yss ) @ Res ) ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b,Yss: list_l6099054058445139744od_a_b,Res: produc7877445111886203567od_a_b] :
              ( X3
             != ( produc6699211207839096121od_a_b @ X4 @ ( produc883383490548289190od_a_b @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ Yss ) @ Res ) ) ) ) ) ).

% prefixes_in_list_helper.cases
thf(fact_240_transpose_Ocases,axiom,
    ! [X3: list_l6443893005374362810od_a_b] :
      ( ( X3 != nil_li2802039260981550394od_a_b )
     => ( ! [Xss: list_l6443893005374362810od_a_b] :
            ( X3
           != ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ Xss ) )
       => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Xss: list_l6443893005374362810od_a_b] :
              ( X3
             != ( cons_l4798275018037426410od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_241_transpose_Ocases,axiom,
    ! [X3: list_l378912295992385958od_a_b] :
      ( ( X3 != nil_li4771897614291402022od_a_b )
     => ( ! [Xss: list_l378912295992385958od_a_b] :
            ( X3
           != ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ Xss ) )
       => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Xss: list_l378912295992385958od_a_b] :
              ( X3
             != ( cons_l2865286841204467926od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_242_transpose_Ocases,axiom,
    ! [X3: list_list_o] :
      ( ( X3 != nil_list_o )
     => ( ! [Xss: list_list_o] :
            ( X3
           != ( cons_list_o @ nil_o @ Xss ) )
       => ~ ! [X4: $o,Xs3: list_o,Xss: list_list_o] :
              ( X3
             != ( cons_list_o @ ( cons_o @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_243_transpose_Ocases,axiom,
    ! [X3: list_list_nat] :
      ( ( X3 != nil_list_nat )
     => ( ! [Xss: list_list_nat] :
            ( X3
           != ( cons_list_nat @ nil_nat @ Xss ) )
       => ~ ! [X4: nat,Xs3: list_nat,Xss: list_list_nat] :
              ( X3
             != ( cons_list_nat @ ( cons_nat @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_244_transpose_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ( ! [Xss: list_l8778361445553822004od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ Xss ) )
       => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Xss: list_l8778361445553822004od_a_b] :
              ( X3
             != ( cons_l907386227682280420od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_245_transpose_Ocases,axiom,
    ! [X3: list_l6099054058445139744od_a_b] :
      ( ( X3 != nil_li6050065983854590240od_a_b )
     => ( ! [Xss: list_l6099054058445139744od_a_b] :
            ( X3
           != ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ Xss ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Xss: list_l6099054058445139744od_a_b] :
              ( X3
             != ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_246_list_Odistinct_I1_J,axiom,
    ! [X21: product_prod_a_b,X22: list_P1467974523212632366od_a_b] :
      ( nil_Product_prod_a_b
     != ( cons_P7316939131009794654od_a_b @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_247_list_Odistinct_I1_J,axiom,
    ! [X21: list_P1467974523212632366od_a_b,X22: list_l8778361445553822004od_a_b] :
      ( nil_li8635777946366267444od_a_b
     != ( cons_l907386227682280420od_a_b @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_248_list_Odistinct_I1_J,axiom,
    ! [X21: list_f1445794025290330138od_a_b,X22: list_l6099054058445139744od_a_b] :
      ( nil_li6050065983854590240od_a_b
     != ( cons_l7290444712290925776od_a_b @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_249_list_Odistinct_I1_J,axiom,
    ! [X21: $o,X22: list_o] :
      ( nil_o
     != ( cons_o @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_250_list_Odistinct_I1_J,axiom,
    ! [X21: nat,X22: list_nat] :
      ( nil_nat
     != ( cons_nat @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_251_list_Odistinct_I1_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( nil_fs4581119677382125722od_a_b
     != ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_252_list_OdiscI,axiom,
    ! [List: list_P1467974523212632366od_a_b,X21: product_prod_a_b,X22: list_P1467974523212632366od_a_b] :
      ( ( List
        = ( cons_P7316939131009794654od_a_b @ X21 @ X22 ) )
     => ( List != nil_Product_prod_a_b ) ) ).

% list.discI
thf(fact_253_list_OdiscI,axiom,
    ! [List: list_l8778361445553822004od_a_b,X21: list_P1467974523212632366od_a_b,X22: list_l8778361445553822004od_a_b] :
      ( ( List
        = ( cons_l907386227682280420od_a_b @ X21 @ X22 ) )
     => ( List != nil_li8635777946366267444od_a_b ) ) ).

% list.discI
thf(fact_254_list_OdiscI,axiom,
    ! [List: list_l6099054058445139744od_a_b,X21: list_f1445794025290330138od_a_b,X22: list_l6099054058445139744od_a_b] :
      ( ( List
        = ( cons_l7290444712290925776od_a_b @ X21 @ X22 ) )
     => ( List != nil_li6050065983854590240od_a_b ) ) ).

% list.discI
thf(fact_255_list_OdiscI,axiom,
    ! [List: list_o,X21: $o,X22: list_o] :
      ( ( List
        = ( cons_o @ X21 @ X22 ) )
     => ( List != nil_o ) ) ).

% list.discI
thf(fact_256_list_OdiscI,axiom,
    ! [List: list_nat,X21: nat,X22: list_nat] :
      ( ( List
        = ( cons_nat @ X21 @ X22 ) )
     => ( List != nil_nat ) ) ).

% list.discI
thf(fact_257_list_OdiscI,axiom,
    ! [List: list_f1445794025290330138od_a_b,X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( List
        = ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
     => ( List != nil_fs4581119677382125722od_a_b ) ) ).

% list.discI
thf(fact_258_list_Oexhaust,axiom,
    ! [Y3: list_P1467974523212632366od_a_b] :
      ( ( Y3 != nil_Product_prod_a_b )
     => ~ ! [X212: product_prod_a_b,X222: list_P1467974523212632366od_a_b] :
            ( Y3
           != ( cons_P7316939131009794654od_a_b @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_259_list_Oexhaust,axiom,
    ! [Y3: list_l8778361445553822004od_a_b] :
      ( ( Y3 != nil_li8635777946366267444od_a_b )
     => ~ ! [X212: list_P1467974523212632366od_a_b,X222: list_l8778361445553822004od_a_b] :
            ( Y3
           != ( cons_l907386227682280420od_a_b @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_260_list_Oexhaust,axiom,
    ! [Y3: list_l6099054058445139744od_a_b] :
      ( ( Y3 != nil_li6050065983854590240od_a_b )
     => ~ ! [X212: list_f1445794025290330138od_a_b,X222: list_l6099054058445139744od_a_b] :
            ( Y3
           != ( cons_l7290444712290925776od_a_b @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_261_list_Oexhaust,axiom,
    ! [Y3: list_o] :
      ( ( Y3 != nil_o )
     => ~ ! [X212: $o,X222: list_o] :
            ( Y3
           != ( cons_o @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_262_list_Oexhaust,axiom,
    ! [Y3: list_nat] :
      ( ( Y3 != nil_nat )
     => ~ ! [X212: nat,X222: list_nat] :
            ( Y3
           != ( cons_nat @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_263_list_Oexhaust,axiom,
    ! [Y3: list_f1445794025290330138od_a_b] :
      ( ( Y3 != nil_fs4581119677382125722od_a_b )
     => ~ ! [X212: fset_l1334069825099621524od_a_b,X222: list_f1445794025290330138od_a_b] :
            ( Y3
           != ( cons_f6577355434438001738od_a_b @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_264_min__list_Ocases,axiom,
    ! [X3: list_l6099054058445139744od_a_b] :
      ( ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
          ( X3
         != ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) )
     => ( X3 = nil_li6050065983854590240od_a_b ) ) ).

% min_list.cases
thf(fact_265_min__list_Ocases,axiom,
    ! [X3: list_o] :
      ( ! [X4: $o,Xs3: list_o] :
          ( X3
         != ( cons_o @ X4 @ Xs3 ) )
     => ( X3 = nil_o ) ) ).

% min_list.cases
thf(fact_266_min__list_Ocases,axiom,
    ! [X3: list_nat] :
      ( ! [X4: nat,Xs3: list_nat] :
          ( X3
         != ( cons_nat @ X4 @ Xs3 ) )
     => ( X3 = nil_nat ) ) ).

% min_list.cases
thf(fact_267_min__list_Ocases,axiom,
    ! [X3: list_f1445794025290330138od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
          ( X3
         != ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
     => ( X3 = nil_fs4581119677382125722od_a_b ) ) ).

% min_list.cases
thf(fact_268_remdups__adj_Ocases,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( X3 != nil_Product_prod_a_b )
     => ( ! [X4: product_prod_a_b] :
            ( X3
           != ( cons_P7316939131009794654od_a_b @ X4 @ nil_Product_prod_a_b ) )
       => ~ ! [X4: product_prod_a_b,Y: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
              ( X3
             != ( cons_P7316939131009794654od_a_b @ X4 @ ( cons_P7316939131009794654od_a_b @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_269_remdups__adj_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ( ! [X4: list_P1467974523212632366od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ X4 @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X4: list_P1467974523212632366od_a_b,Y: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
              ( X3
             != ( cons_l907386227682280420od_a_b @ X4 @ ( cons_l907386227682280420od_a_b @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_270_remdups__adj_Ocases,axiom,
    ! [X3: list_l6099054058445139744od_a_b] :
      ( ( X3 != nil_li6050065983854590240od_a_b )
     => ( ! [X4: list_f1445794025290330138od_a_b] :
            ( X3
           != ( cons_l7290444712290925776od_a_b @ X4 @ nil_li6050065983854590240od_a_b ) )
       => ~ ! [X4: list_f1445794025290330138od_a_b,Y: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
              ( X3
             != ( cons_l7290444712290925776od_a_b @ X4 @ ( cons_l7290444712290925776od_a_b @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_271_remdups__adj_Ocases,axiom,
    ! [X3: list_o] :
      ( ( X3 != nil_o )
     => ( ! [X4: $o] :
            ( X3
           != ( cons_o @ X4 @ nil_o ) )
       => ~ ! [X4: $o,Y: $o,Xs3: list_o] :
              ( X3
             != ( cons_o @ X4 @ ( cons_o @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_272_remdups__adj_Ocases,axiom,
    ! [X3: list_nat] :
      ( ( X3 != nil_nat )
     => ( ! [X4: nat] :
            ( X3
           != ( cons_nat @ X4 @ nil_nat ) )
       => ~ ! [X4: nat,Y: nat,Xs3: list_nat] :
              ( X3
             != ( cons_nat @ X4 @ ( cons_nat @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_273_remdups__adj_Ocases,axiom,
    ! [X3: list_f1445794025290330138od_a_b] :
      ( ( X3 != nil_fs4581119677382125722od_a_b )
     => ( ! [X4: fset_l1334069825099621524od_a_b] :
            ( X3
           != ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( X3
             != ( cons_f6577355434438001738od_a_b @ X4 @ ( cons_f6577355434438001738od_a_b @ Y @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_274_neq__Nil__conv,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b] :
      ( ( Xs2 != nil_Product_prod_a_b )
      = ( ? [Y4: product_prod_a_b,Ys2: list_P1467974523212632366od_a_b] :
            ( Xs2
            = ( cons_P7316939131009794654od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_275_neq__Nil__conv,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ( Xs2 != nil_li8635777946366267444od_a_b )
      = ( ? [Y4: list_P1467974523212632366od_a_b,Ys2: list_l8778361445553822004od_a_b] :
            ( Xs2
            = ( cons_l907386227682280420od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_276_neq__Nil__conv,axiom,
    ! [Xs2: list_l6099054058445139744od_a_b] :
      ( ( Xs2 != nil_li6050065983854590240od_a_b )
      = ( ? [Y4: list_f1445794025290330138od_a_b,Ys2: list_l6099054058445139744od_a_b] :
            ( Xs2
            = ( cons_l7290444712290925776od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_277_neq__Nil__conv,axiom,
    ! [Xs2: list_o] :
      ( ( Xs2 != nil_o )
      = ( ? [Y4: $o,Ys2: list_o] :
            ( Xs2
            = ( cons_o @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_278_neq__Nil__conv,axiom,
    ! [Xs2: list_nat] :
      ( ( Xs2 != nil_nat )
      = ( ? [Y4: nat,Ys2: list_nat] :
            ( Xs2
            = ( cons_nat @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_279_neq__Nil__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
      = ( ? [Y4: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( Xs2
            = ( cons_f6577355434438001738od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_280_list__induct2_H,axiom,
    ! [P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( P @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b )
     => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] : ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ nil_fs4581119677382125722od_a_b )
       => ( ! [Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] : ( P @ nil_fs4581119677382125722od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) )
         => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_281_list__induct2_H,axiom,
    ! [P: list_o > list_o > $o,Xs2: list_o,Ys3: list_o] :
      ( ( P @ nil_o @ nil_o )
     => ( ! [X4: $o,Xs3: list_o] : ( P @ ( cons_o @ X4 @ Xs3 ) @ nil_o )
       => ( ! [Y: $o,Ys: list_o] : ( P @ nil_o @ ( cons_o @ Y @ Ys ) )
         => ( ! [X4: $o,Xs3: list_o,Y: $o,Ys: list_o] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_o @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_282_list__induct2_H,axiom,
    ! [P: list_o > list_nat > $o,Xs2: list_o,Ys3: list_nat] :
      ( ( P @ nil_o @ nil_nat )
     => ( ! [X4: $o,Xs3: list_o] : ( P @ ( cons_o @ X4 @ Xs3 ) @ nil_nat )
       => ( ! [Y: nat,Ys: list_nat] : ( P @ nil_o @ ( cons_nat @ Y @ Ys ) )
         => ( ! [X4: $o,Xs3: list_o,Y: nat,Ys: list_nat] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_o @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_283_list__induct2_H,axiom,
    ! [P: list_nat > list_o > $o,Xs2: list_nat,Ys3: list_o] :
      ( ( P @ nil_nat @ nil_o )
     => ( ! [X4: nat,Xs3: list_nat] : ( P @ ( cons_nat @ X4 @ Xs3 ) @ nil_o )
       => ( ! [Y: $o,Ys: list_o] : ( P @ nil_nat @ ( cons_o @ Y @ Ys ) )
         => ( ! [X4: nat,Xs3: list_nat,Y: $o,Ys: list_o] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_284_list__induct2_H,axiom,
    ! [P: list_nat > list_nat > $o,Xs2: list_nat,Ys3: list_nat] :
      ( ( P @ nil_nat @ nil_nat )
     => ( ! [X4: nat,Xs3: list_nat] : ( P @ ( cons_nat @ X4 @ Xs3 ) @ nil_nat )
       => ( ! [Y: nat,Ys: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y @ Ys ) )
         => ( ! [X4: nat,Xs3: list_nat,Y: nat,Ys: list_nat] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_285_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_o > $o,Xs2: list_P1467974523212632366od_a_b,Ys3: list_o] :
      ( ( P @ nil_Product_prod_a_b @ nil_o )
     => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ nil_o )
       => ( ! [Y: $o,Ys: list_o] : ( P @ nil_Product_prod_a_b @ ( cons_o @ Y @ Ys ) )
         => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Y: $o,Ys: list_o] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_286_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_nat > $o,Xs2: list_P1467974523212632366od_a_b,Ys3: list_nat] :
      ( ( P @ nil_Product_prod_a_b @ nil_nat )
     => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ nil_nat )
       => ( ! [Y: nat,Ys: list_nat] : ( P @ nil_Product_prod_a_b @ ( cons_nat @ Y @ Ys ) )
         => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Y: nat,Ys: list_nat] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_287_list__induct2_H,axiom,
    ! [P: list_o > list_P1467974523212632366od_a_b > $o,Xs2: list_o,Ys3: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_o @ nil_Product_prod_a_b )
     => ( ! [X4: $o,Xs3: list_o] : ( P @ ( cons_o @ X4 @ Xs3 ) @ nil_Product_prod_a_b )
       => ( ! [Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] : ( P @ nil_o @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) )
         => ( ! [X4: $o,Xs3: list_o,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_o @ X4 @ Xs3 ) @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_288_list__induct2_H,axiom,
    ! [P: list_nat > list_P1467974523212632366od_a_b > $o,Xs2: list_nat,Ys3: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_nat @ nil_Product_prod_a_b )
     => ( ! [X4: nat,Xs3: list_nat] : ( P @ ( cons_nat @ X4 @ Xs3 ) @ nil_Product_prod_a_b )
       => ( ! [Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] : ( P @ nil_nat @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) )
         => ( ! [X4: nat,Xs3: list_nat,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_289_list__induct2_H,axiom,
    ! [P: list_l8778361445553822004od_a_b > list_o > $o,Xs2: list_l8778361445553822004od_a_b,Ys3: list_o] :
      ( ( P @ nil_li8635777946366267444od_a_b @ nil_o )
     => ( ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ nil_o )
       => ( ! [Y: $o,Ys: list_o] : ( P @ nil_li8635777946366267444od_a_b @ ( cons_o @ Y @ Ys ) )
         => ( ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Y: $o,Ys: list_o] :
                ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) )
           => ( P @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_induct2'
thf(fact_290_list__nonempty__induct,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,P: list_P1467974523212632366od_a_b > $o] :
      ( ( Xs2 != nil_Product_prod_a_b )
     => ( ! [X4: product_prod_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ nil_Product_prod_a_b ) )
       => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
              ( ( Xs3 != nil_Product_prod_a_b )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_291_list__nonempty__induct,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,P: list_l8778361445553822004od_a_b > $o] :
      ( ( Xs2 != nil_li8635777946366267444od_a_b )
     => ( ! [X4: list_P1467974523212632366od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X4 @ nil_li8635777946366267444od_a_b ) )
       => ( ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
              ( ( Xs3 != nil_li8635777946366267444od_a_b )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_292_list__nonempty__induct,axiom,
    ! [Xs2: list_l6099054058445139744od_a_b,P: list_l6099054058445139744od_a_b > $o] :
      ( ( Xs2 != nil_li6050065983854590240od_a_b )
     => ( ! [X4: list_f1445794025290330138od_a_b] : ( P @ ( cons_l7290444712290925776od_a_b @ X4 @ nil_li6050065983854590240od_a_b ) )
       => ( ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
              ( ( Xs3 != nil_li6050065983854590240od_a_b )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_293_list__nonempty__induct,axiom,
    ! [Xs2: list_o,P: list_o > $o] :
      ( ( Xs2 != nil_o )
     => ( ! [X4: $o] : ( P @ ( cons_o @ X4 @ nil_o ) )
       => ( ! [X4: $o,Xs3: list_o] :
              ( ( Xs3 != nil_o )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_o @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_294_list__nonempty__induct,axiom,
    ! [Xs2: list_nat,P: list_nat > $o] :
      ( ( Xs2 != nil_nat )
     => ( ! [X4: nat] : ( P @ ( cons_nat @ X4 @ nil_nat ) )
       => ( ! [X4: nat,Xs3: list_nat] :
              ( ( Xs3 != nil_nat )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_nat @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_295_list__nonempty__induct,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > $o] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ! [X4: fset_l1334069825099621524od_a_b] : ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( Xs3 != nil_fs4581119677382125722od_a_b )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_296_prefixes__in__list_Ocases,axiom,
    ! [X3: produc6133449566840171033od_a_b] :
      ( ! [Prev: list_P1467974523212632366od_a_b,Yss: list_l8778361445553822004od_a_b,Res: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc5762985261779254281od_a_b @ nil_Product_prod_a_b @ ( produc8500600352266341008od_a_b @ Prev @ ( produc3466467997744452247od_a_b @ Yss @ Res ) ) ) )
     => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Prev: list_P1467974523212632366od_a_b,Yss: list_l8778361445553822004od_a_b,Res: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc5762985261779254281od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( produc8500600352266341008od_a_b @ Prev @ ( produc3466467997744452247od_a_b @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_297_prefixes__in__list_Ocases,axiom,
    ! [X3: produc6285210691406119693od_a_b] :
      ( ! [Prev: list_l8778361445553822004od_a_b,Yss: list_l6443893005374362810od_a_b,Res: list_l6443893005374362810od_a_b] :
          ( X3
         != ( produc5805445161374616061od_a_b @ nil_li8635777946366267444od_a_b @ ( produc1849413230003979274od_a_b @ Prev @ ( produc9051856215140236695od_a_b @ Yss @ Res ) ) ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Prev: list_l8778361445553822004od_a_b,Yss: list_l6443893005374362810od_a_b,Res: list_l6443893005374362810od_a_b] :
            ( X3
           != ( produc5805445161374616061od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ ( produc1849413230003979274od_a_b @ Prev @ ( produc9051856215140236695od_a_b @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_298_prefixes__in__list_Ocases,axiom,
    ! [X3: produc8905949819191209269od_a_b] :
      ( ! [Prev: list_l6099054058445139744od_a_b,Yss: list_l378912295992385958od_a_b,Res: list_l378912295992385958od_a_b] :
          ( X3
         != ( produc1348991824872107557od_a_b @ nil_li6050065983854590240od_a_b @ ( produc4034718099474179870od_a_b @ Prev @ ( produc8378414639643377047od_a_b @ Yss @ Res ) ) ) )
     => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Prev: list_l6099054058445139744od_a_b,Yss: list_l378912295992385958od_a_b,Res: list_l378912295992385958od_a_b] :
            ( X3
           != ( produc1348991824872107557od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ ( produc4034718099474179870od_a_b @ Prev @ ( produc8378414639643377047od_a_b @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_299_prefixes__in__list_Ocases,axiom,
    ! [X3: produc4872601182145619129list_o] :
      ( ! [Prev: list_o,Yss: list_list_o,Res: list_list_o] :
          ( X3
         != ( produc2209229713021908649list_o @ nil_o @ ( produc9135509632870949792list_o @ Prev @ ( produc2957346356364703511list_o @ Yss @ Res ) ) ) )
     => ~ ! [X4: $o,Xs3: list_o,Prev: list_o,Yss: list_list_o,Res: list_list_o] :
            ( X3
           != ( produc2209229713021908649list_o @ ( cons_o @ X4 @ Xs3 ) @ ( produc9135509632870949792list_o @ Prev @ ( produc2957346356364703511list_o @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_300_prefixes__in__list_Ocases,axiom,
    ! [X3: produc2175610488484699543st_nat] :
      ( ! [Prev: list_nat,Yss: list_list_nat,Res: list_list_nat] :
          ( X3
         != ( produc4774092089535011407st_nat @ nil_nat @ ( produc8807741811528022664st_nat @ Prev @ ( produc7129799990162260089st_nat @ Yss @ Res ) ) ) )
     => ~ ! [X4: nat,Xs3: list_nat,Prev: list_nat,Yss: list_list_nat,Res: list_list_nat] :
            ( X3
           != ( produc4774092089535011407st_nat @ ( cons_nat @ X4 @ Xs3 ) @ ( produc8807741811528022664st_nat @ Prev @ ( produc7129799990162260089st_nat @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_301_prefixes__in__list_Ocases,axiom,
    ! [X3: produc3622972877636639297od_a_b] :
      ( ! [Prev: list_f1445794025290330138od_a_b,Yss: list_l6099054058445139744od_a_b,Res: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc2822848259085985329od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc4801787804591476900od_a_b @ Prev @ ( produc9191391066883749527od_a_b @ Yss @ Res ) ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Prev: list_f1445794025290330138od_a_b,Yss: list_l6099054058445139744od_a_b,Res: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc2822848259085985329od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( produc4801787804591476900od_a_b @ Prev @ ( produc9191391066883749527od_a_b @ Yss @ Res ) ) ) ) ) ).

% prefixes_in_list.cases
thf(fact_302_successively_Ocases,axiom,
    ! [X3: produc3334210663054469735od_a_b] :
      ( ! [P3: product_prod_a_b > product_prod_a_b > $o] :
          ( X3
         != ( produc7704224619955794135od_a_b @ P3 @ nil_Product_prod_a_b ) )
     => ( ! [P3: product_prod_a_b > product_prod_a_b > $o,X4: product_prod_a_b] :
            ( X3
           != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X4 @ nil_Product_prod_a_b ) ) )
       => ~ ! [P3: product_prod_a_b > product_prod_a_b > $o,X4: product_prod_a_b,Y: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X4 @ ( cons_P7316939131009794654od_a_b @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_303_successively_Ocases,axiom,
    ! [X3: produc9134726091994374893od_a_b] :
      ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o] :
          ( X3
         != ( produc7760118425732869085od_a_b @ P3 @ nil_li8635777946366267444od_a_b ) )
     => ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X4: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X4 @ nil_li8635777946366267444od_a_b ) ) )
       => ~ ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X4: list_P1467974523212632366od_a_b,Y: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X4 @ ( cons_l907386227682280420od_a_b @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_304_successively_Ocases,axiom,
    ! [X3: produc4084954254102156249od_a_b] :
      ( ! [P3: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
          ( X3
         != ( produc3708935670247084489od_a_b @ P3 @ nil_li6050065983854590240od_a_b ) )
     => ( ! [P3: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o,X4: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc3708935670247084489od_a_b @ P3 @ ( cons_l7290444712290925776od_a_b @ X4 @ nil_li6050065983854590240od_a_b ) ) )
       => ~ ! [P3: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o,X4: list_f1445794025290330138od_a_b,Y: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
              ( X3
             != ( produc3708935670247084489od_a_b @ P3 @ ( cons_l7290444712290925776od_a_b @ X4 @ ( cons_l7290444712290925776od_a_b @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_305_successively_Ocases,axiom,
    ! [X3: produc8642409424279824599list_o] :
      ( ! [P3: $o > $o > $o] :
          ( X3
         != ( produc8744836578217649351list_o @ P3 @ nil_o ) )
     => ( ! [P3: $o > $o > $o,X4: $o] :
            ( X3
           != ( produc8744836578217649351list_o @ P3 @ ( cons_o @ X4 @ nil_o ) ) )
       => ~ ! [P3: $o > $o > $o,X4: $o,Y: $o,Xs3: list_o] :
              ( X3
             != ( produc8744836578217649351list_o @ P3 @ ( cons_o @ X4 @ ( cons_o @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_306_successively_Ocases,axiom,
    ! [X3: produc254973753779126261st_nat] :
      ( ! [P3: nat > nat > $o] :
          ( X3
         != ( produc4727192421694094319st_nat @ P3 @ nil_nat ) )
     => ( ! [P3: nat > nat > $o,X4: nat] :
            ( X3
           != ( produc4727192421694094319st_nat @ P3 @ ( cons_nat @ X4 @ nil_nat ) ) )
       => ~ ! [P3: nat > nat > $o,X4: nat,Y: nat,Xs3: list_nat] :
              ( X3
             != ( produc4727192421694094319st_nat @ P3 @ ( cons_nat @ X4 @ ( cons_nat @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_307_successively_Ocases,axiom,
    ! [X3: produc7003135847223052371od_a_b] :
      ( ! [P3: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o] :
          ( X3
         != ( produc7711833712884794307od_a_b @ P3 @ nil_fs4581119677382125722od_a_b ) )
     => ( ! [P3: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o,X4: fset_l1334069825099621524od_a_b] :
            ( X3
           != ( produc7711833712884794307od_a_b @ P3 @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) ) )
       => ~ ! [P3: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o,X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( X3
             != ( produc7711833712884794307od_a_b @ P3 @ ( cons_f6577355434438001738od_a_b @ X4 @ ( cons_f6577355434438001738od_a_b @ Y @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_308_sorted__wrt_Ocases,axiom,
    ! [X3: produc3334210663054469735od_a_b] :
      ( ! [P3: product_prod_a_b > product_prod_a_b > $o] :
          ( X3
         != ( produc7704224619955794135od_a_b @ P3 @ nil_Product_prod_a_b ) )
     => ~ ! [P3: product_prod_a_b > product_prod_a_b > $o,X4: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_309_sorted__wrt_Ocases,axiom,
    ! [X3: produc9134726091994374893od_a_b] :
      ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o] :
          ( X3
         != ( produc7760118425732869085od_a_b @ P3 @ nil_li8635777946366267444od_a_b ) )
     => ~ ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X4: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_310_sorted__wrt_Ocases,axiom,
    ! [X3: produc4084954254102156249od_a_b] :
      ( ! [P3: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
          ( X3
         != ( produc3708935670247084489od_a_b @ P3 @ nil_li6050065983854590240od_a_b ) )
     => ~ ! [P3: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o,X4: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc3708935670247084489od_a_b @ P3 @ ( cons_l7290444712290925776od_a_b @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_311_sorted__wrt_Ocases,axiom,
    ! [X3: produc8642409424279824599list_o] :
      ( ! [P3: $o > $o > $o] :
          ( X3
         != ( produc8744836578217649351list_o @ P3 @ nil_o ) )
     => ~ ! [P3: $o > $o > $o,X4: $o,Ys: list_o] :
            ( X3
           != ( produc8744836578217649351list_o @ P3 @ ( cons_o @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_312_sorted__wrt_Ocases,axiom,
    ! [X3: produc254973753779126261st_nat] :
      ( ! [P3: nat > nat > $o] :
          ( X3
         != ( produc4727192421694094319st_nat @ P3 @ nil_nat ) )
     => ~ ! [P3: nat > nat > $o,X4: nat,Ys: list_nat] :
            ( X3
           != ( produc4727192421694094319st_nat @ P3 @ ( cons_nat @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_313_sorted__wrt_Ocases,axiom,
    ! [X3: produc7003135847223052371od_a_b] :
      ( ! [P3: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o] :
          ( X3
         != ( produc7711833712884794307od_a_b @ P3 @ nil_fs4581119677382125722od_a_b ) )
     => ~ ! [P3: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o,X4: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc7711833712884794307od_a_b @ P3 @ ( cons_f6577355434438001738od_a_b @ X4 @ Ys ) ) ) ) ).

% sorted_wrt.cases
thf(fact_314_shuffles_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [Ys: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Ys ) )
     => ( ! [Xs3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ Xs3 @ nil_Product_prod_a_b ) )
       => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_315_shuffles_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [Ys: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Ys ) )
     => ( ! [Xs3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ Xs3 @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Y: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ ( cons_l907386227682280420od_a_b @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_316_shuffles_Ocases,axiom,
    ! [X3: produc6680082661646774695od_a_b] :
      ( ! [Ys: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc9191391066883749527od_a_b @ nil_li6050065983854590240od_a_b @ Ys ) )
     => ( ! [Xs3: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc9191391066883749527od_a_b @ Xs3 @ nil_li6050065983854590240od_a_b ) )
       => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
              ( X3
             != ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ ( cons_l7290444712290925776od_a_b @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_317_shuffles_Ocases,axiom,
    ! [X3: produc7102631898165422375list_o] :
      ( ! [Ys: list_o] :
          ( X3
         != ( produc8435520187683070743list_o @ nil_o @ Ys ) )
     => ( ! [Xs3: list_o] :
            ( X3
           != ( produc8435520187683070743list_o @ Xs3 @ nil_o ) )
       => ~ ! [X4: $o,Xs3: list_o,Y: $o,Ys: list_o] :
              ( X3
             != ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_318_shuffles_Ocases,axiom,
    ! [X3: produc1828647624359046049st_nat] :
      ( ! [Ys: list_nat] :
          ( X3
         != ( produc2694037385005941721st_nat @ nil_nat @ Ys ) )
     => ( ! [Xs3: list_nat] :
            ( X3
           != ( produc2694037385005941721st_nat @ Xs3 @ nil_nat ) )
       => ~ ! [X4: nat,Xs3: list_nat,Y: nat,Ys: list_nat] :
              ( X3
             != ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_319_shuffles_Ocases,axiom,
    ! [X3: produc4243862795798826663od_a_b] :
      ( ! [Ys: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Ys ) )
     => ( ! [Xs3: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc4047984609689601431od_a_b @ Xs3 @ nil_fs4581119677382125722od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
              ( X3
             != ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) ) ) ) ).

% shuffles.cases
thf(fact_320_splice_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [Ys: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Ys ) )
     => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_321_splice_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [Ys: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Ys ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_322_splice_Ocases,axiom,
    ! [X3: produc6680082661646774695od_a_b] :
      ( ! [Ys: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc9191391066883749527od_a_b @ nil_li6050065983854590240od_a_b @ Ys ) )
     => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Ys: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_323_splice_Ocases,axiom,
    ! [X3: produc7102631898165422375list_o] :
      ( ! [Ys: list_o] :
          ( X3
         != ( produc8435520187683070743list_o @ nil_o @ Ys ) )
     => ~ ! [X4: $o,Xs3: list_o,Ys: list_o] :
            ( X3
           != ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_324_splice_Ocases,axiom,
    ! [X3: produc1828647624359046049st_nat] :
      ( ! [Ys: list_nat] :
          ( X3
         != ( produc2694037385005941721st_nat @ nil_nat @ Ys ) )
     => ~ ! [X4: nat,Xs3: list_nat,Ys: list_nat] :
            ( X3
           != ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_325_splice_Ocases,axiom,
    ! [X3: produc4243862795798826663od_a_b] :
      ( ! [Ys: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Ys ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Ys: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ Ys ) ) ) ).

% splice.cases
thf(fact_326_simple__cg__closure__phase__2_H_Ocases,axiom,
    ! [X3: produc8522616430465603254od_a_b] :
      ( ! [B3: $o,Done: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc5559962869320249254od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,B3: $o,Done: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc5559962869320249254od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) ) ) ).

% simple_cg_closure_phase_2'.cases
thf(fact_327_simple__cg__closure__phase__1__helper_Ocases,axiom,
    ! [X3: produc941565555952692937od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,B3: $o,Done: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc4086412101881284409od_a_b @ X4 @ ( produc5559962869320249254od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,X12: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,B3: $o,Done: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc4086412101881284409od_a_b @ X4 @ ( produc5559962869320249254od_a_b @ ( cons_f6577355434438001738od_a_b @ X12 @ Xs3 ) @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper.cases
thf(fact_328_simple__cg__closure__phase__2_H_Osimps_I1_J,axiom,
    ! [B: $o,Done2: list_f1445794025290330138od_a_b] :
      ( ( simple891077427139469213od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B @ Done2 ) )
      = ( produc7489420772309856409od_a_b @ B @ Done2 ) ) ).

% simple_cg_closure_phase_2'.simps(1)
thf(fact_329_simple__cg__empty__def,axiom,
    simple1082100951563891851od_a_b = nil_fs4581119677382125722od_a_b ).

% simple_cg_empty_def
thf(fact_330_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( X3 != nil_Product_prod_a_b )
     => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_331_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_332_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_l6099054058445139744od_a_b] :
      ( ( X3 != nil_li6050065983854590240od_a_b )
     => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
            ( X3
           != ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_333_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_o] :
      ( ( X3 != nil_o )
     => ~ ! [X4: $o,Xs3: list_o] :
            ( X3
           != ( cons_o @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_334_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_nat] :
      ( ( X3 != nil_nat )
     => ~ ! [X4: nat,Xs3: list_nat] :
            ( X3
           != ( cons_nat @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_335_linear__order__from__list__position_H_Ocases,axiom,
    ! [X3: list_f1445794025290330138od_a_b] :
      ( ( X3 != nil_fs4581119677382125722od_a_b )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( X3
           != ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_336_longest__common__prefix_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) ) )
     => ( ! [Uv: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Uv ) )
       => ~ ! [Uu: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc5288560138351607191od_a_b @ Uu @ nil_Product_prod_a_b ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_337_longest__common__prefix_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Y: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ ( cons_l907386227682280420od_a_b @ Y @ Ys ) ) )
     => ( ! [Uv: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Uv ) )
       => ~ ! [Uu: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc3466467997744452247od_a_b @ Uu @ nil_li8635777946366267444od_a_b ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_338_longest__common__prefix_Ocases,axiom,
    ! [X3: produc6680082661646774695od_a_b] :
      ( ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ ( cons_l7290444712290925776od_a_b @ Y @ Ys ) ) )
     => ( ! [Uv: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc9191391066883749527od_a_b @ nil_li6050065983854590240od_a_b @ Uv ) )
       => ~ ! [Uu: list_l6099054058445139744od_a_b] :
              ( X3
             != ( produc9191391066883749527od_a_b @ Uu @ nil_li6050065983854590240od_a_b ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_339_longest__common__prefix_Ocases,axiom,
    ! [X3: produc7102631898165422375list_o] :
      ( ! [X4: $o,Xs3: list_o,Y: $o,Ys: list_o] :
          ( X3
         != ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) )
     => ( ! [Uv: list_o] :
            ( X3
           != ( produc8435520187683070743list_o @ nil_o @ Uv ) )
       => ~ ! [Uu: list_o] :
              ( X3
             != ( produc8435520187683070743list_o @ Uu @ nil_o ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_340_longest__common__prefix_Ocases,axiom,
    ! [X3: produc1828647624359046049st_nat] :
      ( ! [X4: nat,Xs3: list_nat,Y: nat,Ys: list_nat] :
          ( X3
         != ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) )
     => ( ! [Uv: list_nat] :
            ( X3
           != ( produc2694037385005941721st_nat @ nil_nat @ Uv ) )
       => ~ ! [Uu: list_nat] :
              ( X3
             != ( produc2694037385005941721st_nat @ Uu @ nil_nat ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_341_longest__common__prefix_Ocases,axiom,
    ! [X3: produc4243862795798826663od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) )
     => ( ! [Uv: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Uv ) )
       => ~ ! [Uu: list_f1445794025290330138od_a_b] :
              ( X3
             != ( produc4047984609689601431od_a_b @ Uu @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_342_find__remove_H_Ocases,axiom,
    ! [X3: produc6303315885879197575od_a_b] :
      ( ! [P3: product_prod_a_b > $o,Uu: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc4095041172746057401od_a_b @ P3 @ ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Uu ) ) )
     => ~ ! [P3: product_prod_a_b > $o,X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Prev: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc4095041172746057401od_a_b @ P3 @ ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_343_find__remove_H_Ocases,axiom,
    ! [X3: produc8043380187910098957od_a_b] :
      ( ! [P3: list_P1467974523212632366od_a_b > $o,Uu: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc953458198655700415od_a_b @ P3 @ ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Uu ) ) )
     => ~ ! [P3: list_P1467974523212632366od_a_b > $o,X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Prev: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc953458198655700415od_a_b @ P3 @ ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_344_find__remove_H_Ocases,axiom,
    ! [X3: produc6250212354305936633od_a_b] :
      ( ! [P3: list_f1445794025290330138od_a_b > $o,Uu: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc7142155960364849067od_a_b @ P3 @ ( produc9191391066883749527od_a_b @ nil_li6050065983854590240od_a_b @ Uu ) ) )
     => ~ ! [P3: list_f1445794025290330138od_a_b > $o,X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Prev: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc7142155960364849067od_a_b @ P3 @ ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_345_find__remove_H_Ocases,axiom,
    ! [X3: produc1709182781532539895list_o] :
      ( ! [P3: $o > $o,Uu: list_o] :
          ( X3
         != ( produc8772671931130610601list_o @ P3 @ ( produc8435520187683070743list_o @ nil_o @ Uu ) ) )
     => ~ ! [P3: $o > $o,X4: $o,Xs3: list_o,Prev: list_o] :
            ( X3
           != ( produc8772671931130610601list_o @ P3 @ ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_346_find__remove_H_Ocases,axiom,
    ! [X3: produc1950156742809263241st_nat] :
      ( ! [P3: nat > $o,Uu: list_nat] :
          ( X3
         != ( produc1851982983375519865st_nat @ P3 @ ( produc2694037385005941721st_nat @ nil_nat @ Uu ) ) )
     => ~ ! [P3: nat > $o,X4: nat,Xs3: list_nat,Prev: list_nat] :
            ( X3
           != ( produc1851982983375519865st_nat @ P3 @ ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_347_find__remove_H_Ocases,axiom,
    ! [X3: produc8278318776394211699od_a_b] :
      ( ! [P3: fset_l1334069825099621524od_a_b > $o,Uu: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc3242218216111629733od_a_b @ P3 @ ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Uu ) ) )
     => ~ ! [P3: fset_l1334069825099621524od_a_b > $o,X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Prev: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc3242218216111629733od_a_b @ P3 @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_348_find__index_Ocases,axiom,
    ! [X3: produc9068417245363831566od_a_b] :
      ( ! [F: product_prod_a_b > $o] :
          ( X3
         != ( produc114956849241483840od_a_b @ F @ nil_Product_prod_a_b ) )
     => ~ ! [F: product_prod_a_b > $o,X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc114956849241483840od_a_b @ F @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_349_find__index_Ocases,axiom,
    ! [X3: produc3357997149271159322od_a_b] :
      ( ! [F: list_P1467974523212632366od_a_b > $o] :
          ( X3
         != ( produc7526162350219154764od_a_b @ F @ nil_li8635777946366267444od_a_b ) )
     => ~ ! [F: list_P1467974523212632366od_a_b > $o,X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc7526162350219154764od_a_b @ F @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_350_find__index_Ocases,axiom,
    ! [X3: produc8331063474073164274od_a_b] :
      ( ! [F: list_f1445794025290330138od_a_b > $o] :
          ( X3
         != ( produc2726560669223232804od_a_b @ F @ nil_li6050065983854590240od_a_b ) )
     => ~ ! [F: list_f1445794025290330138od_a_b > $o,X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc2726560669223232804od_a_b @ F @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_351_find__index_Ocases,axiom,
    ! [X3: produc4895375484934168814list_o] :
      ( ! [F: $o > $o] :
          ( X3
         != ( produc1450004214998940960list_o @ F @ nil_o ) )
     => ~ ! [F: $o > $o,X4: $o,Xs3: list_o] :
            ( X3
           != ( produc1450004214998940960list_o @ F @ ( cons_o @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_352_find__index_Ocases,axiom,
    ! [X3: produc4226810134323546766st_nat] :
      ( ! [F: nat > $o] :
          ( X3
         != ( produc8587622027977423880st_nat @ F @ nil_nat ) )
     => ~ ! [F: nat > $o,X4: nat,Xs3: list_nat] :
            ( X3
           != ( produc8587622027977423880st_nat @ F @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_353_find__index_Ocases,axiom,
    ! [X3: produc2073128436939348198od_a_b] :
      ( ! [F: fset_l1334069825099621524od_a_b > $o] :
          ( X3
         != ( produc8550268191463221272od_a_b @ F @ nil_fs4581119677382125722od_a_b ) )
     => ~ ! [F: fset_l1334069825099621524od_a_b > $o,X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc8550268191463221272od_a_b @ F @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ) ).

% find_index.cases
thf(fact_354_is__prefix_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [Uu: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Uu ) )
     => ( ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ nil_Product_prod_a_b ) )
       => ~ ! [X4: product_prod_a_b,Xs3: list_P1467974523212632366od_a_b,Y: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X4 @ Xs3 ) @ ( cons_P7316939131009794654od_a_b @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_355_is__prefix_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [Uu: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Uu ) )
     => ( ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X4: list_P1467974523212632366od_a_b,Xs3: list_l8778361445553822004od_a_b,Y: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X4 @ Xs3 ) @ ( cons_l907386227682280420od_a_b @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_356_is__prefix_Ocases,axiom,
    ! [X3: produc6680082661646774695od_a_b] :
      ( ! [Uu: list_l6099054058445139744od_a_b] :
          ( X3
         != ( produc9191391066883749527od_a_b @ nil_li6050065983854590240od_a_b @ Uu ) )
     => ( ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b] :
            ( X3
           != ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ nil_li6050065983854590240od_a_b ) )
       => ~ ! [X4: list_f1445794025290330138od_a_b,Xs3: list_l6099054058445139744od_a_b,Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
              ( X3
             != ( produc9191391066883749527od_a_b @ ( cons_l7290444712290925776od_a_b @ X4 @ Xs3 ) @ ( cons_l7290444712290925776od_a_b @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_357_is__prefix_Ocases,axiom,
    ! [X3: produc7102631898165422375list_o] :
      ( ! [Uu: list_o] :
          ( X3
         != ( produc8435520187683070743list_o @ nil_o @ Uu ) )
     => ( ! [X4: $o,Xs3: list_o] :
            ( X3
           != ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ nil_o ) )
       => ~ ! [X4: $o,Xs3: list_o,Y: $o,Ys: list_o] :
              ( X3
             != ( produc8435520187683070743list_o @ ( cons_o @ X4 @ Xs3 ) @ ( cons_o @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_358_is__prefix_Ocases,axiom,
    ! [X3: produc1828647624359046049st_nat] :
      ( ! [Uu: list_nat] :
          ( X3
         != ( produc2694037385005941721st_nat @ nil_nat @ Uu ) )
     => ( ! [X4: nat,Xs3: list_nat] :
            ( X3
           != ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ nil_nat ) )
       => ~ ! [X4: nat,Xs3: list_nat,Y: nat,Ys: list_nat] :
              ( X3
             != ( produc2694037385005941721st_nat @ ( cons_nat @ X4 @ Xs3 ) @ ( cons_nat @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_359_is__prefix_Ocases,axiom,
    ! [X3: produc4243862795798826663od_a_b] :
      ( ! [Uu: list_f1445794025290330138od_a_b] :
          ( X3
         != ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Uu ) )
     => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( X3
           != ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ nil_fs4581119677382125722od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
              ( X3
             != ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) ) ) ) ).

% is_prefix.cases
thf(fact_360_delete__aux_Ocases,axiom,
    ! [X3: produc263801385964556654od_a_b] :
      ( ! [K: a] :
          ( X3
         != ( produc769044295738804958od_a_b @ K @ nil_Pr5469403351896759365od_a_b ) )
     => ~ ! [K: a,K2: a,V: produc6345636018528648726od_a_b,Xs3: list_P2373415021271773893od_a_b] :
            ( X3
           != ( produc769044295738804958od_a_b @ K @ ( cons_P1362141854008209397od_a_b @ ( produc458170271728203695od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_361_delete__aux_Ocases,axiom,
    ! [X3: produc4803344270401830612od_a_b] :
      ( ! [K: a] :
          ( X3
         != ( produc2488690576206217668od_a_b @ K @ nil_Pr2185010156820804907od_a_b ) )
     => ~ ! [K: a,K2: a,V: produc3520053589329427452od_a_b,Xs3: list_P2891578699137632811od_a_b] :
            ( X3
           != ( produc2488690576206217668od_a_b @ K @ ( cons_P1301695370724503771od_a_b @ ( produc5260523172840707349od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_362_delete__aux_Ocases,axiom,
    ! [X3: produc6268931404698553153od_b_d] :
      ( ! [K: a] :
          ( X3
         != ( produc225460191387392689od_b_d @ K @ nil_Pr6868600557816461464od_b_d ) )
     => ~ ! [K: a,K2: a,V: product_prod_b_d,Xs3: list_P6112925938187837720od_b_d] :
            ( X3
           != ( produc225460191387392689od_b_d @ K @ ( cons_P8864836314872337480od_b_d @ ( produc6867761809215060226od_b_d @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_363_delete__aux_Ocases,axiom,
    ! [X3: produc6427713924023405888od_b_c] :
      ( ! [K: a] :
          ( X3
         != ( produc2746644709676428336od_b_c @ K @ nil_Pr6797566517770115479od_b_c ) )
     => ~ ! [K: a,K2: a,V: product_prod_b_c,Xs3: list_P8634110456476873367od_b_c] :
            ( X3
           != ( produc2746644709676428336od_b_c @ K @ ( cons_P8793802274825991495od_b_c @ ( produc6867761804911831425od_b_c @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_364_delete__aux_Ocases,axiom,
    ! [X3: produc2639161875728825943od_a_b] :
      ( ! [K: a] :
          ( X3
         != ( produc6643264353547226055od_a_b @ K @ nil_Product_prod_a_b ) )
     => ~ ! [K: a,K2: a,V: b,Xs3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc6643264353547226055od_a_b @ K @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_365_delete__aux_Ocases,axiom,
    ! [X3: produc4943249325152908478od_a_b] :
      ( ! [K: $o] :
          ( X3
         != ( produc336006402058072110od_a_b @ K @ nil_Pr7302809325368845999od_a_b ) )
     => ~ ! [K: $o,K2: $o,V: list_f1445794025290330138od_a_b,Xs3: list_P3574414722980446895od_a_b] :
            ( X3
           != ( produc336006402058072110od_a_b @ K @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_366_delete__aux_Ocases,axiom,
    ! [X3: produc8178655232312819025od_a_b] :
      ( ! [K: $o] :
          ( X3
         != ( produc7187370450469132609od_a_b @ K @ nil_Pr3614377049866306882od_a_b ) )
     => ~ ! [K: $o,K2: $o,V: produc2518759752815613485od_a_b,Xs3: list_P5302045529885307074od_a_b] :
            ( X3
           != ( produc7187370450469132609od_a_b @ K @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_367_delete__aux_Ocases,axiom,
    ! [X3: produc3633803565885464646od_a_b] :
      ( ! [K: fset_l1334069825099621524od_a_b] :
          ( X3
         != ( produc5841801390880218294od_a_b @ K @ nil_Pr1838250474468212019od_a_b ) )
     => ~ ! [K: fset_l1334069825099621524od_a_b,K2: fset_l1334069825099621524od_a_b,V: list_f1445794025290330138od_a_b,Xs3: list_P5488608094462411443od_a_b] :
            ( X3
           != ( produc5841801390880218294od_a_b @ K @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ).

% delete_aux.cases
thf(fact_368_sublists_Osimps_I1_J,axiom,
    ( ( sublis5610707822503107526od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ nil_li2802039260981550394od_a_b ) ) ).

% sublists.simps(1)
thf(fact_369_sublists_Osimps_I1_J,axiom,
    ( ( sublis4548404825810117298od_a_b @ nil_li6050065983854590240od_a_b )
    = ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ nil_li4771897614291402022od_a_b ) ) ).

% sublists.simps(1)
thf(fact_370_sublists_Osimps_I1_J,axiom,
    ( ( sublists_o @ nil_o )
    = ( cons_list_o @ nil_o @ nil_list_o ) ) ).

% sublists.simps(1)
thf(fact_371_sublists_Osimps_I1_J,axiom,
    ( ( sublis2270850047155729216od_a_b @ nil_Product_prod_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% sublists.simps(1)
thf(fact_372_sublists_Osimps_I1_J,axiom,
    ( ( sublis7484350909052568364od_a_b @ nil_fs4581119677382125722od_a_b )
    = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) ) ).

% sublists.simps(1)
thf(fact_373_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix1498375871760299040od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ nil_li2802039260981550394od_a_b ) ) ).

% Util.suffixes.simps(1)
thf(fact_374_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix6313696937464205580od_a_b @ nil_li6050065983854590240od_a_b )
    = ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ nil_li4771897614291402022od_a_b ) ) ).

% Util.suffixes.simps(1)
thf(fact_375_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffixes_o @ nil_o )
    = ( cons_list_o @ nil_o @ nil_list_o ) ) ).

% Util.suffixes.simps(1)
thf(fact_376_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix4939239918433288346od_a_b @ nil_Product_prod_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% Util.suffixes.simps(1)
thf(fact_377_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix4455840324713621126od_a_b @ nil_fs4581119677382125722od_a_b )
    = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) ) ).

% Util.suffixes.simps(1)
thf(fact_378_pow__list_Osimps_I1_J,axiom,
    ( ( pow_li6114394920801268517od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ nil_li2802039260981550394od_a_b ) ) ).

% pow_list.simps(1)
thf(fact_379_pow__list_Osimps_I1_J,axiom,
    ( ( pow_li8436028492934955793od_a_b @ nil_li6050065983854590240od_a_b )
    = ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ nil_li4771897614291402022od_a_b ) ) ).

% pow_list.simps(1)
thf(fact_380_pow__list_Osimps_I1_J,axiom,
    ( ( pow_list_o @ nil_o )
    = ( cons_list_o @ nil_o @ nil_list_o ) ) ).

% pow_list.simps(1)
thf(fact_381_pow__list_Osimps_I1_J,axiom,
    ( ( pow_li7128575976297350687od_a_b @ nil_Product_prod_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% pow_list.simps(1)
thf(fact_382_pow__list_Osimps_I1_J,axiom,
    ( ( pow_li5660269712609304331od_a_b @ nil_fs4581119677382125722od_a_b )
    = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) ) ).

% pow_list.simps(1)
thf(fact_383_simple__cg__closure__phase__2_H_Opinduct,axiom,
    ! [A0: list_f1445794025290330138od_a_b,A1: produc2313482920965681321od_a_b,P: list_f1445794025290330138od_a_b > produc2313482920965681321od_a_b > $o] :
      ( ( accp_P8702517312824989759od_a_b @ simple6863691286768149176od_a_b @ ( produc5559962869320249254od_a_b @ A0 @ A1 ) )
     => ( ! [B3: $o,Done: list_f1445794025290330138od_a_b] :
            ( ( accp_P8702517312824989759od_a_b @ simple6863691286768149176od_a_b @ ( produc5559962869320249254od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) )
           => ( P @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,B3: $o,Done: list_f1445794025290330138od_a_b] :
              ( ( accp_P8702517312824989759od_a_b @ simple6863691286768149176od_a_b @ ( produc5559962869320249254od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) )
             => ( ! [Xb: $o,Y5: produc2518759752815613485od_a_b] :
                    ( ( ( produc1286801380576301484od_a_b @ Xb @ Y5 )
                      = ( simple4112306255986741752od_a_b @ X4 @ Xs3 ) )
                   => ! [Xaa: fset_l1334069825099621524od_a_b,Ya: list_f1445794025290330138od_a_b] :
                        ( ( ( produc6212510018049267869od_a_b @ Xaa @ Ya )
                          = Y5 )
                       => ( Xb
                         => ( P @ Ya @ ( produc7489420772309856409od_a_b @ $true @ ( cons_f6577355434438001738od_a_b @ Xaa @ Done ) ) ) ) ) )
               => ( ! [Xb: $o,Y5: produc2518759752815613485od_a_b] :
                      ( ( ( produc1286801380576301484od_a_b @ Xb @ Y5 )
                        = ( simple4112306255986741752od_a_b @ X4 @ Xs3 ) )
                     => ( ? [Xaa: fset_l1334069825099621524od_a_b,Ya: list_f1445794025290330138od_a_b] :
                            ( ( produc6212510018049267869od_a_b @ Xaa @ Ya )
                            = Y5 )
                       => ( ~ Xb
                         => ( P @ Xs3 @ ( produc7489420772309856409od_a_b @ B3 @ ( cons_f6577355434438001738od_a_b @ X4 @ Done ) ) ) ) ) )
                 => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( produc7489420772309856409od_a_b @ B3 @ Done ) ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% simple_cg_closure_phase_2'.pinduct
thf(fact_384_product__lists_Osimps_I1_J,axiom,
    ( ( produc5179936861586982537od_a_b @ nil_li4771897614291402022od_a_b )
    = ( cons_l2865286841204467926od_a_b @ nil_li6050065983854590240od_a_b @ nil_li4771897614291402022od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_385_product__lists_Osimps_I1_J,axiom,
    ( ( product_lists_o @ nil_list_o )
    = ( cons_list_o @ nil_o @ nil_list_o ) ) ).

% product_lists.simps(1)
thf(fact_386_product__lists_Osimps_I1_J,axiom,
    ( ( produc2086904765359242883od_a_b @ nil_li6050065983854590240od_a_b )
    = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_387_product__lists_Osimps_I1_J,axiom,
    ( ( produc5891818806577749399od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_388_listrel_Osimps,axiom,
    ! [A1: list_f1445794025290330138od_a_b,A22: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ A1 @ A22 ) @ ( listre6775573709112125169od_a_b @ R ) )
      = ( ( ( A1 = nil_fs4581119677382125722od_a_b )
          & ( A22 = nil_fs4581119677382125722od_a_b ) )
        | ? [X5: fset_l1334069825099621524od_a_b,Y4: fset_l1334069825099621524od_a_b,Xs4: list_f1445794025290330138od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( A1
              = ( cons_f6577355434438001738od_a_b @ X5 @ Xs4 ) )
            & ( A22
              = ( cons_f6577355434438001738od_a_b @ Y4 @ Ys2 ) )
            & ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X5 @ Y4 ) @ R )
            & ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs4 @ Ys2 ) @ ( listre6775573709112125169od_a_b @ R ) ) ) ) ) ).

% listrel.simps
thf(fact_389_listrel_Osimps,axiom,
    ! [A1: list_o,A22: list_l6099054058445139744od_a_b,R: set_Pr121319624013539721od_a_b] :
      ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ A1 @ A22 ) @ ( listre8201142255725533427od_a_b @ R ) )
      = ( ( ( A1 = nil_o )
          & ( A22 = nil_li6050065983854590240od_a_b ) )
        | ? [X5: $o,Y4: list_f1445794025290330138od_a_b,Xs4: list_o,Ys2: list_l6099054058445139744od_a_b] :
            ( ( A1
              = ( cons_o @ X5 @ Xs4 ) )
            & ( A22
              = ( cons_l7290444712290925776od_a_b @ Y4 @ Ys2 ) )
            & ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X5 @ Y4 ) @ R )
            & ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs4 @ Ys2 ) @ ( listre8201142255725533427od_a_b @ R ) ) ) ) ) ).

% listrel.simps
thf(fact_390_listrel_Osimps,axiom,
    ! [A1: list_o,A22: list_P5488608094462411443od_a_b,R: set_Pr5622538825374275996od_a_b] :
      ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ A1 @ A22 ) @ ( listre3706061411988323334od_a_b @ R ) )
      = ( ( ( A1 = nil_o )
          & ( A22 = nil_Pr1838250474468212019od_a_b ) )
        | ? [X5: $o,Y4: produc2518759752815613485od_a_b,Xs4: list_o,Ys2: list_P5488608094462411443od_a_b] :
            ( ( A1
              = ( cons_o @ X5 @ Xs4 ) )
            & ( A22
              = ( cons_P7745750895690215651od_a_b @ Y4 @ Ys2 ) )
            & ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X5 @ Y4 ) @ R )
            & ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs4 @ Ys2 ) @ ( listre3706061411988323334od_a_b @ R ) ) ) ) ) ).

% listrel.simps
thf(fact_391_listrel_Osimps,axiom,
    ! [A1: list_f1445794025290330138od_a_b,A22: list_l6099054058445139744od_a_b,R: set_Pr1051027220935592077od_a_b] :
      ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ A1 @ A22 ) @ ( listre5187687223414087671od_a_b @ R ) )
      = ( ( ( A1 = nil_fs4581119677382125722od_a_b )
          & ( A22 = nil_li6050065983854590240od_a_b ) )
        | ? [X5: fset_l1334069825099621524od_a_b,Y4: list_f1445794025290330138od_a_b,Xs4: list_f1445794025290330138od_a_b,Ys2: list_l6099054058445139744od_a_b] :
            ( ( A1
              = ( cons_f6577355434438001738od_a_b @ X5 @ Xs4 ) )
            & ( A22
              = ( cons_l7290444712290925776od_a_b @ Y4 @ Ys2 ) )
            & ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X5 @ Y4 ) @ R )
            & ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs4 @ Ys2 ) @ ( listre5187687223414087671od_a_b @ R ) ) ) ) ) ).

% listrel.simps
thf(fact_392_subseqs__refl,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( subseq3159716953272533757od_a_b @ Xs2 ) ) ) ).

% subseqs_refl
thf(fact_393_Cons__in__subseqsD,axiom,
    ! [Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b,Xs2: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) @ ( set_li5045283583078295363od_a_b @ ( subseq3159716953272533757od_a_b @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ Ys3 @ ( set_li5045283583078295363od_a_b @ ( subseq3159716953272533757od_a_b @ Xs2 ) ) ) ) ).

% Cons_in_subseqsD
thf(fact_394_Cons__in__subseqsD,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member7551773913232940227od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) @ ( set_li8217014873844115759od_a_b @ ( subseq8423821483446685161od_a_b @ Xs2 ) ) )
     => ( member7551773913232940227od_a_b @ Ys3 @ ( set_li8217014873844115759od_a_b @ ( subseq8423821483446685161od_a_b @ Xs2 ) ) ) ) ).

% Cons_in_subseqsD
thf(fact_395_simple__cg__closure__phase__2_H_Opsimps_I1_J,axiom,
    ! [B: $o,Done2: list_f1445794025290330138od_a_b] :
      ( ( accp_P8702517312824989759od_a_b @ simple6863691286768149176od_a_b @ ( produc5559962869320249254od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B @ Done2 ) ) )
     => ( ( simple891077427139469213od_a_b @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B @ Done2 ) )
        = ( produc7489420772309856409od_a_b @ B @ Done2 ) ) ) ).

% simple_cg_closure_phase_2'.psimps(1)
thf(fact_396_listrel_OCons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,R: set_Pr2242436922956002695od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R )
     => ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre6775573709112125169od_a_b @ R ) )
       => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) @ ( listre6775573709112125169od_a_b @ R ) ) ) ) ).

% listrel.Cons
thf(fact_397_listrel_OCons,axiom,
    ! [X3: $o,Y3: list_f1445794025290330138od_a_b,R: set_Pr121319624013539721od_a_b,Xs2: list_o,Ys3: list_l6099054058445139744od_a_b] :
      ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) @ R )
     => ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs2 @ Ys3 ) @ ( listre8201142255725533427od_a_b @ R ) )
       => ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ ( cons_o @ X3 @ Xs2 ) @ ( cons_l7290444712290925776od_a_b @ Y3 @ Ys3 ) ) @ ( listre8201142255725533427od_a_b @ R ) ) ) ) ).

% listrel.Cons
thf(fact_398_listrel_OCons,axiom,
    ! [X3: $o,Y3: produc2518759752815613485od_a_b,R: set_Pr5622538825374275996od_a_b,Xs2: list_o,Ys3: list_P5488608094462411443od_a_b] :
      ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) @ R )
     => ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs2 @ Ys3 ) @ ( listre3706061411988323334od_a_b @ R ) )
       => ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ ( cons_o @ X3 @ Xs2 ) @ ( cons_P7745750895690215651od_a_b @ Y3 @ Ys3 ) ) @ ( listre3706061411988323334od_a_b @ R ) ) ) ) ).

% listrel.Cons
thf(fact_399_listrel_OCons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b,R: set_Pr1051027220935592077od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_l6099054058445139744od_a_b] :
      ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) @ R )
     => ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs2 @ Ys3 ) @ ( listre5187687223414087671od_a_b @ R ) )
       => ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_l7290444712290925776od_a_b @ Y3 @ Ys3 ) ) @ ( listre5187687223414087671od_a_b @ R ) ) ) ) ).

% listrel.Cons
thf(fact_400_listrel__Cons1,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) @ Xs2 ) @ ( listre6775573709112125169od_a_b @ R ) )
     => ~ ! [Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ Y @ Ys ) )
           => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ Y3 @ Y ) @ R )
             => ~ ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Ys3 @ Ys ) @ ( listre6775573709112125169od_a_b @ R ) ) ) ) ) ).

% listrel_Cons1
thf(fact_401_listrel__Cons1,axiom,
    ! [Y3: $o,Ys3: list_o,Xs2: list_l6099054058445139744od_a_b,R: set_Pr121319624013539721od_a_b] :
      ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ ( cons_o @ Y3 @ Ys3 ) @ Xs2 ) @ ( listre8201142255725533427od_a_b @ R ) )
     => ~ ! [Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
            ( ( Xs2
              = ( cons_l7290444712290925776od_a_b @ Y @ Ys ) )
           => ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ Y3 @ Y ) @ R )
             => ~ ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Ys3 @ Ys ) @ ( listre8201142255725533427od_a_b @ R ) ) ) ) ) ).

% listrel_Cons1
thf(fact_402_listrel__Cons1,axiom,
    ! [Y3: $o,Ys3: list_o,Xs2: list_P5488608094462411443od_a_b,R: set_Pr5622538825374275996od_a_b] :
      ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ ( cons_o @ Y3 @ Ys3 ) @ Xs2 ) @ ( listre3706061411988323334od_a_b @ R ) )
     => ~ ! [Y: produc2518759752815613485od_a_b,Ys: list_P5488608094462411443od_a_b] :
            ( ( Xs2
              = ( cons_P7745750895690215651od_a_b @ Y @ Ys ) )
           => ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ Y3 @ Y ) @ R )
             => ~ ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Ys3 @ Ys ) @ ( listre3706061411988323334od_a_b @ R ) ) ) ) ) ).

% listrel_Cons1
thf(fact_403_listrel__Cons1,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b,R: set_Pr1051027220935592077od_a_b] :
      ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) @ Xs2 ) @ ( listre5187687223414087671od_a_b @ R ) )
     => ~ ! [Y: list_f1445794025290330138od_a_b,Ys: list_l6099054058445139744od_a_b] :
            ( ( Xs2
              = ( cons_l7290444712290925776od_a_b @ Y @ Ys ) )
           => ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ Y3 @ Y ) @ R )
             => ~ ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Ys3 @ Ys ) @ ( listre5187687223414087671od_a_b @ R ) ) ) ) ) ).

% listrel_Cons1
thf(fact_404_listrel__Cons2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) @ ( listre6775573709112125169od_a_b @ R ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
           => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Y3 ) @ R )
             => ~ ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs3 @ Ys3 ) @ ( listre6775573709112125169od_a_b @ R ) ) ) ) ) ).

% listrel_Cons2
thf(fact_405_listrel__Cons2,axiom,
    ! [Xs2: list_o,Y3: list_f1445794025290330138od_a_b,Ys3: list_l6099054058445139744od_a_b,R: set_Pr121319624013539721od_a_b] :
      ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs2 @ ( cons_l7290444712290925776od_a_b @ Y3 @ Ys3 ) ) @ ( listre8201142255725533427od_a_b @ R ) )
     => ~ ! [X4: $o,Xs3: list_o] :
            ( ( Xs2
              = ( cons_o @ X4 @ Xs3 ) )
           => ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y3 ) @ R )
             => ~ ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs3 @ Ys3 ) @ ( listre8201142255725533427od_a_b @ R ) ) ) ) ) ).

% listrel_Cons2
thf(fact_406_listrel__Cons2,axiom,
    ! [Xs2: list_o,Y3: produc2518759752815613485od_a_b,Ys3: list_P5488608094462411443od_a_b,R: set_Pr5622538825374275996od_a_b] :
      ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs2 @ ( cons_P7745750895690215651od_a_b @ Y3 @ Ys3 ) ) @ ( listre3706061411988323334od_a_b @ R ) )
     => ~ ! [X4: $o,Xs3: list_o] :
            ( ( Xs2
              = ( cons_o @ X4 @ Xs3 ) )
           => ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y3 ) @ R )
             => ~ ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs3 @ Ys3 ) @ ( listre3706061411988323334od_a_b @ R ) ) ) ) ) ).

% listrel_Cons2
thf(fact_407_listrel__Cons2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b,Ys3: list_l6099054058445139744od_a_b,R: set_Pr1051027220935592077od_a_b] :
      ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs2 @ ( cons_l7290444712290925776od_a_b @ Y3 @ Ys3 ) ) @ ( listre5187687223414087671od_a_b @ R ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
           => ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y3 ) @ R )
             => ~ ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs3 @ Ys3 ) @ ( listre5187687223414087671od_a_b @ R ) ) ) ) ) ).

% listrel_Cons2
thf(fact_408_listrel_Ocases,axiom,
    ! [A1: list_f1445794025290330138od_a_b,A22: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ A1 @ A22 ) @ ( listre6775573709112125169od_a_b @ R ) )
     => ( ( ( A1 = nil_fs4581119677382125722od_a_b )
         => ( A22 != nil_fs4581119677382125722od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( A1
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ! [Ys: list_f1445794025290330138od_a_b] :
                  ( ( A22
                    = ( cons_f6577355434438001738od_a_b @ Y @ Ys ) )
                 => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Y ) @ R )
                   => ~ ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs3 @ Ys ) @ ( listre6775573709112125169od_a_b @ R ) ) ) ) ) ) ) ).

% listrel.cases
thf(fact_409_listrel_Ocases,axiom,
    ! [A1: list_o,A22: list_l6099054058445139744od_a_b,R: set_Pr121319624013539721od_a_b] :
      ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ A1 @ A22 ) @ ( listre8201142255725533427od_a_b @ R ) )
     => ( ( ( A1 = nil_o )
         => ( A22 != nil_li6050065983854590240od_a_b ) )
       => ~ ! [X4: $o,Y: list_f1445794025290330138od_a_b,Xs3: list_o] :
              ( ( A1
                = ( cons_o @ X4 @ Xs3 ) )
             => ! [Ys: list_l6099054058445139744od_a_b] :
                  ( ( A22
                    = ( cons_l7290444712290925776od_a_b @ Y @ Ys ) )
                 => ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ R )
                   => ~ ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs3 @ Ys ) @ ( listre8201142255725533427od_a_b @ R ) ) ) ) ) ) ) ).

% listrel.cases
thf(fact_410_listrel_Ocases,axiom,
    ! [A1: list_o,A22: list_P5488608094462411443od_a_b,R: set_Pr5622538825374275996od_a_b] :
      ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ A1 @ A22 ) @ ( listre3706061411988323334od_a_b @ R ) )
     => ( ( ( A1 = nil_o )
         => ( A22 != nil_Pr1838250474468212019od_a_b ) )
       => ~ ! [X4: $o,Y: produc2518759752815613485od_a_b,Xs3: list_o] :
              ( ( A1
                = ( cons_o @ X4 @ Xs3 ) )
             => ! [Ys: list_P5488608094462411443od_a_b] :
                  ( ( A22
                    = ( cons_P7745750895690215651od_a_b @ Y @ Ys ) )
                 => ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ R )
                   => ~ ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs3 @ Ys ) @ ( listre3706061411988323334od_a_b @ R ) ) ) ) ) ) ) ).

% listrel.cases
thf(fact_411_listrel_Ocases,axiom,
    ! [A1: list_f1445794025290330138od_a_b,A22: list_l6099054058445139744od_a_b,R: set_Pr1051027220935592077od_a_b] :
      ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ A1 @ A22 ) @ ( listre5187687223414087671od_a_b @ R ) )
     => ( ( ( A1 = nil_fs4581119677382125722od_a_b )
         => ( A22 != nil_li6050065983854590240od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( A1
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ! [Ys: list_l6099054058445139744od_a_b] :
                  ( ( A22
                    = ( cons_l7290444712290925776od_a_b @ Y @ Ys ) )
                 => ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ R )
                   => ~ ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs3 @ Ys ) @ ( listre5187687223414087671od_a_b @ R ) ) ) ) ) ) ) ).

% listrel.cases
thf(fact_412_update__with__aux_Osimps_I1_J,axiom,
    ! [V2: list_f1445794025290330138od_a_b,K3: $o,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b] :
      ( ( update7744615274700815744_a_b_o @ V2 @ K3 @ F2 @ nil_Pr7302809325368845999od_a_b )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ V2 ) ) @ nil_Pr7302809325368845999od_a_b ) ) ).

% update_with_aux.simps(1)
thf(fact_413_update__with__aux_Osimps_I1_J,axiom,
    ! [V2: produc2518759752815613485od_a_b,K3: $o,F2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b] :
      ( ( update2008830506971281325_a_b_o @ V2 @ K3 @ F2 @ nil_Pr3614377049866306882od_a_b )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ V2 ) ) @ nil_Pr3614377049866306882od_a_b ) ) ).

% update_with_aux.simps(1)
thf(fact_414_update__with__aux_Osimps_I1_J,axiom,
    ! [V2: list_f1445794025290330138od_a_b,K3: fset_l1334069825099621524od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b] :
      ( ( update1355849682342953596od_a_b @ V2 @ K3 @ F2 @ nil_Pr1838250474468212019od_a_b )
      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ ( F2 @ V2 ) ) @ nil_Pr1838250474468212019od_a_b ) ) ).

% update_with_aux.simps(1)
thf(fact_415_suffixes_Oelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_l6099054058445139744od_a_b] :
      ( ( ( suffix4455840324713621126od_a_b @ X3 )
        = Y3 )
     => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
         => ( Y3
           != ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( X3
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ( Y3
               != ( append1675525773727384373od_a_b @ ( suffix4455840324713621126od_a_b @ Xs3 ) @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ nil_li6050065983854590240od_a_b ) ) ) ) ) ) ).

% suffixes.elims
thf(fact_416_map__default_Osimps_I1_J,axiom,
    ! [K3: $o,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b] :
      ( ( map_de6169289306397452762od_a_b @ K3 @ V2 @ F2 @ nil_Pr7302809325368845999od_a_b )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V2 ) @ nil_Pr7302809325368845999od_a_b ) ) ).

% map_default.simps(1)
thf(fact_417_map__default_Osimps_I1_J,axiom,
    ! [K3: $o,V2: produc2518759752815613485od_a_b,F2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b] :
      ( ( map_de5747135492376268781od_a_b @ K3 @ V2 @ F2 @ nil_Pr3614377049866306882od_a_b )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V2 ) @ nil_Pr3614377049866306882od_a_b ) ) ).

% map_default.simps(1)
thf(fact_418_map__default_Osimps_I1_J,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b] :
      ( ( map_de5790008637807865694od_a_b @ K3 @ V2 @ F2 @ nil_Pr1838250474468212019od_a_b )
      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V2 ) @ nil_Pr1838250474468212019od_a_b ) ) ).

% map_default.simps(1)
thf(fact_419_delete__aux__eq__Nil__conv,axiom,
    ! [K3: $o,Ts: list_P3574414722980446895od_a_b] :
      ( ( ( delete6197099393584013480od_a_b @ K3 @ Ts )
        = nil_Pr7302809325368845999od_a_b )
      = ( ( Ts = nil_Pr7302809325368845999od_a_b )
        | ? [V3: list_f1445794025290330138od_a_b] :
            ( Ts
            = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V3 ) @ nil_Pr7302809325368845999od_a_b ) ) ) ) ).

% delete_aux_eq_Nil_conv
thf(fact_420_delete__aux__eq__Nil__conv,axiom,
    ! [K3: $o,Ts: list_P5302045529885307074od_a_b] :
      ( ( ( delete3629537940609567931od_a_b @ K3 @ Ts )
        = nil_Pr3614377049866306882od_a_b )
      = ( ( Ts = nil_Pr3614377049866306882od_a_b )
        | ? [V3: produc2518759752815613485od_a_b] :
            ( Ts
            = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V3 ) @ nil_Pr3614377049866306882od_a_b ) ) ) ) ).

% delete_aux_eq_Nil_conv
thf(fact_421_delete__aux__eq__Nil__conv,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,Ts: list_P5488608094462411443od_a_b] :
      ( ( ( delete3925988326758032172od_a_b @ K3 @ Ts )
        = nil_Pr1838250474468212019od_a_b )
      = ( ( Ts = nil_Pr1838250474468212019od_a_b )
        | ? [V3: list_f1445794025290330138od_a_b] :
            ( Ts
            = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V3 ) @ nil_Pr1838250474468212019od_a_b ) ) ) ) ).

% delete_aux_eq_Nil_conv
thf(fact_422_delete__aux_Oelims,axiom,
    ! [X3: $o,Xa: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( delete6197099393584013480od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( ( Xa = nil_Pr7302809325368845999od_a_b )
         => ( Y3 != nil_Pr7302809325368845999od_a_b ) )
       => ~ ! [K2: $o,V: list_f1445794025290330138od_a_b,Xs3: list_P3574414722980446895od_a_b] :
              ( ( Xa
                = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ Xs3 ) )
             => ~ ( ( ( X3 = K2 )
                   => ( Y3 = Xs3 ) )
                  & ( ( X3 = ~ K2 )
                   => ( Y3
                      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ ( delete6197099393584013480od_a_b @ X3 @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.elims
thf(fact_423_delete__aux_Oelims,axiom,
    ! [X3: $o,Xa: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( delete3629537940609567931od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( ( Xa = nil_Pr3614377049866306882od_a_b )
         => ( Y3 != nil_Pr3614377049866306882od_a_b ) )
       => ~ ! [K2: $o,V: produc2518759752815613485od_a_b,Xs3: list_P5302045529885307074od_a_b] :
              ( ( Xa
                = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ Xs3 ) )
             => ~ ( ( ( X3 = K2 )
                   => ( Y3 = Xs3 ) )
                  & ( ( X3 = ~ K2 )
                   => ( Y3
                      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ ( delete3629537940609567931od_a_b @ X3 @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.elims
thf(fact_424_delete__aux_Oelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( delete3925988326758032172od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( ( Xa = nil_Pr1838250474468212019od_a_b )
         => ( Y3 != nil_Pr1838250474468212019od_a_b ) )
       => ~ ! [K2: fset_l1334069825099621524od_a_b,V: list_f1445794025290330138od_a_b,Xs3: list_P5488608094462411443od_a_b] :
              ( ( Xa
                = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ Xs3 ) )
             => ~ ( ( ( X3 = K2 )
                   => ( Y3 = Xs3 ) )
                  & ( ( X3 != K2 )
                   => ( Y3
                      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ ( delete3925988326758032172od_a_b @ X3 @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.elims
thf(fact_425_the__elem__set,axiom,
    ! [X3: fset_l1334069825099621524od_a_b] :
      ( ( the_el4387542105688296585od_a_b @ ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) )
      = X3 ) ).

% the_elem_set
thf(fact_426_Util_Osuffixes_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( suffix4455840324713621126od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append1675525773727384373od_a_b @ ( suffix4455840324713621126od_a_b @ Xs2 ) @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ nil_li6050065983854590240od_a_b ) ) ) ).

% Util.suffixes.simps(2)
thf(fact_427_lexord__Nil__left,axiom,
    ! [Y3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ nil_fs4581119677382125722od_a_b @ Y3 ) @ ( lexord9144254948259057799od_a_b @ R ) )
      = ( ? [A5: fset_l1334069825099621524od_a_b,X5: list_f1445794025290330138od_a_b] :
            ( Y3
            = ( cons_f6577355434438001738od_a_b @ A5 @ X5 ) ) ) ) ).

% lexord_Nil_left
thf(fact_428_append1__eq__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) )
        = ( append2015155619842375983od_a_b @ Ys3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ nil_fs4581119677382125722od_a_b ) ) )
      = ( ( Xs2 = Ys3 )
        & ( X3 = Y3 ) ) ) ).

% append1_eq_conv
thf(fact_429_lexord__cons__cons,axiom,
    ! [A: fset_l1334069825099621524od_a_b,X3: list_f1445794025290330138od_a_b,B: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ X3 ) @ ( cons_f6577355434438001738od_a_b @ B @ Y3 ) ) @ ( lexord9144254948259057799od_a_b @ R ) )
      = ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ A @ B ) @ R )
        | ( ( A = B )
          & ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ X3 @ Y3 ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ) ) ).

% lexord_cons_cons
thf(fact_430_lexord__append__rightI,axiom,
    ! [Y3: list_f1445794025290330138od_a_b,X3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ? [B4: fset_l1334069825099621524od_a_b,Z3: list_f1445794025290330138od_a_b] :
          ( Y3
          = ( cons_f6577355434438001738od_a_b @ B4 @ Z3 ) )
     => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ X3 @ ( append2015155619842375983od_a_b @ X3 @ Y3 ) ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ).

% lexord_append_rightI
thf(fact_431_Cons__eq__appendI,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs1: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b] :
      ( ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs1 )
        = Ys3 )
     => ( ( Xs2
          = ( append2015155619842375983od_a_b @ Xs1 @ Zs ) )
       => ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
          = ( append2015155619842375983od_a_b @ Ys3 @ Zs ) ) ) ) ).

% Cons_eq_appendI
thf(fact_432_append__Cons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( append2015155619842375983od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ Ys3 )
      = ( cons_f6577355434438001738od_a_b @ X3 @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) ) ) ).

% append_Cons
thf(fact_433_list__set__sym,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ X3 @ Y3 ) )
      = ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ Y3 @ X3 ) ) ) ).

% list_set_sym
thf(fact_434_list__prefix__elem,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Ys3: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( append7557446516274476873od_a_b @ Xs2 @ Ys3 ) ) )
     => ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Ys3 ) )
       => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% list_prefix_elem
thf(fact_435_list__prefix__elem,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) ) )
     => ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Ys3 ) )
       => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% list_prefix_elem
thf(fact_436_list__concat__non__elem,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Ys3: list_l8778361445553822004od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Ys3 ) )
       => ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( append7557446516274476873od_a_b @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_437_list__concat__non__elem,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Ys3 ) )
       => ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_438_lexord__append__left__rightI,axiom,
    ! [A: fset_l1334069825099621524od_a_b,B: fset_l1334069825099621524od_a_b,R: set_Pr2242436922956002695od_a_b,U: list_f1445794025290330138od_a_b,X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ A @ B ) @ R )
     => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ U @ ( cons_f6577355434438001738od_a_b @ A @ X3 ) ) @ ( append2015155619842375983od_a_b @ U @ ( cons_f6577355434438001738od_a_b @ B @ Y3 ) ) ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ).

% lexord_append_left_rightI
thf(fact_439_lexord__same__pref__iff,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ ( append2015155619842375983od_a_b @ Xs2 @ Zs ) ) @ ( lexord9144254948259057799od_a_b @ R ) )
      = ( ? [X5: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
            & ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X5 @ X5 ) @ R ) )
        | ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Ys3 @ Zs ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ) ).

% lexord_same_pref_iff
thf(fact_440_rev__induct,axiom,
    ! [P: list_f1445794025290330138od_a_b > $o,Xs2: list_f1445794025290330138od_a_b] :
      ( ( P @ nil_fs4581119677382125722od_a_b )
     => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
            ( ( P @ Xs3 )
           => ( P @ ( append2015155619842375983od_a_b @ Xs3 @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) ) ) )
       => ( P @ Xs2 ) ) ) ).

% rev_induct
thf(fact_441_rev__exhaust,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ~ ! [Ys: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b] :
            ( Xs2
           != ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ Y @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% rev_exhaust
thf(fact_442_Cons__eq__append__conv,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b] :
      ( ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
        = ( append2015155619842375983od_a_b @ Ys3 @ Zs ) )
      = ( ( ( Ys3 = nil_fs4581119677382125722od_a_b )
          & ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
            = Zs ) )
        | ? [Ys4: list_f1445794025290330138od_a_b] :
            ( ( ( cons_f6577355434438001738od_a_b @ X3 @ Ys4 )
              = Ys3 )
            & ( Xs2
              = ( append2015155619842375983od_a_b @ Ys4 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_443_append__eq__Cons__conv,axiom,
    ! [Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( append2015155619842375983od_a_b @ Ys3 @ Zs )
        = ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( ( ( Ys3 = nil_fs4581119677382125722od_a_b )
          & ( Zs
            = ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) )
        | ? [Ys4: list_f1445794025290330138od_a_b] :
            ( ( Ys3
              = ( cons_f6577355434438001738od_a_b @ X3 @ Ys4 ) )
            & ( ( append2015155619842375983od_a_b @ Ys4 @ Zs )
              = Xs2 ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_444_rev__nonempty__induct,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > $o] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ! [X4: fset_l1334069825099621524od_a_b] : ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( Xs3 != nil_fs4581119677382125722od_a_b )
             => ( ( P @ Xs3 )
               => ( P @ ( append2015155619842375983od_a_b @ Xs3 @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) ) ) ) )
         => ( P @ Xs2 ) ) ) ) ).

% rev_nonempty_induct
thf(fact_445_split__list,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ? [Ys: list_l8778361445553822004od_a_b,Zs2: list_l8778361445553822004od_a_b] :
          ( Xs2
          = ( append7557446516274476873od_a_b @ Ys @ ( cons_l907386227682280420od_a_b @ X3 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_446_split__list,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( Xs2
          = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_447_split__list__last,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ? [Ys: list_l8778361445553822004od_a_b,Zs2: list_l8778361445553822004od_a_b] :
          ( ( Xs2
            = ( append7557446516274476873od_a_b @ Ys @ ( cons_l907386227682280420od_a_b @ X3 @ Zs2 ) ) )
          & ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_448_split__list__last,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( ( Xs2
            = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs2 ) ) )
          & ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_449_split__list__prop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b] :
          ( ? [Zs2: list_f1445794025290330138od_a_b] :
              ( Xs2
              = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
          & ( P @ X4 ) ) ) ).

% split_list_prop
thf(fact_450_split__list__first,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ? [Ys: list_l8778361445553822004od_a_b,Zs2: list_l8778361445553822004od_a_b] :
          ( ( Xs2
            = ( append7557446516274476873od_a_b @ Ys @ ( cons_l907386227682280420od_a_b @ X3 @ Zs2 ) ) )
          & ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Ys ) ) ) ) ).

% split_list_first
thf(fact_451_split__list__first,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( ( Xs2
            = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs2 ) ) )
          & ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Ys ) ) ) ) ).

% split_list_first
thf(fact_452_split__list__propE,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ~ ! [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b] :
            ( ? [Zs2: list_f1445794025290330138od_a_b] :
                ( Xs2
                = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
           => ~ ( P @ X4 ) ) ) ).

% split_list_propE
thf(fact_453_append__Cons__eq__iff,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Ys3: list_l8778361445553822004od_a_b,Xs5: list_l8778361445553822004od_a_b,Ys5: list_l8778361445553822004od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Ys3 ) )
       => ( ( ( append7557446516274476873od_a_b @ Xs2 @ ( cons_l907386227682280420od_a_b @ X3 @ Ys3 ) )
            = ( append7557446516274476873od_a_b @ Xs5 @ ( cons_l907386227682280420od_a_b @ X3 @ Ys5 ) ) )
          = ( ( Xs2 = Xs5 )
            & ( Ys3 = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_454_append__Cons__eq__iff,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Xs5: list_f1445794025290330138od_a_b,Ys5: list_f1445794025290330138od_a_b] :
      ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Ys3 ) )
       => ( ( ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Ys3 ) )
            = ( append2015155619842375983od_a_b @ Xs5 @ ( cons_f6577355434438001738od_a_b @ X3 @ Ys5 ) ) )
          = ( ( Xs2 = Xs5 )
            & ( Ys3 = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_455_in__set__conv__decomp,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_l8778361445553822004od_a_b,Zs3: list_l8778361445553822004od_a_b] :
            ( Xs2
            = ( append7557446516274476873od_a_b @ Ys2 @ ( cons_l907386227682280420od_a_b @ X3 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_456_in__set__conv__decomp,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_f1445794025290330138od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( Xs2
            = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_457_split__list__last__prop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( ( Xs2
            = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
          & ( P @ X4 )
          & ! [Xa2: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Xa2 @ ( set_fs4298891544546585641od_a_b @ Zs2 ) )
             => ~ ( P @ Xa2 ) ) ) ) ).

% split_list_last_prop
thf(fact_458_split__list__first__prop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ? [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b] :
          ( ? [Zs2: list_f1445794025290330138od_a_b] :
              ( Xs2
              = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
          & ( P @ X4 )
          & ! [Xa2: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Xa2 @ ( set_fs4298891544546585641od_a_b @ Ys ) )
             => ~ ( P @ Xa2 ) ) ) ) ).

% split_list_first_prop
thf(fact_459_split__list__last__propE,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ~ ! [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa2: fset_l1334069825099621524od_a_b] :
                    ( ( member361094292949318077od_a_b @ Xa2 @ ( set_fs4298891544546585641od_a_b @ Zs2 ) )
                   => ~ ( P @ Xa2 ) ) ) ) ) ).

% split_list_last_propE
thf(fact_460_split__list__first__propE,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ? [X6: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X6 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( P @ X6 ) )
     => ~ ! [Ys: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b] :
            ( ? [Zs2: list_f1445794025290330138od_a_b] :
                ( Xs2
                = ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ X4 @ Zs2 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa2: fset_l1334069825099621524od_a_b] :
                    ( ( member361094292949318077od_a_b @ Xa2 @ ( set_fs4298891544546585641od_a_b @ Ys ) )
                   => ~ ( P @ Xa2 ) ) ) ) ) ).

% split_list_first_propE
thf(fact_461_in__set__conv__decomp__last,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_l8778361445553822004od_a_b,Zs3: list_l8778361445553822004od_a_b] :
            ( ( Xs2
              = ( append7557446516274476873od_a_b @ Ys2 @ ( cons_l907386227682280420od_a_b @ X3 @ Zs3 ) ) )
            & ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_462_in__set__conv__decomp__last,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_f1445794025290330138od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs3 ) ) )
            & ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_463_in__set__conv__decomp__first,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_l8778361445553822004od_a_b,Zs3: list_l8778361445553822004od_a_b] :
            ( ( Xs2
              = ( append7557446516274476873od_a_b @ Ys2 @ ( cons_l907386227682280420od_a_b @ X3 @ Zs3 ) ) )
            & ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Ys2 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_464_in__set__conv__decomp__first,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( ? [Ys2: list_f1445794025290330138od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Zs3 ) ) )
            & ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Ys2 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_465_split__list__last__prop__iff,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ( ? [X5: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
            & ( P @ X5 ) ) )
      = ( ? [Ys2: list_f1445794025290330138od_a_b,X5: fset_l1334069825099621524od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ X5 @ Zs3 ) ) )
            & ( P @ X5 )
            & ! [Y4: fset_l1334069825099621524od_a_b] :
                ( ( member361094292949318077od_a_b @ Y4 @ ( set_fs4298891544546585641od_a_b @ Zs3 ) )
               => ~ ( P @ Y4 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_466_split__list__first__prop__iff,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ( ? [X5: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
            & ( P @ X5 ) ) )
      = ( ? [Ys2: list_f1445794025290330138od_a_b,X5: fset_l1334069825099621524od_a_b] :
            ( ? [Zs3: list_f1445794025290330138od_a_b] :
                ( Xs2
                = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ X5 @ Zs3 ) ) )
            & ( P @ X5 )
            & ! [Y4: fset_l1334069825099621524od_a_b] :
                ( ( member361094292949318077od_a_b @ Y4 @ ( set_fs4298891544546585641od_a_b @ Ys2 ) )
               => ~ ( P @ Y4 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_467_list__ex1__iff,axiom,
    ( list_e3621433171152788727od_a_b
    = ( ^ [P4: list_P1467974523212632366od_a_b > $o,Xs4: list_l8778361445553822004od_a_b] :
        ? [X5: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X5 @ ( set_li5045283583078295363od_a_b @ Xs4 ) )
          & ( P4 @ X5 )
          & ! [Y4: list_P1467974523212632366od_a_b] :
              ( ( ( member6895035109809442519od_a_b @ Y4 @ ( set_li5045283583078295363od_a_b @ Xs4 ) )
                & ( P4 @ Y4 ) )
             => ( Y4 = X5 ) ) ) ) ) ).

% list_ex1_iff
thf(fact_468_list__ex1__iff,axiom,
    ( list_e7381079376597858269od_a_b
    = ( ^ [P4: fset_l1334069825099621524od_a_b > $o,Xs4: list_f1445794025290330138od_a_b] :
        ? [X5: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs4 ) )
          & ( P4 @ X5 )
          & ! [Y4: fset_l1334069825099621524od_a_b] :
              ( ( ( member361094292949318077od_a_b @ Y4 @ ( set_fs4298891544546585641od_a_b @ Xs4 ) )
                & ( P4 @ Y4 ) )
             => ( Y4 = X5 ) ) ) ) ) ).

% list_ex1_iff
thf(fact_469_delete__aux_Osimps_I2_J,axiom,
    ! [K3: $o,K4: $o,V2: list_f1445794025290330138od_a_b,Xs2: list_P3574414722980446895od_a_b] :
      ( ( ( K3 = K4 )
       => ( ( delete6197099393584013480od_a_b @ K3 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = Xs2 ) )
      & ( ( K3 = ~ K4 )
       => ( ( delete6197099393584013480od_a_b @ K3 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K4 @ V2 ) @ ( delete6197099393584013480od_a_b @ K3 @ Xs2 ) ) ) ) ) ).

% delete_aux.simps(2)
thf(fact_470_delete__aux_Osimps_I2_J,axiom,
    ! [K3: $o,K4: $o,V2: produc2518759752815613485od_a_b,Xs2: list_P5302045529885307074od_a_b] :
      ( ( ( K3 = K4 )
       => ( ( delete3629537940609567931od_a_b @ K3 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = Xs2 ) )
      & ( ( K3 = ~ K4 )
       => ( ( delete3629537940609567931od_a_b @ K3 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K4 @ V2 ) @ ( delete3629537940609567931od_a_b @ K3 @ Xs2 ) ) ) ) ) ).

% delete_aux.simps(2)
thf(fact_471_delete__aux_Osimps_I2_J,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,K4: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,Xs2: list_P5488608094462411443od_a_b] :
      ( ( ( K3 = K4 )
       => ( ( delete3925988326758032172od_a_b @ K3 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = Xs2 ) )
      & ( ( K3 != K4 )
       => ( ( delete3925988326758032172od_a_b @ K3 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K4 @ V2 ) @ Xs2 ) )
          = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K4 @ V2 ) @ ( delete3925988326758032172od_a_b @ K3 @ Xs2 ) ) ) ) ) ).

% delete_aux.simps(2)
thf(fact_472_lexord__partial__trans,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,R: set_Pr3015088788472578951od_a_b,Ys3: list_l8778361445553822004od_a_b,Zs: list_l8778361445553822004od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b,Y: list_P1467974523212632366od_a_b,Z4: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
         => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X4 @ Y ) @ R )
           => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Y @ Z4 ) @ R )
             => ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X4 @ Z4 ) @ R ) ) ) )
     => ( ( member4992001953252686800od_a_b @ ( produc3466467997744452247od_a_b @ Xs2 @ Ys3 ) @ ( lexord2488576207029785249od_a_b @ R ) )
       => ( ( member4992001953252686800od_a_b @ ( produc3466467997744452247od_a_b @ Ys3 @ Zs ) @ ( lexord2488576207029785249od_a_b @ R ) )
         => ( member4992001953252686800od_a_b @ ( produc3466467997744452247od_a_b @ Xs2 @ Zs ) @ ( lexord2488576207029785249od_a_b @ R ) ) ) ) ) ).

% lexord_partial_trans
thf(fact_473_lexord__partial__trans,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b,Z4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Y ) @ R )
           => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ Y @ Z4 ) @ R )
             => ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Z4 ) @ R ) ) ) )
     => ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( lexord9144254948259057799od_a_b @ R ) )
       => ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Ys3 @ Zs ) @ ( lexord9144254948259057799od_a_b @ R ) )
         => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Zs ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ) ) ).

% lexord_partial_trans
thf(fact_474_can__select__set__list__ex1,axiom,
    ! [P: fset_l1334069825099621524od_a_b > $o,A4: list_f1445794025290330138od_a_b] :
      ( ( can_se1502477684658679057od_a_b @ P @ ( set_fs4298891544546585641od_a_b @ A4 ) )
      = ( list_e7381079376597858269od_a_b @ P @ A4 ) ) ).

% can_select_set_list_ex1
thf(fact_475_prefixes__snoc,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( prefix4612422245637881633od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) )
      = ( append1675525773727384373od_a_b @ ( prefix4612422245637881633od_a_b @ Xs2 ) @ ( cons_l7290444712290925776od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) @ nil_li6050065983854590240od_a_b ) ) ) ).

% prefixes_snoc
thf(fact_476_suffixes__eq__snoc,axiom,
    ! [Ys3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b,X3: list_f1445794025290330138od_a_b] :
      ( ( ( suffix888123080290511074od_a_b @ Ys3 )
        = ( append1675525773727384373od_a_b @ Xs2 @ ( cons_l7290444712290925776od_a_b @ X3 @ nil_li6050065983854590240od_a_b ) ) )
      = ( ( ( ( Ys3 = nil_fs4581119677382125722od_a_b )
            & ( Xs2 = nil_li6050065983854590240od_a_b ) )
          | ? [Z5: fset_l1334069825099621524od_a_b,Zs3: list_f1445794025290330138od_a_b] :
              ( ( Ys3
                = ( cons_f6577355434438001738od_a_b @ Z5 @ Zs3 ) )
              & ( Xs2
                = ( suffix888123080290511074od_a_b @ Zs3 ) ) ) )
        & ( X3 = Ys3 ) ) ) ).

% suffixes_eq_snoc
thf(fact_477_prefixes__eq__snoc,axiom,
    ! [Ys3: list_f1445794025290330138od_a_b,Xs2: list_l6099054058445139744od_a_b,X3: list_f1445794025290330138od_a_b] :
      ( ( ( prefix4612422245637881633od_a_b @ Ys3 )
        = ( append1675525773727384373od_a_b @ Xs2 @ ( cons_l7290444712290925776od_a_b @ X3 @ nil_li6050065983854590240od_a_b ) ) )
      = ( ( ( ( Ys3 = nil_fs4581119677382125722od_a_b )
            & ( Xs2 = nil_li6050065983854590240od_a_b ) )
          | ? [Z5: fset_l1334069825099621524od_a_b,Zs3: list_f1445794025290330138od_a_b] :
              ( ( Ys3
                = ( append2015155619842375983od_a_b @ Zs3 @ ( cons_f6577355434438001738od_a_b @ Z5 @ nil_fs4581119677382125722od_a_b ) ) )
              & ( Xs2
                = ( prefix4612422245637881633od_a_b @ Zs3 ) ) ) )
        & ( X3 = Ys3 ) ) ) ).

% prefixes_eq_snoc
thf(fact_478_snoc__listrel1__snoc__iff,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) @ ( append2015155619842375983od_a_b @ Ys3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ nil_fs4581119677382125722od_a_b ) ) ) @ ( listre757946421397414515od_a_b @ R ) )
      = ( ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
          & ( X3 = Y3 ) )
        | ( ( Xs2 = Ys3 )
          & ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R ) ) ) ) ).

% snoc_listrel1_snoc_iff
thf(fact_479_map__default_Oelims,axiom,
    ! [X3: $o,Xa: produc2518759752815613485od_a_b,Xb2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Xc: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( map_de5747135492376268781od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( ( Xc = nil_Pr3614377049866306882od_a_b )
         => ( Y3
           != ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Xa ) @ nil_Pr3614377049866306882od_a_b ) ) )
       => ~ ! [P5: produc8937288731615916348od_a_b,Ps: list_P5302045529885307074od_a_b] :
              ( ( Xc
                = ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc2316053142268291992od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ ( Xb2 @ ( produc5480430458100320474od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc2316053142268291992od_a_b @ P5 )
                      = ~ X3 )
                   => ( Y3
                      = ( cons_P7065065391077662962od_a_b @ P5 @ ( map_de5747135492376268781od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) ) ) ) ) ).

% map_default.elims
thf(fact_480_map__default_Oelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_f1445794025290330138od_a_b,Xb2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xc: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( map_de5790008637807865694od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( ( Xc = nil_Pr1838250474468212019od_a_b )
         => ( Y3
           != ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Xa ) @ nil_Pr1838250474468212019od_a_b ) ) )
       => ~ ! [P5: produc2518759752815613485od_a_b,Ps: list_P5488608094462411443od_a_b] :
              ( ( Xc
                = ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc5739577146777995401od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ ( Xb2 @ ( produc396176279405262539od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc5739577146777995401od_a_b @ P5 )
                     != X3 )
                   => ( Y3
                      = ( cons_P7745750895690215651od_a_b @ P5 @ ( map_de5790008637807865694od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) ) ) ) ) ).

% map_default.elims
thf(fact_481_map__default_Oelims,axiom,
    ! [X3: $o,Xa: list_f1445794025290330138od_a_b,Xb2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xc: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( map_de6169289306397452762od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( ( Xc = nil_Pr7302809325368845999od_a_b )
         => ( Y3
           != ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Xa ) @ nil_Pr7302809325368845999od_a_b ) ) )
       => ~ ! [P5: produc2313482920965681321od_a_b,Ps: list_P3574414722980446895od_a_b] :
              ( ( Xc
                = ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc5358503411717041797od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ ( Xb2 @ ( produc2954343059184910791od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc5358503411717041797od_a_b @ P5 )
                      = ~ X3 )
                   => ( Y3
                      = ( cons_P2672142353023029855od_a_b @ P5 @ ( map_de6169289306397452762od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) ) ) ) ) ).

% map_default.elims
thf(fact_482_prod_Ocollapse,axiom,
    ! [Prod: produc8937288731615916348od_a_b] :
      ( ( produc1286801380576301484od_a_b @ ( produc2316053142268291992od_a_b @ Prod ) @ ( produc5480430458100320474od_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_483_prod_Ocollapse,axiom,
    ! [Prod: produc2518759752815613485od_a_b] :
      ( ( produc6212510018049267869od_a_b @ ( produc5739577146777995401od_a_b @ Prod ) @ ( produc396176279405262539od_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_484_prod_Ocollapse,axiom,
    ! [Prod: produc2313482920965681321od_a_b] :
      ( ( produc7489420772309856409od_a_b @ ( produc5358503411717041797od_a_b @ Prod ) @ ( produc2954343059184910791od_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_485_Cons__listrel1__Cons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) @ ( listre757946421397414515od_a_b @ R ) )
      = ( ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R )
          & ( Xs2 = Ys3 ) )
        | ( ( X3 = Y3 )
          & ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) ) ) ) ) ).

% Cons_listrel1_Cons
thf(fact_486_fstI,axiom,
    ! [X3: produc2313482920965681321od_a_b,Y3: $o,Z: list_f1445794025290330138od_a_b] :
      ( ( X3
        = ( produc7489420772309856409od_a_b @ Y3 @ Z ) )
     => ( ( produc5358503411717041797od_a_b @ X3 )
        = Y3 ) ) ).

% fstI
thf(fact_487_fstI,axiom,
    ! [X3: produc8937288731615916348od_a_b,Y3: $o,Z: produc2518759752815613485od_a_b] :
      ( ( X3
        = ( produc1286801380576301484od_a_b @ Y3 @ Z ) )
     => ( ( produc2316053142268291992od_a_b @ X3 )
        = Y3 ) ) ).

% fstI
thf(fact_488_fstI,axiom,
    ! [X3: produc2518759752815613485od_a_b,Y3: fset_l1334069825099621524od_a_b,Z: list_f1445794025290330138od_a_b] :
      ( ( X3
        = ( produc6212510018049267869od_a_b @ Y3 @ Z ) )
     => ( ( produc5739577146777995401od_a_b @ X3 )
        = Y3 ) ) ).

% fstI
thf(fact_489_eq__fst__iff,axiom,
    ! [A: $o,P2: produc2313482920965681321od_a_b] :
      ( ( A
        = ( produc5358503411717041797od_a_b @ P2 ) )
      = ( ? [B5: list_f1445794025290330138od_a_b] :
            ( P2
            = ( produc7489420772309856409od_a_b @ A @ B5 ) ) ) ) ).

% eq_fst_iff
thf(fact_490_eq__fst__iff,axiom,
    ! [A: $o,P2: produc8937288731615916348od_a_b] :
      ( ( A
        = ( produc2316053142268291992od_a_b @ P2 ) )
      = ( ? [B5: produc2518759752815613485od_a_b] :
            ( P2
            = ( produc1286801380576301484od_a_b @ A @ B5 ) ) ) ) ).

% eq_fst_iff
thf(fact_491_eq__fst__iff,axiom,
    ! [A: fset_l1334069825099621524od_a_b,P2: produc2518759752815613485od_a_b] :
      ( ( A
        = ( produc5739577146777995401od_a_b @ P2 ) )
      = ( ? [B5: list_f1445794025290330138od_a_b] :
            ( P2
            = ( produc6212510018049267869od_a_b @ A @ B5 ) ) ) ) ).

% eq_fst_iff
thf(fact_492_fst__eqD,axiom,
    ! [X3: $o,Y3: list_f1445794025290330138od_a_b,A: $o] :
      ( ( ( produc5358503411717041797od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) )
        = A )
     => ( X3 = A ) ) ).

% fst_eqD
thf(fact_493_fst__eqD,axiom,
    ! [X3: $o,Y3: produc2518759752815613485od_a_b,A: $o] :
      ( ( ( produc2316053142268291992od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) )
        = A )
     => ( X3 = A ) ) ).

% fst_eqD
thf(fact_494_fst__eqD,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b,A: fset_l1334069825099621524od_a_b] :
      ( ( ( produc5739577146777995401od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) )
        = A )
     => ( X3 = A ) ) ).

% fst_eqD
thf(fact_495_fst__conv,axiom,
    ! [X1: $o,X2: list_f1445794025290330138od_a_b] :
      ( ( produc5358503411717041797od_a_b @ ( produc7489420772309856409od_a_b @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_496_fst__conv,axiom,
    ! [X1: $o,X2: produc2518759752815613485od_a_b] :
      ( ( produc2316053142268291992od_a_b @ ( produc1286801380576301484od_a_b @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_497_fst__conv,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,X2: list_f1445794025290330138od_a_b] :
      ( ( produc5739577146777995401od_a_b @ ( produc6212510018049267869od_a_b @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_498_prod__eq__iff,axiom,
    ( ( ^ [Y6: produc2313482920965681321od_a_b,Z6: produc2313482920965681321od_a_b] : ( Y6 = Z6 ) )
    = ( ^ [S: produc2313482920965681321od_a_b,T: produc2313482920965681321od_a_b] :
          ( ( ( produc5358503411717041797od_a_b @ S )
            = ( produc5358503411717041797od_a_b @ T ) )
          & ( ( produc2954343059184910791od_a_b @ S )
            = ( produc2954343059184910791od_a_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_499_prod__eqI,axiom,
    ! [P2: produc2313482920965681321od_a_b,Q3: produc2313482920965681321od_a_b] :
      ( ( ( produc5358503411717041797od_a_b @ P2 )
        = ( produc5358503411717041797od_a_b @ Q3 ) )
     => ( ( ( produc2954343059184910791od_a_b @ P2 )
          = ( produc2954343059184910791od_a_b @ Q3 ) )
       => ( P2 = Q3 ) ) ) ).

% prod_eqI
thf(fact_500_prod_Oexpand,axiom,
    ! [Prod: produc2313482920965681321od_a_b,Prod2: produc2313482920965681321od_a_b] :
      ( ( ( ( produc5358503411717041797od_a_b @ Prod )
          = ( produc5358503411717041797od_a_b @ Prod2 ) )
        & ( ( produc2954343059184910791od_a_b @ Prod )
          = ( produc2954343059184910791od_a_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_501_prefixes__in__list__helper_Osimps_I3_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Yss2: list_l6099054058445139744od_a_b,Res2: produc7877445111886203567od_a_b] :
      ( ( ( X3 = Y3 )
       => ( ( simple4255713849812333767od_a_b @ X3 @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) @ Yss2 ) @ Res2 )
          = ( simple4255713849812333767od_a_b @ X3 @ Yss2 @ ( produc1238543672593294367od_a_b @ ( produc4967132223111445515od_a_b @ Res2 ) @ ( cons_l7290444712290925776od_a_b @ Ys3 @ ( produc909441938071963213od_a_b @ Res2 ) ) ) ) ) )
      & ( ( X3 != Y3 )
       => ( ( simple4255713849812333767od_a_b @ X3 @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) @ Yss2 ) @ Res2 )
          = ( simple4255713849812333767od_a_b @ X3 @ Yss2 @ Res2 ) ) ) ) ).

% prefixes_in_list_helper.simps(3)
thf(fact_502_can__select__def,axiom,
    ( can_se1502477684658679057od_a_b
    = ( ^ [P4: fset_l1334069825099621524od_a_b > $o,A6: set_fs5173440902860351732od_a_b] :
        ? [X5: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X5 @ A6 )
          & ( P4 @ X5 )
          & ! [Y4: fset_l1334069825099621524od_a_b] :
              ( ( ( member361094292949318077od_a_b @ Y4 @ A6 )
                & ( P4 @ Y4 ) )
             => ( Y4 = X5 ) ) ) ) ) ).

% can_select_def
thf(fact_503_can__select__def,axiom,
    ( can_se3446867761079811115od_a_b
    = ( ^ [P4: list_P1467974523212632366od_a_b > $o,A6: set_li6306622547289818894od_a_b] :
        ? [X5: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X5 @ A6 )
          & ( P4 @ X5 )
          & ! [Y4: list_P1467974523212632366od_a_b] :
              ( ( ( member6895035109809442519od_a_b @ Y4 @ A6 )
                & ( P4 @ Y4 ) )
             => ( Y4 = X5 ) ) ) ) ) ).

% can_select_def
thf(fact_504_prefixes__in__list__helper__prop_I1_J,axiom,
    ! [X3: product_prod_a_b,Yss2: list_l8778361445553822004od_a_b,Res2: produc8908614768156765891od_a_b] :
      ( ( produc8768225620527925535od_a_b @ ( simple3641185509419956187od_a_b @ X3 @ Yss2 @ Res2 ) )
      = ( ( produc8768225620527925535od_a_b @ Res2 )
        | ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ ( set_li5045283583078295363od_a_b @ Yss2 ) ) ) ) ).

% prefixes_in_list_helper_prop(1)
thf(fact_505_prefixes__prefixes,axiom,
    ! [Ys3: list_P1467974523212632366od_a_b,Xs2: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Ys3 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) )
     => ( ( member6895035109809442519od_a_b @ Zs @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) )
       => ( ( member6895035109809442519od_a_b @ Ys3 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Zs ) ) )
          | ( member6895035109809442519od_a_b @ Zs @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) ) ) ) ) ).

% prefixes_prefixes
thf(fact_506_surjective__pairing,axiom,
    ! [T2: produc8937288731615916348od_a_b] :
      ( T2
      = ( produc1286801380576301484od_a_b @ ( produc2316053142268291992od_a_b @ T2 ) @ ( produc5480430458100320474od_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_507_surjective__pairing,axiom,
    ! [T2: produc2518759752815613485od_a_b] :
      ( T2
      = ( produc6212510018049267869od_a_b @ ( produc5739577146777995401od_a_b @ T2 ) @ ( produc396176279405262539od_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_508_surjective__pairing,axiom,
    ! [T2: produc2313482920965681321od_a_b] :
      ( T2
      = ( produc7489420772309856409od_a_b @ ( produc5358503411717041797od_a_b @ T2 ) @ ( produc2954343059184910791od_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_509_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8937288731615916348od_a_b] :
      ( Prod
      = ( produc1286801380576301484od_a_b @ ( produc2316053142268291992od_a_b @ Prod ) @ ( produc5480430458100320474od_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_510_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2518759752815613485od_a_b] :
      ( Prod
      = ( produc6212510018049267869od_a_b @ ( produc5739577146777995401od_a_b @ Prod ) @ ( produc396176279405262539od_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_511_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2313482920965681321od_a_b] :
      ( Prod
      = ( produc7489420772309856409od_a_b @ ( produc5358503411717041797od_a_b @ Prod ) @ ( produc2954343059184910791od_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_512_prefixes__Cons_I2_J,axiom,
    ! [X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) ) )
     => ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) ) ) ).

% prefixes_Cons(2)
thf(fact_513_prefixes__Cons_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member7551773913232940227od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) ) )
     => ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ Ys3 ) ) ) ) ).

% prefixes_Cons(2)
thf(fact_514_prefixes__Cons_I1_J,axiom,
    ! [X3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs2 ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) ) )
     => ( X3 = Y3 ) ) ).

% prefixes_Cons(1)
thf(fact_515_prefixes__Cons_I1_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member7551773913232940227od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) ) )
     => ( X3 = Y3 ) ) ).

% prefixes_Cons(1)
thf(fact_516_prefixes__set__Nil,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) ) ).

% prefixes_set_Nil
thf(fact_517_prefixes__set__ob,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,Xss2: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xss2 ) ) )
     => ~ ! [Xs: list_P1467974523212632366od_a_b] :
            ( Xss2
           != ( append5335208823350062147od_a_b @ Xs2 @ Xs ) ) ) ).

% prefixes_set_ob
thf(fact_518_prefixes__prepend,axiom,
    ! [Xs5: list_P1467974523212632366od_a_b,Xs2: list_P1467974523212632366od_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs5 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Ys3 @ Xs5 ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ ( append5335208823350062147od_a_b @ Ys3 @ Xs2 ) ) ) ) ) ).

% prefixes_prepend
thf(fact_519_prefixes__in__list__helper_Oelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_l6099054058445139744od_a_b,Xb2: produc7877445111886203567od_a_b,Y3: produc7877445111886203567od_a_b] :
      ( ( ( simple4255713849812333767od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( ( Xa = nil_li6050065983854590240od_a_b )
         => ( Y3 != Xb2 ) )
       => ( ! [Yss: list_l6099054058445139744od_a_b] :
              ( ( Xa
                = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ Yss ) )
             => ( Y3
               != ( simple4255713849812333767od_a_b @ X3 @ Yss @ ( produc1238543672593294367od_a_b @ $true @ ( produc909441938071963213od_a_b @ Xb2 ) ) ) ) )
         => ~ ! [Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b,Yss: list_l6099054058445139744od_a_b] :
                ( ( Xa
                  = ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ Yss ) )
               => ~ ( ( ( X3 = Y )
                     => ( Y3
                        = ( simple4255713849812333767od_a_b @ X3 @ Yss @ ( produc1238543672593294367od_a_b @ ( produc4967132223111445515od_a_b @ Xb2 ) @ ( cons_l7290444712290925776od_a_b @ Ys @ ( produc909441938071963213od_a_b @ Xb2 ) ) ) ) ) )
                    & ( ( X3 != Y )
                     => ( Y3
                        = ( simple4255713849812333767od_a_b @ X3 @ Yss @ Xb2 ) ) ) ) ) ) ) ) ).

% prefixes_in_list_helper.elims
thf(fact_520_set__concat__elem,axiom,
    ! [X3: product_prod_a_b,Xss2: list_l8778361445553822004od_a_b] :
      ( ( member1426531481828664017od_a_b @ X3 @ ( set_Product_prod_a_b2 @ ( concat6071998534011412713od_a_b @ Xss2 ) ) )
     => ~ ! [Xs3: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ Xs3 @ ( set_li5045283583078295363od_a_b @ Xss2 ) )
           => ~ ( member1426531481828664017od_a_b @ X3 @ ( set_Product_prod_a_b2 @ Xs3 ) ) ) ) ).

% set_concat_elem
thf(fact_521_set__concat__elem,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xss2: list_l6443893005374362810od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ Xss2 ) ) )
     => ~ ! [Xs3: list_l8778361445553822004od_a_b] :
            ( ( member7805385913403518557od_a_b @ Xs3 @ ( set_li2519811128146010313od_a_b @ Xss2 ) )
           => ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs3 ) ) ) ) ).

% set_concat_elem
thf(fact_522_set__concat__elem,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xss2: list_l6099054058445139744od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ Xss2 ) ) )
     => ~ ! [Xs3: list_f1445794025290330138od_a_b] :
            ( ( member7551773913232940227od_a_b @ Xs3 @ ( set_li8217014873844115759od_a_b @ Xss2 ) )
           => ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs3 ) ) ) ) ).

% set_concat_elem
thf(fact_523_listrel1I2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
     => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ X3 @ Ys3 ) ) @ ( listre757946421397414515od_a_b @ R ) ) ) ).

% listrel1I2
thf(fact_524_prefixes__prefix__suffix__ob,axiom,
    ! [A: list_P1467974523212632366od_a_b,B: list_P1467974523212632366od_a_b,C2: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ A @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ ( append5335208823350062147od_a_b @ B @ C2 ) ) ) )
     => ( ~ ( member6895035109809442519od_a_b @ A @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ B ) ) )
       => ~ ! [C3: list_P1467974523212632366od_a_b] :
              ( ? [C4: list_P1467974523212632366od_a_b] :
                  ( C2
                  = ( append5335208823350062147od_a_b @ C3 @ C4 ) )
             => ( ( A
                  = ( append5335208823350062147od_a_b @ B @ C3 ) )
               => ( C3 = nil_Product_prod_a_b ) ) ) ) ) ).

% prefixes_prefix_suffix_ob
thf(fact_525_listrel1I1,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,R: set_Pr2242436922956002695od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R )
     => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Xs2 ) ) @ ( listre757946421397414515od_a_b @ R ) ) ) ).

% listrel1I1
thf(fact_526_Cons__listrel1E1,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
     => ( ! [Y: fset_l1334069825099621524od_a_b] :
            ( ( Ys3
              = ( cons_f6577355434438001738od_a_b @ Y @ Xs2 ) )
           => ~ ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y ) @ R ) )
       => ~ ! [Zs2: list_f1445794025290330138od_a_b] :
              ( ( Ys3
                = ( cons_f6577355434438001738od_a_b @ X3 @ Zs2 ) )
             => ~ ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Zs2 ) @ ( listre757946421397414515od_a_b @ R ) ) ) ) ) ).

% Cons_listrel1E1
thf(fact_527_Cons__listrel1E2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) @ ( listre757946421397414515od_a_b @ R ) )
     => ( ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ X4 @ Ys3 ) )
           => ~ ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Y3 ) @ R ) )
       => ~ ! [Zs2: list_f1445794025290330138od_a_b] :
              ( ( Xs2
                = ( cons_f6577355434438001738od_a_b @ Y3 @ Zs2 ) )
             => ~ ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Zs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) ) ) ) ) ).

% Cons_listrel1E2
thf(fact_528_simple__cg__closure__phase__1__helper_H__False,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ~ ( produc2316053142268291992od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) )
     => ( ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 )
        = ( produc1286801380576301484od_a_b @ $false @ ( produc6212510018049267869od_a_b @ X1 @ Xs2 ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_False
thf(fact_529_map__default_Osimps_I2_J,axiom,
    ! [P2: produc8937288731615916348od_a_b,K3: $o,V2: produc2518759752815613485od_a_b,F2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( ( ( produc2316053142268291992od_a_b @ P2 )
          = K3 )
       => ( ( map_de5747135492376268781od_a_b @ K3 @ V2 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ ( produc5480430458100320474od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc2316053142268291992od_a_b @ P2 )
          = ~ K3 )
       => ( ( map_de5747135492376268781od_a_b @ K3 @ V2 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ P2 @ ( map_de5747135492376268781od_a_b @ K3 @ V2 @ F2 @ Ps2 ) ) ) ) ) ).

% map_default.simps(2)
thf(fact_530_map__default_Osimps_I2_J,axiom,
    ! [P2: produc2518759752815613485od_a_b,K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P5488608094462411443od_a_b] :
      ( ( ( ( produc5739577146777995401od_a_b @ P2 )
          = K3 )
       => ( ( map_de5790008637807865694od_a_b @ K3 @ V2 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ ( F2 @ ( produc396176279405262539od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5739577146777995401od_a_b @ P2 )
         != K3 )
       => ( ( map_de5790008637807865694od_a_b @ K3 @ V2 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ P2 @ ( map_de5790008637807865694od_a_b @ K3 @ V2 @ F2 @ Ps2 ) ) ) ) ) ).

% map_default.simps(2)
thf(fact_531_map__default_Osimps_I2_J,axiom,
    ! [P2: produc2313482920965681321od_a_b,K3: $o,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( ( ( produc5358503411717041797od_a_b @ P2 )
          = K3 )
       => ( ( map_de6169289306397452762od_a_b @ K3 @ V2 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ ( produc2954343059184910791od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5358503411717041797od_a_b @ P2 )
          = ~ K3 )
       => ( ( map_de6169289306397452762od_a_b @ K3 @ V2 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ P2 @ ( map_de6169289306397452762od_a_b @ K3 @ V2 @ F2 @ Ps2 ) ) ) ) ) ).

% map_default.simps(2)
thf(fact_532_listrel1E,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b,Y: fset_l1334069825099621524od_a_b] :
            ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ Y ) @ R )
           => ! [Us: list_f1445794025290330138od_a_b,Vs: list_f1445794025290330138od_a_b] :
                ( ( Xs2
                  = ( append2015155619842375983od_a_b @ Us @ ( cons_f6577355434438001738od_a_b @ X4 @ Vs ) ) )
               => ( Ys3
                 != ( append2015155619842375983od_a_b @ Us @ ( cons_f6577355434438001738od_a_b @ Y @ Vs ) ) ) ) ) ) ).

% listrel1E
thf(fact_533_listrel1I,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,R: set_Pr2242436922956002695od_a_b,Xs2: list_f1445794025290330138od_a_b,Us2: list_f1445794025290330138od_a_b,Vs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R )
     => ( ( Xs2
          = ( append2015155619842375983od_a_b @ Us2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Vs2 ) ) )
       => ( ( Ys3
            = ( append2015155619842375983od_a_b @ Us2 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Vs2 ) ) )
         => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) ) ) ) ) ).

% listrel1I
thf(fact_534_update__with__aux_Osimps_I2_J,axiom,
    ! [P2: produc8937288731615916348od_a_b,K3: $o,V2: produc2518759752815613485od_a_b,F2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( ( ( produc2316053142268291992od_a_b @ P2 )
          = K3 )
       => ( ( update2008830506971281325_a_b_o @ V2 @ K3 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ ( produc5480430458100320474od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc2316053142268291992od_a_b @ P2 )
          = ~ K3 )
       => ( ( update2008830506971281325_a_b_o @ V2 @ K3 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ P2 @ ( update2008830506971281325_a_b_o @ V2 @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_535_update__with__aux_Osimps_I2_J,axiom,
    ! [P2: produc2518759752815613485od_a_b,K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P5488608094462411443od_a_b] :
      ( ( ( ( produc5739577146777995401od_a_b @ P2 )
          = K3 )
       => ( ( update1355849682342953596od_a_b @ V2 @ K3 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ ( F2 @ ( produc396176279405262539od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5739577146777995401od_a_b @ P2 )
         != K3 )
       => ( ( update1355849682342953596od_a_b @ V2 @ K3 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ P2 @ ( update1355849682342953596od_a_b @ V2 @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_536_update__with__aux_Osimps_I2_J,axiom,
    ! [P2: produc2313482920965681321od_a_b,K3: $o,V2: list_f1445794025290330138od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( ( ( produc5358503411717041797od_a_b @ P2 )
          = K3 )
       => ( ( update7744615274700815744_a_b_o @ V2 @ K3 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ ( produc2954343059184910791od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5358503411717041797od_a_b @ P2 )
          = ~ K3 )
       => ( ( update7744615274700815744_a_b_o @ V2 @ K3 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ P2 @ ( update7744615274700815744_a_b_o @ V2 @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_537_Sublist_Osuffixes_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( suffix888123080290511074od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append1675525773727384373od_a_b @ ( suffix888123080290511074od_a_b @ Xs2 ) @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ nil_li6050065983854590240od_a_b ) ) ) ).

% Sublist.suffixes.simps(2)
thf(fact_538_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: $o > produc2518759752815613485od_a_b > $o,X3: $o,Y3: produc2518759752815613485od_a_b,A: produc8937288731615916348od_a_b] :
      ( ( P @ X3 @ Y3 )
     => ( ( A
          = ( produc1286801380576301484od_a_b @ X3 @ Y3 ) )
       => ( P @ ( produc2316053142268291992od_a_b @ A ) @ ( produc5480430458100320474od_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_539_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > $o,X3: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b,A: produc2518759752815613485od_a_b] :
      ( ( P @ X3 @ Y3 )
     => ( ( A
          = ( produc6212510018049267869od_a_b @ X3 @ Y3 ) )
       => ( P @ ( produc5739577146777995401od_a_b @ A ) @ ( produc396176279405262539od_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_540_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: $o > list_f1445794025290330138od_a_b > $o,X3: $o,Y3: list_f1445794025290330138od_a_b,A: produc2313482920965681321od_a_b] :
      ( ( P @ X3 @ Y3 )
     => ( ( A
          = ( produc7489420772309856409od_a_b @ X3 @ Y3 ) )
       => ( P @ ( produc5358503411717041797od_a_b @ A ) @ ( produc2954343059184910791od_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_541_conjI__realizer,axiom,
    ! [P: $o > $o,P2: $o,Q2: produc2518759752815613485od_a_b > $o,Q3: produc2518759752815613485od_a_b] :
      ( ( P @ P2 )
     => ( ( Q2 @ Q3 )
       => ( ( P @ ( produc2316053142268291992od_a_b @ ( produc1286801380576301484od_a_b @ P2 @ Q3 ) ) )
          & ( Q2 @ ( produc5480430458100320474od_a_b @ ( produc1286801380576301484od_a_b @ P2 @ Q3 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_542_conjI__realizer,axiom,
    ! [P: fset_l1334069825099621524od_a_b > $o,P2: fset_l1334069825099621524od_a_b,Q2: list_f1445794025290330138od_a_b > $o,Q3: list_f1445794025290330138od_a_b] :
      ( ( P @ P2 )
     => ( ( Q2 @ Q3 )
       => ( ( P @ ( produc5739577146777995401od_a_b @ ( produc6212510018049267869od_a_b @ P2 @ Q3 ) ) )
          & ( Q2 @ ( produc396176279405262539od_a_b @ ( produc6212510018049267869od_a_b @ P2 @ Q3 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_543_conjI__realizer,axiom,
    ! [P: $o > $o,P2: $o,Q2: list_f1445794025290330138od_a_b > $o,Q3: list_f1445794025290330138od_a_b] :
      ( ( P @ P2 )
     => ( ( Q2 @ Q3 )
       => ( ( P @ ( produc5358503411717041797od_a_b @ ( produc7489420772309856409od_a_b @ P2 @ Q3 ) ) )
          & ( Q2 @ ( produc2954343059184910791od_a_b @ ( produc7489420772309856409od_a_b @ P2 @ Q3 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_544_exI__realizer,axiom,
    ! [P: produc2518759752815613485od_a_b > $o > $o,Y3: produc2518759752815613485od_a_b,X3: $o] :
      ( ( P @ Y3 @ X3 )
     => ( P @ ( produc5480430458100320474od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) ) @ ( produc2316053142268291992od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_545_exI__realizer,axiom,
    ! [P: list_f1445794025290330138od_a_b > fset_l1334069825099621524od_a_b > $o,Y3: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( P @ Y3 @ X3 )
     => ( P @ ( produc396176279405262539od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) ) @ ( produc5739577146777995401od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_546_exI__realizer,axiom,
    ! [P: list_f1445794025290330138od_a_b > $o > $o,Y3: list_f1445794025290330138od_a_b,X3: $o] :
      ( ( P @ Y3 @ X3 )
     => ( P @ ( produc2954343059184910791od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) ) @ ( produc5358503411717041797od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_547_map__entry_Oelims,axiom,
    ! [X3: $o,Xa: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Xb2: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( map_en6063826221664084574od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( ( Xb2 = nil_Pr3614377049866306882od_a_b )
         => ( Y3 != nil_Pr3614377049866306882od_a_b ) )
       => ~ ! [P5: produc8937288731615916348od_a_b,Ps: list_P5302045529885307074od_a_b] :
              ( ( Xb2
                = ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc2316053142268291992od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ ( Xa @ ( produc5480430458100320474od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc2316053142268291992od_a_b @ P5 )
                      = ~ X3 )
                   => ( Y3
                      = ( cons_P7065065391077662962od_a_b @ P5 @ ( map_en6063826221664084574od_a_b @ X3 @ Xa @ Ps ) ) ) ) ) ) ) ) ).

% map_entry.elims
thf(fact_548_map__entry_Oelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xb2: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( map_en3197194780112073295od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( ( Xb2 = nil_Pr1838250474468212019od_a_b )
         => ( Y3 != nil_Pr1838250474468212019od_a_b ) )
       => ~ ! [P5: produc2518759752815613485od_a_b,Ps: list_P5488608094462411443od_a_b] :
              ( ( Xb2
                = ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc5739577146777995401od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ ( Xa @ ( produc396176279405262539od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc5739577146777995401od_a_b @ P5 )
                     != X3 )
                   => ( Y3
                      = ( cons_P7745750895690215651od_a_b @ P5 @ ( map_en3197194780112073295od_a_b @ X3 @ Xa @ Ps ) ) ) ) ) ) ) ) ).

% map_entry.elims
thf(fact_549_map__entry_Oelims,axiom,
    ! [X3: $o,Xa: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xb2: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( map_en6964498282550363979od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( ( Xb2 = nil_Pr7302809325368845999od_a_b )
         => ( Y3 != nil_Pr7302809325368845999od_a_b ) )
       => ~ ! [P5: produc2313482920965681321od_a_b,Ps: list_P3574414722980446895od_a_b] :
              ( ( Xb2
                = ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) )
             => ~ ( ( ( ( produc5358503411717041797od_a_b @ P5 )
                      = X3 )
                   => ( Y3
                      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ ( Xa @ ( produc2954343059184910791od_a_b @ P5 ) ) ) @ Ps ) ) )
                  & ( ( ( produc5358503411717041797od_a_b @ P5 )
                      = ~ X3 )
                   => ( Y3
                      = ( cons_P2672142353023029855od_a_b @ P5 @ ( map_en6964498282550363979od_a_b @ X3 @ Xa @ Ps ) ) ) ) ) ) ) ) ).

% map_entry.elims
thf(fact_550_map__default_Opelims,axiom,
    ! [X3: $o,Xa: produc2518759752815613485od_a_b,Xb2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Xc: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( map_de5747135492376268781od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( accp_P3721793906898479404od_a_b @ map_de8168527554739364662od_a_b @ ( produc854895907051729775od_a_b @ X3 @ ( produc6486408844037598248od_a_b @ Xa @ ( produc5077058152184573444od_a_b @ Xb2 @ Xc ) ) ) )
       => ( ( ( Xc = nil_Pr3614377049866306882od_a_b )
           => ( ( Y3
                = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Xa ) @ nil_Pr3614377049866306882od_a_b ) )
             => ~ ( accp_P3721793906898479404od_a_b @ map_de8168527554739364662od_a_b @ ( produc854895907051729775od_a_b @ X3 @ ( produc6486408844037598248od_a_b @ Xa @ ( produc5077058152184573444od_a_b @ Xb2 @ nil_Pr3614377049866306882od_a_b ) ) ) ) ) )
         => ~ ! [P5: produc8937288731615916348od_a_b,Ps: list_P5302045529885307074od_a_b] :
                ( ( Xc
                  = ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc2316053142268291992od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ ( Xb2 @ ( produc5480430458100320474od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc2316053142268291992od_a_b @ P5 )
                        = ~ X3 )
                     => ( Y3
                        = ( cons_P7065065391077662962od_a_b @ P5 @ ( map_de5747135492376268781od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) )
                 => ~ ( accp_P3721793906898479404od_a_b @ map_de8168527554739364662od_a_b @ ( produc854895907051729775od_a_b @ X3 @ ( produc6486408844037598248od_a_b @ Xa @ ( produc5077058152184573444od_a_b @ Xb2 @ ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ) ).

% map_default.pelims
thf(fact_551_map__default_Opelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_f1445794025290330138od_a_b,Xb2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xc: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( map_de5790008637807865694od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( accp_P3807179030927346758od_a_b @ map_de8082232421929852711od_a_b @ ( produc3504098642911543689od_a_b @ X3 @ ( produc7490164133858390470od_a_b @ Xa @ ( produc6795408122287886773od_a_b @ Xb2 @ Xc ) ) ) )
       => ( ( ( Xc = nil_Pr1838250474468212019od_a_b )
           => ( ( Y3
                = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Xa ) @ nil_Pr1838250474468212019od_a_b ) )
             => ~ ( accp_P3807179030927346758od_a_b @ map_de8082232421929852711od_a_b @ ( produc3504098642911543689od_a_b @ X3 @ ( produc7490164133858390470od_a_b @ Xa @ ( produc6795408122287886773od_a_b @ Xb2 @ nil_Pr1838250474468212019od_a_b ) ) ) ) ) )
         => ~ ! [P5: produc2518759752815613485od_a_b,Ps: list_P5488608094462411443od_a_b] :
                ( ( Xc
                  = ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc5739577146777995401od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ ( Xb2 @ ( produc396176279405262539od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc5739577146777995401od_a_b @ P5 )
                       != X3 )
                     => ( Y3
                        = ( cons_P7745750895690215651od_a_b @ P5 @ ( map_de5790008637807865694od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) )
                 => ~ ( accp_P3807179030927346758od_a_b @ map_de8082232421929852711od_a_b @ ( produc3504098642911543689od_a_b @ X3 @ ( produc7490164133858390470od_a_b @ Xa @ ( produc6795408122287886773od_a_b @ Xb2 @ ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ) ).

% map_default.pelims
thf(fact_552_map__default_Opelims,axiom,
    ! [X3: $o,Xa: list_f1445794025290330138od_a_b,Xb2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xc: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( map_de6169289306397452762od_a_b @ X3 @ Xa @ Xb2 @ Xc )
        = Y3 )
     => ( ( accp_P6900864555062981958od_a_b @ map_de1802405036153999395od_a_b @ ( produc4003124953861756041od_a_b @ X3 @ ( produc302915861673359298od_a_b @ Xa @ ( produc2586240828387333809od_a_b @ Xb2 @ Xc ) ) ) )
       => ( ( ( Xc = nil_Pr7302809325368845999od_a_b )
           => ( ( Y3
                = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Xa ) @ nil_Pr7302809325368845999od_a_b ) )
             => ~ ( accp_P6900864555062981958od_a_b @ map_de1802405036153999395od_a_b @ ( produc4003124953861756041od_a_b @ X3 @ ( produc302915861673359298od_a_b @ Xa @ ( produc2586240828387333809od_a_b @ Xb2 @ nil_Pr7302809325368845999od_a_b ) ) ) ) ) )
         => ~ ! [P5: produc2313482920965681321od_a_b,Ps: list_P3574414722980446895od_a_b] :
                ( ( Xc
                  = ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc5358503411717041797od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ ( Xb2 @ ( produc2954343059184910791od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc5358503411717041797od_a_b @ P5 )
                        = ~ X3 )
                     => ( Y3
                        = ( cons_P2672142353023029855od_a_b @ P5 @ ( map_de6169289306397452762od_a_b @ X3 @ Xa @ Xb2 @ Ps ) ) ) ) )
                 => ~ ( accp_P6900864555062981958od_a_b @ map_de1802405036153999395od_a_b @ ( produc4003124953861756041od_a_b @ X3 @ ( produc302915861673359298od_a_b @ Xa @ ( produc2586240828387333809od_a_b @ Xb2 @ ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ) ).

% map_default.pelims
thf(fact_553_prefixes__in__list__helper_Opelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_l6099054058445139744od_a_b,Xb2: produc7877445111886203567od_a_b,Y3: produc7877445111886203567od_a_b] :
      ( ( ( simple4255713849812333767od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( accp_P5339454666067580242od_a_b @ simple5858505605421243878od_a_b @ ( produc6699211207839096121od_a_b @ X3 @ ( produc883383490548289190od_a_b @ Xa @ Xb2 ) ) )
       => ( ( ( Xa = nil_li6050065983854590240od_a_b )
           => ( ( Y3 = Xb2 )
             => ~ ( accp_P5339454666067580242od_a_b @ simple5858505605421243878od_a_b @ ( produc6699211207839096121od_a_b @ X3 @ ( produc883383490548289190od_a_b @ nil_li6050065983854590240od_a_b @ Xb2 ) ) ) ) )
         => ( ! [Yss: list_l6099054058445139744od_a_b] :
                ( ( Xa
                  = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ Yss ) )
               => ( ( Y3
                    = ( simple4255713849812333767od_a_b @ X3 @ Yss @ ( produc1238543672593294367od_a_b @ $true @ ( produc909441938071963213od_a_b @ Xb2 ) ) ) )
                 => ~ ( accp_P5339454666067580242od_a_b @ simple5858505605421243878od_a_b @ ( produc6699211207839096121od_a_b @ X3 @ ( produc883383490548289190od_a_b @ ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ Yss ) @ Xb2 ) ) ) ) )
           => ~ ! [Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b,Yss: list_l6099054058445139744od_a_b] :
                  ( ( Xa
                    = ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ Yss ) )
                 => ( ( ( ( X3 = Y )
                       => ( Y3
                          = ( simple4255713849812333767od_a_b @ X3 @ Yss @ ( produc1238543672593294367od_a_b @ ( produc4967132223111445515od_a_b @ Xb2 ) @ ( cons_l7290444712290925776od_a_b @ Ys @ ( produc909441938071963213od_a_b @ Xb2 ) ) ) ) ) )
                      & ( ( X3 != Y )
                       => ( Y3
                          = ( simple4255713849812333767od_a_b @ X3 @ Yss @ Xb2 ) ) ) )
                   => ~ ( accp_P5339454666067580242od_a_b @ simple5858505605421243878od_a_b @ ( produc6699211207839096121od_a_b @ X3 @ ( produc883383490548289190od_a_b @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ Yss ) @ Xb2 ) ) ) ) ) ) ) ) ) ).

% prefixes_in_list_helper.pelims
thf(fact_554_map__entry_Osimps_I2_J,axiom,
    ! [P2: produc8937288731615916348od_a_b,K3: $o,F2: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( ( ( produc2316053142268291992od_a_b @ P2 )
          = K3 )
       => ( ( map_en6063826221664084574od_a_b @ K3 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ ( produc5480430458100320474od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc2316053142268291992od_a_b @ P2 )
          = ~ K3 )
       => ( ( map_en6063826221664084574od_a_b @ K3 @ F2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ P2 @ ( map_en6063826221664084574od_a_b @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% map_entry.simps(2)
thf(fact_555_map__entry_Osimps_I2_J,axiom,
    ! [P2: produc2518759752815613485od_a_b,K3: fset_l1334069825099621524od_a_b,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P5488608094462411443od_a_b] :
      ( ( ( ( produc5739577146777995401od_a_b @ P2 )
          = K3 )
       => ( ( map_en3197194780112073295od_a_b @ K3 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ ( F2 @ ( produc396176279405262539od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5739577146777995401od_a_b @ P2 )
         != K3 )
       => ( ( map_en3197194780112073295od_a_b @ K3 @ F2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ P2 @ ( map_en3197194780112073295od_a_b @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% map_entry.simps(2)
thf(fact_556_map__entry_Osimps_I2_J,axiom,
    ! [P2: produc2313482920965681321od_a_b,K3: $o,F2: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( ( ( produc5358503411717041797od_a_b @ P2 )
          = K3 )
       => ( ( map_en6964498282550363979od_a_b @ K3 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ ( produc2954343059184910791od_a_b @ P2 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc5358503411717041797od_a_b @ P2 )
          = ~ K3 )
       => ( ( map_en6964498282550363979od_a_b @ K3 @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ P2 @ ( map_en6964498282550363979od_a_b @ K3 @ F2 @ Ps2 ) ) ) ) ) ).

% map_entry.simps(2)
thf(fact_557_exE__realizer_H,axiom,
    ! [P: list_f1445794025290330138od_a_b > $o > $o,P2: produc2313482920965681321od_a_b] :
      ( ( P @ ( produc2954343059184910791od_a_b @ P2 ) @ ( produc5358503411717041797od_a_b @ P2 ) )
     => ~ ! [X4: $o,Y: list_f1445794025290330138od_a_b] :
            ~ ( P @ Y @ X4 ) ) ).

% exE_realizer'
thf(fact_558_map__entry_Opelims,axiom,
    ! [X3: $o,Xa: produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,Xb2: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( map_en6063826221664084574od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( accp_P8597022368939085008od_a_b @ map_en7425035617249803781od_a_b @ ( produc1988051149204433939od_a_b @ X3 @ ( produc5077058152184573444od_a_b @ Xa @ Xb2 ) ) )
       => ( ( ( Xb2 = nil_Pr3614377049866306882od_a_b )
           => ( ( Y3 = nil_Pr3614377049866306882od_a_b )
             => ~ ( accp_P8597022368939085008od_a_b @ map_en7425035617249803781od_a_b @ ( produc1988051149204433939od_a_b @ X3 @ ( produc5077058152184573444od_a_b @ Xa @ nil_Pr3614377049866306882od_a_b ) ) ) ) )
         => ~ ! [P5: produc8937288731615916348od_a_b,Ps: list_P5302045529885307074od_a_b] :
                ( ( Xb2
                  = ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc2316053142268291992od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ ( Xa @ ( produc5480430458100320474od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc2316053142268291992od_a_b @ P5 )
                        = ~ X3 )
                     => ( Y3
                        = ( cons_P7065065391077662962od_a_b @ P5 @ ( map_en6063826221664084574od_a_b @ X3 @ Xa @ Ps ) ) ) ) )
                 => ~ ( accp_P8597022368939085008od_a_b @ map_en7425035617249803781od_a_b @ ( produc1988051149204433939od_a_b @ X3 @ ( produc5077058152184573444od_a_b @ Xa @ ( cons_P7065065391077662962od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ).

% map_entry.pelims
thf(fact_559_map__entry_Opelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xb2: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( map_en3197194780112073295od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( accp_P5581439537166740605od_a_b @ map_en202605468252318070od_a_b @ ( produc1429321633257256512od_a_b @ X3 @ ( produc6795408122287886773od_a_b @ Xa @ Xb2 ) ) )
       => ( ( ( Xb2 = nil_Pr1838250474468212019od_a_b )
           => ( ( Y3 = nil_Pr1838250474468212019od_a_b )
             => ~ ( accp_P5581439537166740605od_a_b @ map_en202605468252318070od_a_b @ ( produc1429321633257256512od_a_b @ X3 @ ( produc6795408122287886773od_a_b @ Xa @ nil_Pr1838250474468212019od_a_b ) ) ) ) )
         => ~ ! [P5: produc2518759752815613485od_a_b,Ps: list_P5488608094462411443od_a_b] :
                ( ( Xb2
                  = ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc5739577146777995401od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ ( Xa @ ( produc396176279405262539od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc5739577146777995401od_a_b @ P5 )
                       != X3 )
                     => ( Y3
                        = ( cons_P7745750895690215651od_a_b @ P5 @ ( map_en3197194780112073295od_a_b @ X3 @ Xa @ Ps ) ) ) ) )
                 => ~ ( accp_P5581439537166740605od_a_b @ map_en202605468252318070od_a_b @ ( produc1429321633257256512od_a_b @ X3 @ ( produc6795408122287886773od_a_b @ Xa @ ( cons_P7745750895690215651od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ).

% map_entry.pelims
thf(fact_560_map__entry_Opelims,axiom,
    ! [X3: $o,Xa: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,Xb2: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( map_en6964498282550363979od_a_b @ X3 @ Xa @ Xb2 )
        = Y3 )
     => ( ( accp_P1594159262757799549od_a_b @ map_en6339584017969766386od_a_b @ ( produc6096372360267053632od_a_b @ X3 @ ( produc2586240828387333809od_a_b @ Xa @ Xb2 ) ) )
       => ( ( ( Xb2 = nil_Pr7302809325368845999od_a_b )
           => ( ( Y3 = nil_Pr7302809325368845999od_a_b )
             => ~ ( accp_P1594159262757799549od_a_b @ map_en6339584017969766386od_a_b @ ( produc6096372360267053632od_a_b @ X3 @ ( produc2586240828387333809od_a_b @ Xa @ nil_Pr7302809325368845999od_a_b ) ) ) ) )
         => ~ ! [P5: produc2313482920965681321od_a_b,Ps: list_P3574414722980446895od_a_b] :
                ( ( Xb2
                  = ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) )
               => ( ( ( ( ( produc5358503411717041797od_a_b @ P5 )
                        = X3 )
                     => ( Y3
                        = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ ( Xa @ ( produc2954343059184910791od_a_b @ P5 ) ) ) @ Ps ) ) )
                    & ( ( ( produc5358503411717041797od_a_b @ P5 )
                        = ~ X3 )
                     => ( Y3
                        = ( cons_P2672142353023029855od_a_b @ P5 @ ( map_en6964498282550363979od_a_b @ X3 @ Xa @ Ps ) ) ) ) )
                 => ~ ( accp_P1594159262757799549od_a_b @ map_en6339584017969766386od_a_b @ ( produc6096372360267053632od_a_b @ X3 @ ( produc2586240828387333809od_a_b @ Xa @ ( cons_P2672142353023029855od_a_b @ P5 @ Ps ) ) ) ) ) ) ) ) ) ).

% map_entry.pelims
thf(fact_561_SuccI,axiom,
    ! [Kl: list_l8778361445553822004od_a_b,K3: list_P1467974523212632366od_a_b,Kl2: set_li948167846089608596od_a_b] :
      ( ( member7805385913403518557od_a_b @ ( append7557446516274476873od_a_b @ Kl @ ( cons_l907386227682280420od_a_b @ K3 @ nil_li8635777946366267444od_a_b ) ) @ Kl2 )
     => ( member6895035109809442519od_a_b @ K3 @ ( bNF_Gr5295578694846582473od_a_b @ Kl2 @ Kl ) ) ) ).

% SuccI
thf(fact_562_SuccI,axiom,
    ! [Kl: list_P1467974523212632366od_a_b,K3: product_prod_a_b,Kl2: set_li6306622547289818894od_a_b] :
      ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Kl @ ( cons_P7316939131009794654od_a_b @ K3 @ nil_Product_prod_a_b ) ) @ Kl2 )
     => ( member1426531481828664017od_a_b @ K3 @ ( bNF_Gr1699325108002784195od_a_b @ Kl2 @ Kl ) ) ) ).

% SuccI
thf(fact_563_SuccI,axiom,
    ! [Kl: list_f1445794025290330138od_a_b,K3: fset_l1334069825099621524od_a_b,Kl2: set_li7540826859550765818od_a_b] :
      ( ( member7551773913232940227od_a_b @ ( append2015155619842375983od_a_b @ Kl @ ( cons_f6577355434438001738od_a_b @ K3 @ nil_fs4581119677382125722od_a_b ) ) @ Kl2 )
     => ( member361094292949318077od_a_b @ K3 @ ( bNF_Gr6941718835010197679od_a_b @ Kl2 @ Kl ) ) ) ).

% SuccI
thf(fact_564_SuccD,axiom,
    ! [K3: product_prod_a_b,Kl2: set_li6306622547289818894od_a_b,Kl: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ K3 @ ( bNF_Gr1699325108002784195od_a_b @ Kl2 @ Kl ) )
     => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Kl @ ( cons_P7316939131009794654od_a_b @ K3 @ nil_Product_prod_a_b ) ) @ Kl2 ) ) ).

% SuccD
thf(fact_565_SuccD,axiom,
    ! [K3: list_P1467974523212632366od_a_b,Kl2: set_li948167846089608596od_a_b,Kl: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ K3 @ ( bNF_Gr5295578694846582473od_a_b @ Kl2 @ Kl ) )
     => ( member7805385913403518557od_a_b @ ( append7557446516274476873od_a_b @ Kl @ ( cons_l907386227682280420od_a_b @ K3 @ nil_li8635777946366267444od_a_b ) ) @ Kl2 ) ) ).

% SuccD
thf(fact_566_SuccD,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,Kl2: set_li7540826859550765818od_a_b,Kl: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ K3 @ ( bNF_Gr6941718835010197679od_a_b @ Kl2 @ Kl ) )
     => ( member7551773913232940227od_a_b @ ( append2015155619842375983od_a_b @ Kl @ ( cons_f6577355434438001738od_a_b @ K3 @ nil_fs4581119677382125722od_a_b ) ) @ Kl2 ) ) ).

% SuccD
thf(fact_567_map__ran__Cons__sel,axiom,
    ! [F2: $o > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,P2: produc2313482920965681321od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( map_ra7768207298033780897od_a_b @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ ( produc5358503411717041797od_a_b @ P2 ) @ ( F2 @ ( produc5358503411717041797od_a_b @ P2 ) @ ( produc2954343059184910791od_a_b @ P2 ) ) ) @ ( map_ra7768207298033780897od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_Cons_sel
thf(fact_568_map__ran__Cons__sel,axiom,
    ! [F2: $o > list_f1445794025290330138od_a_b > produc2518759752815613485od_a_b,P2: produc2313482920965681321od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( map_ra2300569569700106676od_a_b @ F2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ ( produc5358503411717041797od_a_b @ P2 ) @ ( F2 @ ( produc5358503411717041797od_a_b @ P2 ) @ ( produc2954343059184910791od_a_b @ P2 ) ) ) @ ( map_ra2300569569700106676od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_Cons_sel
thf(fact_569_prefixes__set__Cons__insert,axiom,
    ! [W: list_f1445794025290330138od_a_b,Xy: fset_l1334069825099621524od_a_b] :
      ( ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ ( append2015155619842375983od_a_b @ W @ ( cons_f6577355434438001738od_a_b @ Xy @ nil_fs4581119677382125722od_a_b ) ) ) )
      = ( insert38576201109616106od_a_b @ ( append2015155619842375983od_a_b @ W @ ( cons_f6577355434438001738od_a_b @ Xy @ nil_fs4581119677382125722od_a_b ) ) @ ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ W ) ) ) ) ).

% prefixes_set_Cons_insert
thf(fact_570_list_Osimps_I15_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
      = ( insert3249498615411298916od_a_b @ X21 @ ( set_fs4298891544546585641od_a_b @ X22 ) ) ) ).

% list.simps(15)
thf(fact_571_map__ran__simps_I2_J,axiom,
    ! [F2: $o > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,K3: $o,V2: list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( map_ra7768207298033780897od_a_b @ F2 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V2 ) @ Ps2 ) )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ K3 @ V2 ) ) @ ( map_ra7768207298033780897od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_simps(2)
thf(fact_572_map__ran__simps_I2_J,axiom,
    ! [F2: $o > list_f1445794025290330138od_a_b > produc2518759752815613485od_a_b,K3: $o,V2: list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( map_ra2300569569700106676od_a_b @ F2 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V2 ) @ Ps2 ) )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ K3 @ V2 ) ) @ ( map_ra2300569569700106676od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_simps(2)
thf(fact_573_map__ran__simps_I2_J,axiom,
    ! [F2: $o > produc2518759752815613485od_a_b > list_f1445794025290330138od_a_b,K3: $o,V2: produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( map_ra7039145154704061134od_a_b @ F2 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V2 ) @ Ps2 ) )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ ( F2 @ K3 @ V2 ) ) @ ( map_ra7039145154704061134od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_simps(2)
thf(fact_574_map__ran__simps_I2_J,axiom,
    ! [F2: $o > produc2518759752815613485od_a_b > produc2518759752815613485od_a_b,K3: $o,V2: produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( map_ra8397445362931850465od_a_b @ F2 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V2 ) @ Ps2 ) )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ ( F2 @ K3 @ V2 ) ) @ ( map_ra8397445362931850465od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_simps(2)
thf(fact_575_map__ran__simps_I2_J,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b,K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,Ps2: list_P5488608094462411443od_a_b] :
      ( ( map_ra104177868202533149od_a_b @ F2 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V2 ) @ Ps2 ) )
      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ ( F2 @ K3 @ V2 ) ) @ ( map_ra104177868202533149od_a_b @ F2 @ Ps2 ) ) ) ).

% map_ran_simps(2)
thf(fact_576_List_Oset__insert,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( insert2610919176168914352od_a_b @ X3 @ Xs2 ) )
      = ( insert3249498615411298916od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% List.set_insert
thf(fact_577_empty__Shift,axiom,
    ! [Kl2: set_li7540826859550765818od_a_b,K3: fset_l1334069825099621524od_a_b] :
      ( ( member7551773913232940227od_a_b @ nil_fs4581119677382125722od_a_b @ Kl2 )
     => ( ( member361094292949318077od_a_b @ K3 @ ( bNF_Gr6941718835010197679od_a_b @ Kl2 @ nil_fs4581119677382125722od_a_b ) )
       => ( member7551773913232940227od_a_b @ nil_fs4581119677382125722od_a_b @ ( bNF_Gr9187693764577137459od_a_b @ Kl2 @ K3 ) ) ) ) ).

% empty_Shift
thf(fact_578_empty__Shift,axiom,
    ! [Kl2: set_li948167846089608596od_a_b,K3: list_P1467974523212632366od_a_b] :
      ( ( member7805385913403518557od_a_b @ nil_li8635777946366267444od_a_b @ Kl2 )
     => ( ( member6895035109809442519od_a_b @ K3 @ ( bNF_Gr5295578694846582473od_a_b @ Kl2 @ nil_li8635777946366267444od_a_b ) )
       => ( member7805385913403518557od_a_b @ nil_li8635777946366267444od_a_b @ ( bNF_Gr1899121854005402445od_a_b @ Kl2 @ K3 ) ) ) ) ).

% empty_Shift
thf(fact_579_empty__Shift,axiom,
    ! [Kl2: set_li6306622547289818894od_a_b,K3: product_prod_a_b] :
      ( ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ Kl2 )
     => ( ( member1426531481828664017od_a_b @ K3 @ ( bNF_Gr1699325108002784195od_a_b @ Kl2 @ nil_Product_prod_a_b ) )
       => ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ ( bNF_Gr6004602585737257543od_a_b @ Kl2 @ K3 ) ) ) ) ).

% empty_Shift
thf(fact_580_Succ__Shift,axiom,
    ! [Kl2: set_li7540826859550765818od_a_b,K3: fset_l1334069825099621524od_a_b,Kl: list_f1445794025290330138od_a_b] :
      ( ( bNF_Gr6941718835010197679od_a_b @ ( bNF_Gr9187693764577137459od_a_b @ Kl2 @ K3 ) @ Kl )
      = ( bNF_Gr6941718835010197679od_a_b @ Kl2 @ ( cons_f6577355434438001738od_a_b @ K3 @ Kl ) ) ) ).

% Succ_Shift
thf(fact_581_suffixes_Opelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_l6099054058445139744od_a_b] :
      ( ( ( suffix4455840324713621126od_a_b @ X3 )
        = Y3 )
     => ( ( accp_l5651743518013118883od_a_b @ suffix2477028357949749991od_a_b @ X3 )
       => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
           => ( ( Y3
                = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ nil_li6050065983854590240od_a_b ) )
             => ~ ( accp_l5651743518013118883od_a_b @ suffix2477028357949749991od_a_b @ nil_fs4581119677382125722od_a_b ) ) )
         => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
                ( ( X3
                  = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
               => ( ( Y3
                    = ( append1675525773727384373od_a_b @ ( suffix4455840324713621126od_a_b @ Xs3 ) @ ( cons_l7290444712290925776od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ nil_li6050065983854590240od_a_b ) ) )
                 => ~ ( accp_l5651743518013118883od_a_b @ suffix2477028357949749991od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ) ) ) ) ).

% suffixes.pelims
thf(fact_582_prod_Oswap__def,axiom,
    ( produc4657918789097900469_a_b_o
    = ( ^ [P6: produc2087898033365526821_a_b_o] : ( produc7489420772309856409od_a_b @ ( produc9054741096147377475_a_b_o @ P6 ) @ ( produc2235529411824732673_a_b_o @ P6 ) ) ) ) ).

% prod.swap_def
thf(fact_583_prod_Oswap__def,axiom,
    ( produc4156728193461308642_a_b_o
    = ( ^ [P6: produc7103389596696383826_a_b_o] : ( produc1286801380576301484od_a_b @ ( produc208704087999850096_a_b_o @ P6 ) @ ( produc6267698809022597422_a_b_o @ P6 ) ) ) ) ).

% prod.swap_def
thf(fact_584_prod_Oswap__def,axiom,
    ( produc2460326553103436337od_a_b
    = ( ^ [P6: produc8628745980099788577od_a_b] : ( produc6212510018049267869od_a_b @ ( produc1533857828010277567od_a_b @ P6 ) @ ( produc6877258695383010429od_a_b @ P6 ) ) ) ) ).

% prod.swap_def
thf(fact_585_prod_Oswap__def,axiom,
    ( produc7780892788990209593od_a_b
    = ( ^ [P6: produc2313482920965681321od_a_b] : ( produc4366446772417547285_a_b_o @ ( produc2954343059184910791od_a_b @ P6 ) @ ( produc5358503411717041797od_a_b @ P6 ) ) ) ) ).

% prod.swap_def
thf(fact_586_delete__aux_Opelims,axiom,
    ! [X3: $o,Xa: list_P3574414722980446895od_a_b,Y3: list_P3574414722980446895od_a_b] :
      ( ( ( delete6197099393584013480od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( accp_P7875516549118069959od_a_b @ delete8919263077593111253od_a_b @ ( produc336006402058072110od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr7302809325368845999od_a_b )
           => ( ( Y3 = nil_Pr7302809325368845999od_a_b )
             => ~ ( accp_P7875516549118069959od_a_b @ delete8919263077593111253od_a_b @ ( produc336006402058072110od_a_b @ X3 @ nil_Pr7302809325368845999od_a_b ) ) ) )
         => ~ ! [K2: $o,V: list_f1445794025290330138od_a_b,Xs3: list_P3574414722980446895od_a_b] :
                ( ( Xa
                  = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ Xs3 ) )
               => ( ( ( ( X3 = K2 )
                     => ( Y3 = Xs3 ) )
                    & ( ( X3 = ~ K2 )
                     => ( Y3
                        = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ ( delete6197099393584013480od_a_b @ X3 @ Xs3 ) ) ) ) )
                 => ~ ( accp_P7875516549118069959od_a_b @ delete8919263077593111253od_a_b @ ( produc336006402058072110od_a_b @ X3 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.pelims
thf(fact_587_delete__aux_Opelims,axiom,
    ! [X3: $o,Xa: list_P5302045529885307074od_a_b,Y3: list_P5302045529885307074od_a_b] :
      ( ( ( delete3629537940609567931od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( accp_P4593430778603979354od_a_b @ delete2995761608754898920od_a_b @ ( produc7187370450469132609od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr3614377049866306882od_a_b )
           => ( ( Y3 = nil_Pr3614377049866306882od_a_b )
             => ~ ( accp_P4593430778603979354od_a_b @ delete2995761608754898920od_a_b @ ( produc7187370450469132609od_a_b @ X3 @ nil_Pr3614377049866306882od_a_b ) ) ) )
         => ~ ! [K2: $o,V: produc2518759752815613485od_a_b,Xs3: list_P5302045529885307074od_a_b] :
                ( ( Xa
                  = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ Xs3 ) )
               => ( ( ( ( X3 = K2 )
                     => ( Y3 = Xs3 ) )
                    & ( ( X3 = ~ K2 )
                     => ( Y3
                        = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ ( delete3629537940609567931od_a_b @ X3 @ Xs3 ) ) ) ) )
                 => ~ ( accp_P4593430778603979354od_a_b @ delete2995761608754898920od_a_b @ ( produc7187370450469132609od_a_b @ X3 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.pelims
thf(fact_588_delete__aux_Opelims,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xa: list_P5488608094462411443od_a_b,Y3: list_P5488608094462411443od_a_b] :
      ( ( ( delete3925988326758032172od_a_b @ X3 @ Xa )
        = Y3 )
     => ( ( accp_P8600931742201088847od_a_b @ delete7018282185866685657od_a_b @ ( produc5841801390880218294od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr1838250474468212019od_a_b )
           => ( ( Y3 = nil_Pr1838250474468212019od_a_b )
             => ~ ( accp_P8600931742201088847od_a_b @ delete7018282185866685657od_a_b @ ( produc5841801390880218294od_a_b @ X3 @ nil_Pr1838250474468212019od_a_b ) ) ) )
         => ~ ! [K2: fset_l1334069825099621524od_a_b,V: list_f1445794025290330138od_a_b,Xs3: list_P5488608094462411443od_a_b] :
                ( ( Xa
                  = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ Xs3 ) )
               => ( ( ( ( X3 = K2 )
                     => ( Y3 = Xs3 ) )
                    & ( ( X3 != K2 )
                     => ( Y3
                        = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ ( delete3925988326758032172od_a_b @ X3 @ Xs3 ) ) ) ) )
                 => ~ ( accp_P8600931742201088847od_a_b @ delete7018282185866685657od_a_b @ ( produc5841801390880218294od_a_b @ X3 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K2 @ V ) @ Xs3 ) ) ) ) ) ) ) ) ).

% delete_aux.pelims
thf(fact_589_swap__simp,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: $o] :
      ( ( produc4657918789097900469_a_b_o @ ( produc4366446772417547285_a_b_o @ X3 @ Y3 ) )
      = ( produc7489420772309856409od_a_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_590_swap__simp,axiom,
    ! [X3: produc2518759752815613485od_a_b,Y3: $o] :
      ( ( produc4156728193461308642_a_b_o @ ( produc5238447047330606914_a_b_o @ X3 @ Y3 ) )
      = ( produc1286801380576301484od_a_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_591_swap__simp,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( produc2460326553103436337od_a_b @ ( produc7350191566654282897od_a_b @ X3 @ Y3 ) )
      = ( produc6212510018049267869od_a_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_592_swap__simp,axiom,
    ! [X3: $o,Y3: list_f1445794025290330138od_a_b] :
      ( ( produc7780892788990209593od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) )
      = ( produc4366446772417547285_a_b_o @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_593_swap__simp,axiom,
    ! [X3: $o,Y3: produc2518759752815613485od_a_b] :
      ( ( produc205082526707003212od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) )
      = ( produc5238447047330606914_a_b_o @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_594_swap__simp,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( produc1322645004498421309od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) )
      = ( produc7350191566654282897od_a_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_595_fst__swap,axiom,
    ! [X3: produc2313482920965681321od_a_b] :
      ( ( produc2235529411824732673_a_b_o @ ( produc7780892788990209593od_a_b @ X3 ) )
      = ( produc2954343059184910791od_a_b @ X3 ) ) ).

% fst_swap
thf(fact_596_snd__swap,axiom,
    ! [X3: produc2087898033365526821_a_b_o] :
      ( ( produc2954343059184910791od_a_b @ ( produc4657918789097900469_a_b_o @ X3 ) )
      = ( produc2235529411824732673_a_b_o @ X3 ) ) ).

% snd_swap
thf(fact_597_ShiftD,axiom,
    ! [Kl: list_P1467974523212632366od_a_b,Kl2: set_li6306622547289818894od_a_b,K3: product_prod_a_b] :
      ( ( member6895035109809442519od_a_b @ Kl @ ( bNF_Gr6004602585737257543od_a_b @ Kl2 @ K3 ) )
     => ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ K3 @ Kl ) @ Kl2 ) ) ).

% ShiftD
thf(fact_598_ShiftD,axiom,
    ! [Kl: list_f1445794025290330138od_a_b,Kl2: set_li7540826859550765818od_a_b,K3: fset_l1334069825099621524od_a_b] :
      ( ( member7551773913232940227od_a_b @ Kl @ ( bNF_Gr9187693764577137459od_a_b @ Kl2 @ K3 ) )
     => ( member7551773913232940227od_a_b @ ( cons_f6577355434438001738od_a_b @ K3 @ Kl ) @ Kl2 ) ) ).

% ShiftD
thf(fact_599_sublists_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( sublis7484350909052568364od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append1675525773727384373od_a_b @ ( sublis7484350909052568364od_a_b @ Xs2 ) @ ( map_li2254913030204620100od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 ) @ ( prefix4612422245637881633od_a_b @ Xs2 ) ) ) ) ).

% sublists.simps(2)
thf(fact_600_butlast__snoc,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( butlas6970048242682811878od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) )
      = Xs2 ) ).

% butlast_snoc
thf(fact_601_list_Osimps_I9_J,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( map_fs8651439882968028996od_a_b @ F2 @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
      = ( cons_f6577355434438001738od_a_b @ ( F2 @ X21 ) @ ( map_fs8651439882968028996od_a_b @ F2 @ X22 ) ) ) ).

% list.simps(9)
thf(fact_602_Cons__eq__map__D,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
        = ( map_fs8651439882968028996od_a_b @ F2 @ Ys3 ) )
     => ? [Z4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( ( Ys3
            = ( cons_f6577355434438001738od_a_b @ Z4 @ Zs2 ) )
          & ( X3
            = ( F2 @ Z4 ) )
          & ( Xs2
            = ( map_fs8651439882968028996od_a_b @ F2 @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_603_map__eq__Cons__D,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 )
        = ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
     => ? [Z4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b] :
          ( ( Xs2
            = ( cons_f6577355434438001738od_a_b @ Z4 @ Zs2 ) )
          & ( ( F2 @ Z4 )
            = Y3 )
          & ( ( map_fs8651439882968028996od_a_b @ F2 @ Zs2 )
            = Ys3 ) ) ) ).

% map_eq_Cons_D
thf(fact_604_Cons__eq__map__conv,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 )
        = ( map_fs8651439882968028996od_a_b @ F2 @ Ys3 ) )
      = ( ? [Z5: fset_l1334069825099621524od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( Ys3
              = ( cons_f6577355434438001738od_a_b @ Z5 @ Zs3 ) )
            & ( X3
              = ( F2 @ Z5 ) )
            & ( Xs2
              = ( map_fs8651439882968028996od_a_b @ F2 @ Zs3 ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_605_map__eq__Cons__conv,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 )
        = ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
      = ( ? [Z5: fset_l1334069825099621524od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ Z5 @ Zs3 ) )
            & ( ( F2 @ Z5 )
              = Y3 )
            & ( ( map_fs8651439882968028996od_a_b @ F2 @ Zs3 )
              = Ys3 ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_606_map__idI,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,F2: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
         => ( ( F2 @ X4 )
            = X4 ) )
     => ( ( map_li1070312879311380292od_a_b @ F2 @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_607_map__idI,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( F2 @ X4 )
            = X4 ) )
     => ( ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_608_list_Omap__ident__strong,axiom,
    ! [T2: list_l8778361445553822004od_a_b,F2: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b] :
      ( ! [Z4: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ Z4 @ ( set_li5045283583078295363od_a_b @ T2 ) )
         => ( ( F2 @ Z4 )
            = Z4 ) )
     => ( ( map_li1070312879311380292od_a_b @ F2 @ T2 )
        = T2 ) ) ).

% list.map_ident_strong
thf(fact_609_list_Omap__ident__strong,axiom,
    ! [T2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b] :
      ( ! [Z4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ Z4 @ ( set_fs4298891544546585641od_a_b @ T2 ) )
         => ( ( F2 @ Z4 )
            = Z4 ) )
     => ( ( map_fs8651439882968028996od_a_b @ F2 @ T2 )
        = T2 ) ) ).

% list.map_ident_strong
thf(fact_610_list__map__source__elem,axiom,
    ! [X3: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( map_fs2600689390591810526od_a_b @ F2 @ Xs2 ) ) )
     => ? [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( X3
            = ( F2 @ X4 ) ) ) ) ).

% list_map_source_elem
thf(fact_611_list__map__source__elem,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) ) )
     => ? [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( X3
            = ( F2 @ X4 ) ) ) ) ).

% list_map_source_elem
thf(fact_612_set__map__elem,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,F2: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( map_li1070312879311380292od_a_b @ F2 @ Xs2 ) ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b] :
            ( ( Y3
              = ( F2 @ X4 ) )
           => ~ ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% set_map_elem
thf(fact_613_set__map__elem,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( map_fs2600689390591810526od_a_b @ F2 @ Xs2 ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( Y3
              = ( F2 @ X4 ) )
           => ~ ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% set_map_elem
thf(fact_614_set__map__elem,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,F2: list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( map_li7547266996134490026od_a_b @ F2 @ Xs2 ) ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b] :
            ( ( Y3
              = ( F2 @ X4 ) )
           => ~ ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% set_map_elem
thf(fact_615_set__map__elem,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( Y3
              = ( F2 @ X4 ) )
           => ~ ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% set_map_elem
thf(fact_616_map__set,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,F2: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( member6895035109809442519od_a_b @ ( F2 @ X3 ) @ ( set_li5045283583078295363od_a_b @ ( map_li1070312879311380292od_a_b @ F2 @ Xs2 ) ) ) ) ).

% map_set
thf(fact_617_map__set,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,F2: list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( member361094292949318077od_a_b @ ( F2 @ X3 ) @ ( set_fs4298891544546585641od_a_b @ ( map_li7547266996134490026od_a_b @ F2 @ Xs2 ) ) ) ) ).

% map_set
thf(fact_618_map__set,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( member6895035109809442519od_a_b @ ( F2 @ X3 ) @ ( set_li5045283583078295363od_a_b @ ( map_fs2600689390591810526od_a_b @ F2 @ Xs2 ) ) ) ) ).

% map_set
thf(fact_619_map__set,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( member361094292949318077od_a_b @ ( F2 @ X3 ) @ ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) ) ) ) ).

% map_set
thf(fact_620_in__set__butlastD,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( butlas2591555278381536128od_a_b @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% in_set_butlastD
thf(fact_621_in__set__butlastD,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% in_set_butlastD
thf(fact_622_set__concat__map__elem,axiom,
    ! [X3: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_l8778361445553822004od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ ( map_fs6872359466567453668od_a_b @ F2 @ Xs2 ) ) ) )
     => ? [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% set_concat_map_elem
thf(fact_623_set__concat__map__elem,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ ( map_fs7724969689208736458od_a_b @ F2 @ Xs2 ) ) ) )
     => ? [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
          & ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% set_concat_map_elem
thf(fact_624_concat__map__elem,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,F2: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ ( map_li5768186579733914698od_a_b @ F2 @ Xs2 ) ) ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
           => ~ ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% concat_map_elem
thf(fact_625_concat__map__elem,axiom,
    ! [Y3: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_l8778361445553822004od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ ( map_fs6872359466567453668od_a_b @ F2 @ Xs2 ) ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ~ ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% concat_map_elem
thf(fact_626_concat__map__elem,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,F2: list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ ( map_li1484870096797251632od_a_b @ F2 @ Xs2 ) ) ) )
     => ~ ! [X4: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
           => ~ ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% concat_map_elem
thf(fact_627_concat__map__elem,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ ( map_fs7724969689208736458od_a_b @ F2 @ Xs2 ) ) ) )
     => ~ ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ~ ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ ( F2 @ X4 ) ) ) ) ) ).

% concat_map_elem
thf(fact_628_butlast_Osimps_I2_J,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ( Xs2 = nil_fs4581119677382125722od_a_b )
       => ( ( butlas6970048242682811878od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = nil_fs4581119677382125722od_a_b ) )
      & ( ( Xs2 != nil_fs4581119677382125722od_a_b )
       => ( ( butlas6970048242682811878od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = ( cons_f6577355434438001738od_a_b @ X3 @ ( butlas6970048242682811878od_a_b @ Xs2 ) ) ) ) ) ).

% butlast.simps(2)
thf(fact_629_in__set__butlast__appendI,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Ys3: list_l8778361445553822004od_a_b] :
      ( ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( butlas2591555278381536128od_a_b @ Xs2 ) ) )
        | ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( butlas2591555278381536128od_a_b @ Ys3 ) ) ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( butlas2591555278381536128od_a_b @ ( append7557446516274476873od_a_b @ Xs2 @ Ys3 ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_630_in__set__butlast__appendI,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) ) )
        | ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( butlas6970048242682811878od_a_b @ Ys3 ) ) ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( butlas6970048242682811878od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_631_prefixes__butlast__is__prefix,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ ( butlas8142365734376493050od_a_b @ Xs2 ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) ) ).

% prefixes_butlast_is_prefix
thf(fact_632_set__map__subset,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,T2: list_P1467974523212632366od_a_b,F2: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( member6895035109809442519od_a_b @ T2 @ ( set_li5045283583078295363od_a_b @ ( map_li1070312879311380292od_a_b @ F2 @ ( cons_l907386227682280420od_a_b @ X3 @ nil_li8635777946366267444od_a_b ) ) ) )
       => ( member6895035109809442519od_a_b @ T2 @ ( set_li5045283583078295363od_a_b @ ( map_li1070312879311380292od_a_b @ F2 @ Xs2 ) ) ) ) ) ).

% set_map_subset
thf(fact_633_set__map__subset,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,T2: fset_l1334069825099621524od_a_b,F2: list_P1467974523212632366od_a_b > fset_l1334069825099621524od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( member361094292949318077od_a_b @ T2 @ ( set_fs4298891544546585641od_a_b @ ( map_li7547266996134490026od_a_b @ F2 @ ( cons_l907386227682280420od_a_b @ X3 @ nil_li8635777946366267444od_a_b ) ) ) )
       => ( member361094292949318077od_a_b @ T2 @ ( set_fs4298891544546585641od_a_b @ ( map_li7547266996134490026od_a_b @ F2 @ Xs2 ) ) ) ) ) ).

% set_map_subset
thf(fact_634_set__map__subset,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,T2: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( member6895035109809442519od_a_b @ T2 @ ( set_li5045283583078295363od_a_b @ ( map_fs2600689390591810526od_a_b @ F2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) ) )
       => ( member6895035109809442519od_a_b @ T2 @ ( set_li5045283583078295363od_a_b @ ( map_fs2600689390591810526od_a_b @ F2 @ Xs2 ) ) ) ) ) ).

% set_map_subset
thf(fact_635_set__map__subset,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,T2: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( member361094292949318077od_a_b @ T2 @ ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) ) )
       => ( member361094292949318077od_a_b @ T2 @ ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) ) ) ) ) ).

% set_map_subset
thf(fact_636_prefixes_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( prefix4612422245637881633od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( cons_l7290444712290925776od_a_b @ nil_fs4581119677382125722od_a_b @ ( map_li2254913030204620100od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 ) @ ( prefix4612422245637881633od_a_b @ Xs2 ) ) ) ) ).

% prefixes.simps(2)
thf(fact_637_append__butlast__last__id,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( append2015155619842375983od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ ( last_f4009646753867174963od_a_b @ Xs2 ) @ nil_fs4581119677382125722od_a_b ) )
        = Xs2 ) ) ).

% append_butlast_last_id
thf(fact_638_Cons__in__lex,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) @ ( lex_fs1791213440591458046od_a_b @ R ) )
      = ( ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ R )
          & ( ( size_s6068669265016274566od_a_b @ Xs2 )
            = ( size_s6068669265016274566od_a_b @ Ys3 ) ) )
        | ( ( X3 = Y3 )
          & ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( lex_fs1791213440591458046od_a_b @ R ) ) ) ) ) ).

% Cons_in_lex
thf(fact_639_snoc__eq__iff__butlast,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) )
        = Ys3 )
      = ( ( Ys3 != nil_fs4581119677382125722od_a_b )
        & ( ( butlas6970048242682811878od_a_b @ Ys3 )
          = Xs2 )
        & ( ( last_f4009646753867174963od_a_b @ Ys3 )
          = X3 ) ) ) ).

% snoc_eq_iff_butlast
thf(fact_640_rotate1_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( rotate1032322621218768487od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) ) ).

% rotate1.simps(2)
thf(fact_641_last__snoc,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( last_f4009646753867174963od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) )
      = X3 ) ).

% last_snoc
thf(fact_642_append__eq__append__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Us2: list_f1445794025290330138od_a_b,Vs2: list_f1445794025290330138od_a_b] :
      ( ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
          = ( size_s6068669265016274566od_a_b @ Ys3 ) )
        | ( ( size_s6068669265016274566od_a_b @ Us2 )
          = ( size_s6068669265016274566od_a_b @ Vs2 ) ) )
     => ( ( ( append2015155619842375983od_a_b @ Xs2 @ Us2 )
          = ( append2015155619842375983od_a_b @ Ys3 @ Vs2 ) )
        = ( ( Xs2 = Ys3 )
          & ( Us2 = Vs2 ) ) ) ) ).

% append_eq_append_conv
thf(fact_643_length__map,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) )
      = ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% length_map
thf(fact_644_set__rotate1,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( rotate1032322621218768487od_a_b @ Xs2 ) )
      = ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ).

% set_rotate1
thf(fact_645_length__rotate1,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( rotate1032322621218768487od_a_b @ Xs2 ) )
      = ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% length_rotate1
thf(fact_646_neq__if__length__neq,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
       != ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( Xs2 != Ys3 ) ) ).

% neq_if_length_neq
thf(fact_647_Ex__list__of__length,axiom,
    ! [N: nat] :
    ? [Xs3: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ Xs3 )
      = N ) ).

% Ex_list_of_length
thf(fact_648_in__set__product__lists__length,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,Xss2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( produc5891818806577749399od_a_b @ Xss2 ) ) )
     => ( ( size_s3956712670882376602od_a_b @ Xs2 )
        = ( size_s4021047160419372448od_a_b @ Xss2 ) ) ) ).

% in_set_product_lists_length
thf(fact_649_in__set__product__lists__length,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Xss2: list_l6099054058445139744od_a_b] :
      ( ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( produc2086904765359242883od_a_b @ Xss2 ) ) )
     => ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s3205160614079436684od_a_b @ Xss2 ) ) ) ).

% in_set_product_lists_length
thf(fact_650_pair__list__eqI,axiom,
    ! [Xs2: list_P3574414722980446895od_a_b,Ys3: list_P3574414722980446895od_a_b] :
      ( ( ( map_Pr8806166102037958131_a_b_o @ produc5358503411717041797od_a_b @ Xs2 )
        = ( map_Pr8806166102037958131_a_b_o @ produc5358503411717041797od_a_b @ Ys3 ) )
     => ( ( ( map_Pr9157305129235354997od_a_b @ produc2954343059184910791od_a_b @ Xs2 )
          = ( map_Pr9157305129235354997od_a_b @ produc2954343059184910791od_a_b @ Ys3 ) )
       => ( Xs2 = Ys3 ) ) ) ).

% pair_list_eqI
thf(fact_651_list__induct2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( P @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
              ( ( ( size_s6068669265016274566od_a_b @ Xs3 )
                = ( size_s6068669265016274566od_a_b @ Ys ) )
             => ( ( P @ Xs3 @ Ys )
               => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) ) )
         => ( P @ Xs2 @ Ys3 ) ) ) ) ).

% list_induct2
thf(fact_652_list__induct3,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Ys3 )
          = ( size_s6068669265016274566od_a_b @ Zs ) )
       => ( ( P @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b )
         => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b,Z4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b] :
                ( ( ( size_s6068669265016274566od_a_b @ Xs3 )
                  = ( size_s6068669265016274566od_a_b @ Ys ) )
               => ( ( ( size_s6068669265016274566od_a_b @ Ys )
                    = ( size_s6068669265016274566od_a_b @ Zs2 ) )
                 => ( ( P @ Xs3 @ Ys @ Zs2 )
                   => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ ( cons_f6577355434438001738od_a_b @ Z4 @ Zs2 ) ) ) ) )
           => ( P @ Xs2 @ Ys3 @ Zs ) ) ) ) ) ).

% list_induct3
thf(fact_653_list__induct4,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,Ws: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Ys3 )
          = ( size_s6068669265016274566od_a_b @ Zs ) )
       => ( ( ( size_s6068669265016274566od_a_b @ Zs )
            = ( size_s6068669265016274566od_a_b @ Ws ) )
         => ( ( P @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b )
           => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b,Z4: fset_l1334069825099621524od_a_b,Zs2: list_f1445794025290330138od_a_b,W2: fset_l1334069825099621524od_a_b,Ws2: list_f1445794025290330138od_a_b] :
                  ( ( ( size_s6068669265016274566od_a_b @ Xs3 )
                    = ( size_s6068669265016274566od_a_b @ Ys ) )
                 => ( ( ( size_s6068669265016274566od_a_b @ Ys )
                      = ( size_s6068669265016274566od_a_b @ Zs2 ) )
                   => ( ( ( size_s6068669265016274566od_a_b @ Zs2 )
                        = ( size_s6068669265016274566od_a_b @ Ws2 ) )
                     => ( ( P @ Xs3 @ Ys @ Zs2 @ Ws2 )
                       => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) @ ( cons_f6577355434438001738od_a_b @ Z4 @ Zs2 ) @ ( cons_f6577355434438001738od_a_b @ W2 @ Ws2 ) ) ) ) ) )
             => ( P @ Xs2 @ Ys3 @ Zs @ Ws ) ) ) ) ) ) ).

% list_induct4
thf(fact_654_last_Osimps,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ( Xs2 = nil_fs4581119677382125722od_a_b )
       => ( ( last_f4009646753867174963od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = X3 ) )
      & ( ( Xs2 != nil_fs4581119677382125722od_a_b )
       => ( ( last_f4009646753867174963od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = ( last_f4009646753867174963od_a_b @ Xs2 ) ) ) ) ).

% last.simps
thf(fact_655_last__ConsL,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( Xs2 = nil_fs4581119677382125722od_a_b )
     => ( ( last_f4009646753867174963od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
        = X3 ) ) ).

% last_ConsL
thf(fact_656_last__ConsR,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( last_f4009646753867174963od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
        = ( last_f4009646753867174963od_a_b @ Xs2 ) ) ) ).

% last_ConsR
thf(fact_657_last__in__set,axiom,
    ! [As: list_l8778361445553822004od_a_b] :
      ( ( As != nil_li8635777946366267444od_a_b )
     => ( member6895035109809442519od_a_b @ ( last_l1496300474439883853od_a_b @ As ) @ ( set_li5045283583078295363od_a_b @ As ) ) ) ).

% last_in_set
thf(fact_658_last__in__set,axiom,
    ! [As: list_f1445794025290330138od_a_b] :
      ( ( As != nil_fs4581119677382125722od_a_b )
     => ( member361094292949318077od_a_b @ ( last_f4009646753867174963od_a_b @ As ) @ ( set_fs4298891544546585641od_a_b @ As ) ) ) ).

% last_in_set
thf(fact_659_listrel1__eq__len,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
     => ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) ) ) ).

% listrel1_eq_len
thf(fact_660_listrel__eq__len,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre6775573709112125169od_a_b @ R ) )
     => ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) ) ) ).

% listrel_eq_len
thf(fact_661_rev__induct2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( P @ nil_fs4581119677382125722od_a_b @ nil_fs4581119677382125722od_a_b )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
              ( ( ( size_s6068669265016274566od_a_b @ Xs3 )
                = ( size_s6068669265016274566od_a_b @ Ys ) )
             => ( ( P @ Xs3 @ Ys )
               => ( P @ ( append2015155619842375983od_a_b @ Xs3 @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) ) @ ( append2015155619842375983od_a_b @ Ys @ ( cons_f6577355434438001738od_a_b @ Y @ nil_fs4581119677382125722od_a_b ) ) ) ) )
         => ( P @ Xs2 @ Ys3 ) ) ) ) ).

% rev_induct2
thf(fact_662_same__length__different,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != Ys3 )
     => ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
          = ( size_s6068669265016274566od_a_b @ Ys3 ) )
       => ? [Pre: list_f1445794025290330138od_a_b,X4: fset_l1334069825099621524od_a_b,Xs: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys6: list_f1445794025290330138od_a_b] :
            ( ( X4 != Y )
            & ( Xs2
              = ( append2015155619842375983od_a_b @ Pre @ ( append2015155619842375983od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ nil_fs4581119677382125722od_a_b ) @ Xs ) ) )
            & ( Ys3
              = ( append2015155619842375983od_a_b @ Pre @ ( append2015155619842375983od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ nil_fs4581119677382125722od_a_b ) @ Ys6 ) ) ) ) ) ) ).

% same_length_different
thf(fact_663_lexord__sufE,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Qs: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Zs ) @ ( append2015155619842375983od_a_b @ Ys3 @ Qs ) ) @ ( lexord9144254948259057799od_a_b @ R ) )
     => ( ( Xs2 != Ys3 )
       => ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
            = ( size_s6068669265016274566od_a_b @ Ys3 ) )
         => ( ( ( size_s6068669265016274566od_a_b @ Zs )
              = ( size_s6068669265016274566od_a_b @ Qs ) )
           => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ) ) ) ).

% lexord_sufE
thf(fact_664_lex__append__rightI,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b,Vs2: list_f1445794025290330138od_a_b,Us2: list_f1445794025290330138od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( lex_fs1791213440591458046od_a_b @ R ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Vs2 )
          = ( size_s6068669265016274566od_a_b @ Us2 ) )
       => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Us2 ) @ ( append2015155619842375983od_a_b @ Ys3 @ Vs2 ) ) @ ( lex_fs1791213440591458046od_a_b @ R ) ) ) ) ).

% lex_append_rightI
thf(fact_665_lexord__lex,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ X3 @ Y3 ) @ ( lex_fs1791213440591458046od_a_b @ R ) )
      = ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ X3 @ Y3 ) @ ( lexord9144254948259057799od_a_b @ R ) )
        & ( ( size_s6068669265016274566od_a_b @ X3 )
          = ( size_s6068669265016274566od_a_b @ Y3 ) ) ) ) ).

% lexord_lex
thf(fact_666_linear__order__from__list__position_H_Oelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( linear8767015901316240446od_a_b @ X3 )
        = Y3 )
     => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
         => ( Y3 != nil_Pr4252210933832115117od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( X3
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ( Y3
               != ( cons_P1864978001919373149od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ X4 ) @ ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( linear8767015901316240446od_a_b @ Xs3 ) ) ) ) ) ) ) ).

% linear_order_from_list_position'.elims
thf(fact_667_list__ordered__pairs_Oelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( list_o5553444344251545051od_a_b @ X3 )
        = Y3 )
     => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
         => ( Y3 != nil_Pr4252210933832115117od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( X3
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ( Y3
               != ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( list_o5553444344251545051od_a_b @ Xs3 ) ) ) ) ) ) ).

% list_ordered_pairs.elims
thf(fact_668_linear__order__from__list__position_H_Opelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( linear8767015901316240446od_a_b @ X3 )
        = Y3 )
     => ( ( accp_l5651743518013118883od_a_b @ linear273309371191718703od_a_b @ X3 )
       => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
           => ( ( Y3 = nil_Pr4252210933832115117od_a_b )
             => ~ ( accp_l5651743518013118883od_a_b @ linear273309371191718703od_a_b @ nil_fs4581119677382125722od_a_b ) ) )
         => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
                ( ( X3
                  = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
               => ( ( Y3
                    = ( cons_P1864978001919373149od_a_b @ ( produc8099561100433402519od_a_b @ X4 @ X4 ) @ ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( linear8767015901316240446od_a_b @ Xs3 ) ) ) )
                 => ~ ( accp_l5651743518013118883od_a_b @ linear273309371191718703od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ) ) ) ) ).

% linear_order_from_list_position'.pelims
thf(fact_669_non__sym__dist__pairs_H_Oelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( non_sy1352304633095342623od_a_b @ X3 )
        = Y3 )
     => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
         => ( Y3 != nil_Pr4252210933832115117od_a_b ) )
       => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
              ( ( X3
                = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
             => ( Y3
               != ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( non_sy1352304633095342623od_a_b @ Xs3 ) ) ) ) ) ) ).

% non_sym_dist_pairs'.elims
thf(fact_670_list__ordered__pairs_Opelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( list_o5553444344251545051od_a_b @ X3 )
        = Y3 )
     => ( ( accp_l5651743518013118883od_a_b @ list_o2651293876426356178od_a_b @ X3 )
       => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
           => ( ( Y3 = nil_Pr4252210933832115117od_a_b )
             => ~ ( accp_l5651743518013118883od_a_b @ list_o2651293876426356178od_a_b @ nil_fs4581119677382125722od_a_b ) ) )
         => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
                ( ( X3
                  = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
               => ( ( Y3
                    = ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( list_o5553444344251545051od_a_b @ Xs3 ) ) )
                 => ~ ( accp_l5651743518013118883od_a_b @ list_o2651293876426356178od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ) ) ) ) ).

% list_ordered_pairs.pelims
thf(fact_671_non__sym__dist__pairs_H_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( non_sy1352304633095342623od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X3 ) @ Xs2 ) @ ( non_sy1352304633095342623od_a_b @ Xs2 ) ) ) ).

% non_sym_dist_pairs'.simps(2)
thf(fact_672_list__ordered__pairs_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( list_o5553444344251545051od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X3 ) @ Xs2 ) @ ( list_o5553444344251545051od_a_b @ Xs2 ) ) ) ).

% list_ordered_pairs.simps(2)
thf(fact_673_list__ordered__pairs__set__containment,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
       => ( ( X3 != Y3 )
         => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( list_o8928240460966572533od_a_b @ Xs2 ) ) )
            | ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Y3 @ X3 ) @ ( set_Pr1811016573229031484od_a_b @ ( list_o8928240460966572533od_a_b @ Xs2 ) ) ) ) ) ) ) ).

% list_ordered_pairs_set_containment
thf(fact_674_list__ordered__pairs__set__containment,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
       => ( ( X3 != Y3 )
         => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( list_o5553444344251545051od_a_b @ Xs2 ) ) )
            | ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ Y3 @ X3 ) @ ( set_Pr3326995048199123516od_a_b @ ( list_o5553444344251545051od_a_b @ Xs2 ) ) ) ) ) ) ) ).

% list_ordered_pairs_set_containment
thf(fact_675_linear__order__from__list__position_H_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( linear8767015901316240446od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( cons_P1864978001919373149od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ X3 ) @ ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X3 ) @ Xs2 ) @ ( linear8767015901316240446od_a_b @ Xs2 ) ) ) ) ).

% linear_order_from_list_position'.simps(2)
thf(fact_676_non__sym__dist__pairs_H_Opelims,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_P1164858718851775149od_a_b] :
      ( ( ( non_sy1352304633095342623od_a_b @ X3 )
        = Y3 )
     => ( ( accp_l5651743518013118883od_a_b @ non_sy4348299424481621646od_a_b @ X3 )
       => ( ( ( X3 = nil_fs4581119677382125722od_a_b )
           => ( ( Y3 = nil_Pr4252210933832115117od_a_b )
             => ~ ( accp_l5651743518013118883od_a_b @ non_sy4348299424481621646od_a_b @ nil_fs4581119677382125722od_a_b ) ) )
         => ~ ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
                ( ( X3
                  = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
               => ( ( Y3
                    = ( append5873922736804373826od_a_b @ ( map_fs8417695273700992087od_a_b @ ( produc8099561100433402519od_a_b @ X4 ) @ Xs3 ) @ ( non_sy1352304633095342623od_a_b @ Xs3 ) ) )
                 => ~ ( accp_l5651743518013118883od_a_b @ non_sy4348299424481621646od_a_b @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) ) ) ) ) ) ) ).

% non_sym_dist_pairs'.pelims
thf(fact_677_List_Oproduct_Osimps_I2_J,axiom,
    ! [X3: $o,Xs2: list_o,Ys3: list_l6099054058445139744od_a_b] :
      ( ( produc2134592012631421511od_a_b @ ( cons_o @ X3 @ Xs2 ) @ Ys3 )
      = ( append2579811284360515140od_a_b @ ( map_li3123090900592589011od_a_b @ ( produc7489420772309856409od_a_b @ X3 ) @ Ys3 ) @ ( produc2134592012631421511od_a_b @ Xs2 @ Ys3 ) ) ) ).

% List.product.simps(2)
thf(fact_678_List_Oproduct_Osimps_I2_J,axiom,
    ! [X3: $o,Xs2: list_o,Ys3: list_P5488608094462411443od_a_b] :
      ( ( produc7959357592531908954od_a_b @ ( cons_o @ X3 @ Xs2 ) @ Ys3 )
      = ( append4988338609183987159od_a_b @ ( map_Pr4429666502407624467od_a_b @ ( produc1286801380576301484od_a_b @ X3 ) @ Ys3 ) @ ( produc7959357592531908954od_a_b @ Xs2 @ Ys3 ) ) ) ).

% List.product.simps(2)
thf(fact_679_List_Oproduct_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys3: list_l6099054058445139744od_a_b] :
      ( ( produc8535066297417230155od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ Ys3 )
      = ( append5072337359724802120od_a_b @ ( map_li4307878677677536599od_a_b @ ( produc6212510018049267869od_a_b @ X3 ) @ Ys3 ) @ ( produc8535066297417230155od_a_b @ Xs2 @ Ys3 ) ) ) ).

% List.product.simps(2)
thf(fact_680_lexord__sufI,axiom,
    ! [U: list_f1445794025290330138od_a_b,W3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b,V2: list_f1445794025290330138od_a_b,Z: list_f1445794025290330138od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ U @ W3 ) @ ( lexord9144254948259057799od_a_b @ R ) )
     => ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ W3 ) @ ( size_s6068669265016274566od_a_b @ U ) )
       => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ U @ V2 ) @ ( append2015155619842375983od_a_b @ W3 @ Z ) ) @ ( lexord9144254948259057799od_a_b @ R ) ) ) ) ).

% lexord_sufI
thf(fact_681_simple__cg__closure__phase__2__helper__length,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] : ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% simple_cg_closure_phase_2_helper_length
thf(fact_682_simple__cg__closure__phase__1__helper_H__length,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] : ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% simple_cg_closure_phase_1_helper'_length
thf(fact_683_impossible__Cons,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( Xs2
       != ( cons_f6577355434438001738od_a_b @ X3 @ Ys3 ) ) ) ).

% impossible_Cons
thf(fact_684_update_Osimps_I2_J,axiom,
    ! [P2: produc2313482920965681321od_a_b,K3: $o,V2: list_f1445794025290330138od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( ( ( produc5358503411717041797od_a_b @ P2 )
          = K3 )
       => ( ( update8681303028256525566od_a_b @ K3 @ V2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V2 ) @ Ps2 ) ) )
      & ( ( ( produc5358503411717041797od_a_b @ P2 )
          = ~ K3 )
       => ( ( update8681303028256525566od_a_b @ K3 @ V2 @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
          = ( cons_P2672142353023029855od_a_b @ P2 @ ( update8681303028256525566od_a_b @ K3 @ V2 @ Ps2 ) ) ) ) ) ).

% update.simps(2)
thf(fact_685_update_Osimps_I2_J,axiom,
    ! [P2: produc8937288731615916348od_a_b,K3: $o,V2: produc2518759752815613485od_a_b,Ps2: list_P5302045529885307074od_a_b] :
      ( ( ( ( produc2316053142268291992od_a_b @ P2 )
          = K3 )
       => ( ( update3607110547477456657od_a_b @ K3 @ V2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V2 ) @ Ps2 ) ) )
      & ( ( ( produc2316053142268291992od_a_b @ P2 )
          = ~ K3 )
       => ( ( update3607110547477456657od_a_b @ K3 @ V2 @ ( cons_P7065065391077662962od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7065065391077662962od_a_b @ P2 @ ( update3607110547477456657od_a_b @ K3 @ V2 @ Ps2 ) ) ) ) ) ).

% update.simps(2)
thf(fact_686_update_Osimps_I2_J,axiom,
    ! [P2: produc2518759752815613485od_a_b,K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b,Ps2: list_P5488608094462411443od_a_b] :
      ( ( ( ( produc5739577146777995401od_a_b @ P2 )
          = K3 )
       => ( ( update9221375438537324674od_a_b @ K3 @ V2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V2 ) @ Ps2 ) ) )
      & ( ( ( produc5739577146777995401od_a_b @ P2 )
         != K3 )
       => ( ( update9221375438537324674od_a_b @ K3 @ V2 @ ( cons_P7745750895690215651od_a_b @ P2 @ Ps2 ) )
          = ( cons_P7745750895690215651od_a_b @ P2 @ ( update9221375438537324674od_a_b @ K3 @ V2 @ Ps2 ) ) ) ) ) ).

% update.simps(2)
thf(fact_687_update_Osimps_I1_J,axiom,
    ! [K3: $o,V2: list_f1445794025290330138od_a_b] :
      ( ( update8681303028256525566od_a_b @ K3 @ V2 @ nil_Pr7302809325368845999od_a_b )
      = ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V2 ) @ nil_Pr7302809325368845999od_a_b ) ) ).

% update.simps(1)
thf(fact_688_update_Osimps_I1_J,axiom,
    ! [K3: $o,V2: produc2518759752815613485od_a_b] :
      ( ( update3607110547477456657od_a_b @ K3 @ V2 @ nil_Pr3614377049866306882od_a_b )
      = ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V2 ) @ nil_Pr3614377049866306882od_a_b ) ) ).

% update.simps(1)
thf(fact_689_update_Osimps_I1_J,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b] :
      ( ( update9221375438537324674od_a_b @ K3 @ V2 @ nil_Pr1838250474468212019od_a_b )
      = ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V2 ) @ nil_Pr1838250474468212019od_a_b ) ) ).

% update.simps(1)
thf(fact_690_merge__simps_I2_J,axiom,
    ! [Qs: list_P3574414722980446895od_a_b,P2: produc2313482920965681321od_a_b,Ps2: list_P3574414722980446895od_a_b] :
      ( ( merge_9196116298519041767od_a_b @ Qs @ ( cons_P2672142353023029855od_a_b @ P2 @ Ps2 ) )
      = ( update8681303028256525566od_a_b @ ( produc5358503411717041797od_a_b @ P2 ) @ ( produc2954343059184910791od_a_b @ P2 ) @ ( merge_9196116298519041767od_a_b @ Qs @ Ps2 ) ) ) ).

% merge_simps(2)
thf(fact_691_simple__cg__closure__phase__1__length,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] : ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% simple_cg_closure_phase_1_length
thf(fact_692_non__sym__dist__pairs__elems__distinct_I2_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% non_sym_dist_pairs_elems_distinct(2)
thf(fact_693_non__sym__dist__pairs__elems__distinct_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) )
     => ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% non_sym_dist_pairs_elems_distinct(2)
thf(fact_694_non__sym__dist__pairs__elems__distinct_I1_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% non_sym_dist_pairs_elems_distinct(1)
thf(fact_695_non__sym__dist__pairs__elems__distinct_I1_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% non_sym_dist_pairs_elems_distinct(1)
thf(fact_696_non__sym__dist__pairs__elems,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
       => ( ( X3 != Y3 )
         => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) )
            | ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Y3 @ X3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) ) ) ) ) ) ).

% non_sym_dist_pairs_elems
thf(fact_697_non__sym__dist__pairs__elems,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
       => ( ( X3 != Y3 )
         => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) )
            | ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ Y3 @ X3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) ) ) ) ) ) ).

% non_sym_dist_pairs_elems
thf(fact_698_non__sym__dist__pairs__set__iff,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) )
      = ( ( X3 != Y3 )
        & ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
        & ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
        & ~ ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Y3 @ X3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy3462148336120157346od_a_b @ Xs2 ) ) ) ) ) ).

% non_sym_dist_pairs_set_iff
thf(fact_699_non__sym__dist__pairs__set__iff,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) )
      = ( ( X3 != Y3 )
        & ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
        & ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
        & ~ ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ Y3 @ X3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy5167582269473054216od_a_b @ Xs2 ) ) ) ) ) ).

% non_sym_dist_pairs_set_iff
thf(fact_700_simple__cg__closure__phase__1__helper_H__True,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( produc2316053142268291992od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) )
     => ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% simple_cg_closure_phase_1_helper'_True
thf(fact_701_simple__cg__closure__phase__2__helper__True,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( produc2316053142268291992od_a_b @ ( simple4112306255986741752od_a_b @ X3 @ Xs2 ) )
     => ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X3 @ Xs2 ) ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% simple_cg_closure_phase_2_helper_True
thf(fact_702_lenlex__length,axiom,
    ! [Ms: list_f1445794025290330138od_a_b,Ns: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Ms @ Ns ) @ ( lenlex8762485181240705951od_a_b @ R ) )
     => ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Ms ) @ ( size_s6068669265016274566od_a_b @ Ns ) ) ) ).

% lenlex_length
thf(fact_703_lenlex__append1,axiom,
    ! [Us2: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,R2: set_Pr2242436922956002695od_a_b,Vs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Us2 @ Xs2 ) @ ( lenlex8762485181240705951od_a_b @ R2 ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Vs2 )
          = ( size_s6068669265016274566od_a_b @ Ys3 ) )
       => ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( append2015155619842375983od_a_b @ Us2 @ Vs2 ) @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) ) @ ( lenlex8762485181240705951od_a_b @ R2 ) ) ) ) ).

% lenlex_append1
thf(fact_704_length__induct,axiom,
    ! [P: list_f1445794025290330138od_a_b > $o,Xs2: list_f1445794025290330138od_a_b] :
      ( ! [Xs3: list_f1445794025290330138od_a_b] :
          ( ! [Ys7: list_f1445794025290330138od_a_b] :
              ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ Ys7 ) @ ( size_s6068669265016274566od_a_b @ Xs3 ) )
             => ( P @ Ys7 ) )
         => ( P @ Xs3 ) )
     => ( P @ Xs2 ) ) ).

% length_induct
thf(fact_705_Cons__lenlex__iff,axiom,
    ! [M2: fset_l1334069825099621524od_a_b,Ms: list_f1445794025290330138od_a_b,N: fset_l1334069825099621524od_a_b,Ns: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ ( cons_f6577355434438001738od_a_b @ M2 @ Ms ) @ ( cons_f6577355434438001738od_a_b @ N @ Ns ) ) @ ( lenlex8762485181240705951od_a_b @ R ) )
      = ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ Ms ) @ ( size_s6068669265016274566od_a_b @ Ns ) )
        | ( ( ( size_s6068669265016274566od_a_b @ Ms )
            = ( size_s6068669265016274566od_a_b @ Ns ) )
          & ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ M2 @ N ) @ R ) )
        | ( ( M2 = N )
          & ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Ms @ Ns ) @ ( lenlex8762485181240705951od_a_b @ R ) ) ) ) ) ).

% Cons_lenlex_iff
thf(fact_706_simple__cg__closure__phase__1__True,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( produc5358503411717041797od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) )
     => ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% simple_cg_closure_phase_1_True
thf(fact_707_less__prod__simp,axiom,
    ! [X1: $o,Y1: list_f1445794025290330138od_a_b,X2: $o,Y2: list_f1445794025290330138od_a_b] :
      ( ( ord_le4629424078442911573od_a_b @ ( produc7489420772309856409od_a_b @ X1 @ Y1 ) @ ( produc7489420772309856409od_a_b @ X2 @ Y2 ) )
      = ( ( ord_less_o @ X1 @ X2 )
        | ( ( ord_less_eq_o @ X1 @ X2 )
          & ( ord_le7150648013565725894od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_prod_simp
thf(fact_708_less__prod__simp,axiom,
    ! [X1: $o,Y1: produc2518759752815613485od_a_b,X2: $o,Y2: produc2518759752815613485od_a_b] :
      ( ( ord_le5639095759471244264od_a_b @ ( produc1286801380576301484od_a_b @ X1 @ Y1 ) @ ( produc1286801380576301484od_a_b @ X2 @ Y2 ) )
      = ( ( ord_less_o @ X1 @ X2 )
        | ( ( ord_less_eq_o @ X1 @ X2 )
          & ( ord_le1232572551315295961od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_prod_simp
thf(fact_709_less__prod__simp,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,Y1: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,Y2: list_f1445794025290330138od_a_b] :
      ( ( ord_le1232572551315295961od_a_b @ ( produc6212510018049267869od_a_b @ X1 @ Y1 ) @ ( produc6212510018049267869od_a_b @ X2 @ Y2 ) )
      = ( ( ord_le98927018796173120od_a_b @ X1 @ X2 )
        | ( ( ord_le5177564485156961332od_a_b @ X1 @ X2 )
          & ( ord_le7150648013565725894od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_prod_simp
thf(fact_710_less__prod__simp,axiom,
    ! [X1: nat,Y1: nat,X2: nat,Y2: nat] :
      ( ( ord_le1203424502768444845at_nat @ ( product_Pair_nat_nat @ X1 @ Y1 ) @ ( product_Pair_nat_nat @ X2 @ Y2 ) )
      = ( ( ord_less_nat @ X1 @ X2 )
        | ( ( ord_less_eq_nat @ X1 @ X2 )
          & ( ord_less_nat @ Y1 @ Y2 ) ) ) ) ).

% less_prod_simp
thf(fact_711_less__eq__prod__simp,axiom,
    ! [X1: $o,Y1: list_f1445794025290330138od_a_b,X2: $o,Y2: list_f1445794025290330138od_a_b] :
      ( ( ord_le6405569072945473609od_a_b @ ( produc7489420772309856409od_a_b @ X1 @ Y1 ) @ ( produc7489420772309856409od_a_b @ X2 @ Y2 ) )
      = ( ( ord_less_o @ X1 @ X2 )
        | ( ( ord_less_eq_o @ X1 @ X2 )
          & ( ord_le2437917120829568954od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_712_less__eq__prod__simp,axiom,
    ! [X1: $o,Y1: produc2518759752815613485od_a_b,X2: $o,Y2: produc2518759752815613485od_a_b] :
      ( ( ord_le117511869695297756od_a_b @ ( produc1286801380576301484od_a_b @ X1 @ Y1 ) @ ( produc1286801380576301484od_a_b @ X2 @ Y2 ) )
      = ( ( ord_less_o @ X1 @ X2 )
        | ( ( ord_less_eq_o @ X1 @ X2 )
          & ( ord_le1997768708718029od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_713_less__eq__prod__simp,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,Y1: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,Y2: list_f1445794025290330138od_a_b] :
      ( ( ord_le1997768708718029od_a_b @ ( produc6212510018049267869od_a_b @ X1 @ Y1 ) @ ( produc6212510018049267869od_a_b @ X2 @ Y2 ) )
      = ( ( ord_le98927018796173120od_a_b @ X1 @ X2 )
        | ( ( ord_le5177564485156961332od_a_b @ X1 @ X2 )
          & ( ord_le2437917120829568954od_a_b @ Y1 @ Y2 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_714_less__eq__prod__simp,axiom,
    ! [X1: nat,Y1: nat,X2: nat,Y2: nat] :
      ( ( ord_le8460144461188290721at_nat @ ( product_Pair_nat_nat @ X1 @ Y1 ) @ ( product_Pair_nat_nat @ X2 @ Y2 ) )
      = ( ( ord_less_nat @ X1 @ X2 )
        | ( ( ord_less_eq_nat @ X1 @ X2 )
          & ( ord_less_eq_nat @ Y1 @ Y2 ) ) ) ) ).

% less_eq_prod_simp
thf(fact_715_Cons__less__Cons,axiom,
    ! [A: fset_l1334069825099621524od_a_b,X3: list_f1445794025290330138od_a_b,B: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( ord_le7150648013565725894od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ X3 ) @ ( cons_f6577355434438001738od_a_b @ B @ Y3 ) )
      = ( ( ord_le98927018796173120od_a_b @ A @ B )
        | ( ( A = B )
          & ( ord_le7150648013565725894od_a_b @ X3 @ Y3 ) ) ) ) ).

% Cons_less_Cons
thf(fact_716_Cons__less__Cons,axiom,
    ! [A: nat,X3: list_nat,B: nat,Y3: list_nat] :
      ( ( ord_less_list_nat @ ( cons_nat @ A @ X3 ) @ ( cons_nat @ B @ Y3 ) )
      = ( ( ord_less_nat @ A @ B )
        | ( ( A = B )
          & ( ord_less_list_nat @ X3 @ Y3 ) ) ) ) ).

% Cons_less_Cons
thf(fact_717_prod__less__def,axiom,
    ( ord_le4629424078442911573od_a_b
    = ( ^ [X5: produc2313482920965681321od_a_b,Y4: produc2313482920965681321od_a_b] :
          ( ( ord_less_o @ ( produc5358503411717041797od_a_b @ X5 ) @ ( produc5358503411717041797od_a_b @ Y4 ) )
          | ( ( ord_less_eq_o @ ( produc5358503411717041797od_a_b @ X5 ) @ ( produc5358503411717041797od_a_b @ Y4 ) )
            & ( ord_le7150648013565725894od_a_b @ ( produc2954343059184910791od_a_b @ X5 ) @ ( produc2954343059184910791od_a_b @ Y4 ) ) ) ) ) ) ).

% prod_less_def
thf(fact_718_prod__less__def,axiom,
    ( ord_le1203424502768444845at_nat
    = ( ^ [X5: product_prod_nat_nat,Y4: product_prod_nat_nat] :
          ( ( ord_less_nat @ ( product_fst_nat_nat @ X5 ) @ ( product_fst_nat_nat @ Y4 ) )
          | ( ( ord_less_eq_nat @ ( product_fst_nat_nat @ X5 ) @ ( product_fst_nat_nat @ Y4 ) )
            & ( ord_less_nat @ ( product_snd_nat_nat @ X5 ) @ ( product_snd_nat_nat @ Y4 ) ) ) ) ) ) ).

% prod_less_def
thf(fact_719_less__eq__prod__def,axiom,
    ( ord_le6405569072945473609od_a_b
    = ( ^ [X5: produc2313482920965681321od_a_b,Y4: produc2313482920965681321od_a_b] :
          ( ( ord_less_o @ ( produc5358503411717041797od_a_b @ X5 ) @ ( produc5358503411717041797od_a_b @ Y4 ) )
          | ( ( ord_less_eq_o @ ( produc5358503411717041797od_a_b @ X5 ) @ ( produc5358503411717041797od_a_b @ Y4 ) )
            & ( ord_le2437917120829568954od_a_b @ ( produc2954343059184910791od_a_b @ X5 ) @ ( produc2954343059184910791od_a_b @ Y4 ) ) ) ) ) ) ).

% less_eq_prod_def
thf(fact_720_less__eq__prod__def,axiom,
    ( ord_le8460144461188290721at_nat
    = ( ^ [X5: product_prod_nat_nat,Y4: product_prod_nat_nat] :
          ( ( ord_less_nat @ ( product_fst_nat_nat @ X5 ) @ ( product_fst_nat_nat @ Y4 ) )
          | ( ( ord_less_eq_nat @ ( product_fst_nat_nat @ X5 ) @ ( product_fst_nat_nat @ Y4 ) )
            & ( ord_less_eq_nat @ ( product_snd_nat_nat @ X5 ) @ ( product_snd_nat_nat @ Y4 ) ) ) ) ) ) ).

% less_eq_prod_def
thf(fact_721_Cons__le__Cons,axiom,
    ! [A: fset_l1334069825099621524od_a_b,X3: list_f1445794025290330138od_a_b,B: fset_l1334069825099621524od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( ord_le2437917120829568954od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ X3 ) @ ( cons_f6577355434438001738od_a_b @ B @ Y3 ) )
      = ( ( ord_le98927018796173120od_a_b @ A @ B )
        | ( ( A = B )
          & ( ord_le2437917120829568954od_a_b @ X3 @ Y3 ) ) ) ) ).

% Cons_le_Cons
thf(fact_722_Cons__le__Cons,axiom,
    ! [A: nat,X3: list_nat,B: nat,Y3: list_nat] :
      ( ( ord_less_eq_list_nat @ ( cons_nat @ A @ X3 ) @ ( cons_nat @ B @ Y3 ) )
      = ( ( ord_less_nat @ A @ B )
        | ( ( A = B )
          & ( ord_less_eq_list_nat @ X3 @ Y3 ) ) ) ) ).

% Cons_le_Cons
thf(fact_723_subset__code_I1_J,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,B6: set_li6306622547289818894od_a_b] :
      ( ( ord_le153002609085230766od_a_b @ ( set_li5045283583078295363od_a_b @ Xs2 ) @ B6 )
      = ( ! [X5: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ X5 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
           => ( member6895035109809442519od_a_b @ X5 @ B6 ) ) ) ) ).

% subset_code(1)
thf(fact_724_subset__code_I1_J,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,B6: set_fs5173440902860351732od_a_b] :
      ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ B6 )
      = ( ! [X5: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( member361094292949318077od_a_b @ X5 @ B6 ) ) ) ) ).

% subset_code(1)
thf(fact_725_less__list__code_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] : ( ord_le7150648013565725894od_a_b @ nil_fs4581119677382125722od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) ).

% less_list_code(2)
thf(fact_726_Nil__less__Cons,axiom,
    ! [A: fset_l1334069825099621524od_a_b,X3: list_f1445794025290330138od_a_b] : ( ord_le7150648013565725894od_a_b @ nil_fs4581119677382125722od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ X3 ) ) ).

% Nil_less_Cons
thf(fact_727_less__eq__list__code_I3_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ord_le2437917120829568954od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
      = ( ( ord_le98927018796173120od_a_b @ X3 @ Y3 )
        | ( ( X3 = Y3 )
          & ( ord_le2437917120829568954od_a_b @ Xs2 @ Ys3 ) ) ) ) ).

% less_eq_list_code(3)
thf(fact_728_less__eq__list__code_I3_J,axiom,
    ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
      ( ( ord_less_eq_list_nat @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) )
      = ( ( ord_less_nat @ X3 @ Y3 )
        | ( ( X3 = Y3 )
          & ( ord_less_eq_list_nat @ Xs2 @ Ys3 ) ) ) ) ).

% less_eq_list_code(3)
thf(fact_729_less__eq__list__code_I1_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ~ ( ord_le2437917120829568954od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ nil_fs4581119677382125722od_a_b ) ).

% less_eq_list_code(1)
thf(fact_730_set__subset__Cons,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] : ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) ) ).

% set_subset_Cons
thf(fact_731_list__prefix__subset,axiom,
    ! [Ts: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ? [Ys7: list_f1445794025290330138od_a_b] :
          ( Ts
          = ( append2015155619842375983od_a_b @ Xs2 @ Ys7 ) )
     => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Ts ) ) ) ).

% list_prefix_subset
thf(fact_732_list__append__subset3,axiom,
    ! [Xs1: list_f1445794025290330138od_a_b,Ys1: list_f1445794025290330138od_a_b,Xs22: list_f1445794025290330138od_a_b,Ys22: list_f1445794025290330138od_a_b,Xs32: list_f1445794025290330138od_a_b,Ys32: list_f1445794025290330138od_a_b] :
      ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs1 ) @ ( set_fs4298891544546585641od_a_b @ Ys1 ) )
     => ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs22 ) @ ( set_fs4298891544546585641od_a_b @ Ys22 ) )
       => ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs32 ) @ ( set_fs4298891544546585641od_a_b @ Ys32 ) )
         => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ Xs1 @ ( append2015155619842375983od_a_b @ Xs22 @ Xs32 ) ) ) @ ( set_fs4298891544546585641od_a_b @ ( append2015155619842375983od_a_b @ Ys1 @ ( append2015155619842375983od_a_b @ Ys22 @ Ys32 ) ) ) ) ) ) ) ).

% list_append_subset3
thf(fact_733_prefixes__prefix__subset,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) )
     => ( ord_le153002609085230766od_a_b @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Xs2 ) ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) ) ) ).

% prefixes_prefix_subset
thf(fact_734_set__concat__map__sublist,axiom,
    ! [X3: list_P1467974523212632366od_a_b,F2: fset_l1334069825099621524od_a_b > list_l8778361445553822004od_a_b,Xs2: list_f1445794025290330138od_a_b,Xs5: list_f1445794025290330138od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ ( map_fs6872359466567453668od_a_b @ F2 @ Xs2 ) ) ) )
     => ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Xs5 ) )
       => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( concat8700631635091661039od_a_b @ ( map_fs6872359466567453668od_a_b @ F2 @ Xs5 ) ) ) ) ) ) ).

% set_concat_map_sublist
thf(fact_735_set__concat__map__sublist,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,Xs5: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ ( map_fs7724969689208736458od_a_b @ F2 @ Xs2 ) ) ) )
     => ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Xs5 ) )
       => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( concat3179126272939696085od_a_b @ ( map_fs7724969689208736458od_a_b @ F2 @ Xs5 ) ) ) ) ) ) ).

% set_concat_map_sublist
thf(fact_736_less__list__code_I3_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ord_le7150648013565725894od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
      = ( ( ord_le98927018796173120od_a_b @ X3 @ Y3 )
        | ( ( X3 = Y3 )
          & ( ord_le7150648013565725894od_a_b @ Xs2 @ Ys3 ) ) ) ) ).

% less_list_code(3)
thf(fact_737_less__list__code_I3_J,axiom,
    ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
      ( ( ord_less_list_nat @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) )
      = ( ( ord_less_nat @ X3 @ Y3 )
        | ( ( X3 = Y3 )
          & ( ord_less_list_nat @ Xs2 @ Ys3 ) ) ) ) ).

% less_list_code(3)
thf(fact_738_less__prod__def_H,axiom,
    ( ord_le4629424078442911573od_a_b
    = ( ^ [X5: produc2313482920965681321od_a_b,Y4: produc2313482920965681321od_a_b] :
          ( ( ord_less_o @ ( produc5358503411717041797od_a_b @ X5 ) @ ( produc5358503411717041797od_a_b @ Y4 ) )
          | ( ( ( produc5358503411717041797od_a_b @ X5 )
              = ( produc5358503411717041797od_a_b @ Y4 ) )
            & ( ord_le7150648013565725894od_a_b @ ( produc2954343059184910791od_a_b @ X5 ) @ ( produc2954343059184910791od_a_b @ Y4 ) ) ) ) ) ) ).

% less_prod_def'
thf(fact_739_less__prod__def_H,axiom,
    ( ord_le1203424502768444845at_nat
    = ( ^ [X5: product_prod_nat_nat,Y4: product_prod_nat_nat] :
          ( ( ord_less_nat @ ( product_fst_nat_nat @ X5 ) @ ( product_fst_nat_nat @ Y4 ) )
          | ( ( ( product_fst_nat_nat @ X5 )
              = ( product_fst_nat_nat @ Y4 ) )
            & ( ord_less_nat @ ( product_snd_nat_nat @ X5 ) @ ( product_snd_nat_nat @ Y4 ) ) ) ) ) ) ).

% less_prod_def'
thf(fact_740_fsubsetI,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ X4 @ A4 )
         => ( fmembe7722352836199763061od_a_b @ X4 @ B6 ) )
     => ( ord_le5177564485156961332od_a_b @ A4 @ B6 ) ) ).

% fsubsetI
thf(fact_741_lists__of__length__containment,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,T3: list_P1467974523212632366od_a_b,N: nat] :
      ( ( ord_le817736998455962536od_a_b @ ( set_Product_prod_a_b2 @ Xs2 ) @ ( set_Product_prod_a_b2 @ T3 ) )
     => ( ( ( size_s3956712670882376602od_a_b @ Xs2 )
          = N )
       => ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( lists_5148932666697663363od_a_b @ T3 @ N ) ) ) ) ) ).

% lists_of_length_containment
thf(fact_742_lists__of__length__containment,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,T3: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ T3 ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
          = N )
       => ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( lists_98629209091004527od_a_b @ T3 @ N ) ) ) ) ) ).

% lists_of_length_containment
thf(fact_743_listrel__iff__nth,axiom,
    ! [Xs2: list_o,Ys3: list_l6099054058445139744od_a_b,R: set_Pr121319624013539721od_a_b] :
      ( ( member6201332024754097106od_a_b @ ( produc8240772320746637977od_a_b @ Xs2 @ Ys3 ) @ ( listre8201142255725533427od_a_b @ R ) )
      = ( ( ( size_size_list_o @ Xs2 )
          = ( size_s3205160614079436684od_a_b @ Ys3 ) )
        & ! [N2: nat] :
            ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
           => ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ ( nth_o @ Xs2 @ N2 ) @ ( nth_li3998004317099707681od_a_b @ Ys3 @ N2 ) ) @ R ) ) ) ) ).

% listrel_iff_nth
thf(fact_744_listrel__iff__nth,axiom,
    ! [Xs2: list_o,Ys3: list_P5488608094462411443od_a_b,R: set_Pr5622538825374275996od_a_b] :
      ( ( member7237066067024242917od_a_b @ ( produc6961711982280244012od_a_b @ Xs2 @ Ys3 ) @ ( listre3706061411988323334od_a_b @ R ) )
      = ( ( ( size_size_list_o @ Xs2 )
          = ( size_s5774146080724371231od_a_b @ Ys3 ) )
        & ! [N2: nat] :
            ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
           => ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ ( nth_o @ Xs2 @ N2 ) @ ( nth_Pr7741617482765506100od_a_b @ Ys3 @ N2 ) ) @ R ) ) ) ) ).

% listrel_iff_nth
thf(fact_745_listrel__iff__nth,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_l6099054058445139744od_a_b,R: set_Pr1051027220935592077od_a_b] :
      ( ( member6680126217112042070od_a_b @ ( produc8565745453924327965od_a_b @ Xs2 @ Ys3 ) @ ( listre5187687223414087671od_a_b @ R ) )
      = ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
          = ( size_s3205160614079436684od_a_b @ Ys3 ) )
        & ! [N2: nat] :
            ( ( ord_less_nat @ N2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N2 ) @ ( nth_li3998004317099707681od_a_b @ Ys3 @ N2 ) ) @ R ) ) ) ) ).

% listrel_iff_nth
thf(fact_746_listrel__iff__nth,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre6775573709112125169od_a_b @ R ) )
      = ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
          = ( size_s6068669265016274566od_a_b @ Ys3 ) )
        & ! [N2: nat] :
            ( ( ord_less_nat @ N2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N2 ) @ ( nth_fs7310631729605226779od_a_b @ Ys3 @ N2 ) ) @ R ) ) ) ) ).

% listrel_iff_nth
thf(fact_747_simple__cg__closure__phase__1__helper__True,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xss2: list_f1445794025290330138od_a_b,Don: list_f1445794025290330138od_a_b] :
      ( ( produc5358503411717041797od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ $false @ Don ) ) )
     => ( ( Xss2 != nil_fs4581119677382125722od_a_b )
       => ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ $false @ Don ) ) ) ) @ ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xss2 ) @ ( size_s6068669265016274566od_a_b @ Don ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper_True
thf(fact_748_length__append,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
      = ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ ( size_s6068669265016274566od_a_b @ Ys3 ) ) ) ).

% length_append
thf(fact_749_nth__append__length,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Ys3 ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
      = X3 ) ).

% nth_append_length
thf(fact_750_nth__append__length__plus,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,N: nat] :
      ( ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) )
      = ( nth_fs7310631729605226779od_a_b @ Ys3 @ N ) ) ).

% nth_append_length_plus
thf(fact_751_nth__equalityI,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ! [I: nat] :
            ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I )
              = ( nth_fs7310631729605226779od_a_b @ Ys3 @ I ) ) )
       => ( Xs2 = Ys3 ) ) ) ).

% nth_equalityI
thf(fact_752_Skolem__list__nth,axiom,
    ! [K3: nat,P: nat > fset_l1334069825099621524od_a_b > $o] :
      ( ( ! [I2: nat] :
            ( ( ord_less_nat @ I2 @ K3 )
           => ? [X7: fset_l1334069825099621524od_a_b] : ( P @ I2 @ X7 ) ) )
      = ( ? [Xs4: list_f1445794025290330138od_a_b] :
            ( ( ( size_s6068669265016274566od_a_b @ Xs4 )
              = K3 )
            & ! [I2: nat] :
                ( ( ord_less_nat @ I2 @ K3 )
               => ( P @ I2 @ ( nth_fs7310631729605226779od_a_b @ Xs4 @ I2 ) ) ) ) ) ) ).

% Skolem_list_nth
thf(fact_753_list__eq__iff__nth__eq,axiom,
    ( ( ^ [Y6: list_f1445794025290330138od_a_b,Z6: list_f1445794025290330138od_a_b] : ( Y6 = Z6 ) )
    = ( ^ [Xs4: list_f1445794025290330138od_a_b,Ys2: list_f1445794025290330138od_a_b] :
          ( ( ( size_s6068669265016274566od_a_b @ Xs4 )
            = ( size_s6068669265016274566od_a_b @ Ys2 ) )
          & ! [I2: nat] :
              ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs4 ) )
             => ( ( nth_fs7310631729605226779od_a_b @ Xs4 @ I2 )
                = ( nth_fs7310631729605226779od_a_b @ Ys2 @ I2 ) ) ) ) ) ) ).

% list_eq_iff_nth_eq
thf(fact_754_simple__cg__closure__phase__1__helper__length,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xss2: list_f1445794025290330138od_a_b,B: $o,Don: list_f1445794025290330138od_a_b] : ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) @ ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xss2 ) @ ( size_s6068669265016274566od_a_b @ Don ) ) ) ).

% simple_cg_closure_phase_1_helper_length
thf(fact_755_list__property__from__index__property,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,P: list_P1467974523212632366od_a_b > $o,X3: list_P1467974523212632366od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
         => ( P @ ( nth_li6535284973015076149od_a_b @ Xs2 @ I ) ) )
     => ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
       => ( P @ X3 ) ) ) ).

% list_property_from_index_property
thf(fact_756_list__property__from__index__property,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o,X3: fset_l1334069825099621524od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) ) )
     => ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
       => ( P @ X3 ) ) ) ).

% list_property_from_index_property
thf(fact_757_all__set__conv__all__nth,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ( ! [X5: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X5 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( P @ X5 ) ) )
      = ( ! [I2: nat] :
            ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I2 ) ) ) ) ) ).

% all_set_conv_all_nth
thf(fact_758_all__nth__imp__all__set,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,P: list_P1467974523212632366od_a_b > $o,X3: list_P1467974523212632366od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
         => ( P @ ( nth_li6535284973015076149od_a_b @ Xs2 @ I ) ) )
     => ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
       => ( P @ X3 ) ) ) ).

% all_nth_imp_all_set
thf(fact_759_all__nth__imp__all__set,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o,X3: fset_l1334069825099621524od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) ) )
     => ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
       => ( P @ X3 ) ) ) ).

% all_nth_imp_all_set
thf(fact_760_in__set__conv__nth,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
      = ( ? [I2: nat] :
            ( ( ord_less_nat @ I2 @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
            & ( ( nth_li6535284973015076149od_a_b @ Xs2 @ I2 )
              = X3 ) ) ) ) ).

% in_set_conv_nth
thf(fact_761_in__set__conv__nth,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( ? [I2: nat] :
            ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
            & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I2 )
              = X3 ) ) ) ) ).

% in_set_conv_nth
thf(fact_762_list__ball__nth,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ! [X4: fset_l1334069825099621524od_a_b] :
            ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( P @ X4 ) )
       => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) ) ) ) ).

% list_ball_nth
thf(fact_763_nth__mem,axiom,
    ! [N: nat,Xs2: list_l8778361445553822004od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
     => ( member6895035109809442519od_a_b @ ( nth_li6535284973015076149od_a_b @ Xs2 @ N ) @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% nth_mem
thf(fact_764_nth__mem,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( member361094292949318077od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% nth_mem
thf(fact_765_nth__butlast,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) ) )
     => ( ( nth_fs7310631729605226779od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) @ N )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) ) ) ).

% nth_butlast
thf(fact_766_fset__eqI,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b] :
      ( ! [X4: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ X4 @ A4 )
          = ( fmembe7722352836199763061od_a_b @ X4 @ B6 ) )
     => ( A4 = B6 ) ) ).

% fset_eqI
thf(fact_767_fequalityCE,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b,C2: list_P1467974523212632366od_a_b] :
      ( ( A4 = B6 )
     => ( ( ( fmembe7722352836199763061od_a_b @ C2 @ A4 )
         => ~ ( fmembe7722352836199763061od_a_b @ C2 @ B6 ) )
       => ~ ( ~ ( fmembe7722352836199763061od_a_b @ C2 @ A4 )
           => ( fmembe7722352836199763061od_a_b @ C2 @ B6 ) ) ) ) ).

% fequalityCE
thf(fact_768_eq__fmem__trans,axiom,
    ! [A: list_P1467974523212632366od_a_b,B: list_P1467974523212632366od_a_b,A4: fset_l1334069825099621524od_a_b] :
      ( ( A = B )
     => ( ( fmembe7722352836199763061od_a_b @ B @ A4 )
       => ( fmembe7722352836199763061od_a_b @ A @ A4 ) ) ) ).

% eq_fmem_trans
thf(fact_769_eqfset__imp__iff,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b,X3: list_P1467974523212632366od_a_b] :
      ( ( A4 = B6 )
     => ( ( fmembe7722352836199763061od_a_b @ X3 @ A4 )
        = ( fmembe7722352836199763061od_a_b @ X3 @ B6 ) ) ) ).

% eqfset_imp_iff
thf(fact_770_if__split__fmem1,axiom,
    ! [Q2: $o,X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,B: fset_l1334069825099621524od_a_b] :
      ( ( fmembe7722352836199763061od_a_b @ ( if_lis1002476807507936500od_a_b @ Q2 @ X3 @ Y3 ) @ B )
      = ( ( Q2
         => ( fmembe7722352836199763061od_a_b @ X3 @ B ) )
        & ( ~ Q2
         => ( fmembe7722352836199763061od_a_b @ Y3 @ B ) ) ) ) ).

% if_split_fmem1
thf(fact_771_if__split__fmem2,axiom,
    ! [A: list_P1467974523212632366od_a_b,Q2: $o,X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( fmembe7722352836199763061od_a_b @ A @ ( if_fse2516390947016424794od_a_b @ Q2 @ X3 @ Y3 ) )
      = ( ( Q2
         => ( fmembe7722352836199763061od_a_b @ A @ X3 ) )
        & ( ~ Q2
         => ( fmembe7722352836199763061od_a_b @ A @ Y3 ) ) ) ) ).

% if_split_fmem2
thf(fact_772_eqfelem__imp__iff,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,A4: fset_l1334069825099621524od_a_b] :
      ( ( X3 = Y3 )
     => ( ( fmembe7722352836199763061od_a_b @ X3 @ A4 )
        = ( fmembe7722352836199763061od_a_b @ Y3 @ A4 ) ) ) ).

% eqfelem_imp_iff
thf(fact_773_fin__mono,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b,X3: list_P1467974523212632366od_a_b] :
      ( ( ord_le5177564485156961332od_a_b @ A4 @ B6 )
     => ( ( fmembe7722352836199763061od_a_b @ X3 @ A4 )
       => ( fmembe7722352836199763061od_a_b @ X3 @ B6 ) ) ) ).

% fin_mono
thf(fact_774_fsubsetD,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b,C2: list_P1467974523212632366od_a_b] :
      ( ( ord_le5177564485156961332od_a_b @ A4 @ B6 )
     => ( ( fmembe7722352836199763061od_a_b @ C2 @ A4 )
       => ( fmembe7722352836199763061od_a_b @ C2 @ B6 ) ) ) ).

% fsubsetD
thf(fact_775_pfsubsetD,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,B6: fset_l1334069825099621524od_a_b,C2: list_P1467974523212632366od_a_b] :
      ( ( ord_le98927018796173120od_a_b @ A4 @ B6 )
     => ( ( fmembe7722352836199763061od_a_b @ C2 @ A4 )
       => ( fmembe7722352836199763061od_a_b @ C2 @ B6 ) ) ) ).

% pfsubsetD
thf(fact_776_lists__of__length__elems,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,T3: list_P1467974523212632366od_a_b,N: nat] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( lists_5148932666697663363od_a_b @ T3 @ N ) ) )
     => ( ord_le817736998455962536od_a_b @ ( set_Product_prod_a_b2 @ Xs2 ) @ ( set_Product_prod_a_b2 @ T3 ) ) ) ).

% lists_of_length_elems
thf(fact_777_lists__of__length__elems,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,T3: list_f1445794025290330138od_a_b,N: nat] :
      ( ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( lists_98629209091004527od_a_b @ T3 @ N ) ) )
     => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ T3 ) ) ) ).

% lists_of_length_elems
thf(fact_778_lists__of__length__length,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,T3: list_P1467974523212632366od_a_b,N: nat] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( lists_5148932666697663363od_a_b @ T3 @ N ) ) )
     => ( ( size_s3956712670882376602od_a_b @ Xs2 )
        = N ) ) ).

% lists_of_length_length
thf(fact_779_lists__of__length__length,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,T3: list_f1445794025290330138od_a_b,N: nat] :
      ( ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( lists_98629209091004527od_a_b @ T3 @ N ) ) )
     => ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = N ) ) ).

% lists_of_length_length
thf(fact_780_list__append__idx__prop2,axiom,
    ! [Xs5: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,Ys5: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b > $o] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs5 )
        = ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ( size_s6068669265016274566od_a_b @ Ys5 )
          = ( size_s6068669265016274566od_a_b @ Ys3 ) )
       => ( ( ! [I2: nat] :
                ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
               => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I2 ) @ ( nth_fs7310631729605226779od_a_b @ Xs5 @ I2 ) ) ) )
          = ( ! [J: nat] :
                ( ( ( ord_less_nat @ J @ ( size_s6068669265016274566od_a_b @ ( append2015155619842375983od_a_b @ Ys3 @ Xs2 ) ) )
                  & ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Ys3 ) @ J ) )
               => ( P @ ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Ys3 @ Xs2 ) @ J ) @ ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Ys5 @ Xs5 ) @ J ) ) ) ) ) ) ) ).

% list_append_idx_prop2
thf(fact_781_list__append__idx__prop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,P: fset_l1334069825099621524od_a_b > $o,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ! [I2: nat] :
            ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( P @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I2 ) ) ) )
      = ( ! [J: nat] :
            ( ( ( ord_less_nat @ J @ ( size_s6068669265016274566od_a_b @ ( append2015155619842375983od_a_b @ Ys3 @ Xs2 ) ) )
              & ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Ys3 ) @ J ) )
           => ( P @ ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Ys3 @ Xs2 ) @ J ) ) ) ) ) ).

% list_append_idx_prop
thf(fact_782_simple__cg__closure__phase__1__helper_Osimps_I1_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,B: $o,Done2: list_f1445794025290330138od_a_b] :
      ( ( simple257211598216488121od_a_b @ X3 @ nil_fs4581119677382125722od_a_b @ ( produc7489420772309856409od_a_b @ B @ Done2 ) )
      = ( produc7489420772309856409od_a_b @ B @ Done2 ) ) ).

% simple_cg_closure_phase_1_helper.simps(1)
thf(fact_783_updates__append1,axiom,
    ! [Ks: list_f1445794025290330138od_a_b,Vs2: list_f1445794025290330138od_a_b,K3: fset_l1334069825099621524od_a_b,Al: list_P1164858718851775149od_a_b] :
      ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ Ks ) @ ( size_s6068669265016274566od_a_b @ Vs2 ) )
     => ( ( update696951664350256759od_a_b @ ( append2015155619842375983od_a_b @ Ks @ ( cons_f6577355434438001738od_a_b @ K3 @ nil_fs4581119677382125722od_a_b ) ) @ Vs2 @ Al )
        = ( update1532413134665826556od_a_b @ K3 @ ( nth_fs7310631729605226779od_a_b @ Vs2 @ ( size_s6068669265016274566od_a_b @ Ks ) ) @ ( update696951664350256759od_a_b @ Ks @ Vs2 @ Al ) ) ) ) ).

% updates_append1
thf(fact_784_subrelI,axiom,
    ! [R: set_Pr121319624013539721od_a_b,S2: set_Pr121319624013539721od_a_b] :
      ( ! [X4: $o,Y: list_f1445794025290330138od_a_b] :
          ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ R )
         => ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ S2 ) )
     => ( ord_le7778196599191822633od_a_b @ R @ S2 ) ) ).

% subrelI
thf(fact_785_subrelI,axiom,
    ! [R: set_Pr5622538825374275996od_a_b,S2: set_Pr5622538825374275996od_a_b] :
      ( ! [X4: $o,Y: produc2518759752815613485od_a_b] :
          ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ R )
         => ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ S2 ) )
     => ( ord_le4232407541035512124od_a_b @ R @ S2 ) ) ).

% subrelI
thf(fact_786_subrelI,axiom,
    ! [R: set_Pr1051027220935592077od_a_b,S2: set_Pr1051027220935592077od_a_b] :
      ( ! [X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b] :
          ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ R )
         => ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ S2 ) )
     => ( ord_le8991869396981723181od_a_b @ R @ S2 ) ) ).

% subrelI
thf(fact_787_listrel1__iff__update,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( listre757946421397414515od_a_b @ R ) )
      = ( ? [Y4: fset_l1334069825099621524od_a_b,N2: nat] :
            ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N2 ) @ Y4 ) @ R )
            & ( ord_less_nat @ N2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
            & ( Ys3
              = ( list_u7851604859245713154od_a_b @ Xs2 @ N2 @ Y4 ) ) ) ) ) ).

% listrel1_iff_update
thf(fact_788_non__sym__dist__pairs_H__indices,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy1352304633095342623od_a_b @ Xs2 ) ) )
       => ? [I: nat,J2: nat] :
            ( ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I )
              = X3 )
            & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ J2 )
              = Y3 )
            & ( ord_less_nat @ I @ J2 )
            & ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
            & ( ord_less_nat @ J2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ) ) ).

% non_sym_dist_pairs'_indices
thf(fact_789_length__list__update,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,I3: nat,X3: fset_l1334069825099621524od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) )
      = ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% length_list_update
thf(fact_790_list__update__beyond,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,I3: nat,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ I3 )
     => ( ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 )
        = Xs2 ) ) ).

% list_update_beyond
thf(fact_791_updates__append__drop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,Al: list_P1164858718851775149od_a_b] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( update696951664350256759od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Zs ) @ Ys3 @ Al )
        = ( update696951664350256759od_a_b @ Xs2 @ Ys3 @ Al ) ) ) ).

% updates_append_drop
thf(fact_792_updates__append2__drop,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b,Al: list_P1164858718851775149od_a_b] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( size_s6068669265016274566od_a_b @ Ys3 ) )
     => ( ( update696951664350256759od_a_b @ Xs2 @ ( append2015155619842375983od_a_b @ Ys3 @ Zs ) @ Al )
        = ( update696951664350256759od_a_b @ Xs2 @ Ys3 @ Al ) ) ) ).

% updates_append2_drop
thf(fact_793_updates__simps_I3_J,axiom,
    ! [K3: fset_l1334069825099621524od_a_b,Ks: list_f1445794025290330138od_a_b,V2: fset_l1334069825099621524od_a_b,Vs2: list_f1445794025290330138od_a_b,Ps2: list_P1164858718851775149od_a_b] :
      ( ( update696951664350256759od_a_b @ ( cons_f6577355434438001738od_a_b @ K3 @ Ks ) @ ( cons_f6577355434438001738od_a_b @ V2 @ Vs2 ) @ Ps2 )
      = ( update696951664350256759od_a_b @ Ks @ Vs2 @ ( update1532413134665826556od_a_b @ K3 @ V2 @ Ps2 ) ) ) ).

% updates_simps(3)
thf(fact_794_list__update__length,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( list_u7851604859245713154od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ Ys3 ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ Y3 )
      = ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) ) ) ).

% list_update_length
thf(fact_795_nth__list__update__eq,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( nth_fs7310631729605226779od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) @ I3 )
        = X3 ) ) ).

% nth_list_update_eq
thf(fact_796_set__swap,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,J3: nat] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ord_less_nat @ J3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( set_fs4298891544546585641od_a_b @ ( list_u7851604859245713154od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) ) @ J3 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) ) )
          = ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% set_swap
thf(fact_797_distinct__swap,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,J3: nat] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ord_less_nat @ J3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( distin1329390416381046541od_a_b @ ( list_u7851604859245713154od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) ) @ J3 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) ) )
          = ( distin1329390416381046541od_a_b @ Xs2 ) ) ) ) ).

% distinct_swap
thf(fact_798_updates__list__update__drop,axiom,
    ! [Ks: list_f1445794025290330138od_a_b,I3: nat,Vs2: list_f1445794025290330138od_a_b,V2: fset_l1334069825099621524od_a_b,Al: list_P1164858718851775149od_a_b] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Ks ) @ I3 )
     => ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Vs2 ) )
       => ( ( update696951664350256759od_a_b @ Ks @ ( list_u7851604859245713154od_a_b @ Vs2 @ I3 @ V2 ) @ Al )
          = ( update696951664350256759od_a_b @ Ks @ Vs2 @ Al ) ) ) ) ).

% updates_list_update_drop
thf(fact_799_distinct__length__2__or__more,axiom,
    ! [A: fset_l1334069825099621524od_a_b,B: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( distin1329390416381046541od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ ( cons_f6577355434438001738od_a_b @ B @ Xs2 ) ) )
      = ( ( A != B )
        & ( distin1329390416381046541od_a_b @ ( cons_f6577355434438001738od_a_b @ A @ Xs2 ) )
        & ( distin1329390416381046541od_a_b @ ( cons_f6577355434438001738od_a_b @ B @ Xs2 ) ) ) ) ).

% distinct_length_2_or_more
thf(fact_800_distinct__set__subseqs,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( distin6974803764735332205od_a_b @ ( map_li1742795277881387806od_a_b @ set_fs4298891544546585641od_a_b @ ( subseq8423821483446685161od_a_b @ Xs2 ) ) ) ) ).

% distinct_set_subseqs
thf(fact_801_distinct__singleton,axiom,
    ! [X3: fset_l1334069825099621524od_a_b] : ( distin1329390416381046541od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) ).

% distinct_singleton
thf(fact_802_distinct_Osimps_I2_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( distin3617893958516599847od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ Xs2 ) )
      = ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
        & ( distin3617893958516599847od_a_b @ Xs2 ) ) ) ).

% distinct.simps(2)
thf(fact_803_distinct_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( distin1329390416381046541od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
        & ( distin1329390416381046541od_a_b @ Xs2 ) ) ) ).

% distinct.simps(2)
thf(fact_804_set__update__subsetI,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,A4: set_li6306622547289818894od_a_b,X3: list_P1467974523212632366od_a_b,I3: nat] :
      ( ( ord_le153002609085230766od_a_b @ ( set_li5045283583078295363od_a_b @ Xs2 ) @ A4 )
     => ( ( member6895035109809442519od_a_b @ X3 @ A4 )
       => ( ord_le153002609085230766od_a_b @ ( set_li5045283583078295363od_a_b @ ( list_u6451611954593206940od_a_b @ Xs2 @ I3 @ X3 ) ) @ A4 ) ) ) ).

% set_update_subsetI
thf(fact_805_set__update__subsetI,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,A4: set_fs5173440902860351732od_a_b,X3: fset_l1334069825099621524od_a_b,I3: nat] :
      ( ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ A4 )
     => ( ( member361094292949318077od_a_b @ X3 @ A4 )
       => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) ) @ A4 ) ) ) ).

% set_update_subsetI
thf(fact_806_subseqs__distinctD,axiom,
    ! [Ys3: list_P1467974523212632366od_a_b,Xs2: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Ys3 @ ( set_li5045283583078295363od_a_b @ ( subseq3159716953272533757od_a_b @ Xs2 ) ) )
     => ( ( distin132333874345289761od_a_b @ Xs2 )
       => ( distin132333874345289761od_a_b @ Ys3 ) ) ) ).

% subseqs_distinctD
thf(fact_807_not__distinct__decomp,axiom,
    ! [Ws: list_f1445794025290330138od_a_b] :
      ( ~ ( distin1329390416381046541od_a_b @ Ws )
     => ? [Xs3: list_f1445794025290330138od_a_b,Ys: list_f1445794025290330138od_a_b,Zs2: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b] :
          ( Ws
          = ( append2015155619842375983od_a_b @ Xs3 @ ( append2015155619842375983od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ nil_fs4581119677382125722od_a_b ) @ ( append2015155619842375983od_a_b @ Ys @ ( append2015155619842375983od_a_b @ ( cons_f6577355434438001738od_a_b @ Y @ nil_fs4581119677382125722od_a_b ) @ Zs2 ) ) ) ) ) ) ).

% not_distinct_decomp
thf(fact_808_not__distinct__conv__prefix,axiom,
    ! [As: list_l8778361445553822004od_a_b] :
      ( ( ~ ( distin3617893958516599847od_a_b @ As ) )
      = ( ? [Xs4: list_l8778361445553822004od_a_b,Y4: list_P1467974523212632366od_a_b,Ys2: list_l8778361445553822004od_a_b] :
            ( ( member6895035109809442519od_a_b @ Y4 @ ( set_li5045283583078295363od_a_b @ Xs4 ) )
            & ( distin3617893958516599847od_a_b @ Xs4 )
            & ( As
              = ( append7557446516274476873od_a_b @ Xs4 @ ( cons_l907386227682280420od_a_b @ Y4 @ Ys2 ) ) ) ) ) ) ).

% not_distinct_conv_prefix
thf(fact_809_not__distinct__conv__prefix,axiom,
    ! [As: list_f1445794025290330138od_a_b] :
      ( ( ~ ( distin1329390416381046541od_a_b @ As ) )
      = ( ? [Xs4: list_f1445794025290330138od_a_b,Y4: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( member361094292949318077od_a_b @ Y4 @ ( set_fs4298891544546585641od_a_b @ Xs4 ) )
            & ( distin1329390416381046541od_a_b @ Xs4 )
            & ( As
              = ( append2015155619842375983od_a_b @ Xs4 @ ( cons_f6577355434438001738od_a_b @ Y4 @ Ys2 ) ) ) ) ) ) ).

% not_distinct_conv_prefix
thf(fact_810_nth__eq__iff__index__eq,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,I3: nat,J3: nat] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( ord_less_nat @ J3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 )
              = ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) )
            = ( I3 = J3 ) ) ) ) ) ).

% nth_eq_iff_index_eq
thf(fact_811_distinct__conv__nth,axiom,
    ( distin1329390416381046541od_a_b
    = ( ^ [Xs4: list_f1445794025290330138od_a_b] :
        ! [I2: nat] :
          ( ( ord_less_nat @ I2 @ ( size_s6068669265016274566od_a_b @ Xs4 ) )
         => ! [J: nat] :
              ( ( ord_less_nat @ J @ ( size_s6068669265016274566od_a_b @ Xs4 ) )
             => ( ( I2 != J )
               => ( ( nth_fs7310631729605226779od_a_b @ Xs4 @ I2 )
                 != ( nth_fs7310631729605226779od_a_b @ Xs4 @ J ) ) ) ) ) ) ) ).

% distinct_conv_nth
thf(fact_812_non__distinct__repetition__indices__rev,axiom,
    ! [I3: nat,J3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ J3 )
     => ( ( ord_less_nat @ J3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 )
            = ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) )
         => ~ ( distin1329390416381046541od_a_b @ Xs2 ) ) ) ) ).

% non_distinct_repetition_indices_rev
thf(fact_813_non__distinct__repetition__indices,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ~ ( distin1329390416381046541od_a_b @ Xs2 )
     => ? [I: nat,J2: nat] :
          ( ( ord_less_nat @ I @ J2 )
          & ( ord_less_nat @ J2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
          & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I )
            = ( nth_fs7310631729605226779od_a_b @ Xs2 @ J2 ) ) ) ) ).

% non_distinct_repetition_indices
thf(fact_814_set__update__subset__insert,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,I3: nat,X3: fset_l1334069825099621524od_a_b] : ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) ) @ ( insert3249498615411298916od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% set_update_subset_insert
thf(fact_815_set__update__memI,axiom,
    ! [N: nat,Xs2: list_l8778361445553822004od_a_b,X3: list_P1467974523212632366od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( list_u6451611954593206940od_a_b @ Xs2 @ N @ X3 ) ) ) ) ).

% set_update_memI
thf(fact_816_set__update__memI,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ N @ X3 ) ) ) ) ).

% set_update_memI
thf(fact_817_list__update__append1,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( list_u7851604859245713154od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ I3 @ X3 )
        = ( append2015155619842375983od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) @ Ys3 ) ) ) ).

% list_update_append1
thf(fact_818_list__update__same__conv,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 )
          = Xs2 )
        = ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 )
          = X3 ) ) ) ).

% list_update_same_conv
thf(fact_819_nth__list__update,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,J3: nat,X3: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ( I3 = J3 )
         => ( ( nth_fs7310631729605226779od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) @ J3 )
            = X3 ) )
        & ( ( I3 != J3 )
         => ( ( nth_fs7310631729605226779od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ X3 ) @ J3 )
            = ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) ) ) ) ) ).

% nth_list_update
thf(fact_820_distinct__Ex1,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,X3: list_P1467974523212632366od_a_b] :
      ( ( distin3617893958516599847od_a_b @ Xs2 )
     => ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
       => ? [X4: nat] :
            ( ( ord_less_nat @ X4 @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
            & ( ( nth_li6535284973015076149od_a_b @ Xs2 @ X4 )
              = X3 )
            & ! [Y5: nat] :
                ( ( ( ord_less_nat @ Y5 @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
                  & ( ( nth_li6535284973015076149od_a_b @ Xs2 @ Y5 )
                    = X3 ) )
               => ( Y5 = X4 ) ) ) ) ) ).

% distinct_Ex1
thf(fact_821_distinct__Ex1,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
       => ? [X4: nat] :
            ( ( ord_less_nat @ X4 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
            & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ X4 )
              = X3 )
            & ! [Y5: nat] :
                ( ( ( ord_less_nat @ Y5 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
                  & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ Y5 )
                    = X3 ) )
               => ( Y5 = X4 ) ) ) ) ) ).

% distinct_Ex1
thf(fact_822_non__sym__dist__pairs_H__elems__distinct_I1_J,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( distin3617893958516599847od_a_b @ Xs2 )
     => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy4621517932026394681od_a_b @ Xs2 ) ) )
       => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% non_sym_dist_pairs'_elems_distinct(1)
thf(fact_823_non__sym__dist__pairs_H__elems__distinct_I1_J,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy1352304633095342623od_a_b @ Xs2 ) ) )
       => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% non_sym_dist_pairs'_elems_distinct(1)
thf(fact_824_non__sym__dist__pairs_H__elems__distinct_I2_J,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( distin3617893958516599847od_a_b @ Xs2 )
     => ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y3 ) @ ( set_Pr1811016573229031484od_a_b @ ( non_sy4621517932026394681od_a_b @ Xs2 ) ) )
       => ( member6895035109809442519od_a_b @ Y3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ) ).

% non_sym_dist_pairs'_elems_distinct(2)
thf(fact_825_non__sym__dist__pairs_H__elems__distinct_I2_J,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ X3 @ Y3 ) @ ( set_Pr3326995048199123516od_a_b @ ( non_sy1352304633095342623od_a_b @ Xs2 ) ) )
       => ( member361094292949318077od_a_b @ Y3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ) ).

% non_sym_dist_pairs'_elems_distinct(2)
thf(fact_826_eq__key__imp__eq__value,axiom,
    ! [Xs2: list_P3574414722980446895od_a_b,K3: $o,V1: list_f1445794025290330138od_a_b,V22: list_f1445794025290330138od_a_b] :
      ( ( distinct_o @ ( map_Pr8806166102037958131_a_b_o @ produc5358503411717041797od_a_b @ Xs2 ) )
     => ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V1 ) @ ( set_Pr6076554551450486590od_a_b @ Xs2 ) )
       => ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ K3 @ V22 ) @ ( set_Pr6076554551450486590od_a_b @ Xs2 ) )
         => ( V1 = V22 ) ) ) ) ).

% eq_key_imp_eq_value
thf(fact_827_eq__key__imp__eq__value,axiom,
    ! [Xs2: list_P5302045529885307074od_a_b,K3: $o,V1: produc2518759752815613485od_a_b,V22: produc2518759752815613485od_a_b] :
      ( ( distinct_o @ ( map_Pr56420267031402400_a_b_o @ produc2316053142268291992od_a_b @ Xs2 ) )
     => ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V1 ) @ ( set_Pr3486397488485167313od_a_b @ Xs2 ) )
       => ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ K3 @ V22 ) @ ( set_Pr3486397488485167313od_a_b @ Xs2 ) )
         => ( V1 = V22 ) ) ) ) ).

% eq_key_imp_eq_value
thf(fact_828_eq__key__imp__eq__value,axiom,
    ! [Xs2: list_P5488608094462411443od_a_b,K3: fset_l1334069825099621524od_a_b,V1: list_f1445794025290330138od_a_b,V22: list_f1445794025290330138od_a_b] :
      ( ( distin1329390416381046541od_a_b @ ( map_Pr4898593741463396971od_a_b @ produc5739577146777995401od_a_b @ Xs2 ) )
     => ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V1 ) @ ( set_Pr6825554078267013186od_a_b @ Xs2 ) )
       => ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ K3 @ V22 ) @ ( set_Pr6825554078267013186od_a_b @ Xs2 ) )
         => ( V1 = V22 ) ) ) ) ).

% eq_key_imp_eq_value
thf(fact_829_nth__enumerate__eq,axiom,
    ! [M2: nat,Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ord_less_nat @ M2 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( nth_Pr5342818094514074866od_a_b @ ( enumer6431117045728783481od_a_b @ N @ Xs2 ) @ M2 )
        = ( produc8653188414478805099od_a_b @ ( plus_plus_nat @ N @ M2 ) @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ M2 ) ) ) ) ).

% nth_enumerate_eq
thf(fact_830_append__one__prefix,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Xs2 @ Ys3 )
     => ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ ( size_s6068669265016274566od_a_b @ Ys3 ) )
       => ( prefix7449001915862371055od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ ( nth_fs7310631729605226779od_a_b @ Ys3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) @ nil_fs4581119677382125722od_a_b ) ) @ Ys3 ) ) ) ).

% append_one_prefix
thf(fact_831_Cons__prefix__Cons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
      = ( ( X3 = Y3 )
        & ( prefix7449001915862371055od_a_b @ Xs2 @ Ys3 ) ) ) ).

% Cons_prefix_Cons
thf(fact_832_length__enumerate,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s1491918145416384605od_a_b @ ( enumer6431117045728783481od_a_b @ N @ Xs2 ) )
      = ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% length_enumerate
thf(fact_833_in__set__prefixes,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) )
      = ( prefix3118977441345254915od_a_b @ Xs2 @ Ys3 ) ) ).

% in_set_prefixes
thf(fact_834_prefix__snoc,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Xs2 @ ( append2015155619842375983od_a_b @ Ys3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ nil_fs4581119677382125722od_a_b ) ) )
      = ( ( Xs2
          = ( append2015155619842375983od_a_b @ Ys3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ nil_fs4581119677382125722od_a_b ) ) )
        | ( prefix7449001915862371055od_a_b @ Xs2 @ Ys3 ) ) ) ).

% prefix_snoc
thf(fact_835_not__prefix__induct,axiom,
    ! [Ps2: list_f1445794025290330138od_a_b,Ls: list_f1445794025290330138od_a_b,P: list_f1445794025290330138od_a_b > list_f1445794025290330138od_a_b > $o] :
      ( ~ ( prefix7449001915862371055od_a_b @ Ps2 @ Ls )
     => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] : ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ nil_fs4581119677382125722od_a_b )
       => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
              ( ( X4 != Y )
             => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) )
         => ( ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b,Y: fset_l1334069825099621524od_a_b,Ys: list_f1445794025290330138od_a_b] :
                ( ( X4 = Y )
               => ( ~ ( prefix7449001915862371055od_a_b @ Xs3 @ Ys )
                 => ( ( P @ Xs3 @ Ys )
                   => ( P @ ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) @ ( cons_f6577355434438001738od_a_b @ Y @ Ys ) ) ) ) )
           => ( P @ Ps2 @ Ls ) ) ) ) ) ).

% not_prefix_induct
thf(fact_836_not__prefix__cases,axiom,
    ! [Ps2: list_f1445794025290330138od_a_b,Ls: list_f1445794025290330138od_a_b] :
      ( ~ ( prefix7449001915862371055od_a_b @ Ps2 @ Ls )
     => ( ( ( Ps2 != nil_fs4581119677382125722od_a_b )
         => ( Ls != nil_fs4581119677382125722od_a_b ) )
       => ( ! [A3: fset_l1334069825099621524od_a_b,As2: list_f1445794025290330138od_a_b] :
              ( ( Ps2
                = ( cons_f6577355434438001738od_a_b @ A3 @ As2 ) )
             => ! [X4: fset_l1334069825099621524od_a_b,Xs3: list_f1445794025290330138od_a_b] :
                  ( ( Ls
                    = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
                 => ( ( X4 = A3 )
                   => ( prefix7449001915862371055od_a_b @ As2 @ Xs3 ) ) ) )
         => ~ ! [A3: fset_l1334069825099621524od_a_b] :
                ( ? [As2: list_f1445794025290330138od_a_b] :
                    ( Ps2
                    = ( cons_f6577355434438001738od_a_b @ A3 @ As2 ) )
               => ! [X4: fset_l1334069825099621524od_a_b] :
                    ( ? [Xs3: list_f1445794025290330138od_a_b] :
                        ( Ls
                        = ( cons_f6577355434438001738od_a_b @ X4 @ Xs3 ) )
                   => ( X4 = A3 ) ) ) ) ) ) ).

% not_prefix_cases
thf(fact_837_prefix__Cons,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
      = ( ( Xs2 = nil_fs4581119677382125722od_a_b )
        | ? [Zs3: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ Y3 @ Zs3 ) )
            & ( prefix7449001915862371055od_a_b @ Zs3 @ Ys3 ) ) ) ) ).

% prefix_Cons
thf(fact_838_prefix__code_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ~ ( prefix7449001915862371055od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ nil_fs4581119677382125722od_a_b ) ).

% prefix_code(2)
thf(fact_839_set__mono__prefix,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Xs2 @ Ys3 )
     => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Ys3 ) ) ) ).

% set_mono_prefix
thf(fact_840_prefix__length__prefix,axiom,
    ! [Ps2: list_f1445794025290330138od_a_b,Xs2: list_f1445794025290330138od_a_b,Qs: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Ps2 @ Xs2 )
     => ( ( prefix7449001915862371055od_a_b @ Qs @ Xs2 )
       => ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Ps2 ) @ ( size_s6068669265016274566od_a_b @ Qs ) )
         => ( prefix7449001915862371055od_a_b @ Ps2 @ Qs ) ) ) ) ).

% prefix_length_prefix
thf(fact_841_prefix__length__le,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( prefix7449001915862371055od_a_b @ Xs2 @ Ys3 )
     => ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ ( size_s6068669265016274566od_a_b @ Ys3 ) ) ) ).

% prefix_length_le
thf(fact_842_enumerate__append__eq,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( enumer6431117045728783481od_a_b @ N @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
      = ( append7576980629738617822od_a_b @ ( enumer6431117045728783481od_a_b @ N @ Xs2 ) @ ( enumer6431117045728783481od_a_b @ ( plus_plus_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) @ Ys3 ) ) ) ).

% enumerate_append_eq
thf(fact_843_in__set__enumerate__eq,axiom,
    ! [P2: produc6829992310584780345od_a_b,N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member3914385324806363600od_a_b @ P2 @ ( set_Pr3993988432441487460od_a_b @ ( enumer6431117045728783481od_a_b @ N @ Xs2 ) ) )
      = ( ( ord_less_eq_nat @ N @ ( produc3138289943185643391od_a_b @ P2 ) )
        & ( ord_less_nat @ ( produc3138289943185643391od_a_b @ P2 ) @ ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) )
        & ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( minus_minus_nat @ ( produc3138289943185643391od_a_b @ P2 ) @ N ) )
          = ( produc2570711435215982525od_a_b @ P2 ) ) ) ) ).

% in_set_enumerate_eq
thf(fact_844_length__prefixes,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s3205160614079436684od_a_b @ ( prefix4612422245637881633od_a_b @ Xs2 ) )
      = ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) ) ).

% length_prefixes
thf(fact_845_lex__take__index,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ Xs2 @ Ys3 ) @ ( lex_fs1791213440591458046od_a_b @ R ) )
     => ~ ! [I: nat] :
            ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
           => ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Ys3 ) )
             => ( ( ( take_f8758302346742390914od_a_b @ I @ Xs2 )
                  = ( take_f8758302346742390914od_a_b @ I @ Ys3 ) )
               => ~ ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) @ ( nth_fs7310631729605226779od_a_b @ Ys3 @ I ) ) @ R ) ) ) ) ) ).

% lex_take_index
thf(fact_846_take__all,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N )
     => ( ( take_f8758302346742390914od_a_b @ N @ Xs2 )
        = Xs2 ) ) ).

% take_all
thf(fact_847_take__all__iff,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( take_f8758302346742390914od_a_b @ N @ Xs2 )
        = Xs2 )
      = ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) ) ).

% take_all_iff
thf(fact_848_take__append,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( take_f8758302346742390914od_a_b @ N @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
      = ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) @ ( take_f8758302346742390914od_a_b @ ( minus_minus_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) @ Ys3 ) ) ) ).

% take_append
thf(fact_849_length__butlast,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) )
      = ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) ) ).

% length_butlast
thf(fact_850_rotate1__length01,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat )
     => ( ( rotate1032322621218768487od_a_b @ Xs2 )
        = Xs2 ) ) ).

% rotate1_length01
thf(fact_851_butlast__list__update,axiom,
    ! [K3: nat,Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ( K3
          = ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) )
       => ( ( butlas6970048242682811878od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ K3 @ X3 ) )
          = ( butlas6970048242682811878od_a_b @ Xs2 ) ) )
      & ( ( K3
         != ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) )
       => ( ( butlas6970048242682811878od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ K3 @ X3 ) )
          = ( list_u7851604859245713154od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) @ K3 @ X3 ) ) ) ) ).

% butlast_list_update
thf(fact_852_butlast__take,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( butlas6970048242682811878od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) )
        = ( take_f8758302346742390914od_a_b @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs2 ) ) ) ).

% butlast_take
thf(fact_853_in__set__takeD,axiom,
    ! [X3: list_P1467974523212632366od_a_b,N: nat,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( take_l2578627034827611164od_a_b @ N @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% in_set_takeD
thf(fact_854_in__set__takeD,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% in_set_takeD
thf(fact_855_butlast__conv__take,axiom,
    ( butlas6970048242682811878od_a_b
    = ( ^ [Xs4: list_f1445794025290330138od_a_b] : ( take_f8758302346742390914od_a_b @ ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs4 ) @ one_one_nat ) @ Xs4 ) ) ) ).

% butlast_conv_take
thf(fact_856_set__take__subset,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] : ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) ) @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ).

% set_take_subset
thf(fact_857_take__diff,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,J3: nat] :
      ( ( ord_less_eq_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ J3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( I3 != J3 )
         => ( ( take_f8758302346742390914od_a_b @ I3 @ Xs2 )
           != ( take_f8758302346742390914od_a_b @ J3 @ Xs2 ) ) ) ) ) ).

% take_diff
thf(fact_858_last__conv__nth,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( last_f4009646753867174963od_a_b @ Xs2 )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) ) ) ) ).

% last_conv_nth
thf(fact_859_last__list__update,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,K3: nat,X3: fset_l1334069825099621524od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( ( K3
            = ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) )
         => ( ( last_f4009646753867174963od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ K3 @ X3 ) )
            = X3 ) )
        & ( ( K3
           != ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) )
         => ( ( last_f4009646753867174963od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ K3 @ X3 ) )
            = ( last_f4009646753867174963od_a_b @ Xs2 ) ) ) ) ) ).

% last_list_update
thf(fact_860_set__take__subset__set__take,axiom,
    ! [M2: nat,N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ M2 @ N )
     => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ M2 @ Xs2 ) ) @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) ) ) ) ).

% set_take_subset_set_take
thf(fact_861_take__le,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( take_f8758302346742390914od_a_b @ I3 @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
        = ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) ) ) ).

% take_le
thf(fact_862_distinct__not__in__prefix,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ! [I: nat,X4: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ ( take_l2578627034827611164od_a_b @ I @ Xs2 ) ) )
         => ( ( nth_li6535284973015076149od_a_b @ Xs2 @ I )
           != X4 ) )
     => ( distin3617893958516599847od_a_b @ Xs2 ) ) ).

% distinct_not_in_prefix
thf(fact_863_distinct__not__in__prefix,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ! [I: nat,X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ I @ Xs2 ) ) )
         => ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I )
           != X4 ) )
     => ( distin1329390416381046541od_a_b @ Xs2 ) ) ).

% distinct_not_in_prefix
thf(fact_864_take__butlast,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( take_f8758302346742390914od_a_b @ N @ ( butlas6970048242682811878od_a_b @ Xs2 ) )
        = ( take_f8758302346742390914od_a_b @ N @ Xs2 ) ) ) ).

% take_butlast
thf(fact_865_butlast__take__le,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ I3 @ ( size_s6068669265016274566od_a_b @ ( butlas6970048242682811878od_a_b @ Xs2 ) ) )
     => ( ( take_f8758302346742390914od_a_b @ I3 @ ( butlas6970048242682811878od_a_b @ Xs2 ) )
        = ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) ) ) ).

% butlast_take_le
thf(fact_866_prefixes__take__iff,axiom,
    ! [Xs2: list_P1467974523212632366od_a_b,Ys3: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Xs2 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Ys3 ) ) )
      = ( ( take_P1986783999826777750od_a_b @ ( size_s3956712670882376602od_a_b @ Xs2 ) @ Ys3 )
        = Xs2 ) ) ).

% prefixes_take_iff
thf(fact_867_prefixes__take__iff,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( member7551773913232940227od_a_b @ Xs2 @ ( set_li8217014873844115759od_a_b @ ( prefix4612422245637881633od_a_b @ Ys3 ) ) )
      = ( ( take_f8758302346742390914od_a_b @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ Ys3 )
        = Xs2 ) ) ).

% prefixes_take_iff
thf(fact_868_nth__take__lemma,axiom,
    ! [K3: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ K3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ K3 @ ( size_s6068669265016274566od_a_b @ Ys3 ) )
       => ( ! [I: nat] :
              ( ( ord_less_nat @ I @ K3 )
             => ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ I )
                = ( nth_fs7310631729605226779od_a_b @ Ys3 @ I ) ) )
         => ( ( take_f8758302346742390914od_a_b @ K3 @ Xs2 )
            = ( take_f8758302346742390914od_a_b @ K3 @ Ys3 ) ) ) ) ) ).

% nth_take_lemma
thf(fact_869_nth__append,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ N )
          = ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) ) )
      & ( ~ ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( nth_fs7310631729605226779od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ N )
          = ( nth_fs7310631729605226779od_a_b @ Ys3 @ ( minus_minus_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ) ) ) ).

% nth_append
thf(fact_870_list__update__append,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( list_u7851604859245713154od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ N @ X3 )
          = ( append2015155619842375983od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ N @ X3 ) @ Ys3 ) ) )
      & ( ~ ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( list_u7851604859245713154od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) @ N @ X3 )
          = ( append2015155619842375983od_a_b @ Xs2 @ ( list_u7851604859245713154od_a_b @ Ys3 @ ( minus_minus_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) @ X3 ) ) ) ) ) ).

% list_update_append
thf(fact_871_list__distinct__prefix,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
         => ~ ( member6895035109809442519od_a_b @ ( nth_li6535284973015076149od_a_b @ Xs2 @ I ) @ ( set_li5045283583078295363od_a_b @ ( take_l2578627034827611164od_a_b @ I @ Xs2 ) ) ) )
     => ( distin3617893958516599847od_a_b @ Xs2 ) ) ).

% list_distinct_prefix
thf(fact_872_list__distinct__prefix,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ~ ( member361094292949318077od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ I @ Xs2 ) ) ) )
     => ( distin1329390416381046541od_a_b @ Xs2 ) ) ).

% list_distinct_prefix
thf(fact_873_take__Suc__conv__app__nth,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( take_f8758302346742390914od_a_b @ ( suc @ I3 ) @ Xs2 )
        = ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% take_Suc_conv_app_nth
thf(fact_874_nth__Cons__pos,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ N )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).

% nth_Cons_pos
thf(fact_875_lexord__take__index__conv,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b,R: set_Pr2242436922956002695od_a_b] :
      ( ( member2549368600341536720od_a_b @ ( produc4047984609689601431od_a_b @ X3 @ Y3 ) @ ( lexord9144254948259057799od_a_b @ R ) )
      = ( ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ X3 ) @ ( size_s6068669265016274566od_a_b @ Y3 ) )
          & ( ( take_f8758302346742390914od_a_b @ ( size_s6068669265016274566od_a_b @ X3 ) @ Y3 )
            = X3 ) )
        | ? [I2: nat] :
            ( ( ord_less_nat @ I2 @ ( ord_min_nat @ ( size_s6068669265016274566od_a_b @ X3 ) @ ( size_s6068669265016274566od_a_b @ Y3 ) ) )
            & ( ( take_f8758302346742390914od_a_b @ I2 @ X3 )
              = ( take_f8758302346742390914od_a_b @ I2 @ Y3 ) )
            & ( member2847915659457029072od_a_b @ ( produc8099561100433402519od_a_b @ ( nth_fs7310631729605226779od_a_b @ X3 @ I2 ) @ ( nth_fs7310631729605226779od_a_b @ Y3 @ I2 ) ) @ R ) ) ) ) ).

% lexord_take_index_conv
thf(fact_876_length__0__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = zero_zero_nat )
      = ( Xs2 = nil_fs4581119677382125722od_a_b ) ) ).

% length_0_conv
thf(fact_877_nth__Cons__Suc,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( suc @ N ) )
      = ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) ) ).

% nth_Cons_Suc
thf(fact_878_nth__Cons__0,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ zero_zero_nat )
      = X3 ) ).

% nth_Cons_0
thf(fact_879_take__Suc__Cons,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( take_f8758302346742390914od_a_b @ ( suc @ N ) @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( cons_f6577355434438001738od_a_b @ X3 @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) ) ) ).

% take_Suc_Cons
thf(fact_880_length__take,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) )
      = ( ord_min_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) ) ).

% length_take
thf(fact_881_length__greater__0__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
      = ( Xs2 != nil_fs4581119677382125722od_a_b ) ) ).

% length_greater_0_conv
thf(fact_882_enumerate__simps_I2_J,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( enumer6431117045728783481od_a_b @ N @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( cons_P1524207422287465219od_a_b @ ( produc8653188414478805099od_a_b @ N @ X3 ) @ ( enumer6431117045728783481od_a_b @ ( suc @ N ) @ Xs2 ) ) ) ).

% enumerate_simps(2)
thf(fact_883_length__suffixes,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s3205160614079436684od_a_b @ ( suffix888123080290511074od_a_b @ Xs2 ) )
      = ( suc @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% length_suffixes
thf(fact_884_list_Osize_I4_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
      = ( plus_plus_nat @ ( size_s6068669265016274566od_a_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).

% list.size(4)
thf(fact_885_monotone__function__with__limit__witness__helper,axiom,
    ! [F2: nat > nat,K3: nat] :
      ( ! [I: nat,J2: nat] :
          ( ( ord_less_eq_nat @ I @ J2 )
         => ( ord_less_eq_nat @ ( F2 @ I ) @ ( F2 @ J2 ) ) )
     => ( ! [I: nat,J2: nat] :
            ( ( ord_less_nat @ I @ J2 )
           => ( ( ( F2 @ I )
                = ( F2 @ J2 ) )
             => ! [M3: nat] :
                  ( ( ord_less_eq_nat @ J2 @ M3 )
                 => ( ( F2 @ I )
                    = ( F2 @ M3 ) ) ) ) )
       => ( ! [I: nat] : ( ord_less_eq_nat @ ( F2 @ I ) @ K3 )
         => ~ ! [X4: nat] :
                ( ( ( F2 @ ( suc @ X4 ) )
                  = ( F2 @ X4 ) )
               => ~ ( ord_less_eq_nat @ X4 @ ( minus_minus_nat @ K3 @ ( F2 @ zero_zero_nat ) ) ) ) ) ) ) ).

% monotone_function_with_limit_witness_helper
thf(fact_886_minimal__fixpoint__helper_I1_J,axiom,
    ! [F2: nat > nat,P: nat > $o,K3: nat,X3: nat] :
      ( ( F2
        = ( ^ [X5: nat] : ( if_nat @ ( P @ X5 ) @ X5 @ ( F2 @ ( suc @ X5 ) ) ) ) )
     => ( ! [X4: nat] :
            ( ( ord_less_eq_nat @ K3 @ X4 )
           => ( P @ X4 ) )
       => ( P @ ( F2 @ X3 ) ) ) ) ).

% minimal_fixpoint_helper(1)
thf(fact_887_recursion__renaming__helper,axiom,
    ! [F1: nat > nat,P: nat > $o,F22: nat > nat,K3: nat] :
      ( ( F1
        = ( ^ [X5: nat] : ( if_nat @ ( P @ X5 ) @ X5 @ ( F1 @ ( suc @ X5 ) ) ) ) )
     => ( ( F22
          = ( ^ [X5: nat] : ( if_nat @ ( P @ X5 ) @ X5 @ ( F22 @ ( suc @ X5 ) ) ) ) )
       => ( ! [X4: nat] :
              ( ( ord_less_eq_nat @ K3 @ X4 )
             => ( P @ X4 ) )
         => ( F1 = F22 ) ) ) ) ).

% recursion_renaming_helper
thf(fact_888_length__Cons,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( suc @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% length_Cons
thf(fact_889_length__Suc__conv,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( suc @ N ) )
      = ( ? [Y4: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ Y4 @ Ys2 ) )
            & ( ( size_s6068669265016274566od_a_b @ Ys2 )
              = N ) ) ) ) ).

% length_Suc_conv
thf(fact_890_Suc__length__conv,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( suc @ N )
        = ( size_s6068669265016274566od_a_b @ Xs2 ) )
      = ( ? [Y4: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ Y4 @ Ys2 ) )
            & ( ( size_s6068669265016274566od_a_b @ Ys2 )
              = N ) ) ) ) ).

% Suc_length_conv
thf(fact_891_minimal__fixpoint__helper_I2_J,axiom,
    ! [F2: nat > nat,P: nat > $o,K3: nat,X3: nat,X8: nat] :
      ( ( F2
        = ( ^ [X5: nat] : ( if_nat @ ( P @ X5 ) @ X5 @ ( F2 @ ( suc @ X5 ) ) ) ) )
     => ( ! [X4: nat] :
            ( ( ord_less_eq_nat @ K3 @ X4 )
           => ( P @ X4 ) )
       => ( ( ord_less_eq_nat @ X3 @ X8 )
         => ( ( ord_less_nat @ X8 @ ( F2 @ X3 ) )
           => ~ ( P @ X8 ) ) ) ) ) ).

% minimal_fixpoint_helper(2)
thf(fact_892_list__update__code_I3_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,I3: nat,Y3: fset_l1334069825099621524od_a_b] :
      ( ( list_u7851604859245713154od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ ( suc @ I3 ) @ Y3 )
      = ( cons_f6577355434438001738od_a_b @ X3 @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ Y3 ) ) ) ).

% list_update_code(3)
thf(fact_893_list_Osize_I3_J,axiom,
    ( ( size_s6068669265016274566od_a_b @ nil_fs4581119677382125722od_a_b )
    = zero_zero_nat ) ).

% list.size(3)
thf(fact_894_list__update__code_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( list_u7851604859245713154od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ zero_zero_nat @ Y3 )
      = ( cons_f6577355434438001738od_a_b @ Y3 @ Xs2 ) ) ).

% list_update_code(2)
thf(fact_895_Suc__le__length__iff,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
      = ( ? [X5: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( cons_f6577355434438001738od_a_b @ X5 @ Ys2 ) )
            & ( ord_less_eq_nat @ N @ ( size_s6068669265016274566od_a_b @ Ys2 ) ) ) ) ) ).

% Suc_le_length_iff
thf(fact_896_list__index__fun__gt,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > nat,J3: nat,I3: nat] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ ( suc @ I ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( ord_less_nat @ ( F2 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( suc @ I ) ) ) @ ( F2 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) ) ) )
     => ( ( ord_less_nat @ J3 @ I3 )
       => ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( ord_less_nat @ ( F2 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) ) @ ( F2 @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ J3 ) ) ) ) ) ) ).

% list_index_fun_gt
thf(fact_897_length__pos__if__in__set,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ord_less_nat @ zero_zero_nat @ ( size_s4021047160419372448od_a_b @ Xs2 ) ) ) ).

% length_pos_if_in_set
thf(fact_898_length__pos__if__in__set,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ord_less_nat @ zero_zero_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% length_pos_if_in_set
thf(fact_899_length__append__singleton,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ ( cons_f6577355434438001738od_a_b @ X3 @ nil_fs4581119677382125722od_a_b ) ) )
      = ( suc @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% length_append_singleton
thf(fact_900_length__Suc__conv__rev,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ( size_s6068669265016274566od_a_b @ Xs2 )
        = ( suc @ N ) )
      = ( ? [Y4: fset_l1334069825099621524od_a_b,Ys2: list_f1445794025290330138od_a_b] :
            ( ( Xs2
              = ( append2015155619842375983od_a_b @ Ys2 @ ( cons_f6577355434438001738od_a_b @ Y4 @ nil_fs4581119677382125722od_a_b ) ) )
            & ( ( size_s6068669265016274566od_a_b @ Ys2 )
              = N ) ) ) ) ).

% length_Suc_conv_rev
thf(fact_901_nth__Cons_H,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( N = zero_zero_nat )
       => ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ N )
          = X3 ) )
      & ( ( N != zero_zero_nat )
       => ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ N )
          = ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).

% nth_Cons'
thf(fact_902_ordered__list__distinct,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ ( suc @ I ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( ord_le98927018796173120od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( suc @ I ) ) ) )
     => ( distin1329390416381046541od_a_b @ Xs2 ) ) ).

% ordered_list_distinct
thf(fact_903_ordered__list__distinct,axiom,
    ! [Xs2: list_nat] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_nat @ Xs2 ) )
         => ( ord_less_nat @ ( nth_nat @ Xs2 @ I ) @ ( nth_nat @ Xs2 @ ( suc @ I ) ) ) )
     => ( distinct_nat @ Xs2 ) ) ).

% ordered_list_distinct
thf(fact_904_ordered__list__distinct__rev,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ ( suc @ I ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
         => ( ord_le98927018796173120od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( suc @ I ) ) @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I ) ) )
     => ( distin1329390416381046541od_a_b @ Xs2 ) ) ).

% ordered_list_distinct_rev
thf(fact_905_ordered__list__distinct__rev,axiom,
    ! [Xs2: list_nat] :
      ( ! [I: nat] :
          ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_nat @ Xs2 ) )
         => ( ord_less_nat @ ( nth_nat @ Xs2 @ ( suc @ I ) ) @ ( nth_nat @ Xs2 @ I ) ) )
     => ( distinct_nat @ Xs2 ) ) ).

% ordered_list_distinct_rev
thf(fact_906_take__last__index,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( last_f4009646753867174963od_a_b @ ( take_f8758302346742390914od_a_b @ ( suc @ I3 ) @ Xs2 ) )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) ) ) ).

% take_last_index
thf(fact_907_nth__equal__first__eq,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,N: nat] :
      ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ N @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
       => ( ( ( nth_li6535284973015076149od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ Xs2 ) @ N )
            = X3 )
          = ( N = zero_zero_nat ) ) ) ) ).

% nth_equal_first_eq
thf(fact_908_nth__equal__first__eq,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ N )
            = X3 )
          = ( N = zero_zero_nat ) ) ) ) ).

% nth_equal_first_eq
thf(fact_909_nth__non__equal__first__eq,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( X3 != Y3 )
     => ( ( ( nth_fs7310631729605226779od_a_b @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) @ N )
          = Y3 )
        = ( ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
            = Y3 )
          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).

% nth_non_equal_first_eq
thf(fact_910_take__Cons_H,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( N = zero_zero_nat )
       => ( ( take_f8758302346742390914od_a_b @ N @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = nil_fs4581119677382125722od_a_b ) )
      & ( ( N != zero_zero_nat )
       => ( ( take_f8758302346742390914od_a_b @ N @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = ( cons_f6577355434438001738od_a_b @ X3 @ ( take_f8758302346742390914od_a_b @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs2 ) ) ) ) ) ).

% take_Cons'
thf(fact_911_list__contains__last__take,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ? [I: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ I )
          & ( ord_less_eq_nat @ I @ ( size_s4021047160419372448od_a_b @ Xs2 ) )
          & ( ( last_l1496300474439883853od_a_b @ ( take_l2578627034827611164od_a_b @ I @ Xs2 ) )
            = X3 ) ) ) ).

% list_contains_last_take
thf(fact_912_list__contains__last__take,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ? [I: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ I )
          & ( ord_less_eq_nat @ I @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
          & ( ( last_f4009646753867174963od_a_b @ ( take_f8758302346742390914od_a_b @ I @ Xs2 ) )
            = X3 ) ) ) ).

% list_contains_last_take
thf(fact_913_length__n__lists__elem,axiom,
    ! [Ys3: list_P1467974523212632366od_a_b,N: nat,Xs2: list_P1467974523212632366od_a_b] :
      ( ( member6895035109809442519od_a_b @ Ys3 @ ( set_li5045283583078295363od_a_b @ ( n_list8012392503361751734od_a_b @ N @ Xs2 ) ) )
     => ( ( size_s3956712670882376602od_a_b @ Ys3 )
        = N ) ) ).

% length_n_lists_elem
thf(fact_914_length__n__lists__elem,axiom,
    ! [Ys3: list_f1445794025290330138od_a_b,N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member7551773913232940227od_a_b @ Ys3 @ ( set_li8217014873844115759od_a_b @ ( n_list7006363026360775842od_a_b @ N @ Xs2 ) ) )
     => ( ( size_s6068669265016274566od_a_b @ Ys3 )
        = N ) ) ).

% length_n_lists_elem
thf(fact_915_size__prod__simp,axiom,
    ( basic_8042737028673046454od_a_b
    = ( ^ [F3: $o > nat,G: list_f1445794025290330138od_a_b > nat,P6: produc2313482920965681321od_a_b] : ( plus_plus_nat @ ( plus_plus_nat @ ( F3 @ ( produc5358503411717041797od_a_b @ P6 ) ) @ ( G @ ( produc2954343059184910791od_a_b @ P6 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).

% size_prod_simp
thf(fact_916_list__index__split__set,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( set_fs4298891544546585641od_a_b @ Xs2 )
        = ( set_fs4298891544546585641od_a_b @ ( cons_f6577355434438001738od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) @ ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) @ ( drop_f570763960254934490od_a_b @ ( suc @ I3 ) @ Xs2 ) ) ) ) ) ) ).

% list_index_split_set
thf(fact_917_drop__Suc__Cons,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( drop_f570763960254934490od_a_b @ ( suc @ N ) @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
      = ( drop_f570763960254934490od_a_b @ N @ Xs2 ) ) ).

% drop_Suc_Cons
thf(fact_918_length__drop,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) )
      = ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) ) ).

% length_drop
thf(fact_919_drop__eq__Nil2,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( nil_fs4581119677382125722od_a_b
        = ( drop_f570763960254934490od_a_b @ N @ Xs2 ) )
      = ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) ) ).

% drop_eq_Nil2
thf(fact_920_drop__eq__Nil,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( drop_f570763960254934490od_a_b @ N @ Xs2 )
        = nil_fs4581119677382125722od_a_b )
      = ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N ) ) ).

% drop_eq_Nil
thf(fact_921_drop__all,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ N )
     => ( ( drop_f570763960254934490od_a_b @ N @ Xs2 )
        = nil_fs4581119677382125722od_a_b ) ) ).

% drop_all
thf(fact_922_drop__append,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( drop_f570763960254934490od_a_b @ N @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
      = ( append2015155619842375983od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) @ ( drop_f570763960254934490od_a_b @ ( minus_minus_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) @ Ys3 ) ) ) ).

% drop_append
thf(fact_923_last__drop,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( last_f4009646753867174963od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) )
        = ( last_f4009646753867174963od_a_b @ Xs2 ) ) ) ).

% last_drop
thf(fact_924_nth__drop,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,I3: nat] :
      ( ( ord_less_eq_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( nth_fs7310631729605226779od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) @ I3 )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( plus_plus_nat @ N @ I3 ) ) ) ) ).

% nth_drop
thf(fact_925_set__drop__subset,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] : ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) ) @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ).

% set_drop_subset
thf(fact_926_nth__via__drop,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b,Y3: fset_l1334069825099621524od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( ( drop_f570763960254934490od_a_b @ N @ Xs2 )
        = ( cons_f6577355434438001738od_a_b @ Y3 @ Ys3 ) )
     => ( ( nth_fs7310631729605226779od_a_b @ Xs2 @ N )
        = Y3 ) ) ).

% nth_via_drop
thf(fact_927_in__set__dropD,axiom,
    ! [X3: list_P1467974523212632366od_a_b,N: nat,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( drop_l4132970615840781684od_a_b @ N @ Xs2 ) ) )
     => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% in_set_dropD
thf(fact_928_in__set__dropD,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) ) )
     => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% in_set_dropD
thf(fact_929_set__drop__subset__set__drop,axiom,
    ! [N: nat,M2: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_eq_nat @ N @ M2 )
     => ( ord_le8981612867897606292od_a_b @ ( set_fs4298891544546585641od_a_b @ ( drop_f570763960254934490od_a_b @ M2 @ Xs2 ) ) @ ( set_fs4298891544546585641od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) ) ) ) ).

% set_drop_subset_set_drop
thf(fact_930_append__eq__conv__conj,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b,Zs: list_f1445794025290330138od_a_b] :
      ( ( ( append2015155619842375983od_a_b @ Xs2 @ Ys3 )
        = Zs )
      = ( ( Xs2
          = ( take_f8758302346742390914od_a_b @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ Zs ) )
        & ( Ys3
          = ( drop_f570763960254934490od_a_b @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ Zs ) ) ) ) ).

% append_eq_conv_conj
thf(fact_931_drop__Cons_H,axiom,
    ! [N: nat,X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( N = zero_zero_nat )
       => ( ( drop_f570763960254934490od_a_b @ N @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) ) )
      & ( ( N != zero_zero_nat )
       => ( ( drop_f570763960254934490od_a_b @ N @ ( cons_f6577355434438001738od_a_b @ X3 @ Xs2 ) )
          = ( drop_f570763960254934490od_a_b @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs2 ) ) ) ) ).

% drop_Cons'
thf(fact_932_append__eq__append__conv__if,axiom,
    ! [Xs_1: list_f1445794025290330138od_a_b,Xs_2: list_f1445794025290330138od_a_b,Ys_1: list_f1445794025290330138od_a_b,Ys_2: list_f1445794025290330138od_a_b] :
      ( ( ( append2015155619842375983od_a_b @ Xs_1 @ Xs_2 )
        = ( append2015155619842375983od_a_b @ Ys_1 @ Ys_2 ) )
      = ( ( ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs_1 ) @ ( size_s6068669265016274566od_a_b @ Ys_1 ) )
         => ( ( Xs_1
              = ( take_f8758302346742390914od_a_b @ ( size_s6068669265016274566od_a_b @ Xs_1 ) @ Ys_1 ) )
            & ( Xs_2
              = ( append2015155619842375983od_a_b @ ( drop_f570763960254934490od_a_b @ ( size_s6068669265016274566od_a_b @ Xs_1 ) @ Ys_1 ) @ Ys_2 ) ) ) )
        & ( ~ ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Xs_1 ) @ ( size_s6068669265016274566od_a_b @ Ys_1 ) )
         => ( ( ( take_f8758302346742390914od_a_b @ ( size_s6068669265016274566od_a_b @ Ys_1 ) @ Xs_1 )
              = Ys_1 )
            & ( ( append2015155619842375983od_a_b @ ( drop_f570763960254934490od_a_b @ ( size_s6068669265016274566od_a_b @ Ys_1 ) @ Xs_1 ) @ Xs_2 )
              = Ys_2 ) ) ) ) ) ).

% append_eq_append_conv_if
thf(fact_933_Cons__nth__drop__Suc,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( cons_f6577355434438001738od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) @ ( drop_f570763960254934490od_a_b @ ( suc @ I3 ) @ Xs2 ) )
        = ( drop_f570763960254934490od_a_b @ I3 @ Xs2 ) ) ) ).

% Cons_nth_drop_Suc
thf(fact_934_id__take__nth__drop,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( Xs2
        = ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) @ ( drop_f570763960254934490od_a_b @ ( suc @ I3 ) @ Xs2 ) ) ) ) ) ).

% id_take_nth_drop
thf(fact_935_upd__conv__take__nth__drop,axiom,
    ! [I3: nat,Xs2: list_f1445794025290330138od_a_b,A: fset_l1334069825099621524od_a_b] :
      ( ( ord_less_nat @ I3 @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ A )
        = ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ I3 @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ A @ ( drop_f570763960254934490od_a_b @ ( suc @ I3 ) @ Xs2 ) ) ) ) ) ).

% upd_conv_take_nth_drop
thf(fact_936_take__hd__drop,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( append2015155619842375983od_a_b @ ( take_f8758302346742390914od_a_b @ N @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) ) @ nil_fs4581119677382125722od_a_b ) )
        = ( take_f8758302346742390914od_a_b @ ( suc @ N ) @ Xs2 ) ) ) ).

% take_hd_drop
thf(fact_937_list_Oset__sel_I1_J,axiom,
    ! [A: list_l8778361445553822004od_a_b] :
      ( ( A != nil_li8635777946366267444od_a_b )
     => ( member6895035109809442519od_a_b @ ( hd_lis2958756505300214169od_a_b @ A ) @ ( set_li5045283583078295363od_a_b @ A ) ) ) ).

% list.set_sel(1)
thf(fact_938_list_Oset__sel_I1_J,axiom,
    ! [A: list_f1445794025290330138od_a_b] :
      ( ( A != nil_fs4581119677382125722od_a_b )
     => ( member361094292949318077od_a_b @ ( hd_fse7826183927675143039od_a_b @ A ) @ ( set_fs4298891544546585641od_a_b @ A ) ) ) ).

% list.set_sel(1)
thf(fact_939_hd__in__set,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ( Xs2 != nil_li8635777946366267444od_a_b )
     => ( member6895035109809442519od_a_b @ ( hd_lis2958756505300214169od_a_b @ Xs2 ) @ ( set_li5045283583078295363od_a_b @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_940_hd__in__set,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( member361094292949318077od_a_b @ ( hd_fse7826183927675143039od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_941_list_Osel_I1_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( hd_fse7826183927675143039od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
      = X21 ) ).

% list.sel(1)
thf(fact_942_hd__drop__conv__nth,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
     => ( ( hd_fse7826183927675143039od_a_b @ ( drop_f570763960254934490od_a_b @ N @ Xs2 ) )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) ) ) ).

% hd_drop_conv_nth
thf(fact_943_length__tl,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( size_s6068669265016274566od_a_b @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) )
      = ( minus_minus_nat @ ( size_s6068669265016274566od_a_b @ Xs2 ) @ one_one_nat ) ) ).

% length_tl
thf(fact_944_list_Ocollapse,axiom,
    ! [List: list_f1445794025290330138od_a_b] :
      ( ( List != nil_fs4581119677382125722od_a_b )
     => ( ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ List ) @ ( tl_fse1540917908967337859od_a_b @ List ) )
        = List ) ) ).

% list.collapse
thf(fact_945_hd__Cons__tl,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ Xs2 ) @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) )
        = Xs2 ) ) ).

% hd_Cons_tl
thf(fact_946_list_Osel_I3_J,axiom,
    ! [X21: fset_l1334069825099621524od_a_b,X22: list_f1445794025290330138od_a_b] :
      ( ( tl_fse1540917908967337859od_a_b @ ( cons_f6577355434438001738od_a_b @ X21 @ X22 ) )
      = X22 ) ).

% list.sel(3)
thf(fact_947_tl__Nil,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( tl_fse1540917908967337859od_a_b @ Xs2 )
        = nil_fs4581119677382125722od_a_b )
      = ( ( Xs2 = nil_fs4581119677382125722od_a_b )
        | ? [X5: fset_l1334069825099621524od_a_b] :
            ( Xs2
            = ( cons_f6577355434438001738od_a_b @ X5 @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% tl_Nil
thf(fact_948_Nil__tl,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( nil_fs4581119677382125722od_a_b
        = ( tl_fse1540917908967337859od_a_b @ Xs2 ) )
      = ( ( Xs2 = nil_fs4581119677382125722od_a_b )
        | ? [X5: fset_l1334069825099621524od_a_b] :
            ( Xs2
            = ( cons_f6577355434438001738od_a_b @ X5 @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% Nil_tl
thf(fact_949_list_Oset__sel_I2_J,axiom,
    ! [A: list_l8778361445553822004od_a_b,X3: list_P1467974523212632366od_a_b] :
      ( ( A != nil_li8635777946366267444od_a_b )
     => ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ ( tl_lis3067933314816597917od_a_b @ A ) ) )
       => ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ A ) ) ) ) ).

% list.set_sel(2)
thf(fact_950_list_Oset__sel_I2_J,axiom,
    ! [A: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b] :
      ( ( A != nil_fs4581119677382125722od_a_b )
     => ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ ( tl_fse1540917908967337859od_a_b @ A ) ) )
       => ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ A ) ) ) ) ).

% list.set_sel(2)
thf(fact_951_list_Oexhaust__sel,axiom,
    ! [List: list_f1445794025290330138od_a_b] :
      ( ( List != nil_fs4581119677382125722od_a_b )
     => ( List
        = ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ List ) @ ( tl_fse1540917908967337859od_a_b @ List ) ) ) ) ).

% list.exhaust_sel
thf(fact_952_nth__tl,axiom,
    ! [N: nat,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) ) )
     => ( ( nth_fs7310631729605226779od_a_b @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) @ N )
        = ( nth_fs7310631729605226779od_a_b @ Xs2 @ ( suc @ N ) ) ) ) ).

% nth_tl
thf(fact_953_take__Suc,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( take_f8758302346742390914od_a_b @ ( suc @ N ) @ Xs2 )
        = ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ Xs2 ) @ ( take_f8758302346742390914od_a_b @ N @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) ) ) ) ) ).

% take_Suc
thf(fact_954_rotate1__hd__tl,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( Xs2 != nil_fs4581119677382125722od_a_b )
     => ( ( rotate1032322621218768487od_a_b @ Xs2 )
        = ( append2015155619842375983od_a_b @ ( tl_fse1540917908967337859od_a_b @ Xs2 ) @ ( cons_f6577355434438001738od_a_b @ ( hd_fse7826183927675143039od_a_b @ Xs2 ) @ nil_fs4581119677382125722od_a_b ) ) ) ) ).

% rotate1_hd_tl
thf(fact_955_Nitpick_Osize__list__simp_I2_J,axiom,
    ( size_s6068669265016274566od_a_b
    = ( ^ [Xs4: list_f1445794025290330138od_a_b] : ( if_nat @ ( Xs4 = nil_fs4581119677382125722od_a_b ) @ zero_zero_nat @ ( suc @ ( size_s6068669265016274566od_a_b @ ( tl_fse1540917908967337859od_a_b @ Xs4 ) ) ) ) ) ) ).

% Nitpick.size_list_simp(2)
thf(fact_956_size__list__estimation,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: nat,F2: list_P1467974523212632366od_a_b > nat] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( ord_less_nat @ Y3 @ ( F2 @ X3 ) )
       => ( ord_less_nat @ Y3 @ ( size_l6337794300503450422od_a_b @ F2 @ Xs2 ) ) ) ) ).

% size_list_estimation
thf(fact_957_size__list__estimation,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: nat,F2: fset_l1334069825099621524od_a_b > nat] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( ord_less_nat @ Y3 @ ( F2 @ X3 ) )
       => ( ord_less_nat @ Y3 @ ( size_l2153056584847331996od_a_b @ F2 @ Xs2 ) ) ) ) ).

% size_list_estimation
thf(fact_958_size__list__estimation_H,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: nat,F2: list_P1467974523212632366od_a_b > nat] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 ) )
       => ( ord_less_eq_nat @ Y3 @ ( size_l6337794300503450422od_a_b @ F2 @ Xs2 ) ) ) ) ).

% size_list_estimation'
thf(fact_959_size__list__estimation_H,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,Y3: nat,F2: fset_l1334069825099621524od_a_b > nat] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 ) )
       => ( ord_less_eq_nat @ Y3 @ ( size_l2153056584847331996od_a_b @ F2 @ Xs2 ) ) ) ) ).

% size_list_estimation'
thf(fact_960_size__list__pointwise,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,F2: list_P1467974523212632366od_a_b > nat,G2: list_P1467974523212632366od_a_b > nat] :
      ( ! [X4: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ X4 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
         => ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) )
     => ( ord_less_eq_nat @ ( size_l6337794300503450422od_a_b @ F2 @ Xs2 ) @ ( size_l6337794300503450422od_a_b @ G2 @ Xs2 ) ) ) ).

% size_list_pointwise
thf(fact_961_size__list__pointwise,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,F2: fset_l1334069825099621524od_a_b > nat,G2: fset_l1334069825099621524od_a_b > nat] :
      ( ! [X4: fset_l1334069825099621524od_a_b] :
          ( ( member361094292949318077od_a_b @ X4 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ord_less_eq_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) )
     => ( ord_less_eq_nat @ ( size_l2153056584847331996od_a_b @ F2 @ Xs2 ) @ ( size_l2153056584847331996od_a_b @ G2 @ Xs2 ) ) ) ).

% size_list_pointwise
thf(fact_962_path__prepend__t,axiom,
    ! [M4: fsm_li3816064051032718074od_a_b,Q4: list_f1445794025290330138od_a_b,P2: list_P5370328139307421263od_a_b,Q3: list_f1445794025290330138od_a_b,X3: $o,Y3: fset_l1334069825099621524od_a_b] :
      ( ( path_l4848144068100360156od_a_b @ M4 @ Q4 @ P2 )
     => ( ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q3 @ ( produc1286801380576301484od_a_b @ X3 @ ( produc6212510018049267869od_a_b @ Y3 @ Q4 ) ) ) @ ( transi2698755513253879019od_a_b @ M4 ) )
       => ( path_l4848144068100360156od_a_b @ M4 @ Q3 @ ( cons_P383312003685503615od_a_b @ ( produc5205648118086869305od_a_b @ Q3 @ ( produc1286801380576301484od_a_b @ X3 @ ( produc6212510018049267869od_a_b @ Y3 @ Q4 ) ) ) @ P2 ) ) ) ) ).

% path_prepend_t
thf(fact_963_deterministic__alt__def,axiom,
    ( determ8637524772085499191od_a_b
    = ( ^ [M5: fsm_li3816064051032718074od_a_b] :
        ! [Q1: list_f1445794025290330138od_a_b,X5: $o,Y7: fset_l1334069825099621524od_a_b,Y8: fset_l1334069825099621524od_a_b,Q12: list_f1445794025290330138od_a_b,Q13: list_f1445794025290330138od_a_b] :
          ( ( ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X5 @ ( produc6212510018049267869od_a_b @ Y7 @ Q12 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) )
            & ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X5 @ ( produc6212510018049267869od_a_b @ Y8 @ Q13 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) ) )
         => ( ( Y7 = Y8 )
            & ( Q12 = Q13 ) ) ) ) ) ).

% deterministic_alt_def
thf(fact_964_LS__single__transition,axiom,
    ! [X3: a,Y3: b,M4: fsm_d_a_b,Q3: d] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) @ ( lS_d_a_b @ M4 @ Q3 ) )
      = ( ? [X5: produc84550687463314808od_b_d] :
            ( ( member2916658754359974305od_b_d @ X5 @ ( transitions_d_a_b @ M4 ) )
            & ( ( produc2783554870102817108od_b_d @ X5 )
              = Q3 )
            & ( ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ X5 ) )
              = X3 )
            & ( ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ X5 ) ) )
              = Y3 ) ) ) ) ).

% LS_single_transition
thf(fact_965_LS__single__transition,axiom,
    ! [X3: a,Y3: b,M4: fsm_c_a_b,Q3: c] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) @ ( lS_c_a_b @ M4 @ Q3 ) )
      = ( ? [X5: produc6657052613134160568od_b_c] :
            ( ( member265788643176044257od_b_c @ X5 @ ( transitions_c_a_b @ M4 ) )
            & ( ( produc6763838237438281236od_b_c @ X5 )
              = Q3 )
            & ( ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ X5 ) )
              = X3 )
            & ( ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ X5 ) ) )
              = Y3 ) ) ) ) ).

% LS_single_transition
thf(fact_966_LS__prepend__transition,axiom,
    ! [T2: produc84550687463314808od_b_d,M4: fsm_d_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( member2916658754359974305od_b_d @ T2 @ ( transitions_d_a_b @ M4 ) )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) )
       => ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) @ ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) @ Io ) @ ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T2 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_967_LS__prepend__transition,axiom,
    ! [T2: produc6657052613134160568od_b_c,M4: fsm_c_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( member265788643176044257od_b_c @ T2 @ ( transitions_c_a_b @ M4 ) )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) )
       => ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) @ ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) @ Io ) @ ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T2 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_968_language__prefix,axiom,
    ! [Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,M4: fsm_d_a_b,Q3: d] :
      ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_d_a_b @ M4 @ Q3 ) )
     => ( member6895035109809442519od_a_b @ Io1 @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ).

% language_prefix
thf(fact_969_language__prefix,axiom,
    ! [Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,M4: fsm_c_a_b,Q3: c] :
      ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_c_a_b @ M4 @ Q3 ) )
     => ( member6895035109809442519od_a_b @ Io1 @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ).

% language_prefix
thf(fact_970_language__next__transition__ob,axiom,
    ! [X3: a,Y3: b,Ios: list_P1467974523212632366od_a_b,M4: fsm_d_a_b,Q3: d] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ Ios ) @ ( lS_d_a_b @ M4 @ Q3 ) )
     => ~ ! [T4: produc84550687463314808od_b_d] :
            ( ( ( produc2783554870102817108od_b_d @ T4 )
              = Q3 )
           => ( ( member2916658754359974305od_b_d @ T4 @ ( transitions_d_a_b @ M4 ) )
             => ( ( ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T4 ) )
                  = X3 )
               => ( ( ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T4 ) ) )
                    = Y3 )
                 => ~ ( member6895035109809442519od_a_b @ Ios @ ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T4 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_971_language__next__transition__ob,axiom,
    ! [X3: a,Y3: b,Ios: list_P1467974523212632366od_a_b,M4: fsm_c_a_b,Q3: c] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ Ios ) @ ( lS_c_a_b @ M4 @ Q3 ) )
     => ~ ! [T4: produc6657052613134160568od_b_c] :
            ( ( ( produc6763838237438281236od_b_c @ T4 )
              = Q3 )
           => ( ( member265788643176044257od_b_c @ T4 @ ( transitions_c_a_b @ M4 ) )
             => ( ( ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) )
                  = X3 )
               => ( ( ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) ) )
                    = Y3 )
                 => ~ ( member6895035109809442519od_a_b @ Ios @ ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_972_observable__language__transition__target,axiom,
    ! [M4: fsm_d_a_b,T2: produc84550687463314808od_b_d,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member2916658754359974305od_b_d @ T2 @ ( transitions_d_a_b @ M4 ) )
       => ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) @ ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) @ Io ) @ ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T2 ) ) )
         => ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_973_observable__language__transition__target,axiom,
    ! [M4: fsm_c_a_b,T2: produc6657052613134160568od_b_c,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member265788643176044257od_b_c @ T2 @ ( transitions_c_a_b @ M4 ) )
       => ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) @ ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) @ Io ) @ ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T2 ) ) )
         => ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_974_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P1467974523212632366od_a_b,M4: fsm_d_a_b,Q3: d] :
      ( ~ ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ Q3 ) )
     => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M4 ) )
       => ( ( observable_d_a_b @ M4 )
         => ~ ! [Io3: list_P1467974523212632366od_a_b,X4: a,Y: b] :
                ( ? [Io4: list_P1467974523212632366od_a_b] :
                    ( Io
                    = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) @ Io4 ) ) )
               => ( ( member6895035109809442519od_a_b @ Io3 @ ( lS_d_a_b @ M4 @ Q3 ) )
                 => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_975_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P1467974523212632366od_a_b,M4: fsm_c_a_b,Q3: c] :
      ( ~ ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ Q3 ) )
     => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M4 ) )
       => ( ( observable_c_a_b @ M4 )
         => ~ ! [Io3: list_P1467974523212632366od_a_b,X4: a,Y: b] :
                ( ? [Io4: list_P1467974523212632366od_a_b] :
                    ( Io
                    = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) @ Io4 ) ) )
               => ( ( member6895035109809442519od_a_b @ Io3 @ ( lS_c_a_b @ M4 @ Q3 ) )
                 => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_976_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P1467974523212632366od_a_b,M4: fsm_fs1840479945969036537_b_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M4 ) )
       => ( ( observ529373768824785053_b_a_b @ M4 )
         => ~ ! [Io3: list_P1467974523212632366od_a_b,X4: a,Y: b] :
                ( ? [Io4: list_P1467974523212632366od_a_b] :
                    ( Io
                    = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) @ Io4 ) ) )
               => ( ( member6895035109809442519od_a_b @ Io3 @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) )
                 => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) ) @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_977_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P1467974523212632366od_a_b,M4: fsm_li1655959576902402579_b_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M4 ) )
       => ( ( observ3837622365268550711_b_a_b @ M4 )
         => ~ ! [Io3: list_P1467974523212632366od_a_b,X4: a,Y: b] :
                ( ? [Io4: list_P1467974523212632366od_a_b] :
                    ( Io
                    = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) @ Io4 ) ) )
               => ( ( member6895035109809442519od_a_b @ Io3 @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) )
                 => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X4 @ Y ) @ nil_Product_prod_a_b ) ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_978_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P3574414722980446895od_a_b,M4: fsm_fs4691611325187074810od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ~ ( member380949161941006936od_a_b @ Io @ ( lS_fse7711909652459976378od_a_b @ M4 @ Q3 ) )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states817862702784690207od_a_b @ M4 ) )
       => ( ( observ3669562468644736030od_a_b @ M4 )
         => ~ ! [Io3: list_P3574414722980446895od_a_b,X4: $o,Y: list_f1445794025290330138od_a_b] :
                ( ? [Io4: list_P3574414722980446895od_a_b] :
                    ( Io
                    = ( append2579811284360515140od_a_b @ Io3 @ ( append2579811284360515140od_a_b @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ nil_Pr7302809325368845999od_a_b ) @ Io4 ) ) )
               => ( ( member380949161941006936od_a_b @ Io3 @ ( lS_fse7711909652459976378od_a_b @ M4 @ Q3 ) )
                 => ( member380949161941006936od_a_b @ ( append2579811284360515140od_a_b @ Io3 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ nil_Pr7302809325368845999od_a_b ) ) @ ( lS_fse7711909652459976378od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_979_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P3574414722980446895od_a_b,M4: fsm_li6929239050930586644od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ~ ( member380949161941006936od_a_b @ Io @ ( lS_lis5520868105703117908od_a_b @ M4 @ Q3 ) )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states1072089101645958201od_a_b @ M4 ) )
       => ( ( observ5961674566362278840od_a_b @ M4 )
         => ~ ! [Io3: list_P3574414722980446895od_a_b,X4: $o,Y: list_f1445794025290330138od_a_b] :
                ( ? [Io4: list_P3574414722980446895od_a_b] :
                    ( Io
                    = ( append2579811284360515140od_a_b @ Io3 @ ( append2579811284360515140od_a_b @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ nil_Pr7302809325368845999od_a_b ) @ Io4 ) ) )
               => ( ( member380949161941006936od_a_b @ Io3 @ ( lS_lis5520868105703117908od_a_b @ M4 @ Q3 ) )
                 => ( member380949161941006936od_a_b @ ( append2579811284360515140od_a_b @ Io3 @ ( cons_P2672142353023029855od_a_b @ ( produc7489420772309856409od_a_b @ X4 @ Y ) @ nil_Pr7302809325368845999od_a_b ) ) @ ( lS_lis5520868105703117908od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_980_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P5302045529885307074od_a_b,M4: fsm_fs8047552373904900237od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ~ ( member33161170550207851od_a_b @ Io @ ( lS_fse7190820750362262733od_a_b @ M4 @ Q3 ) )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states5841465829182338866od_a_b @ M4 ) )
       => ( ( observ1325349641595455025od_a_b @ M4 )
         => ~ ! [Io3: list_P5302045529885307074od_a_b,X4: $o,Y: produc2518759752815613485od_a_b] :
                ( ? [Io4: list_P5302045529885307074od_a_b] :
                    ( Io
                    = ( append4988338609183987159od_a_b @ Io3 @ ( append4988338609183987159od_a_b @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ nil_Pr3614377049866306882od_a_b ) @ Io4 ) ) )
               => ( ( member33161170550207851od_a_b @ Io3 @ ( lS_fse7190820750362262733od_a_b @ M4 @ Q3 ) )
                 => ( member33161170550207851od_a_b @ ( append4988338609183987159od_a_b @ Io3 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ nil_Pr3614377049866306882od_a_b ) ) @ ( lS_fse7190820750362262733od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_981_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P5302045529885307074od_a_b,M4: fsm_li467911846419323815od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ~ ( member33161170550207851od_a_b @ Io @ ( lS_lis7345120860424838247od_a_b @ M4 @ Q3 ) )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states535247141084106060od_a_b @ M4 ) )
       => ( ( observ9193399924451010507od_a_b @ M4 )
         => ~ ! [Io3: list_P5302045529885307074od_a_b,X4: $o,Y: produc2518759752815613485od_a_b] :
                ( ? [Io4: list_P5302045529885307074od_a_b] :
                    ( Io
                    = ( append4988338609183987159od_a_b @ Io3 @ ( append4988338609183987159od_a_b @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ nil_Pr3614377049866306882od_a_b ) @ Io4 ) ) )
               => ( ( member33161170550207851od_a_b @ Io3 @ ( lS_lis7345120860424838247od_a_b @ M4 @ Q3 ) )
                 => ( member33161170550207851od_a_b @ ( append4988338609183987159od_a_b @ Io3 @ ( cons_P7065065391077662962od_a_b @ ( produc1286801380576301484od_a_b @ X4 @ Y ) @ nil_Pr3614377049866306882od_a_b ) ) @ ( lS_lis7345120860424838247od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_982_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P5488608094462411443od_a_b,M4: fsm_fs3444354198583051774od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ~ ( member3794113899005121500od_a_b @ Io @ ( lS_fse8932539686287297598od_a_b @ M4 @ Q3 ) )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states7817400623188889891od_a_b @ M4 ) )
       => ( ( observ4317395130350675874od_a_b @ M4 )
         => ~ ! [Io3: list_P5488608094462411443od_a_b,X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b] :
                ( ? [Io4: list_P5488608094462411443od_a_b] :
                    ( Io
                    = ( append5072337359724802120od_a_b @ Io3 @ ( append5072337359724802120od_a_b @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ nil_Pr1838250474468212019od_a_b ) @ Io4 ) ) )
               => ( ( member3794113899005121500od_a_b @ Io3 @ ( lS_fse8932539686287297598od_a_b @ M4 @ Q3 ) )
                 => ( member3794113899005121500od_a_b @ ( append5072337359724802120od_a_b @ Io3 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ nil_Pr1838250474468212019od_a_b ) ) @ ( lS_fse8932539686287297598od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_983_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P5488608094462411443od_a_b,M4: fsm_li9174950046736424472od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ~ ( member3794113899005121500od_a_b @ Io @ ( lS_lis5005023478512920792od_a_b @ M4 @ Q3 ) )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states61340070856860733od_a_b @ M4 ) )
       => ( ( observ227875004139865660od_a_b @ M4 )
         => ~ ! [Io3: list_P5488608094462411443od_a_b,X4: fset_l1334069825099621524od_a_b,Y: list_f1445794025290330138od_a_b] :
                ( ? [Io4: list_P5488608094462411443od_a_b] :
                    ( Io
                    = ( append5072337359724802120od_a_b @ Io3 @ ( append5072337359724802120od_a_b @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ nil_Pr1838250474468212019od_a_b ) @ Io4 ) ) )
               => ( ( member3794113899005121500od_a_b @ Io3 @ ( lS_lis5005023478512920792od_a_b @ M4 @ Q3 ) )
                 => ( member3794113899005121500od_a_b @ ( append5072337359724802120od_a_b @ Io3 @ ( cons_P7745750895690215651od_a_b @ ( produc6212510018049267869od_a_b @ X4 @ Y ) @ nil_Pr1838250474468212019od_a_b ) ) @ ( lS_lis5005023478512920792od_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_984_observable__alt__def,axiom,
    ( observ8538549861865788958od_a_b
    = ( ^ [M5: fsm_li3816064051032718074od_a_b] :
        ! [Q1: list_f1445794025290330138od_a_b,X5: $o,Y4: fset_l1334069825099621524od_a_b,Q12: list_f1445794025290330138od_a_b,Q13: list_f1445794025290330138od_a_b] :
          ( ( ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X5 @ ( produc6212510018049267869od_a_b @ Y4 @ Q12 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) )
            & ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X5 @ ( produc6212510018049267869od_a_b @ Y4 @ Q13 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) ) )
         => ( Q12 = Q13 ) ) ) ) ).

% observable_alt_def
thf(fact_985_observable__transition__target__language__eq,axiom,
    ! [M4: fsm_d_a_b,T1: produc84550687463314808od_b_d,T22: produc84550687463314808od_b_d] :
      ( ( ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T1 ) )
        = ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T22 ) ) )
     => ( ( member2916658754359974305od_b_d @ T1 @ ( transitions_d_a_b @ M4 ) )
       => ( ( member2916658754359974305od_b_d @ T22 @ ( transitions_d_a_b @ M4 ) )
         => ( ( ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) )
              = ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) )
           => ( ( ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) ) )
                = ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) ) )
             => ( ( observable_d_a_b @ M4 )
               => ( ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) ) ) )
                  = ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_986_observable__transition__target__language__eq,axiom,
    ! [M4: fsm_c_a_b,T1: produc6657052613134160568od_b_c,T22: produc6657052613134160568od_b_c] :
      ( ( ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T1 ) )
        = ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T22 ) ) )
     => ( ( member265788643176044257od_b_c @ T1 @ ( transitions_c_a_b @ M4 ) )
       => ( ( member265788643176044257od_b_c @ T22 @ ( transitions_c_a_b @ M4 ) )
         => ( ( ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) )
              = ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) )
           => ( ( ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) ) )
                = ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) ) )
             => ( ( observable_c_a_b @ M4 )
               => ( ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) ) ) )
                  = ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_987_observable__transition__target__language__subset,axiom,
    ! [M4: fsm_d_a_b,T1: produc84550687463314808od_b_d,T22: produc84550687463314808od_b_d] :
      ( ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T1 ) ) @ ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T22 ) ) )
     => ( ( member2916658754359974305od_b_d @ T1 @ ( transitions_d_a_b @ M4 ) )
       => ( ( member2916658754359974305od_b_d @ T22 @ ( transitions_d_a_b @ M4 ) )
         => ( ( ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) )
              = ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) )
           => ( ( ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) ) )
                = ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) ) )
             => ( ( observable_d_a_b @ M4 )
               => ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T1 ) ) ) ) @ ( lS_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_988_observable__transition__target__language__subset,axiom,
    ! [M4: fsm_c_a_b,T1: produc6657052613134160568od_b_c,T22: produc6657052613134160568od_b_c] :
      ( ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T1 ) ) @ ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T22 ) ) )
     => ( ( member265788643176044257od_b_c @ T1 @ ( transitions_c_a_b @ M4 ) )
       => ( ( member265788643176044257od_b_c @ T22 @ ( transitions_c_a_b @ M4 ) )
         => ( ( ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) )
              = ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) )
           => ( ( ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) ) )
                = ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) ) )
             => ( ( observable_c_a_b @ M4 )
               => ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T1 ) ) ) ) @ ( lS_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_989_after__is__state,axiom,
    ! [M4: fsm_d_a_b,Io: list_P1467974523212632366od_a_b,Q3: d] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( member_d2 @ ( after_d_a_b @ M4 @ Q3 @ Io ) @ ( states_d_a_b @ M4 ) ) ) ) ).

% after_is_state
thf(fact_990_after__is__state,axiom,
    ! [M4: fsm_c_a_b,Io: list_P1467974523212632366od_a_b,Q3: c] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( member_c2 @ ( after_c_a_b @ M4 @ Q3 @ Io ) @ ( states_c_a_b @ M4 ) ) ) ) ).

% after_is_state
thf(fact_991_after__is__state,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Io: list_P1467974523212632366od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) )
       => ( member361094292949318077od_a_b @ ( after_5198964185542980012_b_a_b @ M4 @ Q3 @ Io ) @ ( states760346292458343070_b_a_b @ M4 ) ) ) ) ).

% after_is_state
thf(fact_992_after__is__state,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Io: list_P1467974523212632366od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) )
       => ( member6895035109809442519od_a_b @ ( after_1595828222394802374_b_a_b @ M4 @ Q3 @ Io ) @ ( states5225472451708754616_b_a_b @ M4 ) ) ) ) ).

% after_is_state
thf(fact_993_observable__after__language__append,axiom,
    ! [M4: fsm_d_a_b,Io1: list_P1467974523212632366od_a_b,Q3: d,Io2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ Q3 @ Io1 ) ) )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ) ).

% observable_after_language_append
thf(fact_994_observable__after__language__append,axiom,
    ! [M4: fsm_c_a_b,Io1: list_P1467974523212632366od_a_b,Q3: c,Io2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ Q3 @ Io1 ) ) )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ) ).

% observable_after_language_append
thf(fact_995_observable__after__language__none,axiom,
    ! [M4: fsm_d_a_b,Io1: list_P1467974523212632366od_a_b,Q3: d,Io2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( ~ ( member6895035109809442519od_a_b @ Io2 @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ Q3 @ Io1 ) ) )
         => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ) ).

% observable_after_language_none
thf(fact_996_observable__after__language__none,axiom,
    ! [M4: fsm_c_a_b,Io1: list_P1467974523212632366od_a_b,Q3: c,Io2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( ~ ( member6895035109809442519od_a_b @ Io2 @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ Q3 @ Io1 ) ) )
         => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io2 ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ) ).

% observable_after_language_none
thf(fact_997_observable__after__eq,axiom,
    ! [M4: fsm_d_a_b,Q3: d,Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( ( after_d_a_b @ M4 @ Q3 @ Io1 )
          = ( after_d_a_b @ M4 @ Q3 @ Io2 ) )
       => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_d_a_b @ M4 @ Q3 ) )
         => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_d_a_b @ M4 @ Q3 ) )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io ) @ ( lS_d_a_b @ M4 @ Q3 ) )
              = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io2 @ Io ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_998_observable__after__eq,axiom,
    ! [M4: fsm_c_a_b,Q3: c,Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( ( after_c_a_b @ M4 @ Q3 @ Io1 )
          = ( after_c_a_b @ M4 @ Q3 @ Io2 ) )
       => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_c_a_b @ M4 @ Q3 ) )
         => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_c_a_b @ M4 @ Q3 ) )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io ) @ ( lS_c_a_b @ M4 @ Q3 ) )
              = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io2 @ Io ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_999_after__language__iff,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Q3: d,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Alpha @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( ( member6895035109809442519od_a_b @ Gamma @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ Q3 @ Alpha ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ) ).

% after_language_iff
thf(fact_1000_after__language__iff,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Q3: c,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Alpha @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( ( member6895035109809442519od_a_b @ Gamma @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ Q3 @ Alpha ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ) ).

% after_language_iff
thf(fact_1001_after__split,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Q3: d] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( ( after_d_a_b @ M4 @ ( after_d_a_b @ M4 @ Q3 @ Alpha ) @ Gamma )
          = ( after_d_a_b @ M4 @ Q3 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_1002_after__split,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Q3: c] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( ( after_c_a_b @ M4 @ ( after_c_a_b @ M4 @ Q3 @ Alpha ) @ Gamma )
          = ( after_c_a_b @ M4 @ Q3 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_1003_after__transition,axiom,
    ! [M4: fsm_li3816064051032718074od_a_b,Q3: list_f1445794025290330138od_a_b,X3: $o,Y3: fset_l1334069825099621524od_a_b,Q4: list_f1445794025290330138od_a_b] :
      ( ( observ8538549861865788958od_a_b @ M4 )
     => ( ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q3 @ ( produc1286801380576301484od_a_b @ X3 @ ( produc6212510018049267869od_a_b @ Y3 @ Q4 ) ) ) @ ( transi2698755513253879019od_a_b @ M4 ) )
       => ( ( after_6635595617298838829od_a_b @ M4 @ Q3 @ ( cons_P2465205493254962905od_a_b @ ( produc6339891136650604691od_a_b @ X3 @ Y3 ) @ nil_Pr7172365244936649513od_a_b ) )
          = Q4 ) ) ) ).

% after_transition
thf(fact_1004_single__input__alt__def,axiom,
    ( single8793350731111814183od_a_b
    = ( ^ [M5: fsm_li3816064051032718074od_a_b] :
        ! [Q1: list_f1445794025290330138od_a_b,X5: $o,X9: $o,Y4: fset_l1334069825099621524od_a_b,Y7: fset_l1334069825099621524od_a_b,Q12: list_f1445794025290330138od_a_b,Q13: list_f1445794025290330138od_a_b] :
          ( ( ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X5 @ ( produc6212510018049267869od_a_b @ Y4 @ Q12 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) )
            & ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q1 @ ( produc1286801380576301484od_a_b @ X9 @ ( produc6212510018049267869od_a_b @ Y7 @ Q13 ) ) ) @ ( transi2698755513253879019od_a_b @ M5 ) ) )
         => ( X5 = X9 ) ) ) ) ).

% single_input_alt_def
thf(fact_1005_distinguish__prepend,axiom,
    ! [M4: fsm_d_a_b,Q14: d,Io: list_P1467974523212632366od_a_b,Q22: d,W3: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ Q14 @ Io ) @ ( after_d_a_b @ M4 @ Q22 @ Io ) @ W3 )
       => ( ( member_d2 @ Q14 @ ( states_d_a_b @ M4 ) )
         => ( ( member_d2 @ Q22 @ ( states_d_a_b @ M4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ Q14 ) )
             => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ Q22 ) )
               => ( distinguishes_d_a_b @ M4 @ Q14 @ Q22 @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_1006_distinguish__prepend,axiom,
    ! [M4: fsm_c_a_b,Q14: c,Io: list_P1467974523212632366od_a_b,Q22: c,W3: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ Q14 @ Io ) @ ( after_c_a_b @ M4 @ Q22 @ Io ) @ W3 )
       => ( ( member_c2 @ Q14 @ ( states_c_a_b @ M4 ) )
         => ( ( member_c2 @ Q22 @ ( states_c_a_b @ M4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ Q14 ) )
             => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ Q22 ) )
               => ( distinguishes_c_a_b @ M4 @ Q14 @ Q22 @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_1007_distinguish__prepend,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Q14: fset_l1334069825099621524od_a_b,Io: list_P1467974523212632366od_a_b,Q22: fset_l1334069825099621524od_a_b,W3: list_P1467974523212632366od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( distin4693659209764571861_b_a_b @ M4 @ ( after_5198964185542980012_b_a_b @ M4 @ Q14 @ Io ) @ ( after_5198964185542980012_b_a_b @ M4 @ Q22 @ Io ) @ W3 )
       => ( ( member361094292949318077od_a_b @ Q14 @ ( states760346292458343070_b_a_b @ M4 ) )
         => ( ( member361094292949318077od_a_b @ Q22 @ ( states760346292458343070_b_a_b @ M4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q14 ) )
             => ( ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q22 ) )
               => ( distin4693659209764571861_b_a_b @ M4 @ Q14 @ Q22 @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_1008_distinguish__prepend,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Q14: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b,Q22: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( distin348325521541145199_b_a_b @ M4 @ ( after_1595828222394802374_b_a_b @ M4 @ Q14 @ Io ) @ ( after_1595828222394802374_b_a_b @ M4 @ Q22 @ Io ) @ W3 )
       => ( ( member6895035109809442519od_a_b @ Q14 @ ( states5225472451708754616_b_a_b @ M4 ) )
         => ( ( member6895035109809442519od_a_b @ Q22 @ ( states5225472451708754616_b_a_b @ M4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q14 ) )
             => ( ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q22 ) )
               => ( distin348325521541145199_b_a_b @ M4 @ Q14 @ Q22 @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_1009_h__obs__None,axiom,
    ! [M4: fsm_li3816064051032718074od_a_b,Q3: list_f1445794025290330138od_a_b,X3: $o,Y3: fset_l1334069825099621524od_a_b] :
      ( ( observ8538549861865788958od_a_b @ M4 )
     => ( ( ( h_obs_1937385545949026089od_a_b @ M4 @ Q3 @ X3 @ Y3 )
          = none_l1130124498050917115od_a_b )
        = ( ~ ? [Q5: list_f1445794025290330138od_a_b] : ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q3 @ ( produc1286801380576301484od_a_b @ X3 @ ( produc6212510018049267869od_a_b @ Y3 @ Q5 ) ) ) @ ( transi2698755513253879019od_a_b @ M4 ) ) ) ) ) ).

% h_obs_None
thf(fact_1010_h__obs__language__single__transition__iff,axiom,
    ! [M4: fsm_d_a_b,X3: a,Y3: b,Q3: d] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) @ ( lS_d_a_b @ M4 @ Q3 ) )
        = ( ( h_obs_d_a_b @ M4 @ Q3 @ X3 @ Y3 )
         != none_d ) ) ) ).

% h_obs_language_single_transition_iff
thf(fact_1011_h__obs__language__single__transition__iff,axiom,
    ! [M4: fsm_c_a_b,X3: a,Y3: b,Q3: c] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) @ ( lS_c_a_b @ M4 @ Q3 ) )
        = ( ( h_obs_c_a_b @ M4 @ Q3 @ X3 @ Y3 )
         != none_c ) ) ) ).

% h_obs_language_single_transition_iff
thf(fact_1012_distinguishes__after__initial__prepend,axiom,
    ! [M4: fsm_d_a_b,Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,X3: a,Y3: b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( ( h_obs_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io1 ) @ X3 @ Y3 )
             != none_d )
           => ( ( ( h_obs_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io2 ) @ X3 @ Y3 )
               != none_d )
             => ( ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io1 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io2 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) ) @ Gamma )
               => ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io1 ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io2 ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ Gamma ) ) ) ) ) ) ) ) ).

% distinguishes_after_initial_prepend
thf(fact_1013_distinguishes__after__initial__prepend,axiom,
    ! [M4: fsm_c_a_b,Io1: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,X3: a,Y3: b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io1 @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Io2 @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( ( h_obs_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io1 ) @ X3 @ Y3 )
             != none_c )
           => ( ( ( h_obs_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io2 ) @ X3 @ Y3 )
               != none_c )
             => ( ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io1 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io2 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) ) @ Gamma )
               => ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io1 ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io2 ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ Gamma ) ) ) ) ) ) ) ) ).

% distinguishes_after_initial_prepend
thf(fact_1014_h__obs__language__append,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,X3: a,Y3: b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( ( h_obs_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ U ) @ X3 @ Y3 )
           != none_d )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ) ) ).

% h_obs_language_append
thf(fact_1015_h__obs__language__append,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,X3: a,Y3: b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( ( h_obs_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ U ) @ X3 @ Y3 )
           != none_c )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y3 ) @ nil_Product_prod_a_b ) ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ) ) ).

% h_obs_language_append
thf(fact_1016_fsm__initial,axiom,
    ! [M4: fsm_d_a_b] : ( member_d2 @ ( initial_d_a_b @ M4 ) @ ( states_d_a_b @ M4 ) ) ).

% fsm_initial
thf(fact_1017_fsm__initial,axiom,
    ! [M4: fsm_c_a_b] : ( member_c2 @ ( initial_c_a_b @ M4 ) @ ( states_c_a_b @ M4 ) ) ).

% fsm_initial
thf(fact_1018_add__transition__with__components__simps_I1_J,axiom,
    ! [M4: fsm_d_a_b,T2: produc84550687463314808od_b_d] :
      ( ( initial_d_a_b @ ( add_tr130567725712866499_d_a_b @ M4 @ T2 ) )
      = ( initial_d_a_b @ M4 ) ) ).

% add_transition_with_components_simps(1)
thf(fact_1019_add__transition__with__components__simps_I1_J,axiom,
    ! [M4: fsm_c_a_b,T2: produc6657052613134160568od_b_c] :
      ( ( initial_c_a_b @ ( add_tr3757721147379511618_c_a_b @ M4 @ T2 ) )
      = ( initial_c_a_b @ M4 ) ) ).

% add_transition_with_components_simps(1)
thf(fact_1020_assms_I7_J,axiom,
    member6895035109809442519od_a_b @ u @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) ).

% assms(7)
thf(fact_1021_assms_I6_J,axiom,
    member6895035109809442519od_a_b @ u @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) ).

% assms(6)
thf(fact_1022_language__contains__empty__sequence,axiom,
    ! [M4: fsm_d_a_b] : ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ).

% language_contains_empty_sequence
thf(fact_1023_language__contains__empty__sequence,axiom,
    ! [M4: fsm_c_a_b] : ( member6895035109809442519od_a_b @ nil_Product_prod_a_b @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ).

% language_contains_empty_sequence
thf(fact_1024_after__language__subset,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Gamma @ Beta ) @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_1025_after__language__subset,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) )
         => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Gamma @ Beta ) @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Alpha ) ) ) ) ) ) ).

% after_language_subset
thf(fact_1026_after__language__append__iff,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Gamma @ Beta ) @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_1027_after__language__append__iff,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Gamma @ Beta ) @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Alpha ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_1028_cyclic__path__pumping,axiom,
    ! [M4: fsm_d_a_b,P2: list_P8454989104189725694od_b_d,N: nat] :
      ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P2 )
     => ( ~ ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ M4 ) @ P2 ) )
       => ? [P5: list_P8454989104189725694od_b_d] :
            ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P5 )
            & ( ord_less_eq_nat @ N @ ( size_s5514198242428051050od_b_d @ P5 ) ) ) ) ) ).

% cyclic_path_pumping
thf(fact_1029_cyclic__path__pumping,axiom,
    ! [M4: fsm_c_a_b,P2: list_P5017272815184427326od_b_c,N: nat] :
      ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P2 )
     => ( ~ ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ M4 ) @ P2 ) )
       => ? [P5: list_P5017272815184427326od_b_c] :
            ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P5 )
            & ( ord_less_eq_nat @ N @ ( size_s2076481953422752682od_b_c @ P5 ) ) ) ) ) ).

% cyclic_path_pumping
thf(fact_1030_after__distinguishes__language,axiom,
    ! [M1: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( member6895035109809442519od_a_b @ Alpha @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
         => ( ( distinguishes_d_a_b @ M1 @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Alpha ) @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             != ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_1031_after__distinguishes__language,axiom,
    ! [M1: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( member6895035109809442519od_a_b @ Alpha @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
       => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
         => ( ( distinguishes_c_a_b @ M1 @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Alpha ) @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             != ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_1032_distinguish__prepend__initial,axiom,
    ! [M4: fsm_d_a_b,Io1: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io1 @ Io ) ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io2 @ Io ) ) @ W3 )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io2 @ Io ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
           => ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io1 ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io2 ) @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_1033_distinguish__prepend__initial,axiom,
    ! [M4: fsm_c_a_b,Io1: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b,Io2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io1 @ Io ) ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ Io2 @ Io ) ) @ W3 )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io1 @ Io ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io2 @ Io ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
           => ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io1 ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io2 ) @ ( append5335208823350062147od_a_b @ Io @ W3 ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_1034_reachable__def,axiom,
    ( reachable_d_a_b
    = ( ^ [M5: fsm_d_a_b,Q6: d] :
        ? [P6: list_P8454989104189725694od_b_d] :
          ( ( path_d_a_b @ M5 @ ( initial_d_a_b @ M5 ) @ P6 )
          & ( ( target_d_a_b @ ( initial_d_a_b @ M5 ) @ P6 )
            = Q6 ) ) ) ) ).

% reachable_def
thf(fact_1035_reachable__def,axiom,
    ( reachable_c_a_b
    = ( ^ [M5: fsm_c_a_b,Q6: c] :
        ? [P6: list_P5017272815184427326od_b_c] :
          ( ( path_c_a_b @ M5 @ ( initial_c_a_b @ M5 ) @ P6 )
          & ( ( target_c_a_b @ ( initial_c_a_b @ M5 ) @ P6 )
            = Q6 ) ) ) ) ).

% reachable_def
thf(fact_1036_pass__io__set__def,axiom,
    ( pass_io_set_d_a_b
    = ( ^ [M5: fsm_d_a_b,Ios2: set_li6306622547289818894od_a_b] :
        ! [Io5: list_P1467974523212632366od_a_b,X5: a,Y4: b] :
          ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y4 ) @ nil_Product_prod_a_b ) ) @ Ios2 )
         => ! [Y7: b] :
              ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ ( lS_d_a_b @ M5 @ ( initial_d_a_b @ M5 ) ) )
             => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_1037_pass__io__set__def,axiom,
    ( pass_io_set_c_a_b
    = ( ^ [M5: fsm_c_a_b,Ios2: set_li6306622547289818894od_a_b] :
        ! [Io5: list_P1467974523212632366od_a_b,X5: a,Y4: b] :
          ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y4 ) @ nil_Product_prod_a_b ) ) @ Ios2 )
         => ! [Y7: b] :
              ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ ( lS_c_a_b @ M5 @ ( initial_c_a_b @ M5 ) ) )
             => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_1038_pass__io__set__maximal__def,axiom,
    ( pass_i6997918733032182053_d_a_b
    = ( ^ [M5: fsm_d_a_b,Ios2: set_li6306622547289818894od_a_b] :
        ! [Io5: list_P1467974523212632366od_a_b,X5: a,Y4: b,Io6: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y4 ) @ nil_Product_prod_a_b ) @ Io6 ) ) @ Ios2 )
         => ! [Y7: b] :
              ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ ( lS_d_a_b @ M5 @ ( initial_d_a_b @ M5 ) ) )
             => ? [Io7: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) @ Io7 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_1039_pass__io__set__maximal__def,axiom,
    ( pass_i1401700117844051364_c_a_b
    = ( ^ [M5: fsm_c_a_b,Ios2: set_li6306622547289818894od_a_b] :
        ! [Io5: list_P1467974523212632366od_a_b,X5: a,Y4: b,Io6: list_P1467974523212632366od_a_b] :
          ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y4 ) @ nil_Product_prod_a_b ) @ Io6 ) ) @ Ios2 )
         => ! [Y7: b] :
              ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) ) @ ( lS_c_a_b @ M5 @ ( initial_c_a_b @ M5 ) ) )
             => ? [Io7: list_P1467974523212632366od_a_b] : ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io5 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X5 @ Y7 ) @ nil_Product_prod_a_b ) @ Io7 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_1040_less_Ohyps,axiom,
    ! [Xss2: list_f1445794025290330138od_a_b,Don: list_f1445794025290330138od_a_b,B: $o] :
      ( ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ Xss2 ) @ ( size_s6068669265016274566od_a_b @ xssa ) )
     => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
            ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Don ) )
           => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
                   => ( ( converge_c_a_b @ m1 @ U2 @ V )
                      & ( converge_d_a_b @ m2 @ U2 @ V ) ) ) ) ) ) )
       => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xss2 ) )
             => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
                     => ( ( converge_c_a_b @ m1 @ U2 @ V )
                        & ( converge_d_a_b @ m2 @ U2 @ V ) ) ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ x2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple891077427139469213od_a_b @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) )
           => ( ( converge_c_a_b @ m1 @ u @ v )
              & ( converge_d_a_b @ m2 @ u @ v ) ) ) ) ) ) ).

% less.hyps
thf(fact_1041_less_Oprems_I2_J,axiom,
    ! [X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ xssa ) )
     => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
       => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
         => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
             => ( ( converge_c_a_b @ m1 @ U @ V2 )
                & ( converge_d_a_b @ m2 @ U @ V2 ) ) ) ) ) ) ) ).

% less.prems(2)
thf(fact_1042_assms_I2_J,axiom,
    ! [X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ xss ) )
     => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
       => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
         => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
             => ( ( converge_c_a_b @ m1 @ U @ V2 )
                & ( converge_d_a_b @ m2 @ U @ V2 ) ) ) ) ) ) ) ).

% assms(2)
thf(fact_1043_assms_I1_J,axiom,
    ! [X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ don ) )
     => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
       => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
         => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
             => ( ( converge_c_a_b @ m1 @ U @ V2 )
                & ( converge_d_a_b @ m2 @ U @ V2 ) ) ) ) ) ) ) ).

% assms(1)
thf(fact_1044_less_Oprems_I1_J,axiom,
    ! [X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ dona ) )
     => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
       => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
         => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ m1 @ ( initial_c_a_b @ m1 ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ m2 @ ( initial_d_a_b @ m2 ) ) )
             => ( ( converge_c_a_b @ m1 @ U @ V2 )
                & ( converge_d_a_b @ m2 @ U @ V2 ) ) ) ) ) ) ) ).

% less.prems(1)
thf(fact_1045_converge__append__iff,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Omega: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( converge_c_a_b @ M4 @ Alpha @ Beta )
       => ( ( converge_c_a_b @ M4 @ Gamma @ ( append5335208823350062147od_a_b @ Alpha @ Omega ) )
          = ( converge_c_a_b @ M4 @ Gamma @ ( append5335208823350062147od_a_b @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_1046_converge__append__iff,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Omega: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( converge_d_a_b @ M4 @ Alpha @ Beta )
       => ( ( converge_d_a_b @ M4 @ Gamma @ ( append5335208823350062147od_a_b @ Alpha @ Omega ) )
          = ( converge_d_a_b @ M4 @ Gamma @ ( append5335208823350062147od_a_b @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_1047_diverge__prefix,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ~ ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) )
           => ~ ( converge_c_a_b @ M4 @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_1048_diverge__prefix,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ~ ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) )
           => ~ ( converge_d_a_b @ M4 @ Alpha @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_1049_converge__append,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( converge_c_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
           => ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_1050_converge__append,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( converge_d_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
           => ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_1051_converge__extend,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( converge_c_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
           => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_1052_converge__extend,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( converge_d_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ Beta @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
           => ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_1053_converge__append__language__iff,axiom,
    ! [M4: fsm_c_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( converge_c_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_1054_converge__append__language__iff,axiom,
    ! [M4: fsm_d_a_b,Alpha: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( converge_d_a_b @ M4 @ Alpha @ Beta )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
          = ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Beta @ Gamma ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_1055_simple__cg__closure__phase__1__helper_H__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_c_a_b,M22: fsm_c_a_b,X2: fset_l1334069825099621524od_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                 => ( ( converge_c_a_b @ M1 @ U2 @ V )
                    & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_snd
thf(fact_1056_simple__cg__closure__phase__1__helper_H__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_c_a_b,M22: fsm_d_a_b,X2: fset_l1334069825099621524od_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                 => ( ( converge_c_a_b @ M1 @ U2 @ V )
                    & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_snd
thf(fact_1057_simple__cg__closure__phase__1__helper_H__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_d_a_b,M22: fsm_c_a_b,X2: fset_l1334069825099621524od_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                 => ( ( converge_d_a_b @ M1 @ U2 @ V )
                    & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_snd
thf(fact_1058_simple__cg__closure__phase__1__helper_H__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_d_a_b,M22: fsm_d_a_b,X2: fset_l1334069825099621524od_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                 => ( ( converge_d_a_b @ M1 @ U2 @ V )
                    & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_snd
thf(fact_1059_simple__cg__closure__phase__1__helper_H__validity__fst,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U2 @ V )
                        & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                         => ( ( converge_c_a_b @ M1 @ U2 @ V )
                            & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U @ V2 )
                        & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_fst
thf(fact_1060_simple__cg__closure__phase__1__helper_H__validity__fst,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U2 @ V )
                        & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                         => ( ( converge_c_a_b @ M1 @ U2 @ V )
                            & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U @ V2 )
                        & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_fst
thf(fact_1061_simple__cg__closure__phase__1__helper_H__validity__fst,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U2 @ V )
                        & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                         => ( ( converge_d_a_b @ M1 @ U2 @ V )
                            & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U @ V2 )
                        & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_fst
thf(fact_1062_simple__cg__closure__phase__1__helper_H__validity__fst,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,X3: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U2 @ V )
                        & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                         => ( ( converge_d_a_b @ M1 @ U2 @ V )
                            & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple8292391143910244688od_a_b @ X3 @ X1 @ Xs2 ) ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U @ V2 )
                        & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper'_validity_fst
thf(fact_1063_simple__cg__closure__phase__2__helper__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_c_a_b,M22: fsm_c_a_b,X2: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                 => ( ( converge_c_a_b @ M1 @ U2 @ V )
                    & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_snd
thf(fact_1064_simple__cg__closure__phase__2__helper__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_c_a_b,M22: fsm_d_a_b,X2: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                 => ( ( converge_c_a_b @ M1 @ U2 @ V )
                    & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_snd
thf(fact_1065_simple__cg__closure__phase__2__helper__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_d_a_b,M22: fsm_c_a_b,X2: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                 => ( ( converge_d_a_b @ M1 @ U2 @ V )
                    & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_snd
thf(fact_1066_simple__cg__closure__phase__2__helper__validity__snd,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,M1: fsm_d_a_b,M22: fsm_d_a_b,X2: fset_l1334069825099621524od_a_b,X1: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
         => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
           => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                 => ( ( converge_d_a_b @ M1 @ U2 @ V )
                    & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
     => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc396176279405262539od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_snd
thf(fact_1067_simple__cg__closure__phase__2__helper__validity__fst,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,M1: fsm_c_a_b,M22: fsm_c_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
         => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
           => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U2 @ V )
                  & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
     => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
            ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_fst
thf(fact_1068_simple__cg__closure__phase__2__helper__validity__fst,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,M1: fsm_c_a_b,M22: fsm_d_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
         => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
           => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U2 @ V )
                  & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
     => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
            ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_c_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_fst
thf(fact_1069_simple__cg__closure__phase__2__helper__validity__fst,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,M1: fsm_d_a_b,M22: fsm_c_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
         => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
           => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U2 @ V )
                  & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
     => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
            ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_fst
thf(fact_1070_simple__cg__closure__phase__2__helper__validity__fst,axiom,
    ! [X1: fset_l1334069825099621524od_a_b,M1: fsm_d_a_b,M22: fsm_d_a_b,Xs2: list_f1445794025290330138od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
          ( ( fmembe7722352836199763061od_a_b @ U2 @ X1 )
         => ( ( fmembe7722352836199763061od_a_b @ V @ X1 )
           => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U2 @ V )
                  & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
     => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
            ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
           => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
       => ( ( fmembe7722352836199763061od_a_b @ U @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
         => ( ( fmembe7722352836199763061od_a_b @ V2 @ ( produc5739577146777995401od_a_b @ ( produc5480430458100320474od_a_b @ ( simple4112306255986741752od_a_b @ X1 @ Xs2 ) ) ) )
           => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
               => ( ( converge_d_a_b @ M1 @ U @ V2 )
                  & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_2_helper_validity_fst
thf(fact_1071_distinguishes__diverge__prefix,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ U ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ V2 ) @ W3 )
       => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
           => ( ( member6895035109809442519od_a_b @ W @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ W3 ) ) )
             => ( ( member6895035109809442519od_a_b @ W @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ U ) ) )
               => ( ( member6895035109809442519od_a_b @ W @ ( lS_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ V2 ) ) )
                 => ~ ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W ) @ ( append5335208823350062147od_a_b @ V2 @ W ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_1072_distinguishes__diverge__prefix,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ U ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ V2 ) @ W3 )
       => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
           => ( ( member6895035109809442519od_a_b @ W @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ W3 ) ) )
             => ( ( member6895035109809442519od_a_b @ W @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ U ) ) )
               => ( ( member6895035109809442519od_a_b @ W @ ( lS_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ V2 ) ) )
                 => ~ ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W ) @ ( append5335208823350062147od_a_b @ V2 @ W ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_1073_simple__cg__closure__phase__1__validity,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,Xs2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
             => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U2 @ V )
                        & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) )
           => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
             => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
               => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U @ V2 )
                      & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_validity
thf(fact_1074_simple__cg__closure__phase__1__validity,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,Xs2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
             => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_c_a_b @ M1 @ U2 @ V )
                        & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) )
           => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
             => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
               => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U @ V2 )
                      & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_validity
thf(fact_1075_simple__cg__closure__phase__1__validity,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,Xs2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
             => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U2 @ V )
                        & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) )
           => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
             => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
               => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U @ V2 )
                      & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_validity
thf(fact_1076_simple__cg__closure__phase__1__validity,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,Xs2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
             => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
               => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                     => ( ( converge_d_a_b @ M1 @ U2 @ V )
                        & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple7196191000754466375od_a_b @ Xs2 ) ) ) )
           => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
             => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
               => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U @ V2 )
                      & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_validity
thf(fact_1077_simple__cg__closure__phase__1__helper__validity,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,X3: fset_l1334069825099621524od_a_b,Don: list_f1445794025290330138od_a_b,Xss2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,B: $o,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Don ) )
               => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                 => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                       => ( ( converge_c_a_b @ M1 @ U2 @ V )
                          & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xss2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                         => ( ( converge_c_a_b @ M1 @ U2 @ V )
                            & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
                 => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                       => ( ( converge_c_a_b @ M1 @ U @ V2 )
                          & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper_validity
thf(fact_1078_simple__cg__closure__phase__1__helper__validity,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,X3: fset_l1334069825099621524od_a_b,Don: list_f1445794025290330138od_a_b,Xss2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,B: $o,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_c_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Don ) )
               => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                 => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                       => ( ( converge_c_a_b @ M1 @ U2 @ V )
                          & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xss2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                         => ( ( converge_c_a_b @ M1 @ U2 @ V )
                            & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
                 => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                       => ( ( converge_c_a_b @ M1 @ U @ V2 )
                          & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper_validity
thf(fact_1079_simple__cg__closure__phase__1__helper__validity,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,X3: fset_l1334069825099621524od_a_b,Don: list_f1445794025290330138od_a_b,Xss2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,B: $o,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Don ) )
               => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                 => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                       => ( ( converge_d_a_b @ M1 @ U2 @ V )
                          & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xss2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                         => ( ( converge_d_a_b @ M1 @ U2 @ V )
                            & ( converge_c_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
                 => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) )
                       => ( ( converge_d_a_b @ M1 @ U @ V2 )
                          & ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper_validity
thf(fact_1080_simple__cg__closure__phase__1__helper__validity,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,X3: fset_l1334069825099621524od_a_b,Don: list_f1445794025290330138od_a_b,Xss2: list_f1445794025290330138od_a_b,X2: fset_l1334069825099621524od_a_b,B: $o,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ! [U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
              ( ( fmembe7722352836199763061od_a_b @ U2 @ X3 )
             => ( ( fmembe7722352836199763061od_a_b @ V @ X3 )
               => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                   => ( ( converge_d_a_b @ M1 @ U2 @ V )
                      & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) )
         => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Don ) )
               => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                 => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                   => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                       => ( ( converge_d_a_b @ M1 @ U2 @ V )
                          & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
           => ( ! [X23: fset_l1334069825099621524od_a_b,U2: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b] :
                  ( ( member361094292949318077od_a_b @ X23 @ ( set_fs4298891544546585641od_a_b @ Xss2 ) )
                 => ( ( fmembe7722352836199763061od_a_b @ U2 @ X23 )
                   => ( ( fmembe7722352836199763061od_a_b @ V @ X23 )
                     => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                       => ( ( member6895035109809442519od_a_b @ U2 @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                         => ( ( converge_d_a_b @ M1 @ U2 @ V )
                            & ( converge_d_a_b @ M22 @ U2 @ V ) ) ) ) ) ) )
             => ( ( member361094292949318077od_a_b @ X2 @ ( set_fs4298891544546585641od_a_b @ ( produc2954343059184910791od_a_b @ ( simple257211598216488121od_a_b @ X3 @ Xss2 @ ( produc7489420772309856409od_a_b @ B @ Don ) ) ) ) )
               => ( ( fmembe7722352836199763061od_a_b @ U @ X2 )
                 => ( ( fmembe7722352836199763061od_a_b @ V2 @ X2 )
                   => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                     => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) )
                       => ( ( converge_d_a_b @ M1 @ U @ V2 )
                          & ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% simple_cg_closure_phase_1_helper_validity
thf(fact_1081_observable__language__next,axiom,
    ! [Io: product_prod_a_b,Ios: list_P1467974523212632366od_a_b,M4: fsm_d_a_b,T2: produc84550687463314808od_b_d] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ Io @ Ios ) @ ( lS_d_a_b @ M4 @ ( produc2783554870102817108od_b_d @ T2 ) ) )
     => ( ( observable_d_a_b @ M4 )
       => ( ( member2916658754359974305od_b_d @ T2 @ ( transitions_d_a_b @ M4 ) )
         => ( ( ( produc3728844969960764142od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) )
              = ( product_fst_a_b @ Io ) )
           => ( ( ( product_fst_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) )
                = ( product_snd_a_b @ Io ) )
             => ( member6895035109809442519od_a_b @ Ios @ ( lS_d_a_b @ ( from_FSM_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) @ ( initial_d_a_b @ ( from_FSM_d_a_b @ M4 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ T2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_1082_observable__language__next,axiom,
    ! [Io: product_prod_a_b,Ios: list_P1467974523212632366od_a_b,M4: fsm_c_a_b,T2: produc6657052613134160568od_b_c] :
      ( ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ Io @ Ios ) @ ( lS_c_a_b @ M4 @ ( produc6763838237438281236od_b_c @ T2 ) ) )
     => ( ( observable_c_a_b @ M4 )
       => ( ( member265788643176044257od_b_c @ T2 @ ( transitions_c_a_b @ M4 ) )
         => ( ( ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) )
              = ( product_fst_a_b @ Io ) )
           => ( ( ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) )
                = ( product_snd_a_b @ Io ) )
             => ( member6895035109809442519od_a_b @ Ios @ ( lS_c_a_b @ ( from_FSM_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) @ ( initial_c_a_b @ ( from_FSM_c_a_b @ M4 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_1083_minimally__distinguishes__no__prefix,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b,W4: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ W3 ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ W3 ) @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( minima1372903217058875368_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ U ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ V2 ) @ ( append5335208823350062147od_a_b @ W3 @ ( append5335208823350062147od_a_b @ W @ W4 ) ) )
           => ( ( W != nil_Product_prod_a_b )
             => ~ ( distinguishes_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ U @ W3 ) ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ V2 @ W3 ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_1084_minimally__distinguishes__no__prefix,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b,W4: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ W3 ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ W3 ) @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( minima5000056638725520487_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ U ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ V2 ) @ ( append5335208823350062147od_a_b @ W3 @ ( append5335208823350062147od_a_b @ W @ W4 ) ) )
           => ( ( W != nil_Product_prod_a_b )
             => ~ ( distinguishes_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ U @ W3 ) ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ V2 @ W3 ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_1085_from__FSM__simps_I1_J,axiom,
    ! [Q3: d,M4: fsm_d_a_b] :
      ( ( member_d2 @ Q3 @ ( states_d_a_b @ M4 ) )
     => ( ( initial_d_a_b @ ( from_FSM_d_a_b @ M4 @ Q3 ) )
        = Q3 ) ) ).

% from_FSM_simps(1)
thf(fact_1086_from__FSM__simps_I1_J,axiom,
    ! [Q3: c,M4: fsm_c_a_b] :
      ( ( member_c2 @ Q3 @ ( states_c_a_b @ M4 ) )
     => ( ( initial_c_a_b @ ( from_FSM_c_a_b @ M4 @ Q3 ) )
        = Q3 ) ) ).

% from_FSM_simps(1)
thf(fact_1087_minimally__distinguishes__ex,axiom,
    ! [Q14: d,M4: fsm_d_a_b,Q22: d] :
      ( ( member_d2 @ Q14 @ ( states_d_a_b @ M4 ) )
     => ( ( member_d2 @ Q22 @ ( states_d_a_b @ M4 ) )
       => ( ( ( lS_d_a_b @ M4 @ Q14 )
           != ( lS_d_a_b @ M4 @ Q22 ) )
         => ~ ! [V: list_P1467974523212632366od_a_b] :
                ~ ( minima1372903217058875368_d_a_b @ M4 @ Q14 @ Q22 @ V ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_1088_minimally__distinguishes__ex,axiom,
    ! [Q14: c,M4: fsm_c_a_b,Q22: c] :
      ( ( member_c2 @ Q14 @ ( states_c_a_b @ M4 ) )
     => ( ( member_c2 @ Q22 @ ( states_c_a_b @ M4 ) )
       => ( ( ( lS_c_a_b @ M4 @ Q14 )
           != ( lS_c_a_b @ M4 @ Q22 ) )
         => ~ ! [V: list_P1467974523212632366od_a_b] :
                ~ ( minima5000056638725520487_c_a_b @ M4 @ Q14 @ Q22 @ V ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_1089_from__FSM__language,axiom,
    ! [Q3: d,M4: fsm_d_a_b] :
      ( ( member_d2 @ Q3 @ ( states_d_a_b @ M4 ) )
     => ( ( lS_d_a_b @ ( from_FSM_d_a_b @ M4 @ Q3 ) @ ( initial_d_a_b @ ( from_FSM_d_a_b @ M4 @ Q3 ) ) )
        = ( lS_d_a_b @ M4 @ Q3 ) ) ) ).

% from_FSM_language
thf(fact_1090_from__FSM__language,axiom,
    ! [Q3: c,M4: fsm_c_a_b] :
      ( ( member_c2 @ Q3 @ ( states_c_a_b @ M4 ) )
     => ( ( lS_c_a_b @ ( from_FSM_c_a_b @ M4 @ Q3 ) @ ( initial_c_a_b @ ( from_FSM_c_a_b @ M4 @ Q3 ) ) )
        = ( lS_c_a_b @ M4 @ Q3 ) ) ) ).

% from_FSM_language
thf(fact_1091_from__FSM__path__initial,axiom,
    ! [Q3: d,M4: fsm_d_a_b,P2: list_P8454989104189725694od_b_d] :
      ( ( member_d2 @ Q3 @ ( states_d_a_b @ M4 ) )
     => ( ( path_d_a_b @ M4 @ Q3 @ P2 )
        = ( path_d_a_b @ ( from_FSM_d_a_b @ M4 @ Q3 ) @ ( initial_d_a_b @ ( from_FSM_d_a_b @ M4 @ Q3 ) ) @ P2 ) ) ) ).

% from_FSM_path_initial
thf(fact_1092_from__FSM__path__initial,axiom,
    ! [Q3: c,M4: fsm_c_a_b,P2: list_P5017272815184427326od_b_c] :
      ( ( member_c2 @ Q3 @ ( states_c_a_b @ M4 ) )
     => ( ( path_c_a_b @ M4 @ Q3 @ P2 )
        = ( path_c_a_b @ ( from_FSM_c_a_b @ M4 @ Q3 ) @ ( initial_c_a_b @ ( from_FSM_c_a_b @ M4 @ Q3 ) ) @ P2 ) ) ) ).

% from_FSM_path_initial
thf(fact_1093_maximal__acyclic__path__deadlock,axiom,
    ! [M4: fsm_d_a_b,P2: list_P8454989104189725694od_b_d] :
      ( ( acyclic_d_a_b @ M4 )
     => ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P2 )
       => ( ( ? [P7: list_P8454989104189725694od_b_d] :
                ( ( P7 != nil_Pr7980766280164352894od_b_d )
                & ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append1298783090030845715od_b_d @ P2 @ P7 ) )
                & ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ M4 ) @ ( append1298783090030845715od_b_d @ P2 @ P7 ) ) ) ) )
         != ( deadlock_state_d_a_b @ M4 @ ( target_d_a_b @ ( initial_d_a_b @ M4 ) @ P2 ) ) ) ) ) ).

% maximal_acyclic_path_deadlock
thf(fact_1094_maximal__acyclic__path__deadlock,axiom,
    ! [M4: fsm_c_a_b,P2: list_P5017272815184427326od_b_c] :
      ( ( acyclic_c_a_b @ M4 )
     => ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P2 )
       => ( ( ? [P7: list_P5017272815184427326od_b_c] :
                ( ( P7 != nil_Pr5329896168980422846od_b_c )
                & ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append7871285015701691475od_b_c @ P2 @ P7 ) )
                & ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ M4 ) @ ( append7871285015701691475od_b_c @ P2 @ P7 ) ) ) ) )
         != ( deadlock_state_c_a_b @ M4 @ ( target_c_a_b @ ( initial_c_a_b @ M4 ) @ P2 ) ) ) ) ) ).

% maximal_acyclic_path_deadlock
thf(fact_1095_acyclic__initial,axiom,
    ! [M4: fsm_d_a_b] :
      ( ( acyclic_d_a_b @ M4 )
     => ~ ? [X6: produc84550687463314808od_b_d] :
            ( ( member2916658754359974305od_b_d @ X6 @ ( transitions_d_a_b @ M4 ) )
            & ( ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ X6 ) ) )
              = ( initial_d_a_b @ M4 ) )
            & ? [P8: list_P8454989104189725694od_b_d] :
                ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P8 )
                & ( ( target_d_a_b @ ( initial_d_a_b @ M4 ) @ P8 )
                  = ( produc2783554870102817108od_b_d @ X6 ) ) ) ) ) ).

% acyclic_initial
thf(fact_1096_acyclic__initial,axiom,
    ! [M4: fsm_c_a_b] :
      ( ( acyclic_c_a_b @ M4 )
     => ~ ? [X6: produc6657052613134160568od_b_c] :
            ( ( member265788643176044257od_b_c @ X6 @ ( transitions_c_a_b @ M4 ) )
            & ( ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ X6 ) ) )
              = ( initial_c_a_b @ M4 ) )
            & ? [P8: list_P5017272815184427326od_b_c] :
                ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P8 )
                & ( ( target_c_a_b @ ( initial_c_a_b @ M4 ) @ P8 )
                  = ( produc6763838237438281236od_b_c @ X6 ) ) ) ) ) ).

% acyclic_initial
thf(fact_1097_cyclic__cycle__rev,axiom,
    ! [M4: fsm_d_a_b,P9: list_P8454989104189725694od_b_d,Q3: d,P2: list_P8454989104189725694od_b_d] :
      ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P9 )
     => ( ( ( target_d_a_b @ ( initial_d_a_b @ M4 ) @ P9 )
          = Q3 )
       => ( ( path_d_a_b @ M4 @ Q3 @ P2 )
         => ( ( P2 != nil_Pr7980766280164352894od_b_d )
           => ( ( ( target_d_a_b @ Q3 @ P2 )
                = Q3 )
             => ~ ( acyclic_d_a_b @ M4 ) ) ) ) ) ) ).

% cyclic_cycle_rev
thf(fact_1098_cyclic__cycle__rev,axiom,
    ! [M4: fsm_c_a_b,P9: list_P5017272815184427326od_b_c,Q3: c,P2: list_P5017272815184427326od_b_c] :
      ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P9 )
     => ( ( ( target_c_a_b @ ( initial_c_a_b @ M4 ) @ P9 )
          = Q3 )
       => ( ( path_c_a_b @ M4 @ Q3 @ P2 )
         => ( ( P2 != nil_Pr5329896168980422846od_b_c )
           => ( ( ( target_c_a_b @ Q3 @ P2 )
                = Q3 )
             => ~ ( acyclic_c_a_b @ M4 ) ) ) ) ) ) ).

% cyclic_cycle_rev
thf(fact_1099_acyclic_Oelims_I3_J,axiom,
    ! [X3: fsm_d_a_b] :
      ( ~ ( acyclic_d_a_b @ X3 )
     => ~ ! [P5: list_P8454989104189725694od_b_d] :
            ( ( path_d_a_b @ X3 @ ( initial_d_a_b @ X3 ) @ P5 )
           => ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ X3 ) @ P5 ) ) ) ) ).

% acyclic.elims(3)
thf(fact_1100_acyclic_Oelims_I3_J,axiom,
    ! [X3: fsm_c_a_b] :
      ( ~ ( acyclic_c_a_b @ X3 )
     => ~ ! [P5: list_P5017272815184427326od_b_c] :
            ( ( path_c_a_b @ X3 @ ( initial_c_a_b @ X3 ) @ P5 )
           => ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ X3 ) @ P5 ) ) ) ) ).

% acyclic.elims(3)
thf(fact_1101_acyclic_Oelims_I2_J,axiom,
    ! [X3: fsm_d_a_b] :
      ( ( acyclic_d_a_b @ X3 )
     => ! [P8: list_P8454989104189725694od_b_d] :
          ( ( path_d_a_b @ X3 @ ( initial_d_a_b @ X3 ) @ P8 )
         => ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ X3 ) @ P8 ) ) ) ) ).

% acyclic.elims(2)
thf(fact_1102_acyclic_Oelims_I2_J,axiom,
    ! [X3: fsm_c_a_b] :
      ( ( acyclic_c_a_b @ X3 )
     => ! [P8: list_P5017272815184427326od_b_c] :
          ( ( path_c_a_b @ X3 @ ( initial_c_a_b @ X3 ) @ P8 )
         => ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ X3 ) @ P8 ) ) ) ) ).

% acyclic.elims(2)
thf(fact_1103_acyclic_Oelims_I1_J,axiom,
    ! [X3: fsm_d_a_b,Y3: $o] :
      ( ( ( acyclic_d_a_b @ X3 )
        = Y3 )
     => ( Y3
        = ( ! [P6: list_P8454989104189725694od_b_d] :
              ( ( path_d_a_b @ X3 @ ( initial_d_a_b @ X3 ) @ P6 )
             => ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ X3 ) @ P6 ) ) ) ) ) ) ).

% acyclic.elims(1)
thf(fact_1104_acyclic_Oelims_I1_J,axiom,
    ! [X3: fsm_c_a_b,Y3: $o] :
      ( ( ( acyclic_c_a_b @ X3 )
        = Y3 )
     => ( Y3
        = ( ! [P6: list_P5017272815184427326od_b_c] :
              ( ( path_c_a_b @ X3 @ ( initial_c_a_b @ X3 ) @ P6 )
             => ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ X3 ) @ P6 ) ) ) ) ) ) ).

% acyclic.elims(1)
thf(fact_1105_acyclic_Osimps,axiom,
    ( acyclic_d_a_b
    = ( ^ [M5: fsm_d_a_b] :
        ! [P6: list_P8454989104189725694od_b_d] :
          ( ( path_d_a_b @ M5 @ ( initial_d_a_b @ M5 ) @ P6 )
         => ( distinct_d @ ( visited_states_d_a_b @ ( initial_d_a_b @ M5 ) @ P6 ) ) ) ) ) ).

% acyclic.simps
thf(fact_1106_acyclic_Osimps,axiom,
    ( acyclic_c_a_b
    = ( ^ [M5: fsm_c_a_b] :
        ! [P6: list_P5017272815184427326od_b_c] :
          ( ( path_c_a_b @ M5 @ ( initial_c_a_b @ M5 ) @ P6 )
         => ( distinct_c @ ( visited_states_c_a_b @ ( initial_c_a_b @ M5 ) @ P6 ) ) ) ) ) ).

% acyclic.simps
thf(fact_1107_acyclic__paths__from__reachable__states,axiom,
    ! [M4: fsm_d_a_b,P9: list_P8454989104189725694od_b_d,Q3: d,P2: list_P8454989104189725694od_b_d] :
      ( ( acyclic_d_a_b @ M4 )
     => ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P9 )
       => ( ( ( target_d_a_b @ ( initial_d_a_b @ M4 ) @ P9 )
            = Q3 )
         => ( ( path_d_a_b @ M4 @ Q3 @ P2 )
           => ( distinct_d @ ( visited_states_d_a_b @ Q3 @ P2 ) ) ) ) ) ) ).

% acyclic_paths_from_reachable_states
thf(fact_1108_acyclic__paths__from__reachable__states,axiom,
    ! [M4: fsm_c_a_b,P9: list_P5017272815184427326od_b_c,Q3: c,P2: list_P5017272815184427326od_b_c] :
      ( ( acyclic_c_a_b @ M4 )
     => ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P9 )
       => ( ( ( target_c_a_b @ ( initial_c_a_b @ M4 ) @ P9 )
            = Q3 )
         => ( ( path_c_a_b @ M4 @ Q3 @ P2 )
           => ( distinct_c @ ( visited_states_c_a_b @ Q3 @ P2 ) ) ) ) ) ) ).

% acyclic_paths_from_reachable_states
thf(fact_1109_acyclic__code,axiom,
    ( acyclic_d_a_b
    = ( ^ [M5: fsm_d_a_b] :
          ~ ? [X5: list_P8454989104189725694od_b_d] :
              ( ( member315062636207077287od_b_d @ X5 @ ( acycli5107599411020016573_d_a_b @ M5 @ ( initial_d_a_b @ M5 ) @ ( minus_minus_nat @ ( size_d_a_b @ M5 ) @ one_one_nat ) ) )
              & ? [Y4: produc84550687463314808od_b_d] :
                  ( ( member2916658754359974305od_b_d @ Y4 @ ( transitions_d_a_b @ M5 ) )
                  & ( ( produc2783554870102817108od_b_d @ Y4 )
                    = ( target_d_a_b @ ( initial_d_a_b @ M5 ) @ X5 ) )
                  & ( member_d2 @ ( product_snd_b_d @ ( produc8648342219374764080od_b_d @ ( produc6645741625167713430od_b_d @ Y4 ) ) ) @ ( set_d2 @ ( visited_states_d_a_b @ ( initial_d_a_b @ M5 ) @ X5 ) ) ) ) ) ) ) ).

% acyclic_code
thf(fact_1110_acyclic__code,axiom,
    ( acyclic_c_a_b
    = ( ^ [M5: fsm_c_a_b] :
          ~ ? [X5: list_P5017272815184427326od_b_c] :
              ( ( member6100718384056554727od_b_c @ X5 @ ( acycli8734752832686661692_c_a_b @ M5 @ ( initial_c_a_b @ M5 ) @ ( minus_minus_nat @ ( size_c_a_b @ M5 ) @ one_one_nat ) ) )
              & ? [Y4: produc6657052613134160568od_b_c] :
                  ( ( member265788643176044257od_b_c @ Y4 @ ( transitions_c_a_b @ M5 ) )
                  & ( ( produc6763838237438281236od_b_c @ Y4 )
                    = ( target_c_a_b @ ( initial_c_a_b @ M5 ) @ X5 ) )
                  & ( member_c2 @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ Y4 ) ) ) @ ( set_c2 @ ( visited_states_c_a_b @ ( initial_c_a_b @ M5 ) @ X5 ) ) ) ) ) ) ) ).

% acyclic_code
thf(fact_1111_LS__from__LS__acyclic,axiom,
    ! [M4: fsm_d_a_b] :
      ( ( acyclic_d_a_b @ M4 )
     => ( ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) )
        = ( lS_acyclic_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_1112_LS__from__LS__acyclic,axiom,
    ! [M4: fsm_c_a_b] :
      ( ( acyclic_c_a_b @ M4 )
     => ( ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) )
        = ( lS_acyclic_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_1113_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Q3: fset_l1334069825099621524od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima3855660599394504998_b_a_b @ M4 @ Q3 @ Io ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_1114_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Q3: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima5690422175864505664_b_a_b @ M4 @ Q3 @ Io ) @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_1115_minimal_Oelims_I3_J,axiom,
    ! [X3: fsm_d_a_b] :
      ( ~ ( minimal_d_a_b @ X3 )
     => ~ ! [X4: d] :
            ( ( member_d2 @ X4 @ ( states_d_a_b @ X3 ) )
           => ! [Xa3: d] :
                ( ( member_d2 @ Xa3 @ ( states_d_a_b @ X3 ) )
               => ( ( X4 != Xa3 )
                 => ( ( lS_d_a_b @ X3 @ X4 )
                   != ( lS_d_a_b @ X3 @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_1116_minimal_Oelims_I3_J,axiom,
    ! [X3: fsm_c_a_b] :
      ( ~ ( minimal_c_a_b @ X3 )
     => ~ ! [X4: c] :
            ( ( member_c2 @ X4 @ ( states_c_a_b @ X3 ) )
           => ! [Xa3: c] :
                ( ( member_c2 @ Xa3 @ ( states_c_a_b @ X3 ) )
               => ( ( X4 != Xa3 )
                 => ( ( lS_c_a_b @ X3 @ X4 )
                   != ( lS_c_a_b @ X3 @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_1117_minimal_Oelims_I2_J,axiom,
    ! [X3: fsm_d_a_b] :
      ( ( minimal_d_a_b @ X3 )
     => ! [X6: d] :
          ( ( member_d2 @ X6 @ ( states_d_a_b @ X3 ) )
         => ! [Xa2: d] :
              ( ( member_d2 @ Xa2 @ ( states_d_a_b @ X3 ) )
             => ( ( X6 != Xa2 )
               => ( ( lS_d_a_b @ X3 @ X6 )
                 != ( lS_d_a_b @ X3 @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_1118_minimal_Oelims_I2_J,axiom,
    ! [X3: fsm_c_a_b] :
      ( ( minimal_c_a_b @ X3 )
     => ! [X6: c] :
          ( ( member_c2 @ X6 @ ( states_c_a_b @ X3 ) )
         => ! [Xa2: c] :
              ( ( member_c2 @ Xa2 @ ( states_c_a_b @ X3 ) )
             => ( ( X6 != Xa2 )
               => ( ( lS_c_a_b @ X3 @ X6 )
                 != ( lS_c_a_b @ X3 @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_1119_minimal_Oelims_I1_J,axiom,
    ! [X3: fsm_d_a_b,Y3: $o] :
      ( ( ( minimal_d_a_b @ X3 )
        = Y3 )
     => ( Y3
        = ( ! [X5: d] :
              ( ( member_d2 @ X5 @ ( states_d_a_b @ X3 ) )
             => ! [Y4: d] :
                  ( ( member_d2 @ Y4 @ ( states_d_a_b @ X3 ) )
                 => ( ( X5 != Y4 )
                   => ( ( lS_d_a_b @ X3 @ X5 )
                     != ( lS_d_a_b @ X3 @ Y4 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_1120_minimal_Oelims_I1_J,axiom,
    ! [X3: fsm_c_a_b,Y3: $o] :
      ( ( ( minimal_c_a_b @ X3 )
        = Y3 )
     => ( Y3
        = ( ! [X5: c] :
              ( ( member_c2 @ X5 @ ( states_c_a_b @ X3 ) )
             => ! [Y4: c] :
                  ( ( member_c2 @ Y4 @ ( states_c_a_b @ X3 ) )
                 => ( ( X5 != Y4 )
                   => ( ( lS_c_a_b @ X3 @ X5 )
                     != ( lS_c_a_b @ X3 @ Y4 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_1121_minimal_Osimps,axiom,
    ( minimal_d_a_b
    = ( ^ [M5: fsm_d_a_b] :
        ! [X5: d] :
          ( ( member_d2 @ X5 @ ( states_d_a_b @ M5 ) )
         => ! [Y4: d] :
              ( ( member_d2 @ Y4 @ ( states_d_a_b @ M5 ) )
             => ( ( X5 != Y4 )
               => ( ( lS_d_a_b @ M5 @ X5 )
                 != ( lS_d_a_b @ M5 @ Y4 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_1122_minimal_Osimps,axiom,
    ( minimal_c_a_b
    = ( ^ [M5: fsm_c_a_b] :
        ! [X5: c] :
          ( ( member_c2 @ X5 @ ( states_c_a_b @ M5 ) )
         => ! [Y4: c] :
              ( ( member_c2 @ Y4 @ ( states_c_a_b @ M5 ) )
             => ( ( X5 != Y4 )
               => ( ( lS_c_a_b @ M5 @ X5 )
                 != ( lS_c_a_b @ M5 @ Y4 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_1123_minimal__alt__def,axiom,
    ( minimal_d_a_b
    = ( ^ [M5: fsm_d_a_b] :
        ! [Q6: d,Q5: d] :
          ( ( member_d2 @ Q6 @ ( states_d_a_b @ M5 ) )
         => ( ( member_d2 @ Q5 @ ( states_d_a_b @ M5 ) )
           => ( ( ( lS_d_a_b @ M5 @ Q6 )
                = ( lS_d_a_b @ M5 @ Q5 ) )
             => ( Q6 = Q5 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_1124_minimal__alt__def,axiom,
    ( minimal_c_a_b
    = ( ^ [M5: fsm_c_a_b] :
        ! [Q6: c,Q5: c] :
          ( ( member_c2 @ Q6 @ ( states_c_a_b @ M5 ) )
         => ( ( member_c2 @ Q5 @ ( states_c_a_b @ M5 ) )
           => ( ( ( lS_c_a_b @ M5 @ Q6 )
                = ( lS_c_a_b @ M5 @ Q5 ) )
             => ( Q6 = Q5 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_1125_converge__trans__2_I1_J,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( minimal_c_a_b @ M4 )
       => ( ( converge_c_a_b @ M4 @ U @ V2 )
         => ( ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ V2 @ W1 ) @ ( append5335208823350062147od_a_b @ V2 @ W22 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_1126_converge__trans__2_I1_J,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( minimal_d_a_b @ M4 )
       => ( ( converge_d_a_b @ M4 @ U @ V2 )
         => ( ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ V2 @ W1 ) @ ( append5335208823350062147od_a_b @ V2 @ W22 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_1127_converge__trans__2_I2_J,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( minimal_c_a_b @ M4 )
       => ( ( converge_c_a_b @ M4 @ U @ V2 )
         => ( ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ V2 @ W22 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_1128_converge__trans__2_I2_J,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( minimal_d_a_b @ M4 )
       => ( ( converge_d_a_b @ M4 @ U @ V2 )
         => ( ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ V2 @ W22 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_1129_converge__trans__2_I3_J,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( minimal_c_a_b @ M4 )
       => ( ( converge_c_a_b @ M4 @ U @ V2 )
         => ( ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_c_a_b @ M4 @ ( append5335208823350062147od_a_b @ V2 @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_1130_converge__trans__2_I3_J,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W1: list_P1467974523212632366od_a_b,W22: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( minimal_d_a_b @ M4 )
       => ( ( converge_d_a_b @ M4 @ U @ V2 )
         => ( ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ U @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) )
            = ( converge_d_a_b @ M4 @ ( append5335208823350062147od_a_b @ V2 @ W1 ) @ ( append5335208823350062147od_a_b @ U @ W22 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_1131_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M4: fsm_d_a_b,Q3: d,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima2688917914611001107_d_a_b @ M4 @ Q3 @ Io ) @ ( lS_d_a_b @ M4 @ Q3 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_1132_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M4: fsm_c_a_b,Q3: c,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima6316071336277646226_c_a_b @ M4 @ Q3 @ Io ) @ ( lS_c_a_b @ M4 @ Q3 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_1133_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Q3: fset_l1334069825099621524od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima3855660599394504998_b_a_b @ M4 @ Q3 @ Io ) @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_1134_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Q3: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M4 ) )
       => ( member6895035109809442519od_a_b @ ( maxima5690422175864505664_b_a_b @ M4 @ Q3 @ Io ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_1135_minimally__distinguishes__after__append__initial,axiom,
    ! [M4: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( minimal_d_a_b @ M4 )
       => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
           => ( ( minima1372903217058875368_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ U ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ V2 ) @ ( append5335208823350062147od_a_b @ W3 @ W ) )
             => ( ( W != nil_Product_prod_a_b )
               => ( minima1372903217058875368_d_a_b @ M4 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ U @ W3 ) ) @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ V2 @ W3 ) ) @ W ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_1136_minimally__distinguishes__after__append__initial,axiom,
    ! [M4: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W3: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( minimal_c_a_b @ M4 )
       => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
         => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
           => ( ( minima5000056638725520487_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ U ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ V2 ) @ ( append5335208823350062147od_a_b @ W3 @ W ) )
             => ( ( W != nil_Product_prod_a_b )
               => ( minima5000056638725520487_c_a_b @ M4 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ U @ W3 ) ) @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ ( append5335208823350062147od_a_b @ V2 @ W3 ) ) @ W ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_1137_distinguish__converge__diverge,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,U3: list_P1467974523212632366od_a_b,V4: list_P1467974523212632366od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( minimal_c_a_b @ M1 )
         => ( ( member6895035109809442519od_a_b @ U3 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
           => ( ( member6895035109809442519od_a_b @ V4 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( converge_c_a_b @ M1 @ U @ U3 )
               => ( ( converge_c_a_b @ M1 @ V2 @ V4 )
                 => ( ( converge_c_a_b @ M22 @ U @ U3 )
                   => ( ( converge_c_a_b @ M22 @ V2 @ V4 )
                     => ( ( distinguishes_c_a_b @ M1 @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ U ) @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U3 @ Gamma ) @ T3 )
                         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V4 @ Gamma ) @ T3 )
                           => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ T3 )
                                = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ T3 ) )
                             => ~ ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_1138_distinguish__converge__diverge,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,U3: list_P1467974523212632366od_a_b,V4: list_P1467974523212632366od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( minimal_c_a_b @ M1 )
         => ( ( member6895035109809442519od_a_b @ U3 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
           => ( ( member6895035109809442519od_a_b @ V4 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
             => ( ( converge_c_a_b @ M1 @ U @ U3 )
               => ( ( converge_c_a_b @ M1 @ V2 @ V4 )
                 => ( ( converge_d_a_b @ M22 @ U @ U3 )
                   => ( ( converge_d_a_b @ M22 @ V2 @ V4 )
                     => ( ( distinguishes_c_a_b @ M1 @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ U ) @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U3 @ Gamma ) @ T3 )
                         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V4 @ Gamma ) @ T3 )
                           => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ T3 )
                                = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ T3 ) )
                             => ~ ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_1139_distinguish__converge__diverge,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,U3: list_P1467974523212632366od_a_b,V4: list_P1467974523212632366od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( minimal_d_a_b @ M1 )
         => ( ( member6895035109809442519od_a_b @ U3 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
           => ( ( member6895035109809442519od_a_b @ V4 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( converge_d_a_b @ M1 @ U @ U3 )
               => ( ( converge_d_a_b @ M1 @ V2 @ V4 )
                 => ( ( converge_c_a_b @ M22 @ U @ U3 )
                   => ( ( converge_c_a_b @ M22 @ V2 @ V4 )
                     => ( ( distinguishes_d_a_b @ M1 @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ U ) @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U3 @ Gamma ) @ T3 )
                         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V4 @ Gamma ) @ T3 )
                           => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ T3 )
                                = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ T3 ) )
                             => ~ ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_1140_distinguish__converge__diverge,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,U3: list_P1467974523212632366od_a_b,V4: list_P1467974523212632366od_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( minimal_d_a_b @ M1 )
         => ( ( member6895035109809442519od_a_b @ U3 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
           => ( ( member6895035109809442519od_a_b @ V4 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
             => ( ( converge_d_a_b @ M1 @ U @ U3 )
               => ( ( converge_d_a_b @ M1 @ V2 @ V4 )
                 => ( ( converge_d_a_b @ M22 @ U @ U3 )
                   => ( ( converge_d_a_b @ M22 @ V2 @ V4 )
                     => ( ( distinguishes_d_a_b @ M1 @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ U ) @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ V2 ) @ Gamma )
                       => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U3 @ Gamma ) @ T3 )
                         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V4 @ Gamma ) @ T3 )
                           => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ T3 )
                                = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ T3 ) )
                             => ~ ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_1141_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M4: fsm_d_a_b,Q14: d,Q22: d,Io: list_P1467974523212632366od_a_b,Io8: list_P1467974523212632366od_a_b] :
      ( ( minima1372903217058875368_d_a_b @ M4 @ Q14 @ Q22 @ Io )
     => ( ( member6895035109809442519od_a_b @ Io8 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Io ) ) )
       => ( ( Io8 != Io )
         => ( member6895035109809442519od_a_b @ Io8 @ ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M4 @ Q14 ) @ ( lS_d_a_b @ M4 @ Q22 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_1142_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M4: fsm_c_a_b,Q14: c,Q22: c,Io: list_P1467974523212632366od_a_b,Io8: list_P1467974523212632366od_a_b] :
      ( ( minima5000056638725520487_c_a_b @ M4 @ Q14 @ Q22 @ Io )
     => ( ( member6895035109809442519od_a_b @ Io8 @ ( set_li5045283583078295363od_a_b @ ( prefix3919435433362254901od_a_b @ Io ) ) )
       => ( ( Io8 != Io )
         => ( member6895035109809442519od_a_b @ Io8 @ ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M4 @ Q14 ) @ ( lS_c_a_b @ M4 @ Q22 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_1143_distinguish__diverge,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( distinguishes_d_a_b @ M1 @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ U ) @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ Gamma ) @ T3 )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ Gamma ) @ T3 )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ T3 )
                      = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ T3 ) )
                   => ~ ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_1144_distinguish__diverge,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( distinguishes_c_a_b @ M1 @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ U ) @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ Gamma ) @ T3 )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ Gamma ) @ T3 )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ T3 )
                      = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ T3 ) )
                   => ~ ( converge_c_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_1145_distinguish__diverge,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( distinguishes_d_a_b @ M1 @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ U ) @ ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ Gamma ) @ T3 )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ Gamma ) @ T3 )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) )
                 => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ T3 )
                      = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ T3 ) )
                   => ~ ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_1146_distinguish__diverge,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,Gamma: list_P1467974523212632366od_a_b,T3: set_li6306622547289818894od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( distinguishes_c_a_b @ M1 @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ U ) @ ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ V2 ) @ Gamma )
         => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ U @ Gamma ) @ T3 )
           => ( ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ V2 @ Gamma ) @ T3 )
             => ( ( member6895035109809442519od_a_b @ U @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
               => ( ( member6895035109809442519od_a_b @ V2 @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) )
                 => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ T3 )
                      = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ T3 ) )
                   => ~ ( converge_d_a_b @ M22 @ U @ V2 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_1147_converge__distinguishable__helper,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_c_a_b,Pi: list_P1467974523212632366od_a_b,Alpha: list_P1467974523212632366od_a_b,Tau: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( minimal_c_a_b @ M1 )
         => ( ( minimal_c_a_b @ M22 )
           => ( ( converge_c_a_b @ M1 @ Pi @ Alpha )
             => ( ( converge_c_a_b @ M22 @ Pi @ Alpha )
               => ( ( converge_c_a_b @ M1 @ Tau @ Beta )
                 => ( ( converge_c_a_b @ M22 @ Tau @ Beta )
                   => ( ( distinguishes_c_a_b @ M22 @ ( after_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) @ Pi ) @ ( after_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) @ Tau ) @ V2 )
                     => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) )
                          = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) ) )
                       => ( ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Pi )
                         != ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Tau ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_1148_converge__distinguishable__helper,axiom,
    ! [M1: fsm_c_a_b,M22: fsm_d_a_b,Pi: list_P1467974523212632366od_a_b,Alpha: list_P1467974523212632366od_a_b,Tau: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( minimal_c_a_b @ M1 )
         => ( ( minimal_d_a_b @ M22 )
           => ( ( converge_c_a_b @ M1 @ Pi @ Alpha )
             => ( ( converge_d_a_b @ M22 @ Pi @ Alpha )
               => ( ( converge_c_a_b @ M1 @ Tau @ Beta )
                 => ( ( converge_d_a_b @ M22 @ Tau @ Beta )
                   => ( ( distinguishes_d_a_b @ M22 @ ( after_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) @ Pi ) @ ( after_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) @ Tau ) @ V2 )
                     => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) )
                          = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) ) )
                       => ( ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Pi )
                         != ( after_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) @ Tau ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_1149_converge__distinguishable__helper,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_c_a_b,Pi: list_P1467974523212632366od_a_b,Alpha: list_P1467974523212632366od_a_b,Tau: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_c_a_b @ M22 )
       => ( ( minimal_d_a_b @ M1 )
         => ( ( minimal_c_a_b @ M22 )
           => ( ( converge_d_a_b @ M1 @ Pi @ Alpha )
             => ( ( converge_c_a_b @ M22 @ Pi @ Alpha )
               => ( ( converge_d_a_b @ M1 @ Tau @ Beta )
                 => ( ( converge_c_a_b @ M22 @ Tau @ Beta )
                   => ( ( distinguishes_c_a_b @ M22 @ ( after_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) @ Pi ) @ ( after_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) @ Tau ) @ V2 )
                     => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) )
                          = ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) ) )
                       => ( ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Pi )
                         != ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Tau ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_1150_converge__distinguishable__helper,axiom,
    ! [M1: fsm_d_a_b,M22: fsm_d_a_b,Pi: list_P1467974523212632366od_a_b,Alpha: list_P1467974523212632366od_a_b,Tau: list_P1467974523212632366od_a_b,Beta: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M1 )
     => ( ( observable_d_a_b @ M22 )
       => ( ( minimal_d_a_b @ M1 )
         => ( ( minimal_d_a_b @ M22 )
           => ( ( converge_d_a_b @ M1 @ Pi @ Alpha )
             => ( ( converge_d_a_b @ M22 @ Pi @ Alpha )
               => ( ( converge_d_a_b @ M1 @ Tau @ Beta )
                 => ( ( converge_d_a_b @ M22 @ Tau @ Beta )
                   => ( ( distinguishes_d_a_b @ M22 @ ( after_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) @ Pi ) @ ( after_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) @ Tau ) @ V2 )
                     => ( ( ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) )
                          = ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Alpha @ V2 ) @ ( insert6792547294658701054od_a_b @ ( append5335208823350062147od_a_b @ Beta @ V2 ) @ bot_bo4036995510831765370od_a_b ) ) ) )
                       => ( ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Pi )
                         != ( after_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) @ Tau ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_1151_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_d_a_b,I4: fsm_d_a_b,QM: d,QI: d,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( observable_d_a_b @ I4 )
       => ( ( member_d2 @ QM @ ( states_d_a_b @ M4 ) )
         => ( ( member_d2 @ QI @ ( states_d_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1152_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_c_a_b,I4: fsm_d_a_b,QM: c,QI: d,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( observable_d_a_b @ I4 )
       => ( ( member_c2 @ QM @ ( states_c_a_b @ M4 ) )
         => ( ( member_d2 @ QI @ ( states_d_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1153_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_d_a_b,I4: fsm_c_a_b,QM: d,QI: c,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( observable_c_a_b @ I4 )
       => ( ( member_d2 @ QM @ ( states_d_a_b @ M4 ) )
         => ( ( member_c2 @ QI @ ( states_c_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1154_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_c_a_b,I4: fsm_c_a_b,QM: c,QI: c,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( observable_c_a_b @ I4 )
       => ( ( member_c2 @ QM @ ( states_c_a_b @ M4 ) )
         => ( ( member_c2 @ QI @ ( states_c_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1155_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_d_a_b,I4: fsm_li1655959576902402579_b_a_b,QM: d,QI: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( observ3837622365268550711_b_a_b @ I4 )
       => ( ( member_d2 @ QM @ ( states_d_a_b @ M4 ) )
         => ( ( member6895035109809442519od_a_b @ QI @ ( states5225472451708754616_b_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1156_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_c_a_b,I4: fsm_li1655959576902402579_b_a_b,QM: c,QI: list_P1467974523212632366od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( observ3837622365268550711_b_a_b @ I4 )
       => ( ( member_c2 @ QM @ ( states_c_a_b @ M4 ) )
         => ( ( member6895035109809442519od_a_b @ QI @ ( states5225472451708754616_b_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_lis474700916027962579_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1157_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,I4: fsm_d_a_b,QM: list_P1467974523212632366od_a_b,QI: d,Io: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( observable_d_a_b @ I4 )
       => ( ( member6895035109809442519od_a_b @ QM @ ( states5225472451708754616_b_a_b @ M4 ) )
         => ( ( member_d2 @ QI @ ( states_d_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1158_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,I4: fsm_c_a_b,QM: list_P1467974523212632366od_a_b,QI: c,Io: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( observable_c_a_b @ I4 )
       => ( ( member6895035109809442519od_a_b @ QM @ ( states5225472451708754616_b_a_b @ M4 ) )
         => ( ( member_c2 @ QI @ ( states_c_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ I4 @ QI ) @ ( lS_lis474700916027962579_b_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1159_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_d_a_b,I4: fsm_fs1840479945969036537_b_a_b,QM: d,QI: fset_l1334069825099621524od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( observ529373768824785053_b_a_b @ I4 )
       => ( ( member_d2 @ QM @ ( states_d_a_b @ M4 ) )
         => ( ( member361094292949318077od_a_b @ QI @ ( states760346292458343070_b_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_d_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1160_minimal__failure__prefix__ob,axiom,
    ! [M4: fsm_c_a_b,I4: fsm_fs1840479945969036537_b_a_b,QM: c,QI: fset_l1334069825099621524od_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( observ529373768824785053_b_a_b @ I4 )
       => ( ( member_c2 @ QM @ ( states_c_a_b @ M4 ) )
         => ( ( member361094292949318077od_a_b @ QI @ ( states760346292458343070_b_a_b @ I4 ) )
           => ( ( member6895035109809442519od_a_b @ Io @ ( minus_5246360636435702261od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
             => ~ ! [Io3: list_P1467974523212632366od_a_b,Xy2: product_prod_a_b] :
                    ( ? [Io4: list_P1467974523212632366od_a_b] :
                        ( Io
                        = ( append5335208823350062147od_a_b @ Io3 @ ( append5335208823350062147od_a_b @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) @ Io4 ) ) )
                   => ( ( member6895035109809442519od_a_b @ Io3 @ ( inf_in4848585719623981052od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) )
                     => ~ ( member6895035109809442519od_a_b @ ( append5335208823350062147od_a_b @ Io3 @ ( cons_P7316939131009794654od_a_b @ Xy2 @ nil_Product_prod_a_b ) ) @ ( minus_5246360636435702261od_a_b @ ( lS_fse7452106412789865273_b_a_b @ I4 @ QI ) @ ( lS_c_a_b @ M4 @ QM ) ) ) ) ) ) ) ) ) ) ).

% minimal_failure_prefix_ob
thf(fact_1161_set__empty2,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( bot_bo4080195304570884960od_a_b
        = ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( Xs2 = nil_fs4581119677382125722od_a_b ) ) ).

% set_empty2
thf(fact_1162_List_Oset__empty,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( set_fs4298891544546585641od_a_b @ Xs2 )
        = bot_bo4080195304570884960od_a_b )
      = ( Xs2 = nil_fs4581119677382125722od_a_b ) ) ).

% List.set_empty
thf(fact_1163_distinct__append,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,Ys3: list_f1445794025290330138od_a_b] :
      ( ( distin1329390416381046541od_a_b @ ( append2015155619842375983od_a_b @ Xs2 @ Ys3 ) )
      = ( ( distin1329390416381046541od_a_b @ Xs2 )
        & ( distin1329390416381046541od_a_b @ Ys3 )
        & ( ( inf_in6210868181720738530od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( set_fs4298891544546585641od_a_b @ Ys3 ) )
          = bot_bo4080195304570884960od_a_b ) ) ) ).

% distinct_append
thf(fact_1164_distinct__list__update,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b,A: list_P1467974523212632366od_a_b,I3: nat] :
      ( ( distin3617893958516599847od_a_b @ Xs2 )
     => ( ~ ( member6895035109809442519od_a_b @ A @ ( minus_5246360636435702261od_a_b @ ( set_li5045283583078295363od_a_b @ Xs2 ) @ ( insert6792547294658701054od_a_b @ ( nth_li6535284973015076149od_a_b @ Xs2 @ I3 ) @ bot_bo4036995510831765370od_a_b ) ) )
       => ( distin3617893958516599847od_a_b @ ( list_u6451611954593206940od_a_b @ Xs2 @ I3 @ A ) ) ) ) ).

% distinct_list_update
thf(fact_1165_distinct__list__update,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,A: fset_l1334069825099621524od_a_b,I3: nat] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ~ ( member361094292949318077od_a_b @ A @ ( minus_8847328276483105883od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( insert3249498615411298916od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ I3 ) @ bot_bo4080195304570884960od_a_b ) ) )
       => ( distin1329390416381046541od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ I3 @ A ) ) ) ) ).

% distinct_list_update
thf(fact_1166_bot__prod__def,axiom,
    ( bot_bo3446722378476343061od_a_b
    = ( produc7489420772309856409od_a_b @ bot_bot_o @ bot_bo8701990416999507078od_a_b ) ) ).

% bot_prod_def
thf(fact_1167_bot__prod__def,axiom,
    ( bot_bo1834714299575479208od_a_b
    = ( produc1286801380576301484od_a_b @ bot_bot_o @ bot_bo4510604746321438361od_a_b ) ) ).

% bot_prod_def
thf(fact_1168_bot__prod__def,axiom,
    ( bot_bo4510604746321438361od_a_b
    = ( produc6212510018049267869od_a_b @ bot_bo5063621712161242880od_a_b @ bot_bo8701990416999507078od_a_b ) ) ).

% bot_prod_def
thf(fact_1169_empty__set,axiom,
    ( bot_bo4080195304570884960od_a_b
    = ( set_fs4298891544546585641od_a_b @ nil_fs4581119677382125722od_a_b ) ) ).

% empty_set
thf(fact_1170_Longest__common__prefix__ex,axiom,
    ! [L: set_li7540826859550765818od_a_b] :
      ( ( L != bot_bo5012769492311455590od_a_b )
     => ? [Ps: list_f1445794025290330138od_a_b] :
          ( ! [X6: list_f1445794025290330138od_a_b] :
              ( ( member7551773913232940227od_a_b @ X6 @ L )
             => ( prefix7449001915862371055od_a_b @ Ps @ X6 ) )
          & ! [Qs2: list_f1445794025290330138od_a_b] :
              ( ! [X4: list_f1445794025290330138od_a_b] :
                  ( ( member7551773913232940227od_a_b @ X4 @ L )
                 => ( prefix7449001915862371055od_a_b @ Qs2 @ X4 ) )
             => ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Qs2 ) @ ( size_s6068669265016274566od_a_b @ Ps ) ) ) ) ) ).

% Longest_common_prefix_ex
thf(fact_1171_Longest__common__prefix__unique,axiom,
    ! [L: set_li7540826859550765818od_a_b] :
      ( ( L != bot_bo5012769492311455590od_a_b )
     => ? [X4: list_f1445794025290330138od_a_b] :
          ( ! [Xa2: list_f1445794025290330138od_a_b] :
              ( ( member7551773913232940227od_a_b @ Xa2 @ L )
             => ( prefix7449001915862371055od_a_b @ X4 @ Xa2 ) )
          & ! [Qs2: list_f1445794025290330138od_a_b] :
              ( ! [Xa3: list_f1445794025290330138od_a_b] :
                  ( ( member7551773913232940227od_a_b @ Xa3 @ L )
                 => ( prefix7449001915862371055od_a_b @ Qs2 @ Xa3 ) )
             => ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Qs2 ) @ ( size_s6068669265016274566od_a_b @ X4 ) ) )
          & ! [Y5: list_f1445794025290330138od_a_b] :
              ( ( ! [Xa3: list_f1445794025290330138od_a_b] :
                    ( ( member7551773913232940227od_a_b @ Xa3 @ L )
                   => ( prefix7449001915862371055od_a_b @ Y5 @ Xa3 ) )
                & ! [Qs3: list_f1445794025290330138od_a_b] :
                    ( ! [Xa2: list_f1445794025290330138od_a_b] :
                        ( ( member7551773913232940227od_a_b @ Xa2 @ L )
                       => ( prefix7449001915862371055od_a_b @ Qs3 @ Xa2 ) )
                   => ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ Qs3 ) @ ( size_s6068669265016274566od_a_b @ Y5 ) ) ) )
             => ( Y5 = X4 ) ) ) ) ).

% Longest_common_prefix_unique
thf(fact_1172_set__update__distinct,axiom,
    ! [Xs2: list_f1445794025290330138od_a_b,N: nat,X3: fset_l1334069825099621524od_a_b] :
      ( ( distin1329390416381046541od_a_b @ Xs2 )
     => ( ( ord_less_nat @ N @ ( size_s6068669265016274566od_a_b @ Xs2 ) )
       => ( ( set_fs4298891544546585641od_a_b @ ( list_u7851604859245713154od_a_b @ Xs2 @ N @ X3 ) )
          = ( insert3249498615411298916od_a_b @ X3 @ ( minus_8847328276483105883od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( insert3249498615411298916od_a_b @ ( nth_fs7310631729605226779od_a_b @ Xs2 @ N ) @ bot_bo4080195304570884960od_a_b ) ) ) ) ) ) ).

% set_update_distinct
thf(fact_1173_deadlock__state__alt__def,axiom,
    ( deadlock_state_d_a_b
    = ( ^ [M5: fsm_d_a_b,Q6: d] : ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M5 @ Q6 ) @ ( insert6792547294658701054od_a_b @ nil_Product_prod_a_b @ bot_bo4036995510831765370od_a_b ) ) ) ) ).

% deadlock_state_alt_def
thf(fact_1174_deadlock__state__alt__def,axiom,
    ( deadlock_state_c_a_b
    = ( ^ [M5: fsm_c_a_b,Q6: c] : ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M5 @ Q6 ) @ ( insert6792547294658701054od_a_b @ nil_Product_prod_a_b @ bot_bo4036995510831765370od_a_b ) ) ) ) ).

% deadlock_state_alt_def
thf(fact_1175_set__take__disj__set__drop__if__distinct,axiom,
    ! [Vs2: list_f1445794025290330138od_a_b,I3: nat,J3: nat] :
      ( ( distin1329390416381046541od_a_b @ Vs2 )
     => ( ( ord_less_eq_nat @ I3 @ J3 )
       => ( ( inf_in6210868181720738530od_a_b @ ( set_fs4298891544546585641od_a_b @ ( take_f8758302346742390914od_a_b @ I3 @ Vs2 ) ) @ ( set_fs4298891544546585641od_a_b @ ( drop_f570763960254934490od_a_b @ J3 @ Vs2 ) ) )
          = bot_bo4080195304570884960od_a_b ) ) ) ).

% set_take_disj_set_drop_if_distinct
thf(fact_1176_distinct__concat,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ( distin3617893958516599847od_a_b @ Xs2 )
     => ( ! [Ys: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ Ys @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
           => ( distin132333874345289761od_a_b @ Ys ) )
       => ( ! [Ys: list_P1467974523212632366od_a_b,Zs2: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Ys @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
             => ( ( member6895035109809442519od_a_b @ Zs2 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
               => ( ( Ys != Zs2 )
                 => ( ( inf_in8976041639890736118od_a_b @ ( set_Product_prod_a_b2 @ Ys ) @ ( set_Product_prod_a_b2 @ Zs2 ) )
                    = bot_bo3428410327501040244od_a_b ) ) ) )
         => ( distin132333874345289761od_a_b @ ( concat6071998534011412713od_a_b @ Xs2 ) ) ) ) ) ).

% distinct_concat
thf(fact_1177_distinct__concat,axiom,
    ! [Xs2: list_l6099054058445139744od_a_b] :
      ( ( distin5173564018569636371od_a_b @ Xs2 )
     => ( ! [Ys: list_f1445794025290330138od_a_b] :
            ( ( member7551773913232940227od_a_b @ Ys @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
           => ( distin1329390416381046541od_a_b @ Ys ) )
       => ( ! [Ys: list_f1445794025290330138od_a_b,Zs2: list_f1445794025290330138od_a_b] :
              ( ( member7551773913232940227od_a_b @ Ys @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
             => ( ( member7551773913232940227od_a_b @ Zs2 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
               => ( ( Ys != Zs2 )
                 => ( ( inf_in6210868181720738530od_a_b @ ( set_fs4298891544546585641od_a_b @ Ys ) @ ( set_fs4298891544546585641od_a_b @ Zs2 ) )
                    = bot_bo4080195304570884960od_a_b ) ) ) )
         => ( distin1329390416381046541od_a_b @ ( concat3179126272939696085od_a_b @ Xs2 ) ) ) ) ) ).

% distinct_concat
thf(fact_1178_distinct__concat__iff,axiom,
    ! [Xs2: list_l8778361445553822004od_a_b] :
      ( ( distin132333874345289761od_a_b @ ( concat6071998534011412713od_a_b @ Xs2 ) )
      = ( ( distin3617893958516599847od_a_b @ ( remove7800354776472834362od_a_b @ nil_Product_prod_a_b @ Xs2 ) )
        & ! [Ys2: list_P1467974523212632366od_a_b] :
            ( ( member6895035109809442519od_a_b @ Ys2 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
           => ( distin132333874345289761od_a_b @ Ys2 ) )
        & ! [Ys2: list_P1467974523212632366od_a_b,Zs3: list_P1467974523212632366od_a_b] :
            ( ( ( member6895035109809442519od_a_b @ Ys2 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
              & ( member6895035109809442519od_a_b @ Zs3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
              & ( Ys2 != Zs3 ) )
           => ( ( inf_in8976041639890736118od_a_b @ ( set_Product_prod_a_b2 @ Ys2 ) @ ( set_Product_prod_a_b2 @ Zs3 ) )
              = bot_bo3428410327501040244od_a_b ) ) ) ) ).

% distinct_concat_iff
thf(fact_1179_distinct__concat__iff,axiom,
    ! [Xs2: list_l6099054058445139744od_a_b] :
      ( ( distin1329390416381046541od_a_b @ ( concat3179126272939696085od_a_b @ Xs2 ) )
      = ( ( distin5173564018569636371od_a_b @ ( remove6452524568127849510od_a_b @ nil_fs4581119677382125722od_a_b @ Xs2 ) )
        & ! [Ys2: list_f1445794025290330138od_a_b] :
            ( ( member7551773913232940227od_a_b @ Ys2 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
           => ( distin1329390416381046541od_a_b @ Ys2 ) )
        & ! [Ys2: list_f1445794025290330138od_a_b,Zs3: list_f1445794025290330138od_a_b] :
            ( ( ( member7551773913232940227od_a_b @ Ys2 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
              & ( member7551773913232940227od_a_b @ Zs3 @ ( set_li8217014873844115759od_a_b @ Xs2 ) )
              & ( Ys2 != Zs3 ) )
           => ( ( inf_in6210868181720738530od_a_b @ ( set_fs4298891544546585641od_a_b @ Ys2 ) @ ( set_fs4298891544546585641od_a_b @ Zs3 ) )
              = bot_bo4080195304570884960od_a_b ) ) ) ) ).

% distinct_concat_iff
thf(fact_1180_fempty__iff,axiom,
    ! [C2: list_P1467974523212632366od_a_b] :
      ~ ( fmembe7722352836199763061od_a_b @ C2 @ bot_bo5063621712161242880od_a_b ) ).

% fempty_iff
thf(fact_1181_all__not__fin__conv,axiom,
    ! [A4: fset_l1334069825099621524od_a_b] :
      ( ( ! [X5: list_P1467974523212632366od_a_b] :
            ~ ( fmembe7722352836199763061od_a_b @ X5 @ A4 ) )
      = ( A4 = bot_bo5063621712161242880od_a_b ) ) ).

% all_not_fin_conv
thf(fact_1182_removeAll__id,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ~ ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ( remove7800354776472834362od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% removeAll_id
thf(fact_1183_removeAll__id,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ~ ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ( remove7132956074442862240od_a_b @ X3 @ Xs2 )
        = Xs2 ) ) ).

% removeAll_id
thf(fact_1184_set__removeAll,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( remove7132956074442862240od_a_b @ X3 @ Xs2 ) )
      = ( minus_8847328276483105883od_a_b @ ( set_fs4298891544546585641od_a_b @ Xs2 ) @ ( insert3249498615411298916od_a_b @ X3 @ bot_bo4080195304570884960od_a_b ) ) ) ).

% set_removeAll
thf(fact_1185_femptyE,axiom,
    ! [A: list_P1467974523212632366od_a_b] :
      ~ ( fmembe7722352836199763061od_a_b @ A @ bot_bo5063621712161242880od_a_b ) ).

% femptyE
thf(fact_1186_ex__fin__conv,axiom,
    ! [A4: fset_l1334069825099621524od_a_b] :
      ( ( ? [X5: list_P1467974523212632366od_a_b] : ( fmembe7722352836199763061od_a_b @ X5 @ A4 ) )
      = ( A4 != bot_bo5063621712161242880od_a_b ) ) ).

% ex_fin_conv
thf(fact_1187_equalsffemptyD,axiom,
    ! [A4: fset_l1334069825099621524od_a_b,A: list_P1467974523212632366od_a_b] :
      ( ( A4 = bot_bo5063621712161242880od_a_b )
     => ~ ( fmembe7722352836199763061od_a_b @ A @ A4 ) ) ).

% equalsffemptyD
thf(fact_1188_equalsffemptyI,axiom,
    ! [A4: fset_l1334069825099621524od_a_b] :
      ( ! [Y: list_P1467974523212632366od_a_b] :
          ~ ( fmembe7722352836199763061od_a_b @ Y @ A4 )
     => ( A4 = bot_bo5063621712161242880od_a_b ) ) ).

% equalsffemptyI
thf(fact_1189_removeAll_Osimps_I2_J,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ( X3 = Y3 )
       => ( ( remove7132956074442862240od_a_b @ X3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Xs2 ) )
          = ( remove7132956074442862240od_a_b @ X3 @ Xs2 ) ) )
      & ( ( X3 != Y3 )
       => ( ( remove7132956074442862240od_a_b @ X3 @ ( cons_f6577355434438001738od_a_b @ Y3 @ Xs2 ) )
          = ( cons_f6577355434438001738od_a_b @ Y3 @ ( remove7132956074442862240od_a_b @ X3 @ Xs2 ) ) ) ) ) ).

% removeAll.simps(2)
thf(fact_1190_length__removeAll__less__eq,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] : ( ord_less_eq_nat @ ( size_s6068669265016274566od_a_b @ ( remove7132956074442862240od_a_b @ X3 @ Xs2 ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ).

% length_removeAll_less_eq
thf(fact_1191_length__removeAll__less,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
      ( ( member6895035109809442519od_a_b @ X3 @ ( set_li5045283583078295363od_a_b @ Xs2 ) )
     => ( ord_less_nat @ ( size_s4021047160419372448od_a_b @ ( remove7800354776472834362od_a_b @ X3 @ Xs2 ) ) @ ( size_s4021047160419372448od_a_b @ Xs2 ) ) ) ).

% length_removeAll_less
thf(fact_1192_length__removeAll__less,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( member361094292949318077od_a_b @ X3 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( ord_less_nat @ ( size_s6068669265016274566od_a_b @ ( remove7132956074442862240od_a_b @ X3 @ Xs2 ) ) @ ( size_s6068669265016274566od_a_b @ Xs2 ) ) ) ).

% length_removeAll_less
thf(fact_1193_reachable__k__0__initial,axiom,
    ! [M4: fsm_d_a_b] :
      ( ( reachable_k_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ zero_zero_nat )
      = ( insert_d2 @ ( initial_d_a_b @ M4 ) @ bot_bot_set_d ) ) ).

% reachable_k_0_initial
thf(fact_1194_reachable__k__0__initial,axiom,
    ! [M4: fsm_c_a_b] :
      ( ( reachable_k_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ zero_zero_nat )
      = ( insert_c2 @ ( initial_c_a_b @ M4 ) @ bot_bot_set_c ) ) ).

% reachable_k_0_initial
thf(fact_1195_defined__inputs__language__diff,axiom,
    ! [X3: a,M1: fsm_d_a_b,Q14: d,M22: fsm_d_a_b,Q22: d] :
      ( ( member_a2 @ X3 @ ( defined_inputs_d_a_b @ M1 @ Q14 ) )
     => ( ~ ( member_a2 @ X3 @ ( defined_inputs_d_a_b @ M22 @ Q22 ) )
       => ~ ! [Y: b] :
              ~ ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y ) @ nil_Product_prod_a_b ) @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ M1 @ Q14 ) @ ( lS_d_a_b @ M22 @ Q22 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_1196_defined__inputs__language__diff,axiom,
    ! [X3: a,M1: fsm_d_a_b,Q14: d,M22: fsm_c_a_b,Q22: c] :
      ( ( member_a2 @ X3 @ ( defined_inputs_d_a_b @ M1 @ Q14 ) )
     => ( ~ ( member_a2 @ X3 @ ( defined_inputs_c_a_b @ M22 @ Q22 ) )
       => ~ ! [Y: b] :
              ~ ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y ) @ nil_Product_prod_a_b ) @ ( minus_5246360636435702261od_a_b @ ( lS_d_a_b @ M1 @ Q14 ) @ ( lS_c_a_b @ M22 @ Q22 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_1197_defined__inputs__language__diff,axiom,
    ! [X3: a,M1: fsm_c_a_b,Q14: c,M22: fsm_d_a_b,Q22: d] :
      ( ( member_a2 @ X3 @ ( defined_inputs_c_a_b @ M1 @ Q14 ) )
     => ( ~ ( member_a2 @ X3 @ ( defined_inputs_d_a_b @ M22 @ Q22 ) )
       => ~ ! [Y: b] :
              ~ ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y ) @ nil_Product_prod_a_b ) @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ M1 @ Q14 ) @ ( lS_d_a_b @ M22 @ Q22 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_1198_defined__inputs__language__diff,axiom,
    ! [X3: a,M1: fsm_c_a_b,Q14: c,M22: fsm_c_a_b,Q22: c] :
      ( ( member_a2 @ X3 @ ( defined_inputs_c_a_b @ M1 @ Q14 ) )
     => ( ~ ( member_a2 @ X3 @ ( defined_inputs_c_a_b @ M22 @ Q22 ) )
       => ~ ! [Y: b] :
              ~ ( member6895035109809442519od_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ X3 @ Y ) @ nil_Product_prod_a_b ) @ ( minus_5246360636435702261od_a_b @ ( lS_c_a_b @ M1 @ Q14 ) @ ( lS_c_a_b @ M22 @ Q22 ) ) ) ) ) ).

% defined_inputs_language_diff
thf(fact_1199_pair__in__swap__image,axiom,
    ! [Y3: list_f1445794025290330138od_a_b,X3: $o,A4: set_Pr121319624013539721od_a_b] :
      ( ( member2803847055803730254_a_b_o @ ( produc4366446772417547285_a_b_o @ Y3 @ X3 ) @ ( image_3217611746473200321_a_b_o @ produc7780892788990209593od_a_b @ A4 ) )
      = ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1200_pair__in__swap__image,axiom,
    ! [Y3: produc2518759752815613485od_a_b,X3: $o,A4: set_Pr5622538825374275996od_a_b] :
      ( ( member5149209166832238203_a_b_o @ ( produc5238447047330606914_a_b_o @ Y3 @ X3 ) @ ( image_5311508624785544475_a_b_o @ produc205082526707003212od_a_b @ A4 ) )
      = ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1201_pair__in__swap__image,axiom,
    ! [Y3: list_f1445794025290330138od_a_b,X3: fset_l1334069825099621524od_a_b,A4: set_Pr1051027220935592077od_a_b] :
      ( ( member4092356564367800522od_a_b @ ( produc7350191566654282897od_a_b @ Y3 @ X3 ) @ ( image_4146237622769870137od_a_b @ produc1322645004498421309od_a_b @ A4 ) )
      = ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1202_pair__in__swap__image,axiom,
    ! [Y3: $o,X3: list_f1445794025290330138od_a_b,A4: set_Pr2549634154452313093_a_b_o] :
      ( ( member3029431943403884754od_a_b @ ( produc7489420772309856409od_a_b @ Y3 @ X3 ) @ ( image_8940756588869874889od_a_b @ produc4657918789097900469_a_b_o @ A4 ) )
      = ( member2803847055803730254_a_b_o @ ( produc4366446772417547285_a_b_o @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1203_pair__in__swap__image,axiom,
    ! [Y3: $o,X3: produc2518759752815613485od_a_b,A4: set_Pr1979380953684217522_a_b_o] :
      ( ( member6983108301751770725od_a_b @ ( produc1286801380576301484od_a_b @ Y3 @ X3 ) @ ( image_6895954947936813679od_a_b @ produc4156728193461308642_a_b_o @ A4 ) )
      = ( member5149209166832238203_a_b_o @ ( produc5238447047330606914_a_b_o @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1204_pair__in__swap__image,axiom,
    ! [Y3: fset_l1334069825099621524od_a_b,X3: list_f1445794025290330138od_a_b,A4: set_Pr3384986265503004545od_a_b] :
      ( ( member7205742373938401238od_a_b @ ( produc6212510018049267869od_a_b @ Y3 @ X3 ) @ ( image_3785288736868017745od_a_b @ produc2460326553103436337od_a_b @ A4 ) )
      = ( member4092356564367800522od_a_b @ ( produc7350191566654282897od_a_b @ X3 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_1205_list_Oset__map,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,V2: list_f1445794025290330138od_a_b] :
      ( ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ V2 ) )
      = ( image_3633131638523200261od_a_b @ F2 @ ( set_fs4298891544546585641od_a_b @ V2 ) ) ) ).

% list.set_map
thf(fact_1206_image__set,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > fset_l1334069825099621524od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( image_3633131638523200261od_a_b @ F2 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
      = ( set_fs4298891544546585641od_a_b @ ( map_fs8651439882968028996od_a_b @ F2 @ Xs2 ) ) ) ).

% image_set
thf(fact_1207_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: d > d,M1: fsm_d_a_b,M22: fsm_d_a_b,Q3: d] :
      ( ( bij_betw_d_d @ F2 @ ( states_d_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( states_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( states_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M1 @ Q3 ) @ ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1208_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: d > c,M1: fsm_d_a_b,M22: fsm_c_a_b,Q3: d] :
      ( ( bij_betw_d_c @ F2 @ ( states_d_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( states_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( states_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M1 @ Q3 ) @ ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1209_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: c > d,M1: fsm_c_a_b,M22: fsm_d_a_b,Q3: c] :
      ( ( bij_betw_c_d @ F2 @ ( states_c_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( states_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( states_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M1 @ Q3 ) @ ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1210_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: c > c,M1: fsm_c_a_b,M22: fsm_c_a_b,Q3: c] :
      ( ( bij_betw_c_c @ F2 @ ( states_c_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( states_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( states_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M1 @ Q3 ) @ ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1211_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: list_P1467974523212632366od_a_b > d,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_d_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be3428385127041619017_a_b_d @ F2 @ ( states5225472451708754616_b_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states5225472451708754616_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states5225472451708754616_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_lis474700916027962579_b_a_b @ M1 @ Q3 ) @ ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1212_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: list_P1467974523212632366od_a_b > c,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_c_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be3428385127041619016_a_b_c @ F2 @ ( states5225472451708754616_b_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states5225472451708754616_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states5225472451708754616_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_lis474700916027962579_b_a_b @ M1 @ Q3 ) @ ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1213_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > d,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_d_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be6008341014587936483_a_b_d @ F2 @ ( states760346292458343070_b_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states760346292458343070_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states760346292458343070_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_fse7452106412789865273_b_a_b @ M1 @ Q3 ) @ ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1214_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > c,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_c_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be6008341014587936482_a_b_c @ F2 @ ( states760346292458343070_b_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states760346292458343070_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states760346292458343070_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M1 ) )
           => ( ord_le153002609085230766od_a_b @ ( lS_fse7452106412789865273_b_a_b @ M1 @ Q3 ) @ ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1215_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b,M1: fsm_li2173814106350063374od_a_b,M22: fsm_li3816064051032718074od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be5509875313758850402od_a_b @ F2 @ ( states7671667289678552115od_a_b @ M1 ) @ ( states5686850096005743135od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia8636230792963847769od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states7671667289678552115od_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states7671667289678552115od_a_b @ M1 ) )
               => ( ( member6531131955963215218od_a_b @ ( produc4061792103530149689od_a_b @ Q @ ( produc3433936959961524160od_a_b @ X4 @ ( produc5291915255311561905od_a_b @ Y @ Q7 ) ) ) @ ( transi1383219260676973311od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states7671667289678552115od_a_b @ M1 ) )
           => ( ord_le5510395190108133673od_a_b @ ( lS_lis6227585698039082446od_a_b @ M1 @ Q3 ) @ ( lS_lis3357525008826253498od_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1216_language__equivalence__from__isomorphism__helper,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,M1: fsm_fs4038567970311364852od_a_b,M22: fsm_li3816064051032718074od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be1705665232800849660od_a_b @ F2 @ ( states8298490222144566041od_a_b @ M1 ) @ ( states5686850096005743135od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia5383324526419690047od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states8298490222144566041od_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states8298490222144566041od_a_b @ M1 ) )
               => ( ( member7151811798220465266od_a_b @ ( produc6645316577686334777od_a_b @ Q @ ( produc4815424570203850918od_a_b @ X4 @ ( produc8099561100433402519od_a_b @ Y @ Q7 ) ) ) @ ( transi413513904105055205od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states8298490222144566041od_a_b @ M1 ) )
           => ( ord_le5510395190108133673od_a_b @ ( lS_fse3523897189346949940od_a_b @ M1 @ Q3 ) @ ( lS_lis3357525008826253498od_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper
thf(fact_1217_subset__subseqs,axiom,
    ! [X10: set_fs5173440902860351732od_a_b,Xs2: list_f1445794025290330138od_a_b] :
      ( ( ord_le8981612867897606292od_a_b @ X10 @ ( set_fs4298891544546585641od_a_b @ Xs2 ) )
     => ( member3854304715014625821od_a_b @ X10 @ ( image_885551376138370655od_a_b @ set_fs4298891544546585641od_a_b @ ( set_li8217014873844115759od_a_b @ ( subseq8423821483446685161od_a_b @ Xs2 ) ) ) ) ) ).

% subset_subseqs
thf(fact_1218_language__equivalence__from__isomorphism,axiom,
    ! [F2: d > d,M1: fsm_d_a_b,M22: fsm_d_a_b,Q3: d] :
      ( ( bij_betw_d_d @ F2 @ ( states_d_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( states_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( states_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M1 ) )
           => ( ( lS_d_a_b @ M1 @ Q3 )
              = ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1219_language__equivalence__from__isomorphism,axiom,
    ! [F2: d > c,M1: fsm_d_a_b,M22: fsm_c_a_b,Q3: d] :
      ( ( bij_betw_d_c @ F2 @ ( states_d_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( states_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( states_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member_d2 @ Q3 @ ( states_d_a_b @ M1 ) )
           => ( ( lS_d_a_b @ M1 @ Q3 )
              = ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1220_language__equivalence__from__isomorphism,axiom,
    ! [F2: c > d,M1: fsm_c_a_b,M22: fsm_d_a_b,Q3: c] :
      ( ( bij_betw_c_d @ F2 @ ( states_c_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( states_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( states_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M1 ) )
           => ( ( lS_c_a_b @ M1 @ Q3 )
              = ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1221_language__equivalence__from__isomorphism,axiom,
    ! [F2: c > c,M1: fsm_c_a_b,M22: fsm_c_a_b,Q3: c] :
      ( ( bij_betw_c_c @ F2 @ ( states_c_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( states_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( states_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member_c2 @ Q3 @ ( states_c_a_b @ M1 ) )
           => ( ( lS_c_a_b @ M1 @ Q3 )
              = ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1222_language__equivalence__from__isomorphism,axiom,
    ! [F2: list_P1467974523212632366od_a_b > d,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_d_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be3428385127041619017_a_b_d @ F2 @ ( states5225472451708754616_b_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states5225472451708754616_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states5225472451708754616_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M1 ) )
           => ( ( lS_lis474700916027962579_b_a_b @ M1 @ Q3 )
              = ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1223_language__equivalence__from__isomorphism,axiom,
    ! [F2: list_P1467974523212632366od_a_b > c,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_c_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be3428385127041619016_a_b_c @ F2 @ ( states5225472451708754616_b_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states5225472451708754616_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states5225472451708754616_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states5225472451708754616_b_a_b @ M1 ) )
           => ( ( lS_lis474700916027962579_b_a_b @ M1 @ Q3 )
              = ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1224_language__equivalence__from__isomorphism,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > d,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_d_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be6008341014587936483_a_b_d @ F2 @ ( states760346292458343070_b_a_b @ M1 ) @ ( states_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states760346292458343070_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states760346292458343070_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M1 ) )
           => ( ( lS_fse7452106412789865273_b_a_b @ M1 @ Q3 )
              = ( lS_d_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1225_language__equivalence__from__isomorphism,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > c,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_c_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be6008341014587936482_a_b_c @ F2 @ ( states760346292458343070_b_a_b @ M1 ) @ ( states_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states760346292458343070_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states760346292458343070_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states760346292458343070_b_a_b @ M1 ) )
           => ( ( lS_fse7452106412789865273_b_a_b @ M1 @ Q3 )
              = ( lS_c_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1226_language__equivalence__from__isomorphism,axiom,
    ! [F2: list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b,M1: fsm_li2173814106350063374od_a_b,M22: fsm_li3816064051032718074od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( bij_be5509875313758850402od_a_b @ F2 @ ( states7671667289678552115od_a_b @ M1 ) @ ( states5686850096005743135od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia8636230792963847769od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( states7671667289678552115od_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( states7671667289678552115od_a_b @ M1 ) )
               => ( ( member6531131955963215218od_a_b @ ( produc4061792103530149689od_a_b @ Q @ ( produc3433936959961524160od_a_b @ X4 @ ( produc5291915255311561905od_a_b @ Y @ Q7 ) ) ) @ ( transi1383219260676973311od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ( member6895035109809442519od_a_b @ Q3 @ ( states7671667289678552115od_a_b @ M1 ) )
           => ( ( lS_lis6227585698039082446od_a_b @ M1 @ Q3 )
              = ( lS_lis3357525008826253498od_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1227_language__equivalence__from__isomorphism,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,M1: fsm_fs4038567970311364852od_a_b,M22: fsm_li3816064051032718074od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( bij_be1705665232800849660od_a_b @ F2 @ ( states8298490222144566041od_a_b @ M1 ) @ ( states5686850096005743135od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia5383324526419690047od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( states8298490222144566041od_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( states8298490222144566041od_a_b @ M1 ) )
               => ( ( member7151811798220465266od_a_b @ ( produc6645316577686334777od_a_b @ Q @ ( produc4815424570203850918od_a_b @ X4 @ ( produc8099561100433402519od_a_b @ Y @ Q7 ) ) ) @ ( transi413513904105055205od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ( member361094292949318077od_a_b @ Q3 @ ( states8298490222144566041od_a_b @ M1 ) )
           => ( ( lS_fse3523897189346949940od_a_b @ M1 @ Q3 )
              = ( lS_lis3357525008826253498od_a_b @ M22 @ ( F2 @ Q3 ) ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism
thf(fact_1228_rename__states__isomorphism__language,axiom,
    ! [F2: d > d,M4: fsm_d_a_b] :
      ( ( bij_betw_d_d @ F2 @ ( states_d_a_b @ M4 ) @ ( image_d_d @ F2 @ ( states_d_a_b @ M4 ) ) )
     => ( ( lS_d_a_b @ ( rename6211310769420509491_a_b_d @ M4 @ F2 ) @ ( initial_d_a_b @ ( rename6211310769420509491_a_b_d @ M4 @ F2 ) ) )
        = ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ).

% rename_states_isomorphism_language
thf(fact_1229_rename__states__isomorphism__language,axiom,
    ! [F2: c > d,M4: fsm_c_a_b] :
      ( ( bij_betw_c_d @ F2 @ ( states_c_a_b @ M4 ) @ ( image_c_d @ F2 @ ( states_c_a_b @ M4 ) ) )
     => ( ( lS_d_a_b @ ( rename4723348732125710964_a_b_d @ M4 @ F2 ) @ ( initial_d_a_b @ ( rename4723348732125710964_a_b_d @ M4 @ F2 ) ) )
        = ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ).

% rename_states_isomorphism_language
thf(fact_1230_rename__states__isomorphism__language,axiom,
    ! [F2: d > c,M4: fsm_d_a_b] :
      ( ( bij_betw_d_c @ F2 @ ( states_d_a_b @ M4 ) @ ( image_d_c @ F2 @ ( states_d_a_b @ M4 ) ) )
     => ( ( lS_c_a_b @ ( rename6211310769420509490_a_b_c @ M4 @ F2 ) @ ( initial_c_a_b @ ( rename6211310769420509490_a_b_c @ M4 @ F2 ) ) )
        = ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) ) ) ).

% rename_states_isomorphism_language
thf(fact_1231_rename__states__isomorphism__language,axiom,
    ! [F2: c > c,M4: fsm_c_a_b] :
      ( ( bij_betw_c_c @ F2 @ ( states_c_a_b @ M4 ) @ ( image_c_c @ F2 @ ( states_c_a_b @ M4 ) ) )
     => ( ( lS_c_a_b @ ( rename4723348732125710963_a_b_c @ M4 @ F2 ) @ ( initial_c_a_b @ ( rename4723348732125710963_a_b_c @ M4 @ F2 ) ) )
        = ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) ) ) ).

% rename_states_isomorphism_language
thf(fact_1232_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: d > d,M1: fsm_d_a_b,M22: fsm_d_a_b] :
      ( ( bij_betw_d_d @ F2 @ ( reacha2749672884579446598_d_a_b @ M1 ) @ ( reacha2749672884579446598_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( reacha2749672884579446598_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( reacha2749672884579446598_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1233_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: d > c,M1: fsm_d_a_b,M22: fsm_c_a_b] :
      ( ( bij_betw_d_c @ F2 @ ( reacha2749672884579446598_d_a_b @ M1 ) @ ( reacha6376826306246091717_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_d_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: d,X4: a,Y: b,Q7: d] :
              ( ( member_d2 @ Q @ ( reacha2749672884579446598_d_a_b @ M1 ) )
             => ( ( member_d2 @ Q7 @ ( reacha2749672884579446598_d_a_b @ M1 ) )
               => ( ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ Q @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ Q7 ) ) ) @ ( transitions_d_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_d_a_b @ M1 @ ( initial_d_a_b @ M1 ) ) @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1234_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: c > d,M1: fsm_c_a_b,M22: fsm_d_a_b] :
      ( ( bij_betw_c_d @ F2 @ ( reacha6376826306246091717_c_a_b @ M1 ) @ ( reacha2749672884579446598_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( reacha6376826306246091717_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( reacha6376826306246091717_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1235_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: c > c,M1: fsm_c_a_b,M22: fsm_c_a_b] :
      ( ( bij_betw_c_c @ F2 @ ( reacha6376826306246091717_c_a_b @ M1 ) @ ( reacha6376826306246091717_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initial_c_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: c,X4: a,Y: b,Q7: c] :
              ( ( member_c2 @ Q @ ( reacha6376826306246091717_c_a_b @ M1 ) )
             => ( ( member_c2 @ Q7 @ ( reacha6376826306246091717_c_a_b @ M1 ) )
               => ( ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ Q @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ Q7 ) ) ) @ ( transitions_c_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_c_a_b @ M1 @ ( initial_c_a_b @ M1 ) ) @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1236_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: list_P1467974523212632366od_a_b > d,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_d_a_b] :
      ( ( bij_be3428385127041619017_a_b_d @ F2 @ ( reacha5660761788860886259_b_a_b @ M1 ) @ ( reacha2749672884579446598_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( reacha5660761788860886259_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( reacha5660761788860886259_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_lis474700916027962579_b_a_b @ M1 @ ( initia1111342868025077214_b_a_b @ M1 ) ) @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1237_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: list_P1467974523212632366od_a_b > c,M1: fsm_li1655959576902402579_b_a_b,M22: fsm_c_a_b] :
      ( ( bij_be3428385127041619016_a_b_c @ F2 @ ( reacha5660761788860886259_b_a_b @ M1 ) @ ( reacha6376826306246091717_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia1111342868025077214_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: a,Y: b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( reacha5660761788860886259_b_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( reacha5660761788860886259_b_a_b @ M1 ) )
               => ( ( member5376971474732164961od_a_b @ ( produc8932199587862418344od_a_b @ Q @ ( produc458170271728203695od_a_b @ X4 @ ( produc1126366459492273030od_a_b @ Y @ Q7 ) ) ) @ ( transi705733371584467844_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_lis474700916027962579_b_a_b @ M1 @ ( initia1111342868025077214_b_a_b @ M1 ) ) @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1238_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > d,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_d_a_b] :
      ( ( bij_be6008341014587936483_a_b_d @ F2 @ ( reacha2755017045781758809_b_a_b @ M1 ) @ ( reacha2749672884579446598_d_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_d_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( reacha2755017045781758809_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( reacha2755017045781758809_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member2916658754359974305od_b_d @ ( produc4320412792819862376od_b_d @ ( F2 @ Q ) @ ( produc6867761809215060226od_b_d @ X4 @ ( product_Pair_b_d @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_d_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_fse7452106412789865273_b_a_b @ M1 @ ( initia2961132633701536452_b_a_b @ M1 ) ) @ ( lS_d_a_b @ M22 @ ( initial_d_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1239_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > c,M1: fsm_fs1840479945969036537_b_a_b,M22: fsm_c_a_b] :
      ( ( bij_be6008341014587936482_a_b_c @ F2 @ ( reacha2755017045781758809_b_a_b @ M1 ) @ ( reacha6376826306246091717_c_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia2961132633701536452_b_a_b @ M1 ) )
          = ( initial_c_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: a,Y: b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( reacha2755017045781758809_b_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( reacha2755017045781758809_b_a_b @ M1 ) )
               => ( ( member8515146061811315169od_a_b @ ( produc4314678409971068200od_a_b @ Q @ ( produc5260523172840707349od_a_b @ X4 @ ( produc912194690294371052od_a_b @ Y @ Q7 ) ) ) @ ( transi2241535490925309290_b_a_b @ M1 ) )
                  = ( member265788643176044257od_b_c @ ( produc8300696160155326504od_b_c @ ( F2 @ Q ) @ ( produc6867761804911831425od_b_c @ X4 @ ( product_Pair_b_c @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transitions_c_a_b @ M22 ) ) ) ) )
         => ( ord_le153002609085230766od_a_b @ ( lS_fse7452106412789865273_b_a_b @ M1 @ ( initia2961132633701536452_b_a_b @ M1 ) ) @ ( lS_c_a_b @ M22 @ ( initial_c_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1240_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: list_P1467974523212632366od_a_b > list_f1445794025290330138od_a_b,M1: fsm_li2173814106350063374od_a_b,M22: fsm_li3816064051032718074od_a_b] :
      ( ( bij_be5509875313758850402od_a_b @ F2 @ ( reacha4791805987247240686od_a_b @ M1 ) @ ( reacha7494367349399693530od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia8636230792963847769od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: list_P1467974523212632366od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: list_P1467974523212632366od_a_b] :
              ( ( member6895035109809442519od_a_b @ Q @ ( reacha4791805987247240686od_a_b @ M1 ) )
             => ( ( member6895035109809442519od_a_b @ Q7 @ ( reacha4791805987247240686od_a_b @ M1 ) )
               => ( ( member6531131955963215218od_a_b @ ( produc4061792103530149689od_a_b @ Q @ ( produc3433936959961524160od_a_b @ X4 @ ( produc5291915255311561905od_a_b @ Y @ Q7 ) ) ) @ ( transi1383219260676973311od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ord_le5510395190108133673od_a_b @ ( lS_lis6227585698039082446od_a_b @ M1 @ ( initia8636230792963847769od_a_b @ M1 ) ) @ ( lS_lis3357525008826253498od_a_b @ M22 @ ( initia3208193535625315909od_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1241_language__equivalence__from__isomorphism__helper__reachable,axiom,
    ! [F2: fset_l1334069825099621524od_a_b > list_f1445794025290330138od_a_b,M1: fsm_fs4038567970311364852od_a_b,M22: fsm_li3816064051032718074od_a_b] :
      ( ( bij_be1705665232800849660od_a_b @ F2 @ ( reacha3719139522904929108od_a_b @ M1 ) @ ( reacha7494367349399693530od_a_b @ M22 ) )
     => ( ( ( F2 @ ( initia5383324526419690047od_a_b @ M1 ) )
          = ( initia3208193535625315909od_a_b @ M22 ) )
       => ( ! [Q: fset_l1334069825099621524od_a_b,X4: $o,Y: fset_l1334069825099621524od_a_b,Q7: fset_l1334069825099621524od_a_b] :
              ( ( member361094292949318077od_a_b @ Q @ ( reacha3719139522904929108od_a_b @ M1 ) )
             => ( ( member361094292949318077od_a_b @ Q7 @ ( reacha3719139522904929108od_a_b @ M1 ) )
               => ( ( member7151811798220465266od_a_b @ ( produc6645316577686334777od_a_b @ Q @ ( produc4815424570203850918od_a_b @ X4 @ ( produc8099561100433402519od_a_b @ Y @ Q7 ) ) ) @ ( transi413513904105055205od_a_b @ M1 ) )
                  = ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ ( F2 @ Q ) @ ( produc1286801380576301484od_a_b @ X4 @ ( produc6212510018049267869od_a_b @ Y @ ( F2 @ Q7 ) ) ) ) @ ( transi2698755513253879019od_a_b @ M22 ) ) ) ) )
         => ( ord_le5510395190108133673od_a_b @ ( lS_fse3523897189346949940od_a_b @ M1 @ ( initia5383324526419690047od_a_b @ M1 ) ) @ ( lS_lis3357525008826253498od_a_b @ M22 @ ( initia3208193535625315909od_a_b @ M22 ) ) ) ) ) ) ).

% language_equivalence_from_isomorphism_helper_reachable
thf(fact_1242_rename__states__simps_I1_J,axiom,
    ! [M4: fsm_d_a_b,F2: d > d] :
      ( ( initial_d_a_b @ ( rename6211310769420509491_a_b_d @ M4 @ F2 ) )
      = ( F2 @ ( initial_d_a_b @ M4 ) ) ) ).

% rename_states_simps(1)
thf(fact_1243_rename__states__simps_I1_J,axiom,
    ! [M4: fsm_c_a_b,F2: c > d] :
      ( ( initial_d_a_b @ ( rename4723348732125710964_a_b_d @ M4 @ F2 ) )
      = ( F2 @ ( initial_c_a_b @ M4 ) ) ) ).

% rename_states_simps(1)
thf(fact_1244_rename__states__simps_I1_J,axiom,
    ! [M4: fsm_d_a_b,F2: d > c] :
      ( ( initial_c_a_b @ ( rename6211310769420509490_a_b_c @ M4 @ F2 ) )
      = ( F2 @ ( initial_d_a_b @ M4 ) ) ) ).

% rename_states_simps(1)
thf(fact_1245_rename__states__simps_I1_J,axiom,
    ! [M4: fsm_c_a_b,F2: c > c] :
      ( ( initial_c_a_b @ ( rename4723348732125710963_a_b_c @ M4 @ F2 ) )
      = ( F2 @ ( initial_c_a_b @ M4 ) ) ) ).

% rename_states_simps(1)
thf(fact_1246_reachable__states__intro,axiom,
    ! [M4: fsm_d_a_b,P2: list_P8454989104189725694od_b_d] :
      ( ( path_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ P2 )
     => ( member_d2 @ ( target_d_a_b @ ( initial_d_a_b @ M4 ) @ P2 ) @ ( reacha2749672884579446598_d_a_b @ M4 ) ) ) ).

% reachable_states_intro
thf(fact_1247_reachable__states__intro,axiom,
    ! [M4: fsm_c_a_b,P2: list_P5017272815184427326od_b_c] :
      ( ( path_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ P2 )
     => ( member_c2 @ ( target_c_a_b @ ( initial_c_a_b @ M4 ) @ P2 ) @ ( reacha6376826306246091717_c_a_b @ M4 ) ) ) ).

% reachable_states_intro
thf(fact_1248_after__reachable,axiom,
    ! [M4: fsm_d_a_b,Io: list_P1467974523212632366od_a_b,Q3: d] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ Q3 ) )
       => ( ( member_d2 @ Q3 @ ( reacha2749672884579446598_d_a_b @ M4 ) )
         => ( member_d2 @ ( after_d_a_b @ M4 @ Q3 @ Io ) @ ( reacha2749672884579446598_d_a_b @ M4 ) ) ) ) ) ).

% after_reachable
thf(fact_1249_after__reachable,axiom,
    ! [M4: fsm_c_a_b,Io: list_P1467974523212632366od_a_b,Q3: c] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ Q3 ) )
       => ( ( member_c2 @ Q3 @ ( reacha6376826306246091717_c_a_b @ M4 ) )
         => ( member_c2 @ ( after_c_a_b @ M4 @ Q3 @ Io ) @ ( reacha6376826306246091717_c_a_b @ M4 ) ) ) ) ) ).

% after_reachable
thf(fact_1250_after__reachable,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Io: list_P1467974523212632366od_a_b,Q3: fset_l1334069825099621524od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ Q3 ) )
       => ( ( member361094292949318077od_a_b @ Q3 @ ( reacha2755017045781758809_b_a_b @ M4 ) )
         => ( member361094292949318077od_a_b @ ( after_5198964185542980012_b_a_b @ M4 @ Q3 @ Io ) @ ( reacha2755017045781758809_b_a_b @ M4 ) ) ) ) ) ).

% after_reachable
thf(fact_1251_after__reachable,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Io: list_P1467974523212632366od_a_b,Q3: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ Q3 ) )
       => ( ( member6895035109809442519od_a_b @ Q3 @ ( reacha5660761788860886259_b_a_b @ M4 ) )
         => ( member6895035109809442519od_a_b @ ( after_1595828222394802374_b_a_b @ M4 @ Q3 @ Io ) @ ( reacha5660761788860886259_b_a_b @ M4 ) ) ) ) ) ).

% after_reachable
thf(fact_1252_reachable__states__initial,axiom,
    ! [M4: fsm_d_a_b] : ( member_d2 @ ( initial_d_a_b @ M4 ) @ ( reacha2749672884579446598_d_a_b @ M4 ) ) ).

% reachable_states_initial
thf(fact_1253_reachable__states__initial,axiom,
    ! [M4: fsm_c_a_b] : ( member_c2 @ ( initial_c_a_b @ M4 ) @ ( reacha6376826306246091717_c_a_b @ M4 ) ) ).

% reachable_states_initial
thf(fact_1254_after__reachable__initial,axiom,
    ! [M4: fsm_fs1840479945969036537_b_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ529373768824785053_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_fse7452106412789865273_b_a_b @ M4 @ ( initia2961132633701536452_b_a_b @ M4 ) ) )
       => ( member361094292949318077od_a_b @ ( after_5198964185542980012_b_a_b @ M4 @ ( initia2961132633701536452_b_a_b @ M4 ) @ Io ) @ ( reacha2755017045781758809_b_a_b @ M4 ) ) ) ) ).

% after_reachable_initial
thf(fact_1255_after__reachable__initial,axiom,
    ! [M4: fsm_li1655959576902402579_b_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observ3837622365268550711_b_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_lis474700916027962579_b_a_b @ M4 @ ( initia1111342868025077214_b_a_b @ M4 ) ) )
       => ( member6895035109809442519od_a_b @ ( after_1595828222394802374_b_a_b @ M4 @ ( initia1111342868025077214_b_a_b @ M4 ) @ Io ) @ ( reacha5660761788860886259_b_a_b @ M4 ) ) ) ) ).

% after_reachable_initial
thf(fact_1256_after__reachable__initial,axiom,
    ! [M4: fsm_d_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_d_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) ) )
       => ( member_d2 @ ( after_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) @ Io ) @ ( reacha2749672884579446598_d_a_b @ M4 ) ) ) ) ).

% after_reachable_initial
thf(fact_1257_after__reachable__initial,axiom,
    ! [M4: fsm_c_a_b,Io: list_P1467974523212632366od_a_b] :
      ( ( observable_c_a_b @ M4 )
     => ( ( member6895035109809442519od_a_b @ Io @ ( lS_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) ) )
       => ( member_c2 @ ( after_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) @ Io ) @ ( reacha6376826306246091717_c_a_b @ M4 ) ) ) ) ).

% after_reachable_initial
thf(fact_1258_states__initial__deadlock,axiom,
    ! [M4: fsm_d_a_b] :
      ( ( deadlock_state_d_a_b @ M4 @ ( initial_d_a_b @ M4 ) )
     => ( ( reacha2749672884579446598_d_a_b @ M4 )
        = ( insert_d2 @ ( initial_d_a_b @ M4 ) @ bot_bot_set_d ) ) ) ).

% states_initial_deadlock
thf(fact_1259_states__initial__deadlock,axiom,
    ! [M4: fsm_c_a_b] :
      ( ( deadlock_state_c_a_b @ M4 @ ( initial_c_a_b @ M4 ) )
     => ( ( reacha6376826306246091717_c_a_b @ M4 )
        = ( insert_c2 @ ( initial_c_a_b @ M4 ) @ bot_bot_set_c ) ) ) ).

% states_initial_deadlock
thf(fact_1260_acyclic__no__self__loop,axiom,
    ! [M4: fsm_li3816064051032718074od_a_b,Q3: list_f1445794025290330138od_a_b] :
      ( ( acycli2500287621552212143od_a_b @ M4 )
     => ( ( member7551773913232940227od_a_b @ Q3 @ ( reacha7494367349399693530od_a_b @ M4 ) )
       => ~ ? [X6: $o,Y5: fset_l1334069825099621524od_a_b] : ( member9099908583776647538od_a_b @ ( produc5205648118086869305od_a_b @ Q3 @ ( produc1286801380576301484od_a_b @ X6 @ ( produc6212510018049267869od_a_b @ Y5 @ Q3 ) ) ) @ ( transi2698755513253879019od_a_b @ M4 ) ) ) ) ).

% acyclic_no_self_loop

% Helper facts (25)
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( if_nat @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( if_nat @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_I_Eo_J_T,axiom,
    ! [X3: list_o,Y3: list_o] :
      ( ( if_list_o @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_I_Eo_J_T,axiom,
    ! [X3: list_o,Y3: list_o] :
      ( ( if_list_o @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_Itf__a_J_T,axiom,
    ! [X3: list_a,Y3: list_a] :
      ( ( if_list_a @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_Itf__a_J_T,axiom,
    ! [X3: list_a,Y3: list_a] :
      ( ( if_list_a @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_Itf__c_J_T,axiom,
    ! [X3: list_c,Y3: list_c] :
      ( ( if_list_c @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_Itf__c_J_T,axiom,
    ! [X3: list_c,Y3: list_c] :
      ( ( if_list_c @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_Itf__d_J_T,axiom,
    ! [X3: list_d,Y3: list_d] :
      ( ( if_list_d @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_Itf__d_J_T,axiom,
    ! [X3: list_d,Y3: list_d] :
      ( ( if_list_d @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
    ! [X3: list_nat,Y3: list_nat] :
      ( ( if_list_nat @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
    ! [X3: list_nat,Y3: list_nat] :
      ( ( if_list_nat @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_T,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( if_lis1002476807507936500od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_T,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( ( if_lis1002476807507936500od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_T,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( if_fse2516390947016424794od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_T,axiom,
    ! [X3: fset_l1334069825099621524od_a_b,Y3: fset_l1334069825099621524od_a_b] :
      ( ( if_fse2516390947016424794od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_T,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Y3: list_l8778361445553822004od_a_b] :
      ( ( if_lis737310530615849466od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_T,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Y3: list_l8778361445553822004od_a_b] :
      ( ( if_lis737310530615849466od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_T,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( if_lis3379674621698944480od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_T,axiom,
    ! [X3: list_f1445794025290330138od_a_b,Y3: list_f1445794025290330138od_a_b] :
      ( ( if_lis3379674621698944480od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_T,axiom,
    ! [X3: list_l6443893005374362810od_a_b,Y3: list_l6443893005374362810od_a_b] :
      ( ( if_lis8377773601782977152od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_T,axiom,
    ! [X3: list_l6443893005374362810od_a_b,Y3: list_l6443893005374362810od_a_b] :
      ( ( if_lis8377773601782977152od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

thf(help_If_3_1_If_001t__List__Olist_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_T,axiom,
    ! [X3: list_s7922523924679432314od_a_b,Y3: list_s7922523924679432314od_a_b] :
      ( ( if_lis6932009802700144192od_a_b @ $false @ X3 @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Set__Oset_It__FSet__Ofset_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_T,axiom,
    ! [X3: list_s7922523924679432314od_a_b,Y3: list_s7922523924679432314od_a_b] :
      ( ( if_lis6932009802700144192od_a_b @ $true @ X3 @ Y3 )
      = X3 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( simple891077427139469213od_a_b @ ( cons_f6577355434438001738od_a_b @ x3 @ xs2 ) @ ( produc7489420772309856409od_a_b @ ba @ dona ) )
    = ( simple891077427139469213od_a_b @ xs @ ( produc7489420772309856409od_a_b @ $true @ ( cons_f6577355434438001738od_a_b @ x @ dona ) ) ) ) ).

%------------------------------------------------------------------------------