%------------------------------------------------------------------------------
% 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    : Combinable_Wands/0003_CombinableWands/prob_00426_018035__7940600_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2026 ( 555 unt; 742 typ;   0 def)
%            Number of atoms       : 4581 (1597 equ;   0 cnn)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives : 16013 ( 402   ~;  45   |; 677   &;12948   @)
%                                         (   0 <=>;1941  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   8 avg)
%            Number of types       :  117 ( 116 usr)
%            Number of type conns  : 3779 (3779   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  629 ( 626 usr;  14 con; 0-11 aty)
%            Number of variables   : 5367 ( 810   ^;4139   !; 418   ?;5367   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 09:09:10.403
%------------------------------------------------------------------------------
% Could-be-implicit typings (116)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J_J_J,type,
    set_Pr1565700067222966883on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J_J,type,
    produc217507841372899885on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    produc5221327116631553236on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J_J_J,type,
    set_Pr3289333603297600445_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J_J,type,
    produc3057782296003698823_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    set_Pr4305388979797279737on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    produc475038747504217147_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    produc1317171644805857433on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J_J,type,
    set_Pr5308428015838290133_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    produc6455357576889117855_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    set_Pr6185426892591968326on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    produc2521863659554272614on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    set_Pr7975217055296730899_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc2023215532613486146_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc1362221940583236787_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    produc5803078220529002682t_char: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    set_Pr7400413712916508976_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    set_Pr5767439603957941884_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr6040071838687925911_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    set_Pr7332355692443745687on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc2932130718683550586_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc3798933545658027718_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__PartialHeapSA__Ostate_J,type,
    produc3589956252253634615_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    produc177623448699234103on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J_J,type,
    set_Pr2946632083460398663_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    set_Pr4698884584343881589on_val: $tType ).

thf(ty_n_t__PackageLogic__Oaassertion_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    aasser1163550960519286933on_val: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    option8887860577033306220on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    produc4946314520779599207_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc1757238238866670357on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    set_Pr4846723933414538759_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    set_Pr7649655576376376530on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J_J,type,
    set_Pr2871993341207995108r_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc2030649568307348519_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc9003781588162623004on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    produc7776263825685906734r_prat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J_J,type,
    set_Pr1685704261205283783r_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    produc8146610533011921512t_char: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr3348781085009130724_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    set_Pr523392378426063460_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    produc3336119888008106215r_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__PartialHeapSA__Ostate_J,type,
    produc4326932734349944580_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc4357056439811976324_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J_J,type,
    set_Pr401513967981718343_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    produc2489117125269924006t_char: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    produc3646891683153674343_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    set_Pr3996677194857090567t_char: $tType ).

thf(ty_n_t__PackageLogic__Oaassertion_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    aasser7019605857572776418_state: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    option2747342629145793465_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr5323702258453113287_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    produc6071853487833700903t_char: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr4366116562226448461_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    set_Pr4231240917283394591_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
    produc4324712645871441639_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J,type,
    produc1357540302793366807_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc7272280185086996969_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr5527899070135025255_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc948624807956558599_state: $tType ).

thf(ty_n_t__PackageLogic__Oaassertion_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    aasser3179708585289803787_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Mask__Oval_Mt__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J_J,type,
    set_Pr4723104092121316667al_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr1688445902015331925_state: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    set_Pr1004501353197068112on_val: $tType ).

thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    option886743748074664436_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr2391701600042252046_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr2063381651806504974_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr5618112136499017889_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mask__Oval_Mt__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J,type,
    produc2072440392815185925al_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    produc3142500478612311029_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    produc4163891087902651319t_char: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    set_Pr3433046674199179443r_prat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    set_Pr4480099295215233283t_char: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc3882902684156697774_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    produc5876769945872133550_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    produc597591266584407361_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PackageLogic__Oaassertion_It__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    produc2756261550280135502_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J_J,type,
    set_Pr6566877984550221441e_prat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    set_Pr6847263425858009217_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Mask__Oval_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc5122021904355189735on_val: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc6859378861088059299t_char: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J,type,
    set_Pr6546617632949187467al_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr1785066336555260981_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    set_Pr2507339680178222706t_char: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J_J,type,
    set_Pr8803067691650843250ar_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PackageLogic__Oaassertion_It__Mask__Oval_J_Mt__Mask__Oval_J,type,
    produc1707155752992360906al_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
    set_Pr6039890582625207499_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J_J,type,
    set_Pr8996442262779224523e_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J,type,
    produc2654212508281724193e_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    produc6251377953716854561_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J,type,
    produc5503543764249810261al_val: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PosRat__Oprat_J_J,type,
    set_Pr3298805672376727137t_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc8023240190789890773_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc1457211279475724562t_char: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J,type,
    produc7606469099237612818ar_nat: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    set_state_state: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    produc4844402304972151915_state: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J,type,
    produc7334356684927367531e_prat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PosRat__Oprat_J,type,
    produc2235545006120619777t_prat: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    set_option_state: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    set_set_state: $tType ).

thf(ty_n_t__PackageLogic__Oaassertion_It__PartialHeapSA__Ostate_J,type,
    aassertion_state: $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__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
    set_list_char: $tType ).

thf(ty_n_t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    option_state: $tType ).

thf(ty_n_t__PackageLogic__Oaassertion_It__Mask__Oval_J,type,
    aassertion_val: $tType ).

thf(ty_n_t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    set_state: $tType ).

thf(ty_n_t__Option__Ooption_It__Mask__Oval_J,type,
    option_val: $tType ).

thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
    list_char: $tType ).

thf(ty_n_t__Set__Oset_It__PosRat__Oprat_J,type,
    set_prat: $tType ).

thf(ty_n_t__Set__Oset_It__Mask__Oval_J,type,
    set_val: $tType ).

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

thf(ty_n_t__PartialHeapSA__Ostate,type,
    state: $tType ).

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

thf(ty_n_t__PosRat__Oprat,type,
    prat: $tType ).

thf(ty_n_t__Mask__Oval,type,
    val: $tType ).

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

% Explicit typings (626)
thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bNF_Ca2815325664443363616_state: set_Pr1688445902015331925_state > ( option_state > set_state ) > $o ).

thf(sy_c_BNF__Def_OGr_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    bNF_Gr7520394057480975179on_val: set_Pr3433046674199179443r_prat > ( ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > option_val ) > set_Pr7649655576376376530on_val ).

thf(sy_c_BNF__Def_OGr_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    bNF_Gr_state_state: set_state > ( state > state ) > set_Pr1785066336555260981_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    bNF_Gr71701291235176519t_char: set_state > ( state > nat ) > ( state > list_char ) > set_Pr2507339680178222706t_char ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr8144397171961131434_state: set_state > ( state > option_state ) > ( state > option_state ) > set_Pr1688445902015331925_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    bNF_Gr7364880804673765603_state: set_state > ( state > state ) > ( state > state > state ) > set_Pr2391701600042252046_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    bNF_Gr947463461346416350_state: set_state > ( state > state ) > ( state > produc3882902684156697774_state ) > set_Pr4231240917283394591_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    bNF_Gr1645861816300964896_state: set_state > ( state > prat ) > ( state > state ) > set_Pr6039890582625207499_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr8363538844033681878_state: set_state > ( state > prat ) > ( state > set_state ) > set_Pr6847263425858009217_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    bNF_Gr5554302884217825927t_char: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > nat ) > ( produc3882902684156697774_state > list_char ) > set_Pr2507339680178222706t_char ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr4913868530397957098_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > option_state ) > ( produc3882902684156697774_state > option_state ) > set_Pr1688445902015331925_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    bNF_Gr5413576055295359779_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > state ) > ( produc3882902684156697774_state > state > state ) > set_Pr2391701600042252046_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    bNF_Gr5432878666621363808_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > prat ) > ( produc3882902684156697774_state > state ) > set_Pr6039890582625207499_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr6818451474134737942_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > prat ) > ( produc3882902684156697774_state > set_state ) > set_Pr6847263425858009217_state ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    bNF_Gr2250442185837678927_state: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > prat ) > ( produc7272280185086996969_state > state ) > set_Pr6039890582625207499_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr63754628658600314_state: set_Pr1688445902015331925_state > ( option_state > option_state ) > set_Pr1688445902015331925_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    bNF_Gr6805951496242791002_state: set_Pr1785066336555260981_state > ( state > state ) > set_Pr1785066336555260981_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr621135371174781015_state: set_option_state > set_Pr1688445902015331925_state > ( option_state > option_state ) > set_Pr1688445902015331925_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr8759033791985395207_state: set_state > set_Pr1688445902015331925_state > ( state > option_state ) > set_Pr1785066336555260981_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    bNF_Gr4114592414835599415_state: set_state > set_Pr1785066336555260981_state > ( state > state ) > set_Pr1785066336555260981_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr4364826243083562601_state: set_Pr7649655576376376530on_val > set_Pr1688445902015331925_state > ( produc9003781588162623004on_val > option_state ) > set_Pr4305388979797279737on_val ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr919661598790814775_state: set_Pr2391701600042252046_state > set_Pr1688445902015331925_state > ( produc3882902684156697774_state > option_state ) > set_Pr4846723933414538759_state ).

thf(sy_c_BNF__Greatest__Fixpoint_OrelInvImage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    bNF_Gr5630821380644201398_state: set_Pr4231240917283394591_state > set_Pr1688445902015331925_state > ( produc7272280185086996969_state > option_state ) > set_Pr7975217055296730899_state ).

thf(sy_c_CombinableWands_OR,type,
    r: state > state > state ).

thf(sy_c_CombinableWands_Obinary,type,
    binary: set_state > $o ).

thf(sy_c_CombinableWands_Obinary__mask,type,
    binary_mask: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ).

thf(sy_c_CombinableWands_Ocombinable,type,
    combinable: set_state > $o ).

thf(sy_c_CombinableWands_Ocomp__min__mask,type,
    comp_min_mask: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ).

thf(sy_c_CombinableWands_Ocwand,type,
    cwand: set_state > set_state > set_state ).

thf(sy_c_CombinableWands_Ointuitionistic,type,
    intuitionistic: set_state > $o ).

thf(sy_c_CombinableWands_Omultiply,type,
    multiply: prat > state > state ).

thf(sy_c_CombinableWands_Omultiply__rel,type,
    multiply_rel: produc4844402304972151915_state > produc4844402304972151915_state > $o ).

thf(sy_c_CombinableWands_Omultiply__sem__assertion,type,
    multip8064567061438756306ertion: prat > set_state > set_state ).

thf(sy_c_CombinableWands_Omultiply__sem__assertion__rel,type,
    multip8073008153270241703on_rel: produc6251377953716854561_state > produc6251377953716854561_state > $o ).

thf(sy_c_CombinableWands_Oscalable,type,
    scalable: state > state > $o ).

thf(sy_c_CombinableWands_Oscaled,type,
    scaled: state > set_state ).

thf(sy_c_CombinableWands_Owand,type,
    wand: set_state > set_state > set_state ).

thf(sy_c_Fun_Oid_001t__Mask__Oval,type,
    id_val: val > val ).

thf(sy_c_Fun_Oid_001t__PartialHeapSA__Ostate,type,
    id_state: state > state ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    id_Pro1402184692240358763on_val: produc9003781588162623004on_val > produc9003781588162623004on_val ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    id_Pro6264179822262827651t_char: produc1457211279475724562t_char > produc1457211279475724562t_char ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    id_Pro8715877757508063718_state: produc3142500478612311029_state > produc3142500478612311029_state ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    id_Pro689249233197853983_state: produc3882902684156697774_state > produc3882902684156697774_state ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    id_Pro2933125508726022968_state: produc7272280185086996969_state > produc7272280185086996969_state ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    id_Pro5916511905602125660_state: produc4844402304972151915_state > produc4844402304972151915_state ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    id_Pro8860473219607035410_state: produc6251377953716854561_state > produc6251377953716854561_state ).

thf(sy_c_Fun__Def_OTHE__default_001t__PartialHeapSA__Ostate,type,
    fun_TH8221542053827138557_state: state > ( state > $o ) > state ).

thf(sy_c_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    if_option_state: $o > option_state > option_state > option_state ).

thf(sy_c_If_001t__PartialHeapSA__Ostate,type,
    if_state: $o > state > state > state ).

thf(sy_c_If_001t__PosRat__Oprat,type,
    if_prat: $o > prat > prat > prat ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_Eo_J_J,type,
    sup_su4175861339346331443_val_o: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J,type,
    sup_su1536542383718553321char_o: ( nat > list_char > $o ) > ( nat > list_char > $o ) > nat > list_char > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    sup_su2989194110892726342tate_o: ( option_state > option_state > $o ) > ( option_state > option_state > $o ) > option_state > option_state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PartialHeapSA__Ostate_M_062_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    sup_su1108609720783396685tate_o: ( state > ( state > state ) > $o ) > ( state > ( state > state ) > $o ) > state > ( state > state ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PartialHeapSA__Ostate_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_Eo_J_J,type,
    sup_su1162340662190093652tate_o: ( state > produc3882902684156697774_state > $o ) > ( state > produc3882902684156697774_state > $o ) > state > produc3882902684156697774_state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
    sup_sup_state_o: ( state > $o ) > ( state > $o ) > state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PosRat__Oprat_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
    sup_sup_prat_state_o: ( prat > state > $o ) > ( prat > state > $o ) > prat > state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PosRat__Oprat_M_062_It__Set__Oset_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    sup_su7614437069348798106tate_o: ( prat > set_state > $o ) > ( prat > set_state > $o ) > prat > set_state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_Eo_J,type,
    sup_su3200866414790943751_val_o: ( produc9003781588162623004on_val > $o ) > ( produc9003781588162623004on_val > $o ) > produc9003781588162623004on_val > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
    sup_su1130956725435522171tate_o: ( produc3882902684156697774_state > $o ) > ( produc3882902684156697774_state > $o ) > produc3882902684156697774_state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_Eo_J,type,
    sup_su4345871077856951546tate_o: ( produc7272280185086996969_state > $o ) > ( produc7272280185086996969_state > $o ) > produc7272280185086996969_state > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    sup_sup_set_state: set_state > set_state > set_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    sup_su7506060154676209150on_val: set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Mask__Oval_Mt__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J_J,type,
    sup_su4800132526891881063al_val: set_Pr4723104092121316667al_val > set_Pr4723104092121316667al_val > set_Pr4723104092121316667al_val ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    sup_su7899656352754981958t_char: set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    sup_su5006661989123481129_state: set_Pr1688445902015331925_state > set_Pr1688445902015331925_state > set_Pr1688445902015331925_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    sup_su1984960714304006370_state: set_Pr2391701600042252046_state > set_Pr2391701600042252046_state > set_Pr2391701600042252046_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    sup_su3837536599209510219_state: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
    sup_su1826719071296284831_state: set_Pr6039890582625207499_state > set_Pr6039890582625207499_state > set_Pr6039890582625207499_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    sup_su5611131606495579221_state: set_Pr6847263425858009217_state > set_Pr6847263425858009217_state > set_Pr6847263425858009217_state ).

thf(sy_c_Map_Omap__add_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    map_ad2908576761495157028ar_val: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Mask_Oadd__acc_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    add_ac6043276672051819257t_char: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat > produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Oadd__masks_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    add_ma6586698345353345811t_char: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Oadd__masks__rel_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    add_ma2412268806269088278t_char: produc5803078220529002682t_char > produc5803078220529002682t_char > $o ).

thf(sy_c_Mask_Oempty__mask_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    empty_6616431780912394577r_prat: ( produc1457211279475724562t_char > prat ) > prat ).

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    empty_6102255041883331742on_val: produc9003781588162623004on_val > prat ).

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    empty_3446695950879338768t_char: produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    empty_3913122416104905065_state: produc4844402304972151915_state > prat ).

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    empty_5541330147480151071_state: produc6251377953716854561_state > prat ).

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    empty_4129289814623480215on_val: produc1317171644805857433on_val > prat ).

thf(sy_c_Mask_Oempty__mask__rel_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    empty_3412554051312619034r_prat: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    empty_5847456986941130773on_val: produc9003781588162623004on_val > produc9003781588162623004on_val > $o ).

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    empty_8141283858255108185t_char: produc1457211279475724562t_char > produc1457211279475724562t_char > $o ).

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    empty_5283331674940636722_state: produc4844402304972151915_state > produc4844402304972151915_state > $o ).

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    empty_7304051301540881640_state: produc6251377953716854561_state > produc6251377953716854561_state > $o ).

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    empty_1698368654852286560on_val: produc1317171644805857433on_val > produc1317171644805857433on_val > $o ).

thf(sy_c_Mask_Ofull__mask,type,
    full_mask: produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Ogreater__mask_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    greate7680731506090375811t_char: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Mask_Omultiply__mask,type,
    multiply_mask: prat > ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Onull_001t__Nat__Onat,type,
    null_nat: nat ).

thf(sy_c_Mask_Opre__get__m_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    pre_ge8481574585653477131on_val: produc9003781588162623004on_val > produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Opre__get__m_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    pre_ge2740421702909910421t_char: produc1457211279475724562t_char > nat ).

thf(sy_c_Mask_Opre__get__m_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    pre_get_m_prat_state: produc4844402304972151915_state > prat ).

thf(sy_c_Mask_Opre__get__m_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    pre_ge1435879308799382564_state: produc6251377953716854561_state > prat ).

thf(sy_c_Mask_Opre__get__m_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    pre_ge6899797224320663452on_val: produc1317171644805857433on_val > produc9003781588162623004on_val ).

thf(sy_c_Mask_Opre__get__m__rel_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    pre_ge4462515927930180886on_val: produc9003781588162623004on_val > produc9003781588162623004on_val > $o ).

thf(sy_c_Mask_Opre__get__m__rel_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    pre_ge8748858970926381898t_char: produc1457211279475724562t_char > produc1457211279475724562t_char > $o ).

thf(sy_c_Mask_Opre__get__m__rel_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    pre_ge6835382860682234787_state: produc4844402304972151915_state > produc4844402304972151915_state > $o ).

thf(sy_c_Mask_Opre__get__m__rel_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    pre_ge4013444835548200281_state: produc6251377953716854561_state > produc6251377953716854561_state > $o ).

thf(sy_c_Mask_Opre__get__m__rel_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    pre_ge1694281482089598673on_val: produc1317171644805857433on_val > produc1317171644805857433on_val > $o ).

thf(sy_c_Mask_Ouni__mask_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    uni_ma6578582744724537101t_char: produc1457211279475724562t_char > prat > produc1457211279475724562t_char > prat ).

thf(sy_c_Mask_Oupper__bounded,type,
    upper_bounded: ( produc1457211279475724562t_char > prat ) > prat > $o ).

thf(sy_c_Mask_Ovalid__mask,type,
    valid_mask: ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Mask_Ovalid__mask__rel,type,
    valid_mask_rel: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Mask_Ovalid__null,type,
    valid_null: ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Option_Ooption_ONone_001t__Mask__Oval,type,
    none_val: option_val ).

thf(sy_c_Option_Ooption_ONone_001t__PartialHeapSA__Ostate,type,
    none_state: option_state ).

thf(sy_c_Option_Ooption_OSome_001t__Mask__Oval,type,
    some_val: val > option_val ).

thf(sy_c_Option_Ooption_OSome_001t__PartialHeapSA__Ostate,type,
    some_state: state > option_state ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    some_P2581650809551911671on_val: produc9003781588162623004on_val > option8887860577033306220on_val ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    some_P5383513176685068947_state: produc3882902684156697774_state > option886743748074664436_state ).

thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    some_P6297086604321900740_state: produc7272280185086996969_state > option2747342629145793465_state ).

thf(sy_c_Option_Ooption_Othe_001t__Mask__Oval,type,
    the_val: option_val > val ).

thf(sy_c_Option_Ooption_Othe_001t__PartialHeapSA__Ostate,type,
    the_state: option_state > state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bot_bot_set_state: set_state ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_Eo_J_J,type,
    ord_le3852884270828607079_val_o: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_Eo_J_J,type,
    ord_le6723339807950303054prat_o: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ) > ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_Eo_J,type,
    ord_le2830794348966088778prat_o: ( ( produc1457211279475724562t_char > prat ) > $o ) > ( ( produc1457211279475724562t_char > prat ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J,type,
    ord_le2712619360209801397char_o: ( nat > list_char > $o ) > ( nat > list_char > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    ord_le2052508915978315794tate_o: ( option_state > option_state > $o ) > ( option_state > option_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_062_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    ord_le1106678366802930969tate_o: ( state > ( state > state ) > $o ) > ( state > ( state > state ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_Eo_J_J,type,
    ord_le6704609105599929480tate_o: ( state > produc3882902684156697774_state > $o ) > ( state > produc3882902684156697774_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
    ord_less_eq_state_o: ( state > $o ) > ( state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PosRat__Oprat_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
    ord_le9040380983013460636tate_o: ( prat > state > $o ) > ( prat > state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PosRat__Oprat_M_062_It__Set__Oset_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    ord_le8830457724327557734tate_o: ( prat > set_state > $o ) > ( prat > set_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_Eo_J_J,type,
    ord_le616650860478780142_val_o: ( produc9003781588162623004on_val > produc9003781588162623004on_val > $o ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_Eo_J,type,
    ord_le6140313152057869779_val_o: ( produc9003781588162623004on_val > $o ) > ( produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
    ord_le8077393285996101039tate_o: ( produc3882902684156697774_state > $o ) > ( produc3882902684156697774_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_Eo_J,type,
    ord_le7281427340513060550tate_o: ( produc7272280185086996969_state > $o ) > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_M_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
    ord_le2599682012455951694tate_o: ( produc4844402304972151915_state > produc4844402304972151915_state > $o ) > ( produc4844402304972151915_state > produc4844402304972151915_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_M_Eo_J,type,
    ord_le5681876185599785522tate_o: ( produc4844402304972151915_state > $o ) > ( produc4844402304972151915_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_M_Eo_J_J,type,
    ord_le249087669307848398tate_o: ( produc6251377953716854561_state > produc6251377953716854561_state > $o ) > ( produc6251377953716854561_state > produc6251377953716854561_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
    ord_le8699832056682887676tate_o: ( produc6251377953716854561_state > $o ) > ( produc6251377953716854561_state > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_M_062_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_M_Eo_J_J,type,
    ord_le2319172193063290574_val_o: ( produc1317171644805857433on_val > produc1317171644805857433on_val > $o ) > ( produc1317171644805857433on_val > produc1317171644805857433on_val > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_M_Eo_J,type,
    ord_le8528861841627966596_val_o: ( produc1317171644805857433on_val > $o ) > ( produc1317171644805857433on_val > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    ord_le2494988322063910608_state: set_state > set_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le6155467803786297262_state: set_Pr2063381651806504974_state > set_Pr2063381651806504974_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J_J,type,
    ord_le2122960673345045316r_prat: set_Pr2871993341207995108r_prat > set_Pr2871993341207995108r_prat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    ord_le6900622908513426738on_val: set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J_J,type,
    ord_le3387867619833322002ar_nat: set_Pr8803067691650843250ar_nat > set_Pr8803067691650843250ar_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    ord_le6315511645215477266t_char: set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    ord_le6423325748750870005_state: set_Pr1688445902015331925_state > set_Pr1688445902015331925_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    ord_le6483787752022044334_state: set_Pr2391701600042252046_state > set_Pr2391701600042252046_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le2777189432094499797_state: set_Pr1785066336555260981_state > set_Pr1785066336555260981_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J_J,type,
    ord_le3218748728643905899e_prat: set_Pr8996442262779224523e_prat > set_Pr8996442262779224523e_prat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    ord_le2093392236560368951on_val: set_Pr7332355692443745687on_val > set_Pr7332355692443745687on_val > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    ord_le4032880777312351359_state: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    ord_le6305643028697367044_state: set_Pr523392378426063460_state > set_Pr523392378426063460_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le262197048489888875_state: set_Pr6039890582625207499_state > set_Pr6039890582625207499_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    ord_le5761494056910127137_state: set_Pr6847263425858009217_state > set_Pr6847263425858009217_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le801108382804549175_state: set_Pr6040071838687925911_state > set_Pr6040071838687925911_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le4167756422255405229_state: set_Pr4366116562226448461_state > set_Pr4366116562226448461_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__PartialHeapSA__Ostate_J_J,type,
    ord_le9131031735280434308_state: set_Pr3348781085009130724_state > set_Pr3348781085009130724_state > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J_J,type,
    ord_le5481108615602339361e_prat: set_Pr6566877984550221441e_prat > set_Pr6566877984550221441e_prat > $o ).

thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    order_2642746146112740183_state: ( set_state > $o ) > set_state ).

thf(sy_c_PackageLogic_Oaassertion_OAImp_001t__Mask__Oval,type,
    aImp_val: ( val > $o ) > aassertion_val > aassertion_val ).

thf(sy_c_PackageLogic_Oaassertion_OAImp_001t__PartialHeapSA__Ostate,type,
    aImp_state: ( state > $o ) > aassertion_state > aassertion_state ).

thf(sy_c_PackageLogic_Oaassertion_OASem_001t__Mask__Oval,type,
    aSem_val: ( val > $o ) > aassertion_val ).

thf(sy_c_PackageLogic_Oaassertion_OASem_001t__PartialHeapSA__Ostate,type,
    aSem_state: ( state > $o ) > aassertion_state ).

thf(sy_c_PackageLogic_Oaassertion_OAStar_001t__Mask__Oval,type,
    aStar_val: aassertion_val > aassertion_val > aassertion_val ).

thf(sy_c_PackageLogic_Oaassertion_OAStar_001t__PartialHeapSA__Ostate,type,
    aStar_state: aassertion_state > aassertion_state > aassertion_state ).

thf(sy_c_PackageLogic_Opackage__logic_001t__Mask__Oval,type,
    package_logic_val: ( val > val > option_val ) > ( val > val ) > val > ( val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_001t__PartialHeapSA__Ostate,type,
    package_logic_state: ( state > state > option_state ) > ( state > state ) > state > ( state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag4549880205214723289on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > produc9003781588162623004on_val > ( produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag9124413901382861105_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > produc3882902684156697774_state ) > produc3882902684156697774_state > ( produc3882902684156697774_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag2204431621656667814_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > produc7272280185086996969_state ) > produc7272280185086996969_state > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Obool__conj_001t__Mask__Oval,type,
    packag6750194596558674946nj_val: ( val > $o ) > ( val > $o ) > val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Obool__conj_001t__PartialHeapSA__Ostate,type,
    packag1330488657391168505_state: ( state > $o ) > ( state > $o ) > state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Mask__Oval,type,
    packag2085742556458808647ic_val: ( val > val > option_val ) > ( val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__PartialHeapSA__Ostate,type,
    packag8361946002163212404_state: ( state > state > option_state ) > ( state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag1465513459401564630on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag1930333982449825652_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag1160585701684337059_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__Mask__Oval,type,
    packag4897621287243763553al_val: ( val > val > option_val ) > val > ( val > val > val ) > aassertion_val > aassertion_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__PartialHeapSA__Ostate,type,
    packag6192661653625646554_state: ( state > state > option_state ) > state > ( state > state > state ) > aassertion_state > aassertion_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag8228529196479615804on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > ( produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val ) > aasser1163550960519286933on_val > aasser1163550960519286933on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag4438072966337169294_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > produc3882902684156697774_state > ( produc3882902684156697774_state > produc3882902684156697774_state > produc3882902684156697774_state ) > aasser3179708585289803787_state > aasser3179708585289803787_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag7261830501500456713_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > produc7272280185086996969_state > ( produc7272280185086996969_state > produc7272280185086996969_state > produc7272280185086996969_state ) > aasser7019605857572776418_state > aasser7019605857572776418_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__standard_001t__Mask__Oval,type,
    packag685230357167683994rd_val: ( val > val > option_val ) > val > aassertion_val > aassertion_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__standard_001t__PartialHeapSA__Ostate,type,
    packag7096211993527611489_state: ( state > state > option_state ) > state > aassertion_state > aassertion_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__standard_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag6258220590826782659on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > aasser1163550960519286933on_val > aasser1163550960519286933on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__standard_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag3130788337556013255_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > produc3882902684156697774_state > aasser3179708585289803787_state > aasser3179708585289803787_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__standard_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag8077625386405451152_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > produc7272280185086996969_state > aasser7019605857572776418_state > aasser7019605857572776418_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__pruner_001t__PartialHeapSA__Ostate,type,
    packag2456304381420842418_state: ( state > state > option_state ) > ( state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__pure__cond_001t__Mask__Oval,type,
    packag6714868506247462167nd_val: ( val > val > option_val ) > ( val > val ) > ( val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__pure__cond_001t__PartialHeapSA__Ostate,type,
    packag6595153354952283300_state: ( state > state > option_state ) > ( state > state ) > ( state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__transformer_001t__Mask__Oval,type,
    packag4175576287423129206er_val: ( val > val > option_val ) > val > ( val > val ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__transformer_001t__PartialHeapSA__Ostate,type,
    packag4817583915586052229_state: ( state > state > option_state ) > state > ( state > state ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__transformer_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag5955012701910386663on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__transformer_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag5827594511758291363_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > produc3882902684156697774_state > ( produc3882902684156697774_state > produc3882902684156697774_state ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Omono__transformer_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag3884151059541177780_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > produc7272280185086996969_state > ( produc7272280185086996969_state > produc7272280185086996969_state ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs_001t__Mask__Oval,type,
    packag2280635229005757181hs_val: ( val > val > option_val ) > ( val > val ) > ( val > $o ) > val > val > set_Pr4723104092121316667al_val > ( val > $o ) > aassertion_val > val > val > set_Pr4723104092121316667al_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs_001t__PartialHeapSA__Ostate,type,
    packag3171892606229212990_state: ( state > state > option_state ) > ( state > state ) > ( state > $o ) > state > state > set_Pr4231240917283394591_state > ( state > $o ) > aassertion_state > state > state > set_Pr4231240917283394591_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag6843733491101478048on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > ( produc9003781588162623004on_val > $o ) > produc9003781588162623004on_val > produc9003781588162623004on_val > set_Pr1565700067222966883on_val > ( produc9003781588162623004on_val > $o ) > aasser1163550960519286933on_val > produc9003781588162623004on_val > produc9003781588162623004on_val > set_Pr1565700067222966883on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag4061699384143886122_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > produc3882902684156697774_state ) > ( produc3882902684156697774_state > $o ) > produc3882902684156697774_state > produc3882902684156697774_state > set_Pr5308428015838290133_state > ( produc3882902684156697774_state > $o ) > aasser3179708585289803787_state > produc3882902684156697774_state > produc3882902684156697774_state > set_Pr5308428015838290133_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag3630742828623380589_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > produc7272280185086996969_state ) > ( produc7272280185086996969_state > $o ) > produc7272280185086996969_state > produc7272280185086996969_state > set_Pr3289333603297600445_state > ( produc7272280185086996969_state > $o ) > aasser7019605857572776418_state > produc7272280185086996969_state > produc7272280185086996969_state > set_Pr3289333603297600445_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs__connection_001t__Mask__Oval,type,
    packag1944724486178758143on_val: ( val > val > option_val ) > ( val > val ) > ( val > $o ) > val > val > set_Pr4723104092121316667al_val > ( val > $o ) > aassertion_val > val > val > set_Pr4723104092121316667al_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__rhs__connection_001t__PartialHeapSA__Ostate,type,
    packag2054414653763826108_state: ( state > state > option_state ) > ( state > state ) > ( state > $o ) > state > state > set_Pr4231240917283394591_state > ( state > $o ) > aassertion_state > state > state > set_Pr4231240917283394591_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__sat_001t__Mask__Oval,type,
    packag5057539306968662900at_val: ( val > val > option_val ) > ( val > val ) > ( val > $o ) > aassertion_val > val > val > val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opackage__sat_001t__PartialHeapSA__Ostate,type,
    packag8070727096299822599_state: ( state > state > option_state ) > ( state > state ) > ( state > $o ) > aassertion_state > state > state > state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__Mask__Oval_001t__Mask__Oval_001_062_It__Mask__Oval_Mt__Mask__Oval_J,type,
    packag3202507263771882441al_val: ( val > val > option_val ) > set_Pr4723104092121316667al_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    packag4152378406607043437_state: ( state > state > option_state ) > set_Pr4231240917283394591_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag9013619817833129428_state: ( state > state > option_state ) > set_Pr523392378426063460_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    packag161099568566171125on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr1565700067222966883on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag1386629450763126729_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > set_Pr5308428015838290133_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Opure__remains_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    packag3875795242785447337_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > set_Pr3289333603297600445_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat_001t__Mask__Oval,type,
    package_sat_val: ( val > val > option_val ) > aassertion_val > val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat_001t__PartialHeapSA__Ostate,type,
    package_sat_state: ( state > state > option_state ) > aassertion_state > state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag3677137384183703351on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > aasser1163550960519286933on_val > produc9003781588162623004on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag2518615827549365843_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > aasser3179708585289803787_state > produc3882902684156697774_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag4865960244449834244_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > aasser7019605857572776418_state > produc7272280185086996969_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat__rel_001t__Mask__Oval,type,
    package_sat_rel_val: produc1707155752992360906al_val > produc1707155752992360906al_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Osat__rel_001t__PartialHeapSA__Ostate,type,
    packag1918864394588125018_state: produc2756261550280135502_state > produc2756261550280135502_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ovalid__package__set_001t__Mask__Oval,type,
    packag7517340229427718612et_val: ( val > val > option_val ) > ( val > val ) > val > set_Pr4723104092121316667al_val > val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ovalid__package__set_001t__PartialHeapSA__Ostate,type,
    packag3877571396724326311_state: ( state > state > option_state ) > ( state > state ) > state > set_Pr4231240917283394591_state > state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion_001t__Mask__Oval,type,
    packag5732365195153136185on_val: ( val > val > option_val ) > ( val > val ) > aassertion_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion_001t__PartialHeapSA__Ostate,type,
    packag7298478212905792770_state: ( state > state > option_state ) > ( state > state ) > aassertion_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    packag5541956234368469604on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > aasser1163550960519286933on_val > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    packag8517968027831007846_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > produc3882902684156697774_state ) > aasser3179708585289803787_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    packag6254535061403973169_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > produc7272280185086996969_state ) > aasser7019605857572776418_state > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Owf__assertion__rel_001t__PartialHeapSA__Ostate,type,
    packag4834522500328176237_state: aassertion_state > aassertion_state > $o ).

thf(sy_c_PartialHeapSA_Oadd__set,type,
    add_set: set_state > set_state > set_state ).

thf(sy_c_PartialHeapSA_Oadd__states,type,
    add_states: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val ).

thf(sy_c_PartialHeapSA_Oadd__states__rel,type,
    add_states_rel: produc1317171644805857433on_val > produc1317171644805857433on_val > $o ).

thf(sy_c_PartialHeapSA_Ocompatible,type,
    compatible: produc9003781588162623004on_val > produc9003781588162623004on_val > $o ).

thf(sy_c_PartialHeapSA_Ocompatible__heaps,type,
    compatible_heaps: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_PartialHeapSA_Ocompatible__options_001t__Mask__Oval,type,
    compat7209469420100717861ns_val: option_val > option_val > $o ).

thf(sy_c_PartialHeapSA_Ocompatible__options_001t__PartialHeapSA__Ostate,type,
    compat2278460363914054422_state: option_state > option_state > $o ).

thf(sy_c_PartialHeapSA_Ocompatible__options__rel_001t__Mask__Oval,type,
    compat8294034345482142370el_val: produc5122021904355189735on_val > produc5122021904355189735on_val > $o ).

thf(sy_c_PartialHeapSA_Ocompatible__options__rel_001t__PartialHeapSA__Ostate,type,
    compat1844074344818064729_state: produc3142500478612311029_state > produc3142500478612311029_state > $o ).

thf(sy_c_PartialHeapSA_Ocore,type,
    core: state > state ).

thf(sy_c_PartialHeapSA_Odefined,type,
    defined: state > state > $o ).

thf(sy_c_PartialHeapSA_Oempty__heap_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    empty_7512026568161686585ar_val: produc1457211279475724562t_char > option_val ).

thf(sy_c_PartialHeapSA_Oget__h,type,
    get_h: state > produc1457211279475724562t_char > option_val ).

thf(sy_c_PartialHeapSA_Oget__h__rel,type,
    get_h_rel: state > state > $o ).

thf(sy_c_PartialHeapSA_Oget__m,type,
    get_m: state > produc1457211279475724562t_char > prat ).

thf(sy_c_PartialHeapSA_Oget__m__rel,type,
    get_m_rel: state > state > $o ).

thf(sy_c_PartialHeapSA_Ogreater,type,
    greater: state > state > $o ).

thf(sy_c_PartialHeapSA_Ogreater__set,type,
    greater_set: set_state > set_state > $o ).

thf(sy_c_PartialHeapSA_Olarger__heap_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    larger1532547405891354081ar_val: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_PartialHeapSA_Ominus,type,
    minus: state > state > state ).

thf(sy_c_PartialHeapSA_Oplus,type,
    plus: state > state > option_state ).

thf(sy_c_PartialHeapSA_Ostable,type,
    stable: state > $o ).

thf(sy_c_PartialHeapSA_Ostate_OAbs__state,type,
    abs_state: produc9003781588162623004on_val > state ).

thf(sy_c_PartialHeapSA_Ostate_ORep__state,type,
    rep_state: state > produc9003781588162623004on_val ).

thf(sy_c_PartialHeapSA_Ounit,type,
    unit: state ).

thf(sy_c_PartialHeapSA_Ovalid__heap,type,
    valid_heap: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_PartialHeapSA_Ovalid__state,type,
    valid_state: produc9003781588162623004on_val > $o ).

thf(sy_c_PartialHeapSA_Ovalid__state__rel,type,
    valid_state_rel: produc9003781588162623004on_val > produc9003781588162623004on_val > $o ).

thf(sy_c_PosRat_Ocomp__one,type,
    comp_one: prat > prat ).

thf(sy_c_PosRat_Ohalf,type,
    half: prat ).

thf(sy_c_PosRat_Opadd,type,
    padd: prat > prat > prat ).

thf(sy_c_PosRat_Opdiv,type,
    pdiv: prat > prat > prat ).

thf(sy_c_PosRat_Opgt,type,
    pgt: prat > prat > $o ).

thf(sy_c_PosRat_Opgte,type,
    pgte: prat > prat > $o ).

thf(sy_c_PosRat_Opinv,type,
    pinv: prat > prat ).

thf(sy_c_PosRat_Opmax,type,
    pmax: prat > prat > prat ).

thf(sy_c_PosRat_Opmin,type,
    pmin: prat > prat > prat ).

thf(sy_c_PosRat_Opmult,type,
    pmult: prat > prat > prat ).

thf(sy_c_PosRat_Opnone,type,
    pnone: prat ).

thf(sy_c_PosRat_Oppos,type,
    ppos: prat > $o ).

thf(sy_c_PosRat_Opwrite,type,
    pwrite: prat ).

thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    produc7013538429079112736t_char: ( nat > list_char > list_char ) > produc4163891087902651319t_char > produc8146610533011921512t_char ).

thf(sy_c_Product__Type_OPair_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc5362444129537099455_state: ( state > state ) > ( state > state ) > produc948624807956558599_state ).

thf(sy_c_Product__Type_OPair_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc4737362649269059174_state: ( state > state ) > state > produc5876769945872133550_state ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc8008623296994167373on_val: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1757238238866670357on_val ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc1897429902272487136r_prat: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > produc7776263825685906734r_prat ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc74620467203698198on_val: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > produc9003781588162623004on_val ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc1164665353665699927r_prat: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > produc3336119888008106215r_prat ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    produc2957999048406202538t_char: ( produc1457211279475724562t_char > prat ) > produc2489117125269924006t_char > produc5803078220529002682t_char ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc2591414526589101846t_char: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > produc2489117125269924006t_char ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
    produc1606739095562851931t_char: list_char > list_char > produc6859378861088059299t_char ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc8702345860417625034ar_nat: list_char > nat > produc7606469099237612818ar_nat ).

thf(sy_c_Product__Type_OPair_001t__Mask__Oval_001_062_It__Mask__Oval_Mt__Mask__Oval_J,type,
    produc303288909735261391al_val: val > ( val > val ) > produc5503543764249810261al_val ).

thf(sy_c_Product__Type_OPair_001t__Mask__Oval_001t__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J,type,
    produc7187740677493149823al_val: val > produc5503543764249810261al_val > produc2072440392815185925al_val ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    produc120197956887798346t_char: nat > list_char > produc1457211279475724562t_char ).

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__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc8776329868854908137t_char: nat > produc1457211279475724562t_char > produc4163891087902651319t_char ).

thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    produc904852209897547607on_val: option_val > option_val > produc5122021904355189735on_val ).

thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    produc9160152616361873709_state: option_state > option_state > produc3142500478612311029_state ).

thf(sy_c_Product__Type_OPair_001t__PackageLogic__Oaassertion_It__Mask__Oval_J_001t__Mask__Oval,type,
    produc1969469836606013754al_val: aassertion_val > val > produc1707155752992360906al_val ).

thf(sy_c_Product__Type_OPair_001t__PackageLogic__Oaassertion_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc6654088501289988998_state: aassertion_state > state > produc2756261550280135502_state ).

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc8632743443909064678_state: state > ( state > state ) > produc3882902684156697774_state ).

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    produc544653723139640077_state: state > state > produc8023240190789890773_state ).

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat,type,
    produc5862297150877942435e_prat: state > prat > produc7334356684927367531e_prat ).

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc5886875603596089627_state: state > produc3882902684156697774_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc5194695453622026300_state: state > produc7272280185086996969_state > produc4357056439811976324_state ).

thf(sy_c_Product__Type_OPair_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    produc6205719116230455971_state: prat > state > produc4844402304972151915_state ).

thf(sy_c_Product__Type_OPair_001t__PosRat__Oprat_001t__PosRat__Oprat,type,
    produc7183142570155660857t_prat: prat > prat > produc2235545006120619777t_prat ).

thf(sy_c_Product__Type_OPair_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc9080284787853255769_state: prat > set_state > produc6251377953716854561_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    produc6949276712527400972on_val: produc9003781588162623004on_val > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > produc5221327116631553236on_val ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc4958730763592889809on_val: produc9003781588162623004on_val > produc9003781588162623004on_val > produc1317171644805857433on_val ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J,type,
    produc6985948203474072671on_val: produc9003781588162623004on_val > produc5221327116631553236on_val > produc217507841372899885on_val ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc8192741843292627479t_char: produc1457211279475724562t_char > produc1457211279475724562t_char > produc6071853487833700903t_char ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    produc2397313312270560215_state: produc3142500478612311029_state > produc3142500478612311029_state > produc4946314520779599207_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc3987245858496418492_state: produc3882902684156697774_state > ( produc3882902684156697774_state > produc3882902684156697774_state ) > produc2023215532613486146_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc7334084071316671761_state: produc3882902684156697774_state > state > produc1357540302793366807_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc2343482328048119831_state: produc3882902684156697774_state > produc3882902684156697774_state > produc2030649568307348519_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc5427679348311974809_state: produc3882902684156697774_state > produc2023215532613486146_state > produc6455357576889117855_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc7648782313880683123_state: produc7272280185086996969_state > ( produc7272280185086996969_state > produc7272280185086996969_state ) > produc475038747504217147_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate,type,
    produc7271836056140555068_state: produc7272280185086996969_state > state > produc4326932734349944580_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc2330690084503141483_state: produc7272280185086996969_state > produc7272280185086996969_state > produc1362221940583236787_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    produc1904032489304825401_state: produc7272280185086996969_state > produc475038747504217147_state > produc3057782296003698823_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    produc8801277691740291671_state: produc4844402304972151915_state > produc4844402304972151915_state > produc4324712645871441639_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    produc516693425924439767_state: produc6251377953716854561_state > produc6251377953716854561_state > produc3646891683153674343_state ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat,type,
    produc5311113300630973017e_prat: set_state > prat > produc2654212508281724193e_prat ).

thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc1834047914073684089_state: set_state > set_state > produc597591266584407361_state ).

thf(sy_c_Product__Type_OSigma_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc3189049046222722799r_prat: set_Pr1004501353197068112on_val > ( ( produc1457211279475724562t_char > option_val ) > set_Pr3433046674199179443r_prat ) > set_Pr2871993341207995108r_prat ).

thf(sy_c_Product__Type_OSigma_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc1366239611153933861on_val: set_Pr3433046674199179443r_prat > ( ( produc1457211279475724562t_char > prat ) > set_Pr1004501353197068112on_val ) > set_Pr7649655576376376530on_val ).

thf(sy_c_Product__Type_OSigma_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc5389449503320859771ar_nat: set_list_char > ( list_char > set_nat ) > set_Pr8803067691650843250ar_nat ).

thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    produc6030673636645808891t_char: set_nat > ( nat > set_list_char ) > set_Pr2507339680178222706t_char ).

thf(sy_c_Product__Type_OSigma_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    produc7708045757989049950_state: set_option_state > ( option_state > set_option_state ) > set_Pr1688445902015331925_state ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc6646226935541082007_state: set_state > ( state > set_state_state ) > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    produc4572292869282958142_state: set_state > ( state > set_state ) > set_Pr1785066336555260981_state ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat,type,
    produc1315363979526694100e_prat: set_state > ( state > set_prat ) > set_Pr8996442262779224523e_prat ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc4123186969287248032on_val: set_state > ( state > set_Pr7649655576376376530on_val ) > set_Pr7332355692443745687on_val ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc2831624448089660202_state: set_state > ( state > set_Pr2391701600042252046_state ) > set_Pr4231240917283394591_state ).

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc8552965988182875245_state: set_state > ( state > set_Pr4231240917283394591_state ) > set_Pr523392378426063460_state ).

thf(sy_c_Product__Type_OSigma_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    produc1658785944879207636_state: set_prat > ( prat > set_state ) > set_Pr6039890582625207499_state ).

thf(sy_c_Product__Type_OSigma_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc4653271056321233546_state: set_prat > ( prat > set_set_state ) > set_Pr6847263425858009217_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__PartialHeapSA__Ostate,type,
    produc556505947853469856_state: set_Pr7649655576376376530on_val > ( produc9003781588162623004on_val > set_state ) > set_Pr6040071838687925911_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc4278832915810242336_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > set_state ) > set_Pr4366116562226448461_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc5372175771586804680_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > set_Pr2391701600042252046_state ) > set_Pr4846723933414538759_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc4180506523417663567_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > set_Pr4231240917283394591_state ) > set_Pr5767439603957941884_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate,type,
    produc1406734553846628205_state: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > set_state ) > set_Pr3348781085009130724_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc2280571527155128015on_val: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > set_Pr7649655576376376530on_val ) > set_Pr6185426892591968326on_val ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc7282391691264310459_state: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > set_Pr2391701600042252046_state ) > set_Pr7400413712916508976_state ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc8058815403421562012_state: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > set_Pr4231240917283394591_state ) > set_Pr7975217055296730899_state ).

thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat,type,
    produc884099569098950794e_prat: set_set_state > ( set_state > set_prat ) > set_Pr6566877984550221441e_prat ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001_Eo,type,
    produc1225464857956169863tate_o: ( state > ( state > state ) > $o ) > produc3882902684156697774_state > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_Eo,type,
    produc3899216655821101094tate_o: ( state > produc3882902684156697774_state > $o ) > produc7272280185086996969_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc7947965470134731869tate_o: ( ( state > state ) > state > $o ) > produc5876769945872133550_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc3696886681956174835_state: ( ( state > state ) > state > produc3882902684156697774_state ) > produc5876769945872133550_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_Eo,type,
    produc5226666187743293259prat_o: ( ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > $o ) > produc7776263825685906734r_prat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc4110721796449090601on_val: ( ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > produc9003781588162623004on_val ) > produc7776263825685906734r_prat > produc9003781588162623004on_val ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc985966260317727453on_val: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val ) > produc9003781588162623004on_val > produc1457211279475724562t_char > option_val ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc5787256515117077072r_prat: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > prat ) > produc9003781588162623004on_val > produc1457211279475724562t_char > prat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_Eo,type,
    produc5248837549992124053_val_o: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > produc9003781588162623004on_val > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    produc2964738055033037937r_prat: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > produc7776263825685906734r_prat ) > produc9003781588162623004on_val > produc7776263825685906734r_prat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc4192255817509754207on_val: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > produc9003781588162623004on_val ) > produc9003781588162623004on_val > produc9003781588162623004on_val ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat_001_Eo,type,
    produc2492928673396900345_nat_o: ( list_char > nat > $o ) > produc7606469099237612818ar_nat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc6166083679720228083t_char: ( list_char > nat > produc1457211279475724562t_char ) > produc7606469099237612818ar_nat > produc1457211279475724562t_char ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mask__Oval_001_062_It__Mask__Oval_Mt__Mask__Oval_J_001_Eo,type,
    produc7666680587469814684_val_o: ( val > ( val > val ) > $o ) > produc5503543764249810261al_val > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Mask__Oval_001t__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_001_Eo,type,
    produc6995717860488419308_val_o: ( val > produc5503543764249810261al_val > $o ) > produc2072440392815185925al_val > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001_Eo,type,
    produc8526122873445342073char_o: ( nat > list_char > $o ) > produc1457211279475724562t_char > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc9163108120003956271ar_nat: ( nat > list_char > nat ) > produc1457211279475724562t_char > nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001t__PartialHeapSA__Ostate,type,
    produc217683206301814297_state: ( nat > list_char > state ) > produc1457211279475724562t_char > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    produc4071494739252518515t_char: ( nat > list_char > produc1457211279475724562t_char ) > produc1457211279475724562t_char > produc1457211279475724562t_char ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc7881066356751411151_state: ( nat > list_char > set_state ) > produc1457211279475724562t_char > set_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc3312000583120074607_state: ( nat > list_char > set_Pr2391701600042252046_state ) > produc1457211279475724562t_char > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
    produc5315882979514849802tate_o: ( option_state > option_state > produc3142500478612311029_state > $o ) > produc3142500478612311029_state > produc3142500478612311029_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001_Eo,type,
    produc6082990154846732246tate_o: ( option_state > option_state > $o ) > produc3142500478612311029_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc7211634496914305532_state: ( option_state > option_state > state ) > produc3142500478612311029_state > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    produc803252138055838771_state: ( option_state > option_state > produc3142500478612311029_state ) > produc3142500478612311029_state > produc3142500478612311029_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc3424155258940669874_state: ( option_state > option_state > set_state ) > produc3142500478612311029_state > set_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc2209043727768083020_state: ( option_state > option_state > set_Pr2391701600042252046_state ) > produc3142500478612311029_state > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
    produc8588859638187112394tate_o: ( state > ( state > state ) > produc3882902684156697774_state > $o ) > produc3882902684156697774_state > produc3882902684156697774_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001_Eo,type,
    produc3645877548210629341tate_o: ( state > ( state > state ) > $o ) > produc3882902684156697774_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc8575939086779714485_state: ( state > ( state > state ) > state ) > produc3882902684156697774_state > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    produc7521540169313256307_state: ( state > ( state > state ) > produc5876769945872133550_state ) > produc3882902684156697774_state > produc5876769945872133550_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc5376313899190161910tate_o: ( state > state > $o ) > produc8023240190789890773_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc4988896184150421299_state: ( state > state > produc8023240190789890773_state ) > produc8023240190789890773_state > produc8023240190789890773_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat_001_Eo,type,
    produc5248533930912372960prat_o: ( state > prat > $o ) > produc7334356684927367531e_prat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    produc772268595108696499_state: ( state > prat > produc4844402304972151915_state ) > produc7334356684927367531e_prat > produc4844402304972151915_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_Eo,type,
    produc3402325802329673236_val_o: ( state > produc9003781588162623004on_val > $o ) > produc177623448699234103on_val > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_Eo_J,type,
    produc6466221716036377566tate_o: ( state > produc3882902684156697774_state > produc7272280185086996969_state > $o ) > produc7272280185086996969_state > produc7272280185086996969_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_Eo,type,
    produc1745419677418529872tate_o: ( state > produc3882902684156697774_state > $o ) > produc7272280185086996969_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc8258182183023037954_state: ( state > produc3882902684156697774_state > state ) > produc7272280185086996969_state > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J,type,
    produc6605482068524530271_state: ( state > produc3882902684156697774_state > produc1357540302793366807_state ) > produc7272280185086996969_state > produc1357540302793366807_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001_Eo,type,
    produc8801812494870056711tate_o: ( state > produc7272280185086996969_state > $o ) > produc4357056439811976324_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc1228703470279370976tate_o: ( prat > state > $o ) > produc4844402304972151915_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    produc5191658985856023922_state: ( prat > state > state ) > produc4844402304972151915_state > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc6727336724318121462_state: ( prat > state > produc3882902684156697774_state ) > produc4844402304972151915_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    produc1922103714420728243_state: ( prat > state > produc4844402304972151915_state ) > produc4844402304972151915_state > produc4844402304972151915_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc2825319096956678952_state: ( prat > state > set_state ) > produc4844402304972151915_state > set_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc4369308447073708118_state: ( prat > state > set_Pr2391701600042252046_state ) > produc4844402304972151915_state > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc569869127943504087_state: ( prat > state > set_Pr4231240917283394591_state ) > produc4844402304972151915_state > set_Pr4231240917283394591_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001_Eo,type,
    produc7925652287191295402tate_o: ( prat > set_state > $o ) > produc6251377953716854561_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc2626907587099862312_state: ( prat > set_state > state ) > produc6251377953716854561_state > state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc8936804542704588736_state: ( prat > set_state > produc3882902684156697774_state ) > produc6251377953716854561_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    produc897481912382009139_state: ( prat > set_state > produc6251377953716854561_state ) > produc6251377953716854561_state > produc6251377953716854561_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc5034060725774254814_state: ( prat > set_state > set_state ) > produc6251377953716854561_state > set_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc9043967962556017184_state: ( prat > set_state > set_Pr2391701600042252046_state ) > produc6251377953716854561_state > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc7793558081207154829_state: ( prat > set_state > set_Pr4231240917283394591_state ) > produc6251377953716854561_state > set_Pr4231240917283394591_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc8998596806100491796tate_o: ( produc9003781588162623004on_val > state > $o ) > produc3589956252253634615_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001_Eo,type,
    produc1935756327278076076tate_o: ( produc3142500478612311029_state > produc3142500478612311029_state > $o ) > produc4946314520779599207_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc2011331576729698010tate_o: ( produc3882902684156697774_state > state > $o ) > produc1357540302793366807_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc5156651381015392551_state: ( produc3882902684156697774_state > state > produc7272280185086996969_state ) > produc1357540302793366807_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_Eo,type,
    produc7167296152490707052tate_o: ( produc3882902684156697774_state > produc3882902684156697774_state > $o ) > produc2030649568307348519_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate_001_Eo,type,
    produc3925133191046228999tate_o: ( produc7272280185086996969_state > state > $o ) > produc4326932734349944580_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_Eo,type,
    produc7822554240239717925_val_o: ( produc7272280185086996969_state > produc9003781588162623004on_val > $o ) > produc2521863659554272614on_val > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001_Eo,type,
    produc3133855996611560728tate_o: ( produc7272280185086996969_state > produc7272280185086996969_state > $o ) > produc1362221940583236787_state > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat_001_Eo,type,
    produc6803115863956348842prat_o: ( set_state > prat > $o ) > produc2654212508281724193e_prat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    produc4505194488364329267_state: ( set_state > prat > produc6251377953716854561_state ) > produc2654212508281724193e_prat > produc6251377953716854561_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc7062428706300765684r_prat: produc7776263825685906734r_prat > produc1457211279475724562t_char > option_val ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc5239619271231976746on_val: produc9003781588162623004on_val > produc1457211279475724562t_char > prat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc5563429021163328950ar_nat: produc7606469099237612818ar_nat > list_char ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    produc6204653154488278070t_char: produc1457211279475724562t_char > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    produc3900939990612242713_state: produc3142500478612311029_state > option_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc7095885521192019410_state: produc3882902684156697774_state > state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    produc6071883272770572025_state: produc8023240190789890773_state > state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat,type,
    produc5687368831847325327e_prat: produc7334356684927367531e_prat > state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc848024588167747631_state: produc7272280185086996969_state > state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc9028042817728042024_state: produc4357056439811976324_state > state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    produc6030790797199838863_state: produc4844402304972151915_state > prat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc7279835715735703621_state: produc6251377953716854561_state > prat ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc3129717363260770749on_val: produc1317171644805857433on_val > produc9003781588162623004on_val ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc2295233055888329765_state: produc1357540302793366807_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc528253918903283203_state: produc2030649568307348519_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc516098375490675028_state: produc3798933545658027718_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate,type,
    produc1881811383391794984_state: produc4326932734349944580_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc3617983543337321920_state: produc2932130718683550586_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat,type,
    produc3510664228513420869e_prat: produc2654212508281724193e_prat > set_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc4142415063207305778r_prat: produc7776263825685906734r_prat > produc1457211279475724562t_char > prat ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc2319605628138516840on_val: produc9003781588162623004on_val > produc1457211279475724562t_char > option_val ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc1259554233722553080ar_nat: produc7606469099237612818ar_nat > nat ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    produc1900778367047502200t_char: produc1457211279475724562t_char > list_char ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    produc9117690093182453595_state: produc3142500478612311029_state > option_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc1734700239402139924_state: produc3882902684156697774_state > state > state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    produc992860721336220475_state: produc8023240190789890773_state > state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat,type,
    produc7795413381861543633e_prat: produc7334356684927367531e_prat > prat ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc6310399636379773037_state: produc7272280185086996969_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc8002322135157487722_state: produc4357056439811976324_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    produc8138835347214057169_state: produc4844402304972151915_state > state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc4944973370551335047_state: produc6251377953716854561_state > set_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc7757608104100355171_state: produc1357540302793366807_state > state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc1543742031010890053_state: produc2030649568307348519_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    produc94328401792989586_state: produc3798933545658027718_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate,type,
    produc856090700821240682_state: produc4326932734349944580_state > state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc3196213569639636478_state: produc2932130718683550586_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat,type,
    produc1175801883329052295e_prat: produc2654212508281724193e_prat > prat ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    produc2543546466205187078_state: produc5876769945872133550_state > produc3882902684156697774_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    produc5819413633627552064r_prat: produc7776263825685906734r_prat > produc9003781588162623004on_val ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc3996604198558763126on_val: produc9003781588162623004on_val > produc7776263825685906734r_prat ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat,type,
    produc4410195085741832554ar_nat: produc7606469099237612818ar_nat > produc1457211279475724562t_char ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    produc5051419219066781674t_char: produc1457211279475724562t_char > produc7606469099237612818ar_nat ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    produc8425362190318354125_state: produc3142500478612311029_state > produc3142500478612311029_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc6438927260845192582_state: produc3882902684156697774_state > produc5876769945872133550_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__PartialHeapSA__Ostate_001t__PosRat__Oprat,type,
    produc6343331096166649923e_prat: produc7334356684927367531e_prat > produc4844402304972151915_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc6564544480275723131_state: produc7272280185086996969_state > produc1357540302793366807_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    produc6686753061519163459_state: produc4844402304972151915_state > produc7334356684927367531e_prat ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    produc1562565776713478649_state: produc6251377953716854561_state > produc2654212508281724193e_prat ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    produc8011752947996305265_state: produc1357540302793366807_state > produc7272280185086996969_state ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__PosRat__Oprat,type,
    produc7016766326345971705e_prat: produc2654212508281724193e_prat > produc6251377953716854561_state ).

thf(sy_c_Product__Type_Oproduct_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc747609993485717659on_val: set_Pr3433046674199179443r_prat > set_Pr1004501353197068112on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Product__Type_Oproduct_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    produc7466003549325918881_state: set_state > set_state_state > set_Pr2391701600042252046_state ).

thf(sy_c_Product__Type_Oproduct_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    produc3518108405486217632_state: set_state > set_Pr2391701600042252046_state > set_Pr4231240917283394591_state ).

thf(sy_c_Relation_Oconversep_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    conver1298275780297188036_state: ( ( state > state ) > state > $o ) > state > ( state > state ) > $o ).

thf(sy_c_Relation_Oconversep_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    conver4900003399366114050r_prat: ( ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > $o ) > ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_Relation_Oconversep_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    conver3077193964297325112on_val: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ) > ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    conver4209408378539545768t_char: ( nat > list_char > $o ) > list_char > nat > $o ).

thf(sy_c_Relation_Oconversep_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    conver5693912221178358411_state: ( option_state > option_state > $o ) > option_state > option_state > $o ).

thf(sy_c_Relation_Oconversep_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    conver5193656574937193540_state: ( state > ( state > state ) > $o ) > ( state > state ) > state > $o ).

thf(sy_c_Relation_Oconversep_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    conver7967167495199203645_state: ( state > produc3882902684156697774_state > $o ) > produc3882902684156697774_state > state > $o ).

thf(sy_c_Relation_Oconversep_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    conversep_prat_state: ( prat > state > $o ) > state > prat > $o ).

thf(sy_c_Relation_Oconversep_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    conver7791356076405787575_state: ( prat > set_state > $o ) > set_state > prat > $o ).

thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    conver191003926065009971_state: ( produc3882902684156697774_state > state > $o ) > state > produc3882902684156697774_state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Odefined_001t__Mask__Oval,type,
    sep_defined_val: ( val > val > option_val ) > val > val > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Odefined_001t__PartialHeapSA__Ostate,type,
    sep_defined_state: ( state > state > option_state ) > state > state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Oequiv_001t__PartialHeapSA__Ostate,type,
    sep_equiv_state: ( state > state > option_state ) > set_state > set_state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Ogreater_001t__Mask__Oval,type,
    sep_greater_val: ( val > val > option_val ) > val > val > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Ogreater_001t__PartialHeapSA__Ostate,type,
    sep_greater_state: ( state > state > option_state ) > state > state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Omax__projection__prop_001t__PartialHeapSA__Ostate,type,
    sep_ma8214210560313151521_state: ( state > state > option_state ) > ( state > $o ) > ( state > state ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Ominus_001t__Mask__Oval,type,
    sep_minus_val: ( val > val > option_val ) > ( val > val ) > val > val > val ).

thf(sy_c_SepAlgebra_Osep__algebra_Ominus_001t__PartialHeapSA__Ostate,type,
    sep_minus_state: ( state > state > option_state ) > ( state > state ) > state > state > state ).

thf(sy_c_SepAlgebra_Osep__algebra_Omono__prop_001t__PartialHeapSA__Ostate,type,
    sep_mono_prop_state: ( state > state > option_state ) > ( state > $o ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Opure_001t__PartialHeapSA__Ostate,type,
    sep_pure_state: ( state > state > option_state ) > state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Osetify_001t__PartialHeapSA__Ostate,type,
    sep_setify_state: ( state > $o ) > set_state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Ounder_001t__PartialHeapSA__Ostate,type,
    sep_under_state: ( state > state > option_state ) > set_state > state > set_state ).

thf(sy_c_SepAlgebra_Osep__algebra_Oup__closed_001t__PartialHeapSA__Ostate,type,
    sep_up_closed_state: ( state > state > option_state ) > set_state > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Oupper__closure_001t__PartialHeapSA__Ostate,type,
    sep_up1246176804924251236_state: ( state > state > option_state ) > set_state > set_state ).

thf(sy_c_Set_OBall_001t__PartialHeapSA__Ostate,type,
    ball_state: set_state > ( state > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    ball_P2871712132005019634on_val: set_Pr7649655576376376530on_val > ( produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    ball_P1066487999220904024_state: set_Pr2391701600042252046_state > ( produc3882902684156697774_state > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    ball_P7403102246598991807_state: set_Pr4231240917283394591_state > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_Set_OCollect_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    collect_state_state: ( ( state > state ) > $o ) > set_state_state ).

thf(sy_c_Set_OCollect_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    collec8455114619259388271on_val: ( ( produc1457211279475724562t_char > option_val ) > $o ) > set_Pr1004501353197068112on_val ).

thf(sy_c_Set_OCollect_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    collec7093475260167521854r_prat: ( ( produc1457211279475724562t_char > prat ) > $o ) > set_Pr3433046674199179443r_prat ).

thf(sy_c_Set_OCollect_001t__PartialHeapSA__Ostate,type,
    collect_state: ( state > $o ) > set_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    collec2388539233454781465_state: ( produc5876769945872133550_state > $o ) > set_Pr2063381651806504974_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    collec6247776740490166275r_prat: ( produc7776263825685906734r_prat > $o ) > set_Pr2871993341207995108r_prat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    collec7475294502966882545on_val: ( produc9003781588162623004on_val > $o ) > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J,type,
    collec8608152508653127293ar_nat: ( produc7606469099237612818ar_nat > $o ) > set_Pr8803067691650843250ar_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Mask__Oval_Mt__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J,type,
    collec8300311316619386842al_val: ( produc2072440392815185925al_val > $o ) > set_Pr4723104092121316667al_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    collec2458894688891239037t_char: ( produc1457211279475724562t_char > $o ) > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    collec8144523193623705312_state: ( produc3142500478612311029_state > $o ) > set_Pr1688445902015331925_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    collec394671971739345689_state: ( produc3882902684156697774_state > $o ) > set_Pr2391701600042252046_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    collec7320380983431419584_state: ( produc8023240190789890773_state > $o ) > set_Pr1785066336555260981_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J,type,
    collec2363146809267008342e_prat: ( produc7334356684927367531e_prat > $o ) > set_Pr8996442262779224523e_prat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    collec4277618271863934242on_val: ( produc177623448699234103on_val > $o ) > set_Pr7332355692443745687on_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    collec906845016635587262_state: ( produc7272280185086996969_state > $o ) > set_Pr4231240917283394591_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    collec8359297238980412527_state: ( produc4357056439811976324_state > $o ) > set_Pr523392378426063460_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    collec9096564466166568534_state: ( produc4844402304972151915_state > $o ) > set_Pr6039890582625207499_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    collec5094083866753559820_state: ( produc6251377953716854561_state > $o ) > set_Pr6847263425858009217_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__PartialHeapSA__Ostate_J,type,
    collec7689951075418334754_state: ( produc3589956252253634615_state > $o ) > set_Pr6040071838687925911_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    collec5166231387257825412on_val: ( produc1317171644805857433on_val > $o ) > set_Pr4305388979797279737on_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J_J_J,type,
    collec3787697688312515330on_val: ( produc217507841372899885on_val > $o ) > set_Pr1565700067222966883on_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    collec6784228404298526930_state: ( produc4946314520779599207_state > $o ) > set_Pr2946632083460398663_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J,type,
    collec4215477171196732908_state: ( produc1357540302793366807_state > $o ) > set_Pr4366116562226448461_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    collec2083760461196787346_state: ( produc2030649568307348519_state > $o ) > set_Pr4846723933414538759_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    collec6806307004801468532_state: ( produc6455357576889117855_state > $o ) > set_Pr5308428015838290133_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__PartialHeapSA__Ostate_J,type,
    collec8329173533518380783_state: ( produc4326932734349944580_state > $o ) > set_Pr3348781085009130724_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    collec7485704936941981521on_val: ( produc2521863659554272614on_val > $o ) > set_Pr6185426892591968326on_val ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    collec4625684881440051358_state: ( produc1362221940583236787_state > $o ) > set_Pr7975217055296730899_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J_J,type,
    collec7677102015826254172_state: ( produc3057782296003698823_state > $o ) > set_Pr3289333603297600445_state ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J,type,
    collec1496918421318429452e_prat: ( produc2654212508281724193e_prat > $o ) > set_Pr6566877984550221441e_prat ).

thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    image_state_state: ( state > state ) > set_state > set_state ).

thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    image_4772210114854293981on_val: ( state > produc9003781588162623004on_val ) > set_state > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_5311902671526399277_state: ( state > produc3882902684156697774_state ) > set_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    image_632992669292831658_state: ( state > produc7272280185086996969_state ) > set_state > set_Pr4231240917283394591_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_5540908381507763077_state: ( produc5876769945872133550_state > produc3882902684156697774_state ) > set_Pr2063381651806504974_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    image_1698057272686278225on_val: ( produc7776263825685906734r_prat > produc9003781588162623004on_val ) > set_Pr2871993341207995108r_prat > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    image_2330660378567450301on_val: ( produc9003781588162623004on_val > produc1457211279475724562t_char > option_val ) > set_Pr7649655576376376530on_val > set_Pr1004501353197068112on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    image_3067683418878703216r_prat: ( produc9003781588162623004on_val > produc1457211279475724562t_char > prat ) > set_Pr7649655576376376530on_val > set_Pr3433046674199179443r_prat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__PartialHeapSA__Ostate,type,
    image_1205529093420515805_state: ( produc9003781588162623004on_val > state ) > set_Pr7649655576376376530on_val > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    image_2943372182239103057r_prat: ( produc9003781588162623004on_val > produc7776263825685906734r_prat ) > set_Pr7649655576376376530on_val > set_Pr2871993341207995108r_prat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    image_4170889944715819327on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_4494208899119068747_state: ( produc9003781588162623004on_val > produc3882902684156697774_state ) > set_Pr7649655576376376530on_val > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    image_3204238854701872908_state: ( produc9003781588162623004on_val > produc7272280185086996969_state ) > set_Pr7649655576376376530on_val > set_Pr4231240917283394591_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    image_688197443715608197t_char: ( produc7606469099237612818ar_nat > produc1457211279475724562t_char ) > set_Pr8803067691650843250ar_nat > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__String__Ochar_J,type,
    image_3034139768025083822t_char: ( produc1457211279475724562t_char > list_char ) > set_Pr2507339680178222706t_char > set_list_char ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Nat__Onat,type,
    image_3548405822317538717ar_nat: ( produc1457211279475724562t_char > nat ) > set_Pr2507339680178222706t_char > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__PartialHeapSA__Ostate,type,
    image_7385172899168281479_state: ( produc1457211279475724562t_char > state ) > set_Pr2507339680178222706t_char > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J,type,
    image_652198164289537669ar_nat: ( produc1457211279475724562t_char > produc7606469099237612818ar_nat ) > set_Pr2507339680178222706t_char > set_Pr8803067691650843250ar_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    image_393491784373993066_state: ( produc3142500478612311029_state > state ) > set_Pr1688445902015331925_state > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    image_3543735668343923269_state: ( produc3142500478612311029_state > produc3142500478612311029_state ) > set_Pr1688445902015331925_state > set_Pr1688445902015331925_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    image_6089932313839440636_state: ( produc3882902684156697774_state > state > state ) > set_Pr2391701600042252046_state > set_state_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_Eo,type,
    image_528283217102427119tate_o: ( produc3882902684156697774_state > $o ) > set_Pr2391701600042252046_state > set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    image_6759111139246981411_state: ( produc3882902684156697774_state > state ) > set_Pr2391701600042252046_state > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    image_2502765500263079301_state: ( produc3882902684156697774_state > produc5876769945872133550_state ) > set_Pr2391701600042252046_state > set_Pr2063381651806504974_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    image_4690842878458256517on_val: ( produc3882902684156697774_state > produc9003781588162623004on_val ) > set_Pr2391701600042252046_state > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_508898238547643525_state: ( produc3882902684156697774_state > produc3882902684156697774_state ) > set_Pr2391701600042252046_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    image_4364510454419742290_state: ( produc3882902684156697774_state > produc7272280185086996969_state ) > set_Pr2391701600042252046_state > set_Pr4231240917283394591_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    image_1391693815708851269_state: ( produc8023240190789890773_state > produc8023240190789890773_state ) > set_Pr1785066336555260981_state > set_Pr1785066336555260981_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    image_8107462086123161541_state: ( produc7334356684927367531e_prat > produc4844402304972151915_state ) > set_Pr8996442262779224523e_prat > set_Pr6039890582625207499_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001_Eo,type,
    image_6262870063963634088tate_o: ( produc7272280185086996969_state > $o ) > set_Pr4231240917283394591_state > set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__PartialHeapSA__Ostate,type,
    image_2710133271811360426_state: ( produc7272280185086996969_state > state ) > set_Pr4231240917283394591_state > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    image_3393013468800240652on_val: ( produc7272280185086996969_state > produc9003781588162623004on_val ) > set_Pr4231240917283394591_state > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_7466395622266389182_state: ( produc7272280185086996969_state > produc3882902684156697774_state ) > set_Pr4231240917283394591_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    image_3064086290059306969_state: ( produc7272280185086996969_state > produc7272280185086996969_state ) > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J,type,
    image_6372718444620452615_state: ( produc7272280185086996969_state > produc1357540302793366807_state ) > set_Pr4231240917283394591_state > set_Pr4366116562226448461_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    image_6883929567913436896_state: ( produc4844402304972151915_state > state ) > set_Pr6039890582625207499_state > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_1979208616201753608_state: ( produc4844402304972151915_state > produc3882902684156697774_state ) > set_Pr6039890582625207499_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J,type,
    image_2830361380300980677e_prat: ( produc4844402304972151915_state > produc7334356684927367531e_prat ) > set_Pr6039890582625207499_state > set_Pr8996442262779224523e_prat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_001t__PartialHeapSA__Ostate,type,
    image_1091725855630477206_state: ( produc6251377953716854561_state > state ) > set_Pr6847263425858009217_state > set_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    image_7417905060788143314_state: ( produc6251377953716854561_state > produc3882902684156697774_state ) > set_Pr6847263425858009217_state > set_Pr2391701600042252046_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J,type,
    image_8313154324233580357e_prat: ( produc6251377953716854561_state > produc2654212508281724193e_prat ) > set_Pr6847263425858009217_state > set_Pr6566877984550221441e_prat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    image_726267498729412871_state: ( produc1357540302793366807_state > produc7272280185086996969_state ) > set_Pr4366116562226448461_state > set_Pr4231240917283394591_state ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    image_8063195947988251461_state: ( produc2654212508281724193e_prat > produc6251377953716854561_state ) > set_Pr6566877984550221441e_prat > set_Pr6847263425858009217_state ).

thf(sy_c_Set_Oinsert_001t__PartialHeapSA__Ostate,type,
    insert_state: state > set_state > set_state ).

thf(sy_c_Typedef_Otype__definition_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    type_d7385716227342696708on_val: ( state > produc9003781588162623004on_val ) > ( produc9003781588162623004on_val > state ) > set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Wellfounded_Oaccp_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    accp_P4765339447491148764r_prat: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ) > ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__PackageLogic__Oaassertion_It__PartialHeapSA__Ostate_J,type,
    accp_a4361485425079813866_state: ( aassertion_state > aassertion_state > $o ) > aassertion_state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__PartialHeapSA__Ostate,type,
    accp_state: ( state > state > $o ) > state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    accp_P4405556307444930259on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > $o ) > produc9003781588162623004on_val > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    accp_P224314924008452035t_char: ( produc5803078220529002682t_char > produc5803078220529002682t_char > $o ) > produc5803078220529002682t_char > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    accp_P8892882183480857371t_char: ( produc1457211279475724562t_char > produc1457211279475724562t_char > $o ) > produc1457211279475724562t_char > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Mask__Oval_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    accp_P4269981079083053040on_val: ( produc5122021904355189735on_val > produc5122021904355189735on_val > $o ) > produc5122021904355189735on_val > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    accp_P7183347322223220350_state: ( produc3142500478612311029_state > produc3142500478612311029_state > $o ) > produc3142500478612311029_state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__PackageLogic__Oaassertion_It__Mask__Oval_J_Mt__Mask__Oval_J,type,
    accp_P7007234769827254483al_val: ( produc1707155752992360906al_val > produc1707155752992360906al_val > $o ) > produc1707155752992360906al_val > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__PackageLogic__Oaassertion_It__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    accp_P1644577663358802135_state: ( produc2756261550280135502_state > produc2756261550280135502_state > $o ) > produc2756261550280135502_state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    accp_P6233459008282737652_state: ( produc4844402304972151915_state > produc4844402304972151915_state > $o ) > produc4844402304972151915_state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    accp_P6554740477754186410_state: ( produc6251377953716854561_state > produc6251377953716854561_state > $o ) > produc6251377953716854561_state > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    accp_P6797916352740768290on_val: ( produc1317171644805857433on_val > produc1317171644805857433on_val > $o ) > produc1317171644805857433on_val > $o ).

thf(sy_c_Wellfounded_Olex__prod_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    lex_pr8780192377291449342on_val: set_Pr1685704261205283783r_prat > set_Pr4698884584343881589on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    lex_pr1681056561245511266t_char: set_Pr1261947904930325089at_nat > set_Pr4480099295215233283t_char > set_Pr3996677194857090567t_char ).

thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    lex_pr8336311929016760645_state: set_Pr1688445902015331925_state > set_Pr1688445902015331925_state > set_Pr2946632083460398663_state ).

thf(sy_c_Wellfounded_Olex__prod_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    lex_pr4041356198452583422_state: set_Pr1785066336555260981_state > set_Pr5527899070135025255_state > set_Pr4846723933414538759_state ).

thf(sy_c_Wellfounded_Olex__prod_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    lex_pr7268379037978345219_state: set_Pr1785066336555260981_state > set_Pr4846723933414538759_state > set_Pr7975217055296730899_state ).

thf(sy_c_Wellfounded_Olex__prod_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    lex_prod_prat_state: set_Pr3298805672376727137t_prat > set_Pr1785066336555260981_state > set_Pr5323702258453113287_state ).

thf(sy_c_Wellfounded_Olex__prod_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    lex_pr1787351029354341489_state: set_Pr3298805672376727137t_prat > set_Pr5618112136499017889_state > set_Pr401513967981718343_state ).

thf(sy_c_Wfrec_Osame__fst_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    same_f8138205353876899841on_val: ( ( produc1457211279475724562t_char > prat ) > $o ) > ( ( produc1457211279475724562t_char > prat ) > set_Pr4698884584343881589on_val ) > set_Pr4305388979797279737on_val ).

thf(sy_c_Wfrec_Osame__fst_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
    same_f652031872680891423t_char: ( nat > $o ) > ( nat > set_Pr4480099295215233283t_char ) > set_Pr3996677194857090567t_char ).

thf(sy_c_Wfrec_Osame__fst_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    same_f2704544105346032002_state: ( option_state > $o ) > ( option_state > set_Pr1688445902015331925_state ) > set_Pr2946632083460398663_state ).

thf(sy_c_Wfrec_Osame__fst_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    same_f3145481655561538747_state: ( state > $o ) > ( state > set_Pr5527899070135025255_state ) > set_Pr4846723933414538759_state ).

thf(sy_c_Wfrec_Osame__fst_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    same_f8765775015391913222_state: ( state > $o ) > ( state > set_Pr4846723933414538759_state ) > set_Pr7975217055296730899_state ).

thf(sy_c_Wfrec_Osame__fst_001t__PosRat__Oprat_001t__PartialHeapSA__Ostate,type,
    same_fst_prat_state: ( prat > $o ) > ( prat > set_Pr1785066336555260981_state ) > set_Pr5323702258453113287_state ).

thf(sy_c_Wfrec_Osame__fst_001t__PosRat__Oprat_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    same_f5333510722715586990_state: ( prat > $o ) > ( prat > set_Pr5618112136499017889_state ) > set_Pr401513967981718343_state ).

thf(sy_c_fChoice_001t__PosRat__Oprat,type,
    fChoice_prat: ( prat > $o ) > prat ).

thf(sy_c_member_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    member_state_state: ( state > state ) > set_state_state > $o ).

thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    member1577473829074448177on_val: ( produc1457211279475724562t_char > option_val ) > set_Pr1004501353197068112on_val > $o ).

thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    member2336342582916103932r_prat: ( produc1457211279475724562t_char > prat ) > set_Pr3433046674199179443r_prat > $o ).

thf(sy_c_member_001_Eo,type,
    member_o: $o > set_o > $o ).

thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
    member_list_char: list_char > set_list_char > $o ).

thf(sy_c_member_001t__Mask__Oval,type,
    member_val: val > set_val > $o ).

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

thf(sy_c_member_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    member_option_state: option_state > set_option_state > $o ).

thf(sy_c_member_001t__PartialHeapSA__Ostate,type,
    member_state: state > set_state > $o ).

thf(sy_c_member_001t__PosRat__Oprat,type,
    member_prat: prat > set_prat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    member6978531283771894448_state: produc948624807956558599_state > set_Pr5527899070135025255_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_Mt__PartialHeapSA__Ostate_J,type,
    member8708878012768793047_state: produc5876769945872133550_state > set_Pr2063381651806504974_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    member5502714215428086462on_val: produc1757238238866670357on_val > set_Pr4698884584343881589on_val > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    member2879030624002546611on_val: produc9003781588162623004on_val > set_Pr7649655576376376530on_val > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    member1381939458143960592r_prat: produc3336119888008106215r_prat > set_Pr1685704261205283783r_prat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
    member6023471406134104908t_char: produc6859378861088059299t_char > set_Pr4480099295215233283t_char > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__Nat__Onat_J,type,
    member6633493567087309371ar_nat: produc7606469099237612818ar_nat > set_Pr8803067691650843250ar_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J,type,
    member331055627401653996al_val: produc5503543764249810261al_val > set_Pr6546617632949187467al_val > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Mask__Oval_Mt__Product____Type__Oprod_It__Mask__Oval_M_062_It__Mask__Oval_Mt__Mask__Oval_J_J_J,type,
    member5640714103519202460al_val: produc2072440392815185925al_val > set_Pr4723104092121316667al_val > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    member484235747325421115t_char: produc1457211279475724562t_char > set_Pr2507339680178222706t_char > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    member3029510603097127326_state: produc3142500478612311029_state > set_Pr1688445902015331925_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    member6715010751053357271_state: produc3882902684156697774_state > set_Pr2391701600042252046_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    member753036827967488894_state: produc8023240190789890773_state > set_Pr1785066336555260981_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__PosRat__Oprat_J,type,
    member8716344949261458452e_prat: produc7334356684927367531e_prat > set_Pr8996442262779224523e_prat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    member7461423308196221312_state: produc7272280185086996969_state > set_Pr4231240917283394591_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    member5752234768399382829_state: produc4357056439811976324_state > set_Pr523392378426063460_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J,type,
    member6226390569306242836_state: produc4844402304972151915_state > set_Pr6039890582625207499_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__PosRat__Oprat_J,type,
    member5208769068039259050t_prat: produc2235545006120619777t_prat > set_Pr3298805672376727137t_prat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    member6708919011922255306_state: produc6251377953716854561_state > set_Pr6847263425858009217_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    member6505152944228695362on_val: produc1317171644805857433on_val > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    member151853725258021968t_char: produc6071853487833700903t_char > set_Pr3996677194857090567t_char > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    member2361837818702807184_state: produc4946314520779599207_state > set_Pr2946632083460398663_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__PartialHeapSA__Ostate_J,type,
    member1546683425902591150_state: produc1357540302793366807_state > set_Pr4366116562226448461_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    member3801449062345016400_state: produc2030649568307348519_state > set_Pr4846723933414538759_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    member4364272472968950365_state: produc3798933545658027718_state > set_Pr5767439603957941884_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__PartialHeapSA__Ostate_J,type,
    member5722111062937351085_state: produc4326932734349944580_state > set_Pr3348781085009130724_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    member3497469645994473233_state: produc2932130718683550586_state > set_Pr7400413712916508976_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
    member14790466581074960_state: produc4324712645871441639_state > set_Pr5323702258453113287_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
    member647386464819295632_state: produc3646891683153674343_state > set_Pr401513967981718343_state > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__PosRat__Oprat_J,type,
    member3111753566487124938e_prat: produc2654212508281724193e_prat > set_Pr6566877984550221441e_prat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__PartialHeapSA__Ostate_J_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    member1976142906092959210_state: produc597591266584407361_state > set_Pr5618112136499017889_state > $o ).

thf(sy_c_member_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    member_set_state: set_state > set_set_state > $o ).

thf(sy_v_A,type,
    a: set_state ).

thf(sy_v_B,type,
    b: set_state ).

thf(sy_v_a____,type,
    a2: prat ).

thf(sy_v_b____,type,
    b2: prat ).

% Relevant facts (1275)
thf(fact_0_asm0,axiom,
    ( ( ppos @ a2 )
    & ( ppos @ b2 )
    & ( pgte @ pwrite @ ( padd @ a2 @ b2 ) ) ) ).

% asm0
thf(fact_1_pgte__antisym,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pgte @ B @ A )
       => ( A = B ) ) ) ).

% pgte_antisym
thf(fact_2_padd__comp__one,axiom,
    ! [X: prat] :
      ( ( pgte @ pwrite @ X )
     => ( ( padd @ X @ ( comp_one @ X ) )
        = pwrite ) ) ).

% padd_comp_one
thf(fact_3_greater__sum__both,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( pgte @ A @ ( padd @ B @ C ) )
     => ? [A1: prat,A2: prat] :
          ( ( A
            = ( padd @ A1 @ A2 ) )
          & ( pgte @ A1 @ B )
          & ( pgte @ A2 @ C ) ) ) ).

% greater_sum_both
thf(fact_4_p__greater__exists,axiom,
    ( pgte
    = ( ^ [A3: prat,B2: prat] :
        ? [R: prat] :
          ( A3
          = ( padd @ B2 @ R ) ) ) ) ).

% p_greater_exists
thf(fact_5_pdiv__smaller,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( ppos @ A )
       => ( pgte @ pwrite @ ( pdiv @ B @ A ) ) ) ) ).

% pdiv_smaller
thf(fact_6_multiply__smaller__pwrite,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ pwrite @ A )
     => ( ( pgte @ pwrite @ B )
       => ( pgte @ pwrite @ ( pmult @ A @ B ) ) ) ) ).

% multiply_smaller_pwrite
thf(fact_7_multiply__twice,axiom,
    ! [A: prat,B: prat,X: state] :
      ( ( ( pgte @ pwrite @ A )
        & ( pgte @ pwrite @ B ) )
     => ( ( multiply @ A @ ( multiply @ B @ X ) )
        = ( multiply @ ( pmult @ A @ B ) @ X ) ) ) ).

% multiply_twice
thf(fact_8_get__h__multiply,axiom,
    ! [P: prat,X: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_h @ ( multiply @ P @ X ) )
        = ( get_h @ X ) ) ) ).

% get_h_multiply
thf(fact_9_padd__one__ineq__sum,axiom,
    ! [A: prat,B: prat,X: prat,Aa: prat,Bb: prat] :
      ( ( ( padd @ A @ B )
        = pwrite )
     => ( ( pgte @ X @ Aa )
       => ( ( pgte @ X @ Bb )
         => ( pgte @ X @ ( padd @ ( pmult @ A @ Aa ) @ ( pmult @ B @ Bb ) ) ) ) ) ) ).

% padd_one_ineq_sum
thf(fact_10_multiply__order,axiom,
    ! [P: prat,A: state,B: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( greater @ A @ B )
       => ( greater @ ( multiply @ P @ A ) @ ( multiply @ P @ B ) ) ) ) ).

% multiply_order
thf(fact_11_pinv__pwrite,axiom,
    ( ( pinv @ pwrite )
    = pwrite ) ).

% pinv_pwrite
thf(fact_12_binary__mask__def,axiom,
    ( binary_mask
    = ( ^ [Pi: produc1457211279475724562t_char > prat,L: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( Pi @ L )
            = pwrite )
          @ pwrite
          @ pnone ) ) ) ).

% binary_mask_def
thf(fact_13_pmult__special_I2_J,axiom,
    ! [X: prat] :
      ( ( pmult @ pnone @ X )
      = pnone ) ).

% pmult_special(2)
thf(fact_14_ppos__add,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ppos @ ( padd @ A @ B ) ) ) ).

% ppos_add
thf(fact_15_ppos__inv,axiom,
    ! [P: prat] :
      ( ( ppos @ P )
     => ( ppos @ ( pinv @ P ) ) ) ).

% ppos_inv
thf(fact_16_padd__asso,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( padd @ ( padd @ A @ B ) @ C )
      = ( padd @ A @ ( padd @ B @ C ) ) ) ).

% padd_asso
thf(fact_17_padd__comm,axiom,
    ( padd
    = ( ^ [A3: prat,B2: prat] : ( padd @ B2 @ A3 ) ) ) ).

% padd_comm
thf(fact_18_padd__zero,axiom,
    ! [A: prat,B: prat] :
      ( ( pnone
        = ( padd @ A @ B ) )
      = ( ( A = pnone )
        & ( B = pnone ) ) ) ).

% padd_zero
thf(fact_19_pmult__comm,axiom,
    ( pmult
    = ( ^ [A3: prat,B2: prat] : ( pmult @ B2 @ A3 ) ) ) ).

% pmult_comm
thf(fact_20_pmult__padd,axiom,
    ! [A: prat,B: prat,X: prat,C: prat,Y: prat] :
      ( ( pmult @ A @ ( padd @ ( pmult @ B @ X ) @ ( pmult @ C @ Y ) ) )
      = ( padd @ ( pmult @ ( pmult @ A @ B ) @ X ) @ ( pmult @ ( pmult @ A @ C ) @ Y ) ) ) ).

% pmult_padd
thf(fact_21_pmult__ppos,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ( ppos @ B )
       => ( ppos @ ( pmult @ A @ B ) ) ) ) ).

% pmult_ppos
thf(fact_22_pmult__distr,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( pmult @ A @ ( padd @ B @ C ) )
      = ( padd @ ( pmult @ A @ B ) @ ( pmult @ A @ C ) ) ) ).

% pmult_distr
thf(fact_23_ppos__eq__pnone,axiom,
    ( ppos
    = ( ^ [P2: prat] : ( P2 != pnone ) ) ) ).

% ppos_eq_pnone
thf(fact_24_padd__cancellative,axiom,
    ! [A: prat,X: prat,B: prat,Y: prat] :
      ( ( A
        = ( padd @ X @ B ) )
     => ( ( A
          = ( padd @ Y @ B ) )
       => ( X = Y ) ) ) ).

% padd_cancellative
thf(fact_25_pmult__pdiv__cancel,axiom,
    ! [A: prat,X: prat] :
      ( ( ppos @ A )
     => ( ( pmult @ A @ ( pdiv @ X @ A ) )
        = X ) ) ).

% pmult_pdiv_cancel
thf(fact_26_pinv__pmult__ok,axiom,
    ! [P: prat] :
      ( ( ppos @ P )
     => ( ( pmult @ P @ ( pinv @ P ) )
        = pwrite ) ) ).

% pinv_pmult_ok
thf(fact_27_pinv__def,axiom,
    ( pinv
    = ( pdiv @ pwrite ) ) ).

% pinv_def
thf(fact_28_sum__coeff,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ( ppos @ B )
       => ( ( padd @ ( pdiv @ A @ ( padd @ A @ B ) ) @ ( pdiv @ B @ ( padd @ A @ B ) ) )
          = pwrite ) ) ) ).

% sum_coeff
thf(fact_29_pmult__order,axiom,
    ! [A: prat,B: prat,P: prat] :
      ( ( pgte @ A @ B )
     => ( pgte @ ( pmult @ P @ A ) @ ( pmult @ B @ P ) ) ) ).

% pmult_order
thf(fact_30_pmult__special_I1_J,axiom,
    ! [X: prat] :
      ( ( pmult @ pwrite @ X )
      = X ) ).

% pmult_special(1)
thf(fact_31_pinv__inverts,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( ppos @ B )
       => ( pgte @ ( pinv @ B ) @ ( pinv @ A ) ) ) ) ).

% pinv_inverts
thf(fact_32_pinv__double__half,axiom,
    ! [P: prat] :
      ( ( ppos @ P )
     => ( ( pmult @ half @ ( pinv @ P ) )
        = ( pinv @ ( padd @ P @ P ) ) ) ) ).

% pinv_double_half
thf(fact_33_get__m__smaller,axiom,
    ! [P: prat,A: state,Hl: produc1457211279475724562t_char] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_m @ ( multiply @ P @ A ) @ Hl )
        = ( pmult @ P @ ( get_m @ A @ Hl ) ) ) ) ).

% get_m_smaller
thf(fact_34_intuitionistic__def,axiom,
    ( intuitionistic
    = ( ^ [A4: set_state] :
        ! [A3: state,B2: state] :
          ( ( ( greater @ A3 @ B2 )
            & ( member_state @ B2 @ A4 ) )
         => ( member_state @ A3 @ A4 ) ) ) ) ).

% intuitionistic_def
thf(fact_35_half__plus__half,axiom,
    ( ( padd @ half @ half )
    = pwrite ) ).

% half_plus_half
thf(fact_36_in__multiply__sem,axiom,
    ! [X: state,P: prat,A5: set_state] :
      ( ( member_state @ X @ ( multip8064567061438756306ertion @ P @ A5 ) )
     => ? [X2: state] :
          ( ( member_state @ X2 @ A5 )
          & ( greater @ X @ ( multiply @ P @ X2 ) ) ) ) ).

% in_multiply_sem
thf(fact_37_pgte__pgt,axiom,
    ! [A: prat,B: prat,C: prat,D: prat] :
      ( ( pgt @ A @ B )
     => ( ( pgte @ C @ D )
       => ( pgt @ ( padd @ A @ C ) @ ( padd @ B @ D ) ) ) ) ).

% pgte_pgt
thf(fact_38_non__scalable__instantiate,axiom,
    ! [W: state,A: state] :
      ( ~ ( scalable @ W @ A )
     => ? [P3: prat] :
          ( ( ppos @ P3 )
          & ( pgte @ pwrite @ P3 )
          & ( defined @ A @ ( multiply @ P3 @ W ) ) ) ) ).

% non_scalable_instantiate
thf(fact_39_PartialSA_Osucc__refl,axiom,
    ! [A: state] : ( greater @ A @ A ) ).

% PartialSA.succ_refl
thf(fact_40_PartialSA_Osucc__trans,axiom,
    ! [A: state,B: state,C: state] :
      ( ( greater @ A @ B )
     => ( ( greater @ B @ C )
       => ( greater @ A @ C ) ) ) ).

% PartialSA.succ_trans
thf(fact_41_PartialSA_Osucc__antisym,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( ( greater @ B @ A )
       => ( A = B ) ) ) ).

% PartialSA.succ_antisym
thf(fact_42_R__smaller,axiom,
    ! [W: state,A: state] : ( greater @ W @ ( r @ A @ W ) ) ).

% R_smaller
thf(fact_43_in__multiply__refl,axiom,
    ! [X: state,A5: set_state,P: prat] :
      ( ( member_state @ X @ A5 )
     => ( member_state @ ( multiply @ P @ X ) @ ( multip8064567061438756306ertion @ P @ A5 ) ) ) ).

% in_multiply_refl
thf(fact_44_R__compatible__same,axiom,
    ! [A: state,W: state] :
      ( ( defined @ A @ W )
     => ( ( r @ A @ W )
        = W ) ) ).

% R_compatible_same
thf(fact_45_mem__Collect__eq,axiom,
    ! [A: produc3882902684156697774_state,P4: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ A @ ( collec394671971739345689_state @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_46_mem__Collect__eq,axiom,
    ! [A: produc7272280185086996969_state,P4: produc7272280185086996969_state > $o] :
      ( ( member7461423308196221312_state @ A @ ( collec906845016635587262_state @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_47_mem__Collect__eq,axiom,
    ! [A: state,P4: state > $o] :
      ( ( member_state @ A @ ( collect_state @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_48_mem__Collect__eq,axiom,
    ! [A: produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ A @ ( collec7475294502966882545on_val @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_49_Collect__mem__eq,axiom,
    ! [A5: set_Pr2391701600042252046_state] :
      ( ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_50_Collect__mem__eq,axiom,
    ! [A5: set_Pr4231240917283394591_state] :
      ( ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_51_Collect__mem__eq,axiom,
    ! [A5: set_state] :
      ( ( collect_state
        @ ^ [X3: state] : ( member_state @ X3 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_52_Collect__mem__eq,axiom,
    ! [A5: set_Pr7649655576376376530on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_53_Collect__cong,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
          = ( Q @ X2 ) )
     => ( ( collec906845016635587262_state @ P4 )
        = ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_cong
thf(fact_54_Collect__cong,axiom,
    ! [P4: state > $o,Q: state > $o] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_state @ P4 )
        = ( collect_state @ Q ) ) ) ).

% Collect_cong
thf(fact_55_Collect__cong,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X2: produc9003781588162623004on_val] :
          ( ( P4 @ X2 )
          = ( Q @ X2 ) )
     => ( ( collec7475294502966882545on_val @ P4 )
        = ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_cong
thf(fact_56_PartialSA_Osmaller__compatible,axiom,
    ! [A6: state,B: state,A: state] :
      ( ( defined @ A6 @ B )
     => ( ( greater @ A6 @ A )
       => ( defined @ A @ B ) ) ) ).

% PartialSA.smaller_compatible
thf(fact_57_state__ext,axiom,
    ! [A: state,B: state] :
      ( ( ( get_h @ A )
        = ( get_h @ B ) )
     => ( ( ( get_m @ A )
          = ( get_m @ B ) )
       => ( A = B ) ) ) ).

% state_ext
thf(fact_58_larger__implies__greater__mask__hl,axiom,
    ! [A: state,B: state,Hl: produc1457211279475724562t_char] :
      ( ( greater @ A @ B )
     => ( pgte @ ( get_m @ A @ Hl ) @ ( get_m @ B @ Hl ) ) ) ).

% larger_implies_greater_mask_hl
thf(fact_59_half__between__0__1,axiom,
    ( ( ppos @ half )
    & ( pgt @ pwrite @ half ) ) ).

% half_between_0_1
thf(fact_60_not__pgte__charact,axiom,
    ! [A: prat,B: prat] :
      ( ( ~ ( pgte @ A @ B ) )
      = ( pgt @ B @ A ) ) ).

% not_pgte_charact
thf(fact_61_pgt__implies__pgte,axiom,
    ! [A: prat,B: prat] :
      ( ( pgt @ A @ B )
     => ( pgte @ A @ B ) ) ).

% pgt_implies_pgte
thf(fact_62_non__scalable__R__charact,axiom,
    ! [W: state,A: state] :
      ( ~ ( scalable @ W @ A )
     => ( ( ( get_m @ ( r @ A @ W ) )
          = ( comp_min_mask @ ( get_m @ A ) @ ( get_m @ W ) ) )
        & ( ( get_h @ ( r @ A @ W ) )
          = ( get_h @ W ) ) ) ) ).

% non_scalable_R_charact
thf(fact_63_scalable__def,axiom,
    ( scalable
    = ( ^ [W2: state,A3: state] :
        ! [X3: state] :
          ( ( member_state @ X3 @ ( scaled @ W2 ) )
         => ~ ( defined @ A3 @ X3 ) ) ) ) ).

% scalable_def
thf(fact_64_get__m__smaller__mask,axiom,
    ! [P: prat,A: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_m @ ( multiply @ P @ A ) )
        = ( multiply_mask @ P @ ( get_m @ A ) ) ) ) ).

% get_m_smaller_mask
thf(fact_65_larger__implies__larger__heap,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( larger1532547405891354081ar_val @ ( get_h @ A ) @ ( get_h @ B ) ) ) ).

% larger_implies_larger_heap
thf(fact_66_combinable__def,axiom,
    ( combinable
    = ( ^ [P5: set_state] :
        ! [Alpha: prat,Beta: prat] :
          ( ( ( ppos @ Alpha )
            & ( ppos @ Beta )
            & ( pgte @ pwrite @ ( padd @ Alpha @ Beta ) ) )
         => ( ord_le2494988322063910608_state @ ( add_set @ ( multip8064567061438756306ertion @ Alpha @ P5 ) @ ( multip8064567061438756306ertion @ Beta @ P5 ) ) @ ( multip8064567061438756306ertion @ ( padd @ Alpha @ Beta ) @ P5 ) ) ) ) ) ).

% combinable_def
thf(fact_67_R__def,axiom,
    ( r
    = ( ^ [A3: state,W2: state] : ( if_state @ ( scalable @ W2 @ A3 ) @ W2 @ ( abs_state @ ( produc74620467203698198on_val @ ( comp_min_mask @ ( get_m @ A3 ) @ ( get_m @ W2 ) ) @ ( get_h @ W2 ) ) ) ) ) ) ).

% R_def
thf(fact_68_pmax__is,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pmax @ A @ B )
        = A ) ) ).

% pmax_is
thf(fact_69_pmin__is,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pmin @ A @ B )
        = B ) ) ).

% pmin_is
thf(fact_70_pmax__smaller,axiom,
    ! [A: prat,B: prat] : ( pgte @ ( pmax @ A @ B ) @ A ) ).

% pmax_smaller
thf(fact_71_pmin__greater,axiom,
    ! [A: prat,B: prat] : ( pgte @ A @ ( pmin @ A @ B ) ) ).

% pmin_greater
thf(fact_72_pmax__is__smaller,axiom,
    ! [X: prat,A: prat,B: prat] :
      ( ( pgte @ X @ A )
     => ( ( pgte @ X @ B )
       => ( pgte @ X @ ( pmax @ A @ B ) ) ) ) ).

% pmax_is_smaller
thf(fact_73_larger__heap__trans,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ B @ C )
       => ( larger1532547405891354081ar_val @ A @ C ) ) ) ).

% larger_heap_trans
thf(fact_74_larger__heap__refl,axiom,
    ! [H: produc1457211279475724562t_char > option_val] : ( larger1532547405891354081ar_val @ H @ H ) ).

% larger_heap_refl
thf(fact_75_larger__heap__anti,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ B @ A )
       => ( A = B ) ) ) ).

% larger_heap_anti
thf(fact_76_PartialSA_Oadd__set__commm,axiom,
    ( add_set
    = ( ^ [A4: set_state,B3: set_state] : ( add_set @ B3 @ A4 ) ) ) ).

% PartialSA.add_set_commm
thf(fact_77_PartialSA_Oadd__set__asso,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( add_set @ ( add_set @ A5 @ B4 ) @ C2 )
      = ( add_set @ A5 @ ( add_set @ B4 @ C2 ) ) ) ).

% PartialSA.add_set_asso
thf(fact_78_valid__state_Ocases,axiom,
    ! [X: produc9003781588162623004on_val] :
      ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc74620467203698198on_val @ Pi2 @ H2 ) ) ).

% valid_state.cases
thf(fact_79_pmax__comm,axiom,
    ( pmax
    = ( ^ [A3: prat,B2: prat] : ( pmax @ B2 @ A3 ) ) ) ).

% pmax_comm
thf(fact_80_pmin__comm,axiom,
    ( pmin
    = ( ^ [A3: prat,B2: prat] : ( pmin @ B2 @ A3 ) ) ) ).

% pmin_comm
thf(fact_81_w__in__scaled,axiom,
    ! [W: state] : ( member_state @ W @ ( scaled @ W ) ) ).

% w_in_scaled
thf(fact_82_pmin__pmax,axiom,
    ! [X: prat,A: prat,B: prat] :
      ( ( pgte @ X @ ( pmin @ A @ B ) )
     => ( X
        = ( pmin @ ( pmax @ X @ A ) @ ( pmax @ X @ B ) ) ) ) ).

% pmin_pmax
thf(fact_83_multiply_Oelims,axiom,
    ! [X: prat,Xa: state,Y: state] :
      ( ( ( multiply @ X @ Xa )
        = Y )
     => ( Y
        = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X @ ( get_m @ Xa ) ) @ ( get_h @ Xa ) ) ) ) ) ).

% multiply.elims
thf(fact_84_multiply_Osimps,axiom,
    ( multiply
    = ( ^ [P2: prat,Phi: state] : ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ P2 @ ( get_m @ Phi ) ) @ ( get_h @ Phi ) ) ) ) ) ).

% multiply.simps
thf(fact_85_comp__min__mask__def,axiom,
    ( comp_min_mask
    = ( ^ [B2: produc1457211279475724562t_char > prat,A3: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char] : ( pmin @ ( A3 @ Hl2 ) @ ( comp_one @ ( B2 @ Hl2 ) ) ) ) ) ).

% comp_min_mask_def
thf(fact_86_binary__def,axiom,
    ( binary
    = ( ^ [A4: set_state] :
        ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member_state @ ( abs_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ X3 ) ) @ ( get_h @ X3 ) ) ) @ A4 ) ) ) ) ).

% binary_def
thf(fact_87_multiply__valid,axiom,
    ! [P: prat,Phi2: state] :
      ( ( pgte @ pwrite @ P )
     => ( valid_state @ ( produc74620467203698198on_val @ ( multiply_mask @ P @ ( get_m @ Phi2 ) ) @ ( get_h @ Phi2 ) ) ) ) ).

% multiply_valid
thf(fact_88_assms,axiom,
    ! [A: prat,B: prat] :
      ( ( ( ppos @ A )
        & ( ppos @ B )
        & ( ( padd @ A @ B )
          = pwrite ) )
     => ( ord_le2494988322063910608_state @ ( add_set @ ( multip8064567061438756306ertion @ A @ ( cwand @ a @ b ) ) @ ( multip8064567061438756306ertion @ B @ ( cwand @ a @ b ) ) ) @ ( cwand @ a @ b ) ) ) ).

% assms
thf(fact_89_multiply__mask__def,axiom,
    ( multiply_mask
    = ( ^ [P2: prat,Pi: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char] : ( pmult @ P2 @ ( Pi @ Hl2 ) ) ) ) ).

% multiply_mask_def
thf(fact_90_subsetI,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X2 @ A5 )
         => ( member7461423308196221312_state @ X2 @ B4 ) )
     => ( ord_le4032880777312351359_state @ A5 @ B4 ) ) ).

% subsetI
thf(fact_91_subsetI,axiom,
    ! [A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X2: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X2 @ A5 )
         => ( member2879030624002546611on_val @ X2 @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A5 @ B4 ) ) ).

% subsetI
thf(fact_92_subsetI,axiom,
    ! [A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X2 @ A5 )
         => ( member6715010751053357271_state @ X2 @ B4 ) )
     => ( ord_le6483787752022044334_state @ A5 @ B4 ) ) ).

% subsetI
thf(fact_93_subsetI,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ A5 )
         => ( member_state @ X2 @ B4 ) )
     => ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ).

% subsetI
thf(fact_94_double__inclusion,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ A5 )
       => ( A5 = B4 ) ) ) ).

% double_inclusion
thf(fact_95_mult__write__mask,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ pwrite @ Pi3 )
      = Pi3 ) ).

% mult_write_mask
thf(fact_96_prod_Oinject,axiom,
    ! [X1: option_state,X22: option_state,Y1: option_state,Y2: option_state] :
      ( ( ( produc9160152616361873709_state @ X1 @ X22 )
        = ( produc9160152616361873709_state @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_97_prod_Oinject,axiom,
    ! [X1: prat,X22: state,Y1: prat,Y2: state] :
      ( ( ( produc6205719116230455971_state @ X1 @ X22 )
        = ( produc6205719116230455971_state @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_98_prod_Oinject,axiom,
    ! [X1: prat,X22: set_state,Y1: prat,Y2: set_state] :
      ( ( ( produc9080284787853255769_state @ X1 @ X22 )
        = ( produc9080284787853255769_state @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_99_prod_Oinject,axiom,
    ! [X1: nat,X22: list_char,Y1: nat,Y2: list_char] :
      ( ( ( produc120197956887798346t_char @ X1 @ X22 )
        = ( produc120197956887798346t_char @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_100_prod_Oinject,axiom,
    ! [X1: produc1457211279475724562t_char > prat,X22: produc1457211279475724562t_char > option_val,Y1: produc1457211279475724562t_char > prat,Y2: produc1457211279475724562t_char > option_val] :
      ( ( ( produc74620467203698198on_val @ X1 @ X22 )
        = ( produc74620467203698198on_val @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_101_old_Oprod_Oinject,axiom,
    ! [A: option_state,B: option_state,A6: option_state,B5: option_state] :
      ( ( ( produc9160152616361873709_state @ A @ B )
        = ( produc9160152616361873709_state @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_102_old_Oprod_Oinject,axiom,
    ! [A: prat,B: state,A6: prat,B5: state] :
      ( ( ( produc6205719116230455971_state @ A @ B )
        = ( produc6205719116230455971_state @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_103_old_Oprod_Oinject,axiom,
    ! [A: prat,B: set_state,A6: prat,B5: set_state] :
      ( ( ( produc9080284787853255769_state @ A @ B )
        = ( produc9080284787853255769_state @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_104_old_Oprod_Oinject,axiom,
    ! [A: nat,B: list_char,A6: nat,B5: list_char] :
      ( ( ( produc120197956887798346t_char @ A @ B )
        = ( produc120197956887798346t_char @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_105_old_Oprod_Oinject,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val,A6: produc1457211279475724562t_char > prat,B5: produc1457211279475724562t_char > option_val] :
      ( ( ( produc74620467203698198on_val @ A @ B )
        = ( produc74620467203698198on_val @ A6 @ B5 ) )
      = ( ( A = A6 )
        & ( B = B5 ) ) ) ).

% old.prod.inject
thf(fact_106_order__refl,axiom,
    ! [X: set_state] : ( ord_le2494988322063910608_state @ X @ X ) ).

% order_refl
thf(fact_107_dual__order_Orefl,axiom,
    ! [A: set_state] : ( ord_le2494988322063910608_state @ A @ A ) ).

% dual_order.refl
thf(fact_108_ssubsetI,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [Pi2: state,H2: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi2 @ H2 ) @ A5 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_109_ssubsetI,axiom,
    ! [A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [Pi2: state,H2: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi2 @ H2 ) @ A5 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_110_ssubsetI,axiom,
    ! [A5: set_Pr1688445902015331925_state,B4: set_Pr1688445902015331925_state] :
      ( ! [Pi2: option_state,H2: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi2 @ H2 ) @ A5 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le6423325748750870005_state @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_111_ssubsetI,axiom,
    ! [A5: set_Pr6039890582625207499_state,B4: set_Pr6039890582625207499_state] :
      ( ! [Pi2: prat,H2: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi2 @ H2 ) @ A5 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le262197048489888875_state @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_112_ssubsetI,axiom,
    ! [A5: set_Pr6847263425858009217_state,B4: set_Pr6847263425858009217_state] :
      ( ! [Pi2: prat,H2: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi2 @ H2 ) @ A5 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le5761494056910127137_state @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_113_ssubsetI,axiom,
    ! [A5: set_Pr2507339680178222706t_char,B4: set_Pr2507339680178222706t_char] :
      ( ! [Pi2: nat,H2: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi2 @ H2 ) @ A5 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le6315511645215477266t_char @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_114_ssubsetI,axiom,
    ! [A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi2 @ H2 ) @ A5 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi2 @ H2 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A5 @ B4 ) ) ).

% ssubsetI
thf(fact_115_add__states_Ocases,axiom,
    ! [X: produc1317171644805857433on_val] :
      ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val,Pi4: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi2 @ H2 ) @ ( produc74620467203698198on_val @ Pi4 @ H3 ) ) ) ).

% add_states.cases
thf(fact_116_order__antisym__conv,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( ord_le2494988322063910608_state @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_117_ord__le__eq__subst,axiom,
    ! [A: set_state,B: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X2 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_118_ord__eq__le__subst,axiom,
    ! [A: set_state,F: set_state > set_state,B: set_state,C: set_state] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ! [X2: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X2 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_119_order__eq__refl,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( X = Y )
     => ( ord_le2494988322063910608_state @ X @ Y ) ) ).

% order_eq_refl
thf(fact_120_order__subst2,axiom,
    ! [A: set_state,B: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ ( F @ B ) @ C )
       => ( ! [X2: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X2 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_121_order__subst1,axiom,
    ! [A: set_state,F: set_state > set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ ( F @ B ) )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ! [X2: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X2 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_122_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A3: set_state,B2: set_state] :
          ( ( ord_le2494988322063910608_state @ A3 @ B2 )
          & ( ord_le2494988322063910608_state @ B2 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_123_antisym,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_124_dual__order_Otrans,axiom,
    ! [B: set_state,A: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ C @ B )
       => ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_125_dual__order_Oantisym,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_126_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A3: set_state,B2: set_state] :
          ( ( ord_le2494988322063910608_state @ B2 @ A3 )
          & ( ord_le2494988322063910608_state @ A3 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_127_order__trans,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ Z2 )
       => ( ord_le2494988322063910608_state @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_128_order_Otrans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% order.trans
thf(fact_129_order__antisym,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_130_ord__le__eq__trans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( B = C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_131_ord__eq__le__trans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( A = B )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_132_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [X3: set_state,Y5: set_state] :
          ( ( ord_le2494988322063910608_state @ X3 @ Y5 )
          & ( ord_le2494988322063910608_state @ Y5 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_133_Pair__inject,axiom,
    ! [A: option_state,B: option_state,A6: option_state,B5: option_state] :
      ( ( ( produc9160152616361873709_state @ A @ B )
        = ( produc9160152616361873709_state @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_134_Pair__inject,axiom,
    ! [A: prat,B: state,A6: prat,B5: state] :
      ( ( ( produc6205719116230455971_state @ A @ B )
        = ( produc6205719116230455971_state @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_135_Pair__inject,axiom,
    ! [A: prat,B: set_state,A6: prat,B5: set_state] :
      ( ( ( produc9080284787853255769_state @ A @ B )
        = ( produc9080284787853255769_state @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_136_Pair__inject,axiom,
    ! [A: nat,B: list_char,A6: nat,B5: list_char] :
      ( ( ( produc120197956887798346t_char @ A @ B )
        = ( produc120197956887798346t_char @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_137_Pair__inject,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val,A6: produc1457211279475724562t_char > prat,B5: produc1457211279475724562t_char > option_val] :
      ( ( ( produc74620467203698198on_val @ A @ B )
        = ( produc74620467203698198on_val @ A6 @ B5 ) )
     => ~ ( ( A = A6 )
         => ( B != B5 ) ) ) ).

% Pair_inject
thf(fact_138_prod__cases,axiom,
    ! [P4: produc3142500478612311029_state > $o,P: produc3142500478612311029_state] :
      ( ! [A7: option_state,B6: option_state] : ( P4 @ ( produc9160152616361873709_state @ A7 @ B6 ) )
     => ( P4 @ P ) ) ).

% prod_cases
thf(fact_139_prod__cases,axiom,
    ! [P4: produc4844402304972151915_state > $o,P: produc4844402304972151915_state] :
      ( ! [A7: prat,B6: state] : ( P4 @ ( produc6205719116230455971_state @ A7 @ B6 ) )
     => ( P4 @ P ) ) ).

% prod_cases
thf(fact_140_prod__cases,axiom,
    ! [P4: produc6251377953716854561_state > $o,P: produc6251377953716854561_state] :
      ( ! [A7: prat,B6: set_state] : ( P4 @ ( produc9080284787853255769_state @ A7 @ B6 ) )
     => ( P4 @ P ) ) ).

% prod_cases
thf(fact_141_prod__cases,axiom,
    ! [P4: produc1457211279475724562t_char > $o,P: produc1457211279475724562t_char] :
      ( ! [A7: nat,B6: list_char] : ( P4 @ ( produc120197956887798346t_char @ A7 @ B6 ) )
     => ( P4 @ P ) ) ).

% prod_cases
thf(fact_142_prod__cases,axiom,
    ! [P4: produc9003781588162623004on_val > $o,P: produc9003781588162623004on_val] :
      ( ! [A7: produc1457211279475724562t_char > prat,B6: produc1457211279475724562t_char > option_val] : ( P4 @ ( produc74620467203698198on_val @ A7 @ B6 ) )
     => ( P4 @ P ) ) ).

% prod_cases
thf(fact_143_surj__pair,axiom,
    ! [P: produc3142500478612311029_state] :
    ? [X2: option_state,Y3: option_state] :
      ( P
      = ( produc9160152616361873709_state @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_144_surj__pair,axiom,
    ! [P: produc4844402304972151915_state] :
    ? [X2: prat,Y3: state] :
      ( P
      = ( produc6205719116230455971_state @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_145_surj__pair,axiom,
    ! [P: produc6251377953716854561_state] :
    ? [X2: prat,Y3: set_state] :
      ( P
      = ( produc9080284787853255769_state @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_146_surj__pair,axiom,
    ! [P: produc1457211279475724562t_char] :
    ? [X2: nat,Y3: list_char] :
      ( P
      = ( produc120197956887798346t_char @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_147_surj__pair,axiom,
    ! [P: produc9003781588162623004on_val] :
    ? [X2: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
      ( P
      = ( produc74620467203698198on_val @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_148_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3142500478612311029_state] :
      ~ ! [A7: option_state,B6: option_state] :
          ( Y
         != ( produc9160152616361873709_state @ A7 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_149_old_Oprod_Oexhaust,axiom,
    ! [Y: produc4844402304972151915_state] :
      ~ ! [A7: prat,B6: state] :
          ( Y
         != ( produc6205719116230455971_state @ A7 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_150_old_Oprod_Oexhaust,axiom,
    ! [Y: produc6251377953716854561_state] :
      ~ ! [A7: prat,B6: set_state] :
          ( Y
         != ( produc9080284787853255769_state @ A7 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_151_old_Oprod_Oexhaust,axiom,
    ! [Y: produc1457211279475724562t_char] :
      ~ ! [A7: nat,B6: list_char] :
          ( Y
         != ( produc120197956887798346t_char @ A7 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_152_old_Oprod_Oexhaust,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ~ ! [A7: produc1457211279475724562t_char > prat,B6: produc1457211279475724562t_char > option_val] :
          ( Y
         != ( produc74620467203698198on_val @ A7 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_153_Collect__mono__iff,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P4 ) @ ( collec906845016635587262_state @ Q ) )
      = ( ! [X3: produc7272280185086996969_state] :
            ( ( P4 @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_154_Collect__mono__iff,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P4 ) @ ( collec7475294502966882545on_val @ Q ) )
      = ( ! [X3: produc9003781588162623004on_val] :
            ( ( P4 @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_155_Collect__mono__iff,axiom,
    ! [P4: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ ( collect_state @ P4 ) @ ( collect_state @ Q ) )
      = ( ! [X3: state] :
            ( ( P4 @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_156_set__eq__subset,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A4: set_state,B3: set_state] :
          ( ( ord_le2494988322063910608_state @ A4 @ B3 )
          & ( ord_le2494988322063910608_state @ B3 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_157_subset__trans,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C2 )
       => ( ord_le2494988322063910608_state @ A5 @ C2 ) ) ) ).

% subset_trans
thf(fact_158_Collect__mono,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
         => ( Q @ X2 ) )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P4 ) @ ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_mono
thf(fact_159_Collect__mono,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X2: produc9003781588162623004on_val] :
          ( ( P4 @ X2 )
         => ( Q @ X2 ) )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P4 ) @ ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_mono
thf(fact_160_Collect__mono,axiom,
    ! [P4: state > $o,Q: state > $o] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
         => ( Q @ X2 ) )
     => ( ord_le2494988322063910608_state @ ( collect_state @ P4 ) @ ( collect_state @ Q ) ) ) ).

% Collect_mono
thf(fact_161_subset__refl,axiom,
    ! [A5: set_state] : ( ord_le2494988322063910608_state @ A5 @ A5 ) ).

% subset_refl
thf(fact_162_subset__iff,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
        ! [T: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ T @ A4 )
         => ( member7461423308196221312_state @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_163_subset__iff,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,B3: set_Pr7649655576376376530on_val] :
        ! [T: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ T @ A4 )
         => ( member2879030624002546611on_val @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_164_subset__iff,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A4: set_Pr2391701600042252046_state,B3: set_Pr2391701600042252046_state] :
        ! [T: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ T @ A4 )
         => ( member6715010751053357271_state @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_165_subset__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A4: set_state,B3: set_state] :
        ! [T: state] :
          ( ( member_state @ T @ A4 )
         => ( member_state @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_166_equalityD2,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( A5 = B4 )
     => ( ord_le2494988322063910608_state @ B4 @ A5 ) ) ).

% equalityD2
thf(fact_167_equalityD1,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( A5 = B4 )
     => ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ).

% equalityD1
thf(fact_168_subset__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
        ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( member7461423308196221312_state @ X3 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_169_subset__eq,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,B3: set_Pr7649655576376376530on_val] :
        ! [X3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X3 @ A4 )
         => ( member2879030624002546611on_val @ X3 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_170_subset__eq,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A4: set_Pr2391701600042252046_state,B3: set_Pr2391701600042252046_state] :
        ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( member6715010751053357271_state @ X3 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_171_subset__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A4: set_state,B3: set_state] :
        ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member_state @ X3 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_172_equalityE,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( A5 = B4 )
     => ~ ( ( ord_le2494988322063910608_state @ A5 @ B4 )
         => ~ ( ord_le2494988322063910608_state @ B4 @ A5 ) ) ) ).

% equalityE
thf(fact_173_subsetD,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ B4 )
     => ( ( member7461423308196221312_state @ C @ A5 )
       => ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_174_subsetD,axiom,
    ! [A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,C: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A5 @ B4 )
     => ( ( member2879030624002546611on_val @ C @ A5 )
       => ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% subsetD
thf(fact_175_subsetD,axiom,
    ! [A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,C: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A5 @ B4 )
     => ( ( member6715010751053357271_state @ C @ A5 )
       => ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_176_subsetD,axiom,
    ! [A5: set_state,B4: set_state,C: state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ( member_state @ C @ A5 )
       => ( member_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_177_in__mono,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,X: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ B4 )
     => ( ( member7461423308196221312_state @ X @ A5 )
       => ( member7461423308196221312_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_178_in__mono,axiom,
    ! [A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A5 @ B4 )
     => ( ( member2879030624002546611on_val @ X @ A5 )
       => ( member2879030624002546611on_val @ X @ B4 ) ) ) ).

% in_mono
thf(fact_179_in__mono,axiom,
    ! [A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,X: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A5 @ B4 )
     => ( ( member6715010751053357271_state @ X @ A5 )
       => ( member6715010751053357271_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_180_in__mono,axiom,
    ! [A5: set_state,B4: set_state,X: state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ( member_state @ X @ A5 )
       => ( member_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_181_valid__bin,axiom,
    ! [A: state] : ( valid_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ A ) ) @ ( get_h @ A ) ) ) ).

% valid_bin
thf(fact_182_binary__same,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( binary @ A5 )
     => ( ( intuitionistic @ B4 )
       => ( ord_le2494988322063910608_state @ ( wand @ A5 @ B4 ) @ ( cwand @ A5 @ B4 ) ) ) ) ).

% binary_same
thf(fact_183_cwand__stronger,axiom,
    ! [A5: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( cwand @ A5 @ B4 ) @ ( wand @ A5 @ B4 ) ) ).

% cwand_stronger
thf(fact_184_greaterI,axiom,
    ! [A: state,B: state] :
      ( ( larger1532547405891354081ar_val @ ( get_h @ A ) @ ( get_h @ B ) )
     => ( ( greate7680731506090375811t_char @ ( get_m @ A ) @ ( get_m @ B ) )
       => ( greater @ A @ B ) ) ) ).

% greaterI
thf(fact_185_multiply_Opelims,axiom,
    ! [X: prat,Xa: state,Y: state] :
      ( ( ( multiply @ X @ Xa )
        = Y )
     => ( ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X @ Xa ) )
       => ~ ( ( Y
              = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X @ ( get_m @ Xa ) ) @ ( get_h @ Xa ) ) ) )
           => ~ ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X @ Xa ) ) ) ) ) ).

% multiply.pelims
thf(fact_186_get__h__m,axiom,
    ( rep_state
    = ( ^ [X3: state] : ( produc74620467203698198on_val @ ( get_m @ X3 ) @ ( get_h @ X3 ) ) ) ) ).

% get_h_m
thf(fact_187_upper__bounded__smaller,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,A: prat,P: prat] :
      ( ( upper_bounded @ Pi3 @ A )
     => ( upper_bounded @ ( multiply_mask @ P @ Pi3 ) @ ( pmult @ P @ A ) ) ) ).

% upper_bounded_smaller
thf(fact_188_relChain__def,axiom,
    ( bNF_Ca2815325664443363616_state
    = ( ^ [R: set_Pr1688445902015331925_state,As: option_state > set_state] :
        ! [I: option_state,J: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ I @ J ) @ R )
         => ( ord_le2494988322063910608_state @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).

% relChain_def
thf(fact_189_valid__mult,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,P: prat] :
      ( ( valid_mask @ Pi3 )
     => ( ( pgte @ pwrite @ P )
       => ( valid_mask @ ( multiply_mask @ P @ Pi3 ) ) ) ) ).

% valid_mult
thf(fact_190_multiply_Ocases,axiom,
    ! [X: produc4844402304972151915_state] :
      ~ ! [P3: prat,Phi3: state] :
          ( X
         != ( produc6205719116230455971_state @ P3 @ Phi3 ) ) ).

% multiply.cases
thf(fact_191_greater__mask__properties_I1_J,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] : ( greate7680731506090375811t_char @ Pi3 @ Pi3 ) ).

% greater_mask_properties(1)
thf(fact_192_greater__mask__properties_I2_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ A @ B )
        & ( greate7680731506090375811t_char @ B @ C ) )
     => ( greate7680731506090375811t_char @ A @ C ) ) ).

% greater_mask_properties(2)
thf(fact_193_greater__mask__properties_I3_J,axiom,
    ! [Pi5: produc1457211279475724562t_char > prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ Pi5 @ Pi3 )
        & ( greate7680731506090375811t_char @ Pi3 @ Pi5 ) )
     => ( Pi3 = Pi5 ) ) ).

% greater_mask_properties(3)
thf(fact_194_Rep__state__inject,axiom,
    ! [X: state,Y: state] :
      ( ( ( rep_state @ X )
        = ( rep_state @ Y ) )
      = ( X = Y ) ) ).

% Rep_state_inject
thf(fact_195_greater__mask__equiv__def,axiom,
    ( greate7680731506090375811t_char
    = ( ^ [Pi6: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat] :
        ! [Hl2: produc1457211279475724562t_char] : ( pgte @ ( Pi6 @ Hl2 ) @ ( Pi @ Hl2 ) ) ) ) ).

% greater_mask_equiv_def
thf(fact_196_greater__maskI,axiom,
    ! [Pi5: produc1457211279475724562t_char > prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ ( Pi5 @ Hl3 ) @ ( Pi3 @ Hl3 ) )
     => ( greate7680731506090375811t_char @ Pi5 @ Pi3 ) ) ).

% greater_maskI
thf(fact_197_mult__greater,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,P: prat] :
      ( ( greate7680731506090375811t_char @ A @ B )
     => ( greate7680731506090375811t_char @ ( multiply_mask @ P @ A ) @ ( multiply_mask @ P @ B ) ) ) ).

% mult_greater
thf(fact_198_Rep__state__inverse,axiom,
    ! [X: state] :
      ( ( abs_state @ ( rep_state @ X ) )
      = X ) ).

% Rep_state_inverse
thf(fact_199_upper__bounded__bigger,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,A: prat,B: prat] :
      ( ( upper_bounded @ Pi3 @ A )
     => ( ( pgte @ B @ A )
       => ( upper_bounded @ Pi3 @ B ) ) ) ).

% upper_bounded_bigger
thf(fact_200_upper__bounded__def,axiom,
    ( upper_bounded
    = ( ^ [Pi: produc1457211279475724562t_char > prat,P2: prat] :
        ! [Hl2: produc1457211279475724562t_char] : ( pgte @ P2 @ ( Pi @ Hl2 ) ) ) ) ).

% upper_bounded_def
thf(fact_201_upper__boundedI,axiom,
    ! [P: prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ P @ ( Pi3 @ Hl3 ) )
     => ( upper_bounded @ Pi3 @ P ) ) ).

% upper_boundedI
thf(fact_202_valid__multiply,axiom,
    ! [A: produc1457211279475724562t_char > prat,Ma: prat,P: prat] :
      ( ( valid_mask @ A )
     => ( ( upper_bounded @ A @ Ma )
       => ( ( pgte @ pwrite @ ( pmult @ Ma @ P ) )
         => ( valid_mask @ ( multiply_mask @ P @ A ) ) ) ) ) ).

% valid_multiply
thf(fact_203_valid__larger__mask,axiom,
    ( valid_mask
    = ( greate7680731506090375811t_char @ full_mask ) ) ).

% valid_larger_mask
thf(fact_204_valid__maskI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi3 @ Hl3 ) )
     => ( ! [F2: list_char] :
            ( ( Pi3 @ ( produc120197956887798346t_char @ null_nat @ F2 ) )
            = pnone )
       => ( valid_mask @ Pi3 ) ) ) ).

% valid_maskI
thf(fact_205_valid__mask_Osimps,axiom,
    ( valid_mask
    = ( ^ [Pi: produc1457211279475724562t_char > prat] :
          ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi @ Hl2 ) )
          & ! [F3: list_char] :
              ( ( Pi @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
              = pnone ) ) ) ) ).

% valid_mask.simps
thf(fact_206_valid__mask_Oelims_I1_J,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X )
        = Y )
     => ( Y
        = ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl2 ) )
          & ! [F3: list_char] :
              ( ( X @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
              = pnone ) ) ) ) ).

% valid_mask.elims(1)
thf(fact_207_valid__mask_Oelims_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X )
     => ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl4 ) )
        & ! [F4: list_char] :
            ( ( X @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
            = pnone ) ) ) ).

% valid_mask.elims(2)
thf(fact_208_valid__mask_Oelims_I3_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X )
     => ~ ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl3 ) )
          & ! [F2: list_char] :
              ( ( X @ ( produc120197956887798346t_char @ null_nat @ F2 ) )
              = pnone ) ) ) ).

% valid_mask.elims(3)
thf(fact_209_subrelI,axiom,
    ! [R2: set_Pr4231240917283394591_state,S: set_Pr4231240917283394591_state] :
      ( ! [X2: state,Y3: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ Y3 ) @ R2 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ Y3 ) @ S ) )
     => ( ord_le4032880777312351359_state @ R2 @ S ) ) ).

% subrelI
thf(fact_210_subrelI,axiom,
    ! [R2: set_Pr2391701600042252046_state,S: set_Pr2391701600042252046_state] :
      ( ! [X2: state,Y3: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X2 @ Y3 ) @ R2 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X2 @ Y3 ) @ S ) )
     => ( ord_le6483787752022044334_state @ R2 @ S ) ) ).

% subrelI
thf(fact_211_subrelI,axiom,
    ! [R2: set_Pr1688445902015331925_state,S: set_Pr1688445902015331925_state] :
      ( ! [X2: option_state,Y3: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X2 @ Y3 ) @ R2 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X2 @ Y3 ) @ S ) )
     => ( ord_le6423325748750870005_state @ R2 @ S ) ) ).

% subrelI
thf(fact_212_subrelI,axiom,
    ! [R2: set_Pr6039890582625207499_state,S: set_Pr6039890582625207499_state] :
      ( ! [X2: prat,Y3: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X2 @ Y3 ) @ R2 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X2 @ Y3 ) @ S ) )
     => ( ord_le262197048489888875_state @ R2 @ S ) ) ).

% subrelI
thf(fact_213_subrelI,axiom,
    ! [R2: set_Pr6847263425858009217_state,S: set_Pr6847263425858009217_state] :
      ( ! [X2: prat,Y3: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X2 @ Y3 ) @ R2 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X2 @ Y3 ) @ S ) )
     => ( ord_le5761494056910127137_state @ R2 @ S ) ) ).

% subrelI
thf(fact_214_subrelI,axiom,
    ! [R2: set_Pr2507339680178222706t_char,S: set_Pr2507339680178222706t_char] :
      ( ! [X2: nat,Y3: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X2 @ Y3 ) @ R2 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X2 @ Y3 ) @ S ) )
     => ( ord_le6315511645215477266t_char @ R2 @ S ) ) ).

% subrelI
thf(fact_215_subrelI,axiom,
    ! [R2: set_Pr7649655576376376530on_val,S: set_Pr7649655576376376530on_val] :
      ( ! [X2: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X2 @ Y3 ) @ R2 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X2 @ Y3 ) @ S ) )
     => ( ord_le6900622908513426738on_val @ R2 @ S ) ) ).

% subrelI
thf(fact_216_valid__state_Osimps,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ Pi3 @ H ) )
      = ( ( valid_mask @ Pi3 )
        & ( valid_heap @ Pi3 @ H ) ) ) ).

% valid_state.simps
thf(fact_217_valid__state_Oelims_I1_J,axiom,
    ! [X: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X )
        = Y )
     => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
           => ( Y
              = ( ~ ( ( valid_mask @ Pi2 )
                    & ( valid_heap @ Pi2 @ H2 ) ) ) ) ) ) ).

% valid_state.elims(1)
thf(fact_218_valid__mask__full__mask,axiom,
    valid_mask @ full_mask ).

% valid_mask_full_mask
thf(fact_219_valid__state_Oelims_I3_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X )
     => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
           => ( ( valid_mask @ Pi2 )
              & ( valid_heap @ Pi2 @ H2 ) ) ) ) ).

% valid_state.elims(3)
thf(fact_220_valid__state_Oelims_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( valid_state @ X )
     => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
           => ~ ( ( valid_mask @ Pi2 )
                & ( valid_heap @ Pi2 @ H2 ) ) ) ) ).

% valid_state.elims(2)
thf(fact_221_valid__null__def,axiom,
    ( valid_null
    = ( ^ [Pi: produc1457211279475724562t_char > prat] :
        ! [F3: list_char] :
          ( ( Pi @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
          = pnone ) ) ) ).

% valid_null_def
thf(fact_222_valid__sum_I2_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( ( upper_bounded @ A @ Ma )
         => ( ( upper_bounded @ B @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( upper_bounded @ ( add_ma6586698345353345811t_char @ A @ B ) @ ( padd @ Ma @ Mb ) ) ) ) ) ) ) ).

% valid_sum(2)
thf(fact_223_valid__sum_I1_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( ( upper_bounded @ A @ Ma )
         => ( ( upper_bounded @ B @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( valid_mask @ ( add_ma6586698345353345811t_char @ A @ B ) ) ) ) ) ) ) ).

% valid_sum(1)
thf(fact_224_greater__mask__uniI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char,R2: prat] :
      ( ( pgte @ ( Pi3 @ Hl ) @ R2 )
     => ( greate7680731506090375811t_char @ Pi3 @ ( uni_ma6578582744724537101t_char @ Hl @ R2 ) ) ) ).

% greater_mask_uniI
thf(fact_225_greater__mask__uni__equiv,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char,R2: prat] :
      ( ( greate7680731506090375811t_char @ Pi3 @ ( uni_ma6578582744724537101t_char @ Hl @ R2 ) )
      = ( pgte @ ( Pi3 @ Hl ) @ R2 ) ) ).

% greater_mask_uni_equiv
thf(fact_226_full__mask__def,axiom,
    ( full_mask
    = ( ^ [Hl2: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( produc6204653154488278070t_char @ Hl2 )
            = null_nat )
          @ pnone
          @ pwrite ) ) ) ).

% full_mask_def
thf(fact_227_valid__mask_Opelims_I1_J,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( Y
              = ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl2 ) )
                & ! [F3: list_char] :
                    ( ( X @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
                    = pnone ) ) )
           => ~ ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X ) ) ) ) ).

% valid_mask.pelims(1)
thf(fact_228_valid__mask_Opelims_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
           => ~ ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl4 ) )
                & ! [F4: list_char] :
                    ( ( X @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
                    = pnone ) ) ) ) ) ).

% valid_mask.pelims(2)
thf(fact_229_add__masks__equiv__valid__null,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat] :
      ( ( valid_null @ ( add_ma6586698345353345811t_char @ A @ B ) )
      = ( ( valid_null @ A )
        & ( valid_null @ B ) ) ) ).

% add_masks_equiv_valid_null
thf(fact_230_add__masks__cancellative,axiom,
    ! [B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ B @ C )
        = ( add_ma6586698345353345811t_char @ B @ D ) )
     => ( C = D ) ) ).

% add_masks_cancellative
thf(fact_231_add__masks__comm,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat] : ( add_ma6586698345353345811t_char @ B2 @ A3 ) ) ) ).

% add_masks_comm
thf(fact_232_add__masks__asso,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( add_ma6586698345353345811t_char @ ( add_ma6586698345353345811t_char @ A @ B ) @ C )
      = ( add_ma6586698345353345811t_char @ A @ ( add_ma6586698345353345811t_char @ B @ C ) ) ) ).

% add_masks_asso
thf(fact_233_fst__eqD,axiom,
    ! [X: option_state,Y: option_state,A: option_state] :
      ( ( ( produc3900939990612242713_state @ ( produc9160152616361873709_state @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_234_fst__eqD,axiom,
    ! [X: prat,Y: state,A: prat] :
      ( ( ( produc6030790797199838863_state @ ( produc6205719116230455971_state @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_235_fst__eqD,axiom,
    ! [X: prat,Y: set_state,A: prat] :
      ( ( ( produc7279835715735703621_state @ ( produc9080284787853255769_state @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_236_fst__eqD,axiom,
    ! [X: nat,Y: list_char,A: nat] :
      ( ( ( produc6204653154488278070t_char @ ( produc120197956887798346t_char @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_237_fst__eqD,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: produc1457211279475724562t_char > option_val,A: produc1457211279475724562t_char > prat] :
      ( ( ( produc5239619271231976746on_val @ ( produc74620467203698198on_val @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_238_fst__conv,axiom,
    ! [X1: option_state,X22: option_state] :
      ( ( produc3900939990612242713_state @ ( produc9160152616361873709_state @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_239_fst__conv,axiom,
    ! [X1: prat,X22: state] :
      ( ( produc6030790797199838863_state @ ( produc6205719116230455971_state @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_240_fst__conv,axiom,
    ! [X1: prat,X22: set_state] :
      ( ( produc7279835715735703621_state @ ( produc9080284787853255769_state @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_241_fst__conv,axiom,
    ! [X1: nat,X22: list_char] :
      ( ( produc6204653154488278070t_char @ ( produc120197956887798346t_char @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_242_fst__conv,axiom,
    ! [X1: produc1457211279475724562t_char > prat,X22: produc1457211279475724562t_char > option_val] :
      ( ( produc5239619271231976746on_val @ ( produc74620467203698198on_val @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_243_upper__valid__aux,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( A
          = ( add_ma6586698345353345811t_char @ B @ C ) )
       => ( valid_mask @ B ) ) ) ).

% upper_valid_aux
thf(fact_244_upper__valid,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( A
          = ( add_ma6586698345353345811t_char @ B @ C ) )
       => ( ( valid_mask @ B )
          & ( valid_mask @ C ) ) ) ) ).

% upper_valid
thf(fact_245_mult__distr__masks,axiom,
    ! [A: prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ A @ ( add_ma6586698345353345811t_char @ B @ C ) )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A @ B ) @ ( multiply_mask @ A @ C ) ) ) ).

% mult_distr_masks
thf(fact_246_add__masks_Oelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa: produc1457211279475724562t_char > prat,Xb: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( padd @ ( X @ Xb ) @ ( Xa @ Xb ) ) ) ) ).

% add_masks.elims
thf(fact_247_add__masks_Osimps,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [Pi6: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char] : ( padd @ ( Pi6 @ Hl2 ) @ ( Pi @ Hl2 ) ) ) ) ).

% add_masks.simps
thf(fact_248_const__sum__mask__greater,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ A @ B )
        = ( add_ma6586698345353345811t_char @ C @ D ) )
     => ( ( greate7680731506090375811t_char @ A @ C )
       => ( greate7680731506090375811t_char @ D @ B ) ) ) ).

% const_sum_mask_greater
thf(fact_249_greater__mask__decomp,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( greate7680731506090375811t_char @ A @ ( add_ma6586698345353345811t_char @ B @ C ) )
     => ? [A1: produc1457211279475724562t_char > prat,A2: produc1457211279475724562t_char > prat] :
          ( ( A
            = ( add_ma6586698345353345811t_char @ A1 @ A2 ) )
          & ( greate7680731506090375811t_char @ A1 @ B )
          & ( greate7680731506090375811t_char @ A2 @ C ) ) ) ).

% greater_mask_decomp
thf(fact_250_greater__mask__def,axiom,
    ( greate7680731506090375811t_char
    = ( ^ [Pi6: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat] :
        ? [R: produc1457211279475724562t_char > prat] :
          ( Pi6
          = ( add_ma6586698345353345811t_char @ Pi @ R ) ) ) ) ).

% greater_mask_def
thf(fact_251_valid__state__decompose,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ A @ B ) @ H ) )
     => ( valid_state @ ( produc74620467203698198on_val @ A @ H ) ) ) ).

% valid_state_decompose
thf(fact_252_mult__add__states,axiom,
    ! [A: prat,B: prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ ( padd @ A @ B ) @ Pi3 )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A @ Pi3 ) @ ( multiply_mask @ B @ Pi3 ) ) ) ).

% mult_add_states
thf(fact_253_compatible__same__mask,axiom,
    ! [A: produc1457211279475724562t_char > prat,W: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ ( add_ma6586698345353345811t_char @ A @ W ) )
     => ( W
        = ( comp_min_mask @ A @ W ) ) ) ).

% compatible_same_mask
thf(fact_254_valid__mask__add__comp__min,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( valid_mask @ ( add_ma6586698345353345811t_char @ ( comp_min_mask @ B @ A ) @ B ) ) ) ) ).

% valid_mask_add_comp_min
thf(fact_255_valid__mask_Opelims_I3_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
           => ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl3 ) )
              & ! [F2: list_char] :
                  ( ( X @ ( produc120197956887798346t_char @ null_nat @ F2 ) )
                  = pnone ) ) ) ) ) ).

% valid_mask.pelims(3)
thf(fact_256_compatibleI,axiom,
    ! [A: state,B: state] :
      ( ( compatible_heaps @ ( get_h @ A ) @ ( get_h @ B ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ A ) @ ( get_m @ B ) ) )
       => ( defined @ A @ B ) ) ) ).

% compatibleI
thf(fact_257_add__acc__uni__mask,axiom,
    ( add_ac6043276672051819257t_char
    = ( ^ [Pi: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char,P2: prat] : ( add_ma6586698345353345811t_char @ Pi @ ( uni_ma6578582744724537101t_char @ Hl2 @ P2 ) ) ) ) ).

% add_acc_uni_mask
thf(fact_258_fstI,axiom,
    ! [X: produc3142500478612311029_state,Y: option_state,Z2: option_state] :
      ( ( X
        = ( produc9160152616361873709_state @ Y @ Z2 ) )
     => ( ( produc3900939990612242713_state @ X )
        = Y ) ) ).

% fstI
thf(fact_259_fstI,axiom,
    ! [X: produc4844402304972151915_state,Y: prat,Z2: state] :
      ( ( X
        = ( produc6205719116230455971_state @ Y @ Z2 ) )
     => ( ( produc6030790797199838863_state @ X )
        = Y ) ) ).

% fstI
thf(fact_260_fstI,axiom,
    ! [X: produc6251377953716854561_state,Y: prat,Z2: set_state] :
      ( ( X
        = ( produc9080284787853255769_state @ Y @ Z2 ) )
     => ( ( produc7279835715735703621_state @ X )
        = Y ) ) ).

% fstI
thf(fact_261_fstI,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat,Z2: list_char] :
      ( ( X
        = ( produc120197956887798346t_char @ Y @ Z2 ) )
     => ( ( produc6204653154488278070t_char @ X )
        = Y ) ) ).

% fstI
thf(fact_262_fstI,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat,Z2: produc1457211279475724562t_char > option_val] :
      ( ( X
        = ( produc74620467203698198on_val @ Y @ Z2 ) )
     => ( ( produc5239619271231976746on_val @ X )
        = Y ) ) ).

% fstI
thf(fact_263_eq__fst__iff,axiom,
    ! [A: option_state,P: produc3142500478612311029_state] :
      ( ( A
        = ( produc3900939990612242713_state @ P ) )
      = ( ? [B2: option_state] :
            ( P
            = ( produc9160152616361873709_state @ A @ B2 ) ) ) ) ).

% eq_fst_iff
thf(fact_264_eq__fst__iff,axiom,
    ! [A: prat,P: produc4844402304972151915_state] :
      ( ( A
        = ( produc6030790797199838863_state @ P ) )
      = ( ? [B2: state] :
            ( P
            = ( produc6205719116230455971_state @ A @ B2 ) ) ) ) ).

% eq_fst_iff
thf(fact_265_eq__fst__iff,axiom,
    ! [A: prat,P: produc6251377953716854561_state] :
      ( ( A
        = ( produc7279835715735703621_state @ P ) )
      = ( ? [B2: set_state] :
            ( P
            = ( produc9080284787853255769_state @ A @ B2 ) ) ) ) ).

% eq_fst_iff
thf(fact_266_eq__fst__iff,axiom,
    ! [A: nat,P: produc1457211279475724562t_char] :
      ( ( A
        = ( produc6204653154488278070t_char @ P ) )
      = ( ? [B2: list_char] :
            ( P
            = ( produc120197956887798346t_char @ A @ B2 ) ) ) ) ).

% eq_fst_iff
thf(fact_267_eq__fst__iff,axiom,
    ! [A: produc1457211279475724562t_char > prat,P: produc9003781588162623004on_val] :
      ( ( A
        = ( produc5239619271231976746on_val @ P ) )
      = ( ? [B2: produc1457211279475724562t_char > option_val] :
            ( P
            = ( produc74620467203698198on_val @ A @ B2 ) ) ) ) ).

% eq_fst_iff
thf(fact_268_valid__stateI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_mask @ Pi3 )
     => ( ! [Hl3: produc1457211279475724562t_char] :
            ( ( ppos @ ( Pi3 @ Hl3 ) )
           => ( ( H @ Hl3 )
             != none_val ) )
       => ( valid_state @ ( produc74620467203698198on_val @ Pi3 @ H ) ) ) ) ).

% valid_stateI
thf(fact_269_same__fstI,axiom,
    ! [P4: prat > $o,X: prat,Y6: state,Y: state,R3: prat > set_Pr1785066336555260981_state] :
      ( ( P4 @ X )
     => ( ( member753036827967488894_state @ ( produc544653723139640077_state @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member14790466581074960_state @ ( produc8801277691740291671_state @ ( produc6205719116230455971_state @ X @ Y6 ) @ ( produc6205719116230455971_state @ X @ Y ) ) @ ( same_fst_prat_state @ P4 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_270_same__fstI,axiom,
    ! [P4: prat > $o,X: prat,Y6: set_state,Y: set_state,R3: prat > set_Pr5618112136499017889_state] :
      ( ( P4 @ X )
     => ( ( member1976142906092959210_state @ ( produc1834047914073684089_state @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member647386464819295632_state @ ( produc516693425924439767_state @ ( produc9080284787853255769_state @ X @ Y6 ) @ ( produc9080284787853255769_state @ X @ Y ) ) @ ( same_f5333510722715586990_state @ P4 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_271_same__fstI,axiom,
    ! [P4: nat > $o,X: nat,Y6: list_char,Y: list_char,R3: nat > set_Pr4480099295215233283t_char] :
      ( ( P4 @ X )
     => ( ( member6023471406134104908t_char @ ( produc1606739095562851931t_char @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member151853725258021968t_char @ ( produc8192741843292627479t_char @ ( produc120197956887798346t_char @ X @ Y6 ) @ ( produc120197956887798346t_char @ X @ Y ) ) @ ( same_f652031872680891423t_char @ P4 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_272_same__fstI,axiom,
    ! [P4: ( produc1457211279475724562t_char > prat ) > $o,X: produc1457211279475724562t_char > prat,Y6: produc1457211279475724562t_char > option_val,Y: produc1457211279475724562t_char > option_val,R3: ( produc1457211279475724562t_char > prat ) > set_Pr4698884584343881589on_val] :
      ( ( P4 @ X )
     => ( ( member5502714215428086462on_val @ ( produc8008623296994167373on_val @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ X @ Y6 ) @ ( produc74620467203698198on_val @ X @ Y ) ) @ ( same_f8138205353876899841on_val @ P4 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_273_same__fstI,axiom,
    ! [P4: option_state > $o,X: option_state,Y6: option_state,Y: option_state,R3: option_state > set_Pr1688445902015331925_state] :
      ( ( P4 @ X )
     => ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Y6 @ Y ) @ ( R3 @ X ) )
       => ( member2361837818702807184_state @ ( produc2397313312270560215_state @ ( produc9160152616361873709_state @ X @ Y6 ) @ ( produc9160152616361873709_state @ X @ Y ) ) @ ( same_f2704544105346032002_state @ P4 @ R3 ) ) ) ) ).

% same_fstI
thf(fact_274_add__masks_Opelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa: produc1457211279475724562t_char > prat,Xb: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa @ Xb )
        = Y )
     => ( ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa @ Xb ) ) )
       => ~ ( ( Y
              = ( padd @ ( X @ Xb ) @ ( Xa @ Xb ) ) )
           => ~ ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa @ Xb ) ) ) ) ) ) ).

% add_masks.pelims
thf(fact_275_get__m_Osimps,axiom,
    ( get_m
    = ( ^ [A3: state] : ( produc5239619271231976746on_val @ ( rep_state @ A3 ) ) ) ) ).

% get_m.simps
thf(fact_276_get__m_Oelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X )
        = Y )
     => ( Y
        = ( produc5239619271231976746on_val @ ( rep_state @ X ) ) ) ) ).

% get_m.elims
thf(fact_277_get__pre_I2_J,axiom,
    ( get_m
    = ( ^ [X3: state] : ( produc5239619271231976746on_val @ ( rep_state @ X3 ) ) ) ) ).

% get_pre(2)
thf(fact_278_larger__heap__comp,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( compatible_heaps @ A @ C )
       => ( compatible_heaps @ B @ C ) ) ) ).

% larger_heap_comp
thf(fact_279_larger__compatible__sum__heaps,axiom,
    ! [A: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,Y: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ X )
     => ( ( larger1532547405891354081ar_val @ B @ Y )
       => ( ( compatible_heaps @ A @ B )
         => ( compatible_heaps @ X @ Y ) ) ) ) ).

% larger_compatible_sum_heaps
thf(fact_280_valid__heap__def,axiom,
    ( valid_heap
    = ( ^ [Pi: produc1457211279475724562t_char > prat,H4: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi @ Hl2 ) )
         => ( ( H4 @ Hl2 )
           != none_val ) ) ) ) ).

% valid_heap_def
thf(fact_281_valid__heapI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ! [Hl3: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi3 @ Hl3 ) )
         => ( ( H @ Hl3 )
           != none_val ) )
     => ( valid_heap @ Pi3 @ H ) ) ).

% valid_heapI
thf(fact_282_PartialHeapSA_Ostable__def,axiom,
    ( stable
    = ( ^ [Phi: state] :
        ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi @ Hl2 ) )
          = ( ( get_h @ Phi @ Hl2 )
           != none_val ) ) ) ) ).

% PartialHeapSA.stable_def
thf(fact_283_stableI,axiom,
    ! [Phi2: state] :
      ( ! [Hl3: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi2 @ Hl3 ) )
          = ( ( get_h @ Phi2 @ Hl3 )
           != none_val ) )
     => ( stable @ Phi2 ) ) ).

% stableI
thf(fact_284_empty__heap__def,axiom,
    ( empty_7512026568161686585ar_val
    = ( ^ [Hl2: produc1457211279475724562t_char] : none_val ) ) ).

% empty_heap_def
thf(fact_285_pre__get__m_Oelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat] :
      ( ( ( pre_ge2740421702909910421t_char @ X )
        = Y )
     => ( Y
        = ( produc6204653154488278070t_char @ X ) ) ) ).

% pre_get_m.elims
thf(fact_286_pre__get__m_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat] :
      ( ( ( pre_ge8481574585653477131on_val @ X )
        = Y )
     => ( Y
        = ( produc5239619271231976746on_val @ X ) ) ) ).

% pre_get_m.elims
thf(fact_287_pre__get__m_Osimps,axiom,
    pre_ge2740421702909910421t_char = produc6204653154488278070t_char ).

% pre_get_m.simps
thf(fact_288_pre__get__m_Osimps,axiom,
    pre_ge8481574585653477131on_val = produc5239619271231976746on_val ).

% pre_get_m.simps
thf(fact_289_pre__get__m_Opelims,axiom,
    ! [X: produc1317171644805857433on_val,Y: produc9003781588162623004on_val] :
      ( ( ( pre_ge6899797224320663452on_val @ X )
        = Y )
     => ( ( accp_P6797916352740768290on_val @ pre_ge1694281482089598673on_val @ X )
       => ~ ( ( Y
              = ( produc3129717363260770749on_val @ X ) )
           => ~ ( accp_P6797916352740768290on_val @ pre_ge1694281482089598673on_val @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_290_pre__get__m_Opelims,axiom,
    ! [X: produc4844402304972151915_state,Y: prat] :
      ( ( ( pre_get_m_prat_state @ X )
        = Y )
     => ( ( accp_P6233459008282737652_state @ pre_ge6835382860682234787_state @ X )
       => ~ ( ( Y
              = ( produc6030790797199838863_state @ X ) )
           => ~ ( accp_P6233459008282737652_state @ pre_ge6835382860682234787_state @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_291_pre__get__m_Opelims,axiom,
    ! [X: produc6251377953716854561_state,Y: prat] :
      ( ( ( pre_ge1435879308799382564_state @ X )
        = Y )
     => ( ( accp_P6554740477754186410_state @ pre_ge4013444835548200281_state @ X )
       => ~ ( ( Y
              = ( produc7279835715735703621_state @ X ) )
           => ~ ( accp_P6554740477754186410_state @ pre_ge4013444835548200281_state @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_292_pre__get__m_Opelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat] :
      ( ( ( pre_ge2740421702909910421t_char @ X )
        = Y )
     => ( ( accp_P8892882183480857371t_char @ pre_ge8748858970926381898t_char @ X )
       => ~ ( ( Y
              = ( produc6204653154488278070t_char @ X ) )
           => ~ ( accp_P8892882183480857371t_char @ pre_ge8748858970926381898t_char @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_293_pre__get__m_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat] :
      ( ( ( pre_ge8481574585653477131on_val @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ pre_ge4462515927930180886on_val @ X )
       => ~ ( ( Y
              = ( produc5239619271231976746on_val @ X ) )
           => ~ ( accp_P4405556307444930259on_val @ pre_ge4462515927930180886on_val @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_294_valid__state_Opelims_I3_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi2 @ H2 ) )
               => ( ( valid_mask @ Pi2 )
                  & ( valid_heap @ Pi2 @ H2 ) ) ) ) ) ) ).

% valid_state.pelims(3)
thf(fact_295_valid__state_Opelims_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( valid_state @ X )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi2 @ H2 ) )
               => ~ ( ( valid_mask @ Pi2 )
                    & ( valid_heap @ Pi2 @ H2 ) ) ) ) ) ) ).

% valid_state.pelims(2)
thf(fact_296_valid__state_Opelims_I1_J,axiom,
    ! [X: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
             => ( ( Y
                  = ( ( valid_mask @ Pi2 )
                    & ( valid_heap @ Pi2 @ H2 ) ) )
               => ~ ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi2 @ H2 ) ) ) ) ) ) ).

% valid_state.pelims(1)
thf(fact_297_plus__ab__defined,axiom,
    ! [Phi2: state,Phi4: state] :
      ( ( ( plus @ Phi2 @ Phi4 )
       != none_state )
      = ( ( compatible_heaps @ ( get_h @ Phi2 ) @ ( get_h @ Phi4 ) )
        & ( valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ Phi2 ) @ ( get_m @ Phi4 ) ) ) ) ) ).

% plus_ab_defined
thf(fact_298_valid__pre__unit,axiom,
    valid_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ).

% valid_pre_unit
thf(fact_299_fold__atLeastAtMost__nat_Ocases,axiom,
    ! [X: produc8146610533011921512t_char] :
      ~ ! [F2: nat > list_char > list_char,A7: nat,B6: nat,Acc: list_char] :
          ( X
         != ( produc7013538429079112736t_char @ F2 @ ( produc8776329868854908137t_char @ A7 @ ( produc120197956887798346t_char @ B6 @ Acc ) ) ) ) ).

% fold_atLeastAtMost_nat.cases
thf(fact_300_GreatestI2__order,axiom,
    ! [P4: set_state > $o,X: set_state,Q: set_state > $o] :
      ( ( P4 @ X )
     => ( ! [Y3: set_state] :
            ( ( P4 @ Y3 )
           => ( ord_le2494988322063910608_state @ Y3 @ X ) )
       => ( ! [X2: set_state] :
              ( ( P4 @ X2 )
             => ( ! [Y7: set_state] :
                    ( ( P4 @ Y7 )
                   => ( ord_le2494988322063910608_state @ Y7 @ X2 ) )
               => ( Q @ X2 ) ) )
         => ( Q @ ( order_2642746146112740183_state @ P4 ) ) ) ) ) ).

% GreatestI2_order
thf(fact_301_commutative,axiom,
    ( plus
    = ( ^ [A3: state,B2: state] : ( plus @ B2 @ A3 ) ) ) ).

% commutative
thf(fact_302_PartialSA_Odefined__def,axiom,
    ( defined
    = ( ^ [A3: state,B2: state] :
          ( ( plus @ A3 @ B2 )
         != none_state ) ) ) ).

% PartialSA.defined_def
thf(fact_303_valid__empty,axiom,
    valid_mask @ empty_3446695950879338768t_char ).

% valid_empty
thf(fact_304_minus__empty,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( Pi3
      = ( add_ma6586698345353345811t_char @ Pi3 @ empty_3446695950879338768t_char ) ) ).

% minus_empty
thf(fact_305_empty__mask_Osimps,axiom,
    ( empty_3446695950879338768t_char
    = ( ^ [Hl2: produc1457211279475724562t_char] : pnone ) ) ).

% empty_mask.simps
thf(fact_306_empty__mask_Oelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X )
        = Y )
     => ( Y = pnone ) ) ).

% empty_mask.elims
thf(fact_307_Greatest__equality,axiom,
    ! [P4: set_state > $o,X: set_state] :
      ( ( P4 @ X )
     => ( ! [Y3: set_state] :
            ( ( P4 @ Y3 )
           => ( ord_le2494988322063910608_state @ Y3 @ X ) )
       => ( ( order_2642746146112740183_state @ P4 )
          = X ) ) ) ).

% Greatest_equality
thf(fact_308_empty__mask_Opelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X )
        = Y )
     => ( ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_309_empty__mask_Opelims,axiom,
    ! [X: produc1317171644805857433on_val,Y: prat] :
      ( ( ( empty_4129289814623480215on_val @ X )
        = Y )
     => ( ( accp_P6797916352740768290on_val @ empty_1698368654852286560on_val @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6797916352740768290on_val @ empty_1698368654852286560on_val @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_310_empty__mask_Opelims,axiom,
    ! [X: produc4844402304972151915_state,Y: prat] :
      ( ( ( empty_3913122416104905065_state @ X )
        = Y )
     => ( ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_311_empty__mask_Opelims,axiom,
    ! [X: produc6251377953716854561_state,Y: prat] :
      ( ( ( empty_5541330147480151071_state @ X )
        = Y )
     => ( ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_312_empty__mask_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: prat] :
      ( ( ( empty_6102255041883331742on_val @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_313_empty__mask_Opelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: prat] :
      ( ( ( empty_6616431780912394577r_prat @ X )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_314_unit__def,axiom,
    ( unit
    = ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ) ) ).

% unit_def
thf(fact_315_core__def,axiom,
    ( core
    = ( ^ [Phi: state] : ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ ( get_h @ Phi ) ) ) ) ) ).

% core_def
thf(fact_316_in__cwand,axiom,
    ! [A5: set_state,W: state,B4: set_state] :
      ( ! [A7: state,X2: state] :
          ( ( ( member_state @ A7 @ A5 )
            & ( ( some_state @ X2 )
              = ( plus @ ( r @ A7 @ W ) @ A7 ) ) )
         => ( member_state @ X2 @ B4 ) )
     => ( member_state @ W @ ( cwand @ A5 @ B4 ) ) ) ).

% in_cwand
thf(fact_317_unit__charact_I1_J,axiom,
    ( ( get_h @ unit )
    = empty_7512026568161686585ar_val ) ).

% unit_charact(1)
thf(fact_318_PartialSA_Ointuitionistic__def,axiom,
    ! [A5: state > $o] :
      ( ( packag8361946002163212404_state @ plus @ A5 )
      = ( ! [Phi5: state,Phi: state] :
            ( ( ( greater @ Phi5 @ Phi )
              & ( A5 @ Phi ) )
           => ( A5 @ Phi5 ) ) ) ) ).

% PartialSA.intuitionistic_def
thf(fact_319_PartialSA_Omono__prop__def,axiom,
    ! [P4: state > $o] :
      ( ( sep_mono_prop_state @ plus @ P4 )
      = ( ! [X3: state,Y5: state] :
            ( ( ( greater @ Y5 @ X3 )
              & ( P4 @ X3 ) )
           => ( P4 @ Y5 ) ) ) ) ).

% PartialSA.mono_prop_def
thf(fact_320_core__max,axiom,
    ! [X: state,C: state] :
      ( ( ( some_state @ X )
        = ( plus @ X @ C ) )
     => ? [R4: state] :
          ( ( some_state @ ( core @ X ) )
          = ( plus @ C @ R4 ) ) ) ).

% core_max
thf(fact_321_core__sum,axiom,
    ! [C: state,A: state,B: state] :
      ( ( ( some_state @ C )
        = ( plus @ A @ B ) )
     => ( ( some_state @ ( core @ C ) )
        = ( plus @ ( core @ A ) @ ( core @ B ) ) ) ) ).

% core_sum
thf(fact_322_cancellative,axiom,
    ! [A: state,B: state,X: state,Y: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ X ) )
     => ( ( ( some_state @ A )
          = ( plus @ B @ Y ) )
       => ( ( ( core @ X )
            = ( core @ Y ) )
         => ( X = Y ) ) ) ) ).

% cancellative
thf(fact_323_core__is__pure,axiom,
    ! [X: state] :
      ( ( some_state @ ( core @ X ) )
      = ( plus @ ( core @ X ) @ ( core @ X ) ) ) ).

% core_is_pure
thf(fact_324_unit__neutral,axiom,
    ( some_state
    = ( ^ [A3: state] : ( plus @ A3 @ unit ) ) ) ).

% unit_neutral
thf(fact_325_core__is__smaller,axiom,
    ( some_state
    = ( ^ [X3: state] : ( plus @ X3 @ ( core @ X3 ) ) ) ) ).

% core_is_smaller
thf(fact_326_PartialSA_Ounit__core,axiom,
    ( ( core @ unit )
    = unit ) ).

% PartialSA.unit_core
thf(fact_327_PartialSA_Oextract__core,axiom,
    ! [B: state,A: state,X: state] :
      ( ( ( ( some_state @ B )
          = ( plus @ A @ X ) )
        & ( greater @ X @ ( core @ B ) ) )
     => ( ( core @ X )
        = ( core @ B ) ) ) ).

% PartialSA.extract_core
thf(fact_328_PartialSA_Ominus__exists,axiom,
    ! [B: state,A: state] :
      ( ( greater @ B @ A )
     => ? [X2: state] :
          ( ( ( some_state @ B )
            = ( plus @ A @ X2 ) )
          & ( greater @ X2 @ ( core @ B ) ) ) ) ).

% PartialSA.minus_exists
thf(fact_329_PartialSA_Ominus__unique,axiom,
    ! [B: state,A: state,X: state,Y: state] :
      ( ( ( ( some_state @ B )
          = ( plus @ A @ X ) )
        & ( greater @ X @ ( core @ B ) ) )
     => ( ( ( ( some_state @ B )
            = ( plus @ A @ Y ) )
          & ( greater @ Y @ ( core @ B ) ) )
       => ( X = Y ) ) ) ).

% PartialSA.minus_unique
thf(fact_330_PartialSA_Osmaller__than__core,axiom,
    ! [Y: state,X: state,Z2: state] :
      ( ( greater @ Y @ X )
     => ( ( ( some_state @ Z2 )
          = ( plus @ X @ ( core @ Y ) ) )
       => ( ( core @ Z2 )
          = ( core @ Y ) ) ) ) ).

% PartialSA.smaller_than_core
thf(fact_331_PartialSA_Obigger__core__sum__defined,axiom,
    ! [A: state,B: state] :
      ( ( greater @ ( core @ A ) @ B )
     => ( ( some_state @ A )
        = ( plus @ A @ B ) ) ) ).

% PartialSA.bigger_core_sum_defined
thf(fact_332_PartialSA_Ogreater__than__sum__exists,axiom,
    ! [A: state,B: state,B1: state,B22: state] :
      ( ( greater @ A @ B )
     => ( ( ( some_state @ B )
          = ( plus @ B1 @ B22 ) )
       => ? [R4: state] :
            ( ( ( some_state @ A )
              = ( plus @ R4 @ B22 ) )
            & ( greater @ ( core @ R4 ) @ ( core @ A ) )
            & ( greater @ R4 @ B1 ) ) ) ) ).

% PartialSA.greater_than_sum_exists
thf(fact_333_compatible__options_Ocases,axiom,
    ! [X: produc3142500478612311029_state] :
      ( ! [A7: state,B6: state] :
          ( X
         != ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
     => ( ! [Uv: option_state] :
            ( X
           != ( produc9160152616361873709_state @ none_state @ Uv ) )
       => ~ ! [Uu: option_state] :
              ( X
             != ( produc9160152616361873709_state @ Uu @ none_state ) ) ) ) ).

% compatible_options.cases
thf(fact_334_compatible__options_Ocases,axiom,
    ! [X: produc5122021904355189735on_val] :
      ( ! [A7: val,B6: val] :
          ( X
         != ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
     => ( ! [Uv: option_val] :
            ( X
           != ( produc904852209897547607on_val @ none_val @ Uv ) )
       => ~ ! [Uu: option_val] :
              ( X
             != ( produc904852209897547607on_val @ Uu @ none_val ) ) ) ) ).

% compatible_options.cases
thf(fact_335_positivity,axiom,
    ! [A: state,B: state,C: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ C ) )
     => ( ( ( some_state @ C )
          = ( plus @ C @ C ) )
       => ( ( some_state @ A )
          = ( plus @ A @ A ) ) ) ) ).

% positivity
thf(fact_336_asso1,axiom,
    ! [A: state,B: state,Ab: state,C: state,Bc: state] :
      ( ( ( ( plus @ A @ B )
          = ( some_state @ Ab ) )
        & ( ( plus @ B @ C )
          = ( some_state @ Bc ) ) )
     => ( ( plus @ Ab @ C )
        = ( plus @ A @ Bc ) ) ) ).

% asso1
thf(fact_337_PartialSA_Ocore__mono,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( greater @ ( core @ A ) @ ( core @ B ) ) ) ).

% PartialSA.core_mono
thf(fact_338_core__defined_I1_J,axiom,
    ! [Phi2: state] :
      ( ( get_h @ ( core @ Phi2 ) )
      = ( get_h @ Phi2 ) ) ).

% core_defined(1)
thf(fact_339_PartialSA_Osplus_Ocases,axiom,
    ! [X: produc3142500478612311029_state] :
      ( ! [Uu: option_state] :
          ( X
         != ( produc9160152616361873709_state @ none_state @ Uu ) )
     => ( ! [V: state] :
            ( X
           != ( produc9160152616361873709_state @ ( some_state @ V ) @ none_state ) )
       => ~ ! [A7: state,B6: state] :
              ( X
             != ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) ).

% PartialSA.splus.cases
thf(fact_340_larger__heap__def,axiom,
    ( larger1532547405891354081ar_val
    = ( ^ [H5: produc1457211279475724562t_char > option_val,H4: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char,X3: val] :
          ( ( ( H4 @ Hl2 )
            = ( some_val @ X3 ) )
         => ( ( H5 @ Hl2 )
            = ( some_val @ X3 ) ) ) ) ) ).

% larger_heap_def
thf(fact_341_larger__heapI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H6: produc1457211279475724562t_char > option_val] :
      ( ! [Hl3: produc1457211279475724562t_char,X2: val] :
          ( ( ( H @ Hl3 )
            = ( some_val @ X2 ) )
         => ( ( H6 @ Hl3 )
            = ( some_val @ X2 ) ) )
     => ( larger1532547405891354081ar_val @ H6 @ H ) ) ).

% larger_heapI
thf(fact_342_PartialSA_Ounit__smaller,axiom,
    ! [Phi2: state] : ( greater @ Phi2 @ unit ) ).

% PartialSA.unit_smaller
thf(fact_343_stable__unit,axiom,
    stable @ unit ).

% stable_unit
thf(fact_344_PartialSA_Obigger__sum,axiom,
    ! [Phi2: state,A: state,B: state,Phi4: state] :
      ( ( ( some_state @ Phi2 )
        = ( plus @ A @ B ) )
     => ( ( greater @ Phi4 @ Phi2 )
       => ? [B7: state] :
            ( ( greater @ B7 @ B )
            & ( ( some_state @ Phi4 )
              = ( plus @ A @ B7 ) ) ) ) ) ).

% PartialSA.bigger_sum
thf(fact_345_PartialSA_Ogreater__def,axiom,
    ( greater
    = ( ^ [A3: state,B2: state] :
        ? [C3: state] :
          ( ( some_state @ A3 )
          = ( plus @ B2 @ C3 ) ) ) ) ).

% PartialSA.greater_def
thf(fact_346_PartialSA_Ogreater__equiv,axiom,
    ( greater
    = ( ^ [A3: state,B2: state] :
        ? [C3: state] :
          ( ( some_state @ A3 )
          = ( plus @ C3 @ B2 ) ) ) ) ).

% PartialSA.greater_equiv
thf(fact_347_PartialSA_Oaddition__bigger,axiom,
    ! [A6: state,A: state,X4: state,B: state,X: state] :
      ( ( greater @ A6 @ A )
     => ( ( ( some_state @ X4 )
          = ( plus @ A6 @ B ) )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( greater @ X4 @ X ) ) ) ) ).

% PartialSA.addition_bigger
thf(fact_348_PartialSA_Obigger__sum__smaller,axiom,
    ! [C: state,A: state,B: state,A6: state] :
      ( ( ( some_state @ C )
        = ( plus @ A @ B ) )
     => ( ( greater @ A @ A6 )
       => ? [B7: state] :
            ( ( greater @ B7 @ B )
            & ( ( some_state @ C )
              = ( plus @ A6 @ B7 ) ) ) ) ) ).

% PartialSA.bigger_sum_smaller
thf(fact_349_stable__sum,axiom,
    ! [A: state,B: state,X: state] :
      ( ( stable @ A )
     => ( ( stable @ B )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( stable @ X ) ) ) ) ).

% stable_sum
thf(fact_350_PartialSA_Osmaller__compatible__core,axiom,
    ! [Y: state,X: state] :
      ( ( greater @ Y @ X )
     => ( defined @ X @ ( core @ Y ) ) ) ).

% PartialSA.smaller_compatible_core
thf(fact_351_PartialSA_Odefined__sum__move,axiom,
    ! [A: state,B: state,X: state,Y: state,A6: state] :
      ( ( defined @ A @ B )
     => ( ( ( some_state @ B )
          = ( plus @ X @ Y ) )
       => ( ( ( some_state @ A6 )
            = ( plus @ A @ X ) )
         => ( defined @ A6 @ Y ) ) ) ) ).

% PartialSA.defined_sum_move
thf(fact_352_PartialSA_Oadd__set__elem,axiom,
    ! [Phi2: state,A5: set_state,B4: set_state] :
      ( ( member_state @ Phi2 @ ( add_set @ A5 @ B4 ) )
      = ( ? [A3: state,B2: state] :
            ( ( ( some_state @ Phi2 )
              = ( plus @ A3 @ B2 ) )
            & ( member_state @ A3 @ A5 )
            & ( member_state @ B2 @ B4 ) ) ) ) ).

% PartialSA.add_set_elem
thf(fact_353_PartialSA_Ox__elem__set__product,axiom,
    ! [X: state,A5: set_state,B4: set_state] :
      ( ( member_state @ X @ ( add_set @ A5 @ B4 ) )
      = ( ? [A3: state,B2: state] :
            ( ( member_state @ A3 @ A5 )
            & ( member_state @ B2 @ B4 )
            & ( ( some_state @ X )
              = ( plus @ A3 @ B2 ) ) ) ) ) ).

% PartialSA.x_elem_set_product
thf(fact_354_asso2,axiom,
    ! [A: state,B: state,Ab: state,C: state] :
      ( ( ( ( plus @ A @ B )
          = ( some_state @ Ab ) )
        & ( ( plus @ B @ C )
          = none_state ) )
     => ( ( plus @ Ab @ C )
        = none_state ) ) ).

% asso2
thf(fact_355_PartialSA_Oasso3,axiom,
    ! [A: state,B: state,C: state,Bc: state] :
      ( ( ( plus @ A @ B )
        = none_state )
     => ( ( ( plus @ B @ C )
          = ( some_state @ Bc ) )
       => ( ( plus @ A @ Bc )
          = none_state ) ) ) ).

% PartialSA.asso3
thf(fact_356_core__defined_I2_J,axiom,
    ! [Phi2: state] :
      ( ( get_m @ ( core @ Phi2 ) )
      = empty_3446695950879338768t_char ) ).

% core_defined(2)
thf(fact_357_wandI,axiom,
    ! [A5: set_state,W: state,B4: set_state] :
      ( ! [A7: state,X2: state] :
          ( ( ( member_state @ A7 @ A5 )
            & ( ( some_state @ X2 )
              = ( plus @ A7 @ W ) ) )
         => ( member_state @ X2 @ B4 ) )
     => ( member_state @ W @ ( wand @ A5 @ B4 ) ) ) ).

% wandI
thf(fact_358_plus__charact_I1_J,axiom,
    ! [A: state,B: state,X: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ X ) )
     => ( ( get_m @ X )
        = ( add_ma6586698345353345811t_char @ ( get_m @ A ) @ ( get_m @ B ) ) ) ) ).

% plus_charact(1)
thf(fact_359_unit__charact_I2_J,axiom,
    ( ( get_m @ unit )
    = empty_3446695950879338768t_char ) ).

% unit_charact(2)
thf(fact_360_PartialSA_Omono__propI,axiom,
    ! [P4: state > $o] :
      ( ! [X2: state,Y3: state] :
          ( ( ( greater @ Y3 @ X2 )
            & ( P4 @ X2 ) )
         => ( P4 @ Y3 ) )
     => ( sep_mono_prop_state @ plus @ P4 ) ) ).

% PartialSA.mono_propI
thf(fact_361_get__m_Opelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X )
        = Y )
     => ( ( accp_state @ get_m_rel @ X )
       => ~ ( ( Y
              = ( produc5239619271231976746on_val @ ( rep_state @ X ) ) )
           => ~ ( accp_state @ get_m_rel @ X ) ) ) ) ).

% get_m.pelims
thf(fact_362_plus__def,axiom,
    ( plus
    = ( ^ [A3: state,B2: state] : ( if_option_state @ ( compatible @ ( rep_state @ A3 ) @ ( rep_state @ B2 ) ) @ ( some_state @ ( abs_state @ ( add_states @ ( rep_state @ A3 ) @ ( rep_state @ B2 ) ) ) ) @ none_state ) ) ) ).

% plus_def
thf(fact_363_PartialSA_Omono__transformer__def,axiom,
    ! [T2: state > state] :
      ( ( packag4817583915586052229_state @ plus @ unit @ T2 )
      = ( ! [Phi: state,Phi5: state] :
            ( ( greater @ Phi5 @ Phi )
           => ( greater @ ( T2 @ Phi5 ) @ ( T2 @ Phi ) ) )
        & ( ( T2 @ unit )
          = unit ) ) ) ).

% PartialSA.mono_transformer_def
thf(fact_364_PartialSA_Ominus__equiv__def,axiom,
    ! [B: state,A: state] :
      ( ( greater @ B @ A )
     => ( ( ( some_state @ B )
          = ( plus @ A @ ( minus @ B @ A ) ) )
        & ( greater @ ( minus @ B @ A ) @ ( core @ B ) ) ) ) ).

% PartialSA.minus_equiv_def
thf(fact_365_PartialSA_OminusI,axiom,
    ! [B: state,A: state,X: state] :
      ( ( ( some_state @ B )
        = ( plus @ A @ X ) )
     => ( ( greater @ X @ ( core @ B ) )
       => ( X
          = ( minus @ B @ A ) ) ) ) ).

% PartialSA.minusI
thf(fact_366_PartialSA_Obigger__the,axiom,
    ! [A: state,X4: state,Y: state,X: state] :
      ( ( ( some_state @ A )
        = ( plus @ X4 @ Y ) )
     => ( ( greater @ X4 @ X )
       => ( greater @ ( the_state @ ( plus @ ( core @ A ) @ X4 ) ) @ ( the_state @ ( plus @ ( core @ A ) @ X ) ) ) ) ) ).

% PartialSA.bigger_the
thf(fact_367_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ( compat2278460363914054422_state @ X @ Xa )
     => ( ! [A7: state] :
            ( ( X
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa
                  = ( some_state @ B6 ) )
               => ( A7 != B6 ) ) )
       => ( ( X != none_state )
         => ( Xa = none_state ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_368_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ( compat7209469420100717861ns_val @ X @ Xa )
     => ( ! [A7: val] :
            ( ( X
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa
                  = ( some_val @ B6 ) )
               => ( A7 != B6 ) ) )
       => ( ( X != none_val )
         => ( Xa = none_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_369_PartialSA_Ominus__core,axiom,
    ! [A: state,B: state] :
      ( ( core @ ( minus @ A @ B ) )
      = ( core @ A ) ) ).

% PartialSA.minus_core
thf(fact_370_PartialSA_Ominus__core__weaker,axiom,
    ! [A: state,B: state] :
      ( ( core @ ( minus @ A @ B ) )
      = ( minus @ ( core @ A ) @ ( core @ B ) ) ) ).

% PartialSA.minus_core_weaker
thf(fact_371_compatible__heapsI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H6: produc1457211279475724562t_char > option_val] :
      ( ! [Hl3: produc1457211279475724562t_char,A7: val,B6: val] :
          ( ( ( H @ Hl3 )
            = ( some_val @ A7 ) )
         => ( ( ( H6 @ Hl3 )
              = ( some_val @ B6 ) )
           => ( A7 = B6 ) ) )
     => ( compatible_heaps @ H @ H6 ) ) ).

% compatible_heapsI
thf(fact_372_PartialSA_Ogreater__minus__trans,axiom,
    ! [Y: state,X: state,A: state] :
      ( ( greater @ Y @ X )
     => ( ( greater @ X @ A )
       => ( greater @ ( minus @ Y @ A ) @ ( minus @ X @ A ) ) ) ) ).

% PartialSA.greater_minus_trans
thf(fact_373_PartialSA_Ominus__smaller,axiom,
    ! [X: state,A: state] :
      ( ( greater @ X @ A )
     => ( greater @ X @ ( minus @ X @ A ) ) ) ).

% PartialSA.minus_smaller
thf(fact_374_PartialSA_Ominus__default,axiom,
    ! [B: state,A: state] :
      ( ~ ( greater @ B @ A )
     => ( ( minus @ B @ A )
        = B ) ) ).

% PartialSA.minus_default
thf(fact_375_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ~ ( compat2278460363914054422_state @ X @ Xa )
     => ~ ! [A7: state] :
            ( ( X
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa
                  = ( some_state @ B6 ) )
               => ( A7 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_376_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X @ Xa )
     => ~ ! [A7: val] :
            ( ( X
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa
                  = ( some_val @ B6 ) )
               => ( A7 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_377_compatible__options_Osimps_I1_J,axiom,
    ! [A: state,B: state] :
      ( ( compat2278460363914054422_state @ ( some_state @ A ) @ ( some_state @ B ) )
      = ( A = B ) ) ).

% compatible_options.simps(1)
thf(fact_378_compatible__options_Osimps_I1_J,axiom,
    ! [A: val,B: val] :
      ( ( compat7209469420100717861ns_val @ ( some_val @ A ) @ ( some_val @ B ) )
      = ( A = B ) ) ).

% compatible_options.simps(1)
thf(fact_379_compatible__options_Osimps_I3_J,axiom,
    ! [Uu2: option_state] : ( compat2278460363914054422_state @ Uu2 @ none_state ) ).

% compatible_options.simps(3)
thf(fact_380_compatible__options_Osimps_I3_J,axiom,
    ! [Uu2: option_val] : ( compat7209469420100717861ns_val @ Uu2 @ none_val ) ).

% compatible_options.simps(3)
thf(fact_381_compatible__options_Osimps_I2_J,axiom,
    ! [Uv2: option_state] : ( compat2278460363914054422_state @ none_state @ Uv2 ) ).

% compatible_options.simps(2)
thf(fact_382_compatible__options_Osimps_I2_J,axiom,
    ! [Uv2: option_val] : ( compat7209469420100717861ns_val @ none_val @ Uv2 ) ).

% compatible_options.simps(2)
thf(fact_383_compatible__heaps__def,axiom,
    ( compatible_heaps
    = ( ^ [H4: produc1457211279475724562t_char > option_val,H5: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char] : ( compat7209469420100717861ns_val @ ( H4 @ Hl2 ) @ ( H5 @ Hl2 ) ) ) ) ).

% compatible_heaps_def
thf(fact_384_PartialSA_Ominus__equiv__def__any__elem,axiom,
    ! [X: state,A: state,B: state] :
      ( ( ( some_state @ X )
        = ( plus @ A @ B ) )
     => ( ( some_state @ ( minus @ X @ A ) )
        = ( plus @ B @ ( core @ X ) ) ) ) ).

% PartialSA.minus_equiv_def_any_elem
thf(fact_385_PartialSA_Oprove__last__completeness,axiom,
    ! [A6: state,A: state,Nf1: state,F22: state] :
      ( ( greater @ A6 @ A )
     => ( ( ( some_state @ A )
          = ( plus @ Nf1 @ F22 ) )
       => ( greater @ ( minus @ A6 @ Nf1 ) @ F22 ) ) ) ).

% PartialSA.prove_last_completeness
thf(fact_386_PartialSA_Ominus__and__plus,axiom,
    ! [Omega: state,Omega2: state,R2: state,A: state] :
      ( ( ( some_state @ Omega )
        = ( plus @ Omega2 @ R2 ) )
     => ( ( greater @ Omega2 @ A )
       => ( ( some_state @ ( minus @ Omega @ A ) )
          = ( plus @ ( minus @ Omega2 @ A ) @ R2 ) ) ) ) ).

% PartialSA.minus_and_plus
thf(fact_387_PartialSA_Ominus__bigger,axiom,
    ! [X: state,A: state,B: state] :
      ( ( ( some_state @ X )
        = ( plus @ A @ B ) )
     => ( greater @ ( minus @ X @ A ) @ B ) ) ).

% PartialSA.minus_bigger
thf(fact_388_PartialSA_Ominus__some,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( ( some_state @ A )
        = ( plus @ B @ ( minus @ A @ B ) ) ) ) ).

% PartialSA.minus_some
thf(fact_389_PartialSA_Ominus__sum,axiom,
    ! [A: state,B: state,C: state,X: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ C ) )
     => ( ( greater @ X @ A )
       => ( ( minus @ X @ A )
          = ( minus @ ( minus @ X @ B ) @ C ) ) ) ) ).

% PartialSA.minus_sum
thf(fact_390_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_state,Xa: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X @ Xa )
        = Y )
     => ( ! [A7: state] :
            ( ( X
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa
                  = ( some_state @ B6 ) )
               => ( Y
                  = ( A7 != B6 ) ) ) )
       => ( ( ( X = none_state )
           => ~ Y )
         => ~ ( ( Xa = none_state )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_391_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_val,Xa: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X @ Xa )
        = Y )
     => ( ! [A7: val] :
            ( ( X
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa
                  = ( some_val @ B6 ) )
               => ( Y
                  = ( A7 != B6 ) ) ) )
       => ( ( ( X = none_val )
           => ~ Y )
         => ~ ( ( Xa = none_val )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_392_PartialSA_Ovalid__package__setI,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( defined @ A7 @ U )
            & ( greater @ ( core @ A7 ) @ ( core @ U ) )
            & ( packag4817583915586052229_state @ plus @ unit @ T3 )
            & ( greater @ A7 @ ( core @ ( T3 @ F ) ) ) ) )
     => ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F ) ) ).

% PartialSA.valid_package_setI
thf(fact_393_compatible__options_Opelims_I2_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ( compat2278460363914054422_state @ X @ Xa )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa ) )
       => ( ! [A7: state] :
              ( ( X
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
                   => ( A7 != B6 ) ) ) )
         => ( ( ( X = none_state )
             => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa ) ) )
           => ~ ( ( Xa = none_state )
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ none_state ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_394_compatible__options_Opelims_I2_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ( compat7209469420100717861ns_val @ X @ Xa )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa ) )
       => ( ! [A7: val] :
              ( ( X
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
                   => ( A7 != B6 ) ) ) )
         => ( ( ( X = none_val )
             => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa ) ) )
           => ~ ( ( Xa = none_val )
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ none_val ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_395_compatible__options_Opelims_I1_J,axiom,
    ! [X: option_state,Xa: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X @ Xa )
        = Y )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa ) )
       => ( ! [A7: state] :
              ( ( X
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa
                    = ( some_state @ B6 ) )
                 => ( ( Y
                      = ( A7 = B6 ) )
                   => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) )
         => ( ( ( X = none_state )
             => ( Y
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa ) ) ) )
           => ~ ( ( Xa = none_state )
               => ( Y
                 => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ none_state ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_396_compatible__options_Opelims_I1_J,axiom,
    ! [X: option_val,Xa: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X @ Xa )
        = Y )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa ) )
       => ( ! [A7: val] :
              ( ( X
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa
                    = ( some_val @ B6 ) )
                 => ( ( Y
                      = ( A7 = B6 ) )
                   => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) ) ) ) )
         => ( ( ( X = none_val )
             => ( Y
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa ) ) ) )
           => ~ ( ( Xa = none_val )
               => ( Y
                 => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ none_val ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_397_compatible__options_Opelims_I3_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ~ ( compat2278460363914054422_state @ X @ Xa )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa ) )
       => ~ ! [A7: state] :
              ( ( X
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
                   => ( A7 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_398_compatible__options_Opelims_I3_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X @ Xa )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa ) )
       => ~ ! [A7: val] :
              ( ( X
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
                   => ( A7 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_399_compatible__def,axiom,
    ( compatible
    = ( ^ [Phi: produc9003781588162623004on_val,Phi5: produc9003781588162623004on_val] :
          ( ( compatible_heaps @ ( produc2319605628138516840on_val @ Phi ) @ ( produc2319605628138516840on_val @ Phi5 ) )
          & ( valid_mask @ ( add_ma6586698345353345811t_char @ ( produc5239619271231976746on_val @ Phi ) @ ( produc5239619271231976746on_val @ Phi5 ) ) ) ) ) ) ).

% compatible_def
thf(fact_400_PartialSA_Opackage__rhs__connection__instantiate,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state,A: state,U2: state,T2: state > state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
     => ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ ( produc8632743443909064678_state @ U2 @ T2 ) ) @ S2 )
       => ~ ! [Au: state] :
              ( ( ( some_state @ Au )
                = ( plus @ A @ U2 ) )
             => ~ ( ( defined @ Au @ ( minus @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                 => ? [A8: state,U3: state] :
                      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A8 @ ( produc8632743443909064678_state @ U3 @ T2 ) ) @ S3 )
                      & ( greater @ ( core @ A8 ) @ ( core @ A ) )
                      & ( ( plus @ Au @ ( minus @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                        = ( plus @ A8 @ U3 ) )
                      & ( greater @ U3 @ U2 )
                      & ( packag8070727096299822599_state @ plus @ core @ Pc @ A5 @ A8 @ U3 @ U2 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connection_instantiate
thf(fact_401_prod_Ocollapse,axiom,
    ! [Prod: produc3142500478612311029_state] :
      ( ( produc9160152616361873709_state @ ( produc3900939990612242713_state @ Prod ) @ ( produc9117690093182453595_state @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_402_prod_Ocollapse,axiom,
    ! [Prod: produc4844402304972151915_state] :
      ( ( produc6205719116230455971_state @ ( produc6030790797199838863_state @ Prod ) @ ( produc8138835347214057169_state @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_403_prod_Ocollapse,axiom,
    ! [Prod: produc6251377953716854561_state] :
      ( ( produc9080284787853255769_state @ ( produc7279835715735703621_state @ Prod ) @ ( produc4944973370551335047_state @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_404_prod_Ocollapse,axiom,
    ! [Prod: produc1457211279475724562t_char] :
      ( ( produc120197956887798346t_char @ ( produc6204653154488278070t_char @ Prod ) @ ( produc1900778367047502200t_char @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_405_prod_Ocollapse,axiom,
    ! [Prod: produc9003781588162623004on_val] :
      ( ( produc74620467203698198on_val @ ( produc5239619271231976746on_val @ Prod ) @ ( produc2319605628138516840on_val @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_406_snd__eqD,axiom,
    ! [X: option_state,Y: option_state,A: option_state] :
      ( ( ( produc9117690093182453595_state @ ( produc9160152616361873709_state @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_407_snd__eqD,axiom,
    ! [X: prat,Y: state,A: state] :
      ( ( ( produc8138835347214057169_state @ ( produc6205719116230455971_state @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_408_snd__eqD,axiom,
    ! [X: prat,Y: set_state,A: set_state] :
      ( ( ( produc4944973370551335047_state @ ( produc9080284787853255769_state @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_409_snd__eqD,axiom,
    ! [X: nat,Y: list_char,A: list_char] :
      ( ( ( produc1900778367047502200t_char @ ( produc120197956887798346t_char @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_410_snd__eqD,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: produc1457211279475724562t_char > option_val,A: produc1457211279475724562t_char > option_val] :
      ( ( ( produc2319605628138516840on_val @ ( produc74620467203698198on_val @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_411_snd__conv,axiom,
    ! [X1: option_state,X22: option_state] :
      ( ( produc9117690093182453595_state @ ( produc9160152616361873709_state @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_412_snd__conv,axiom,
    ! [X1: prat,X22: state] :
      ( ( produc8138835347214057169_state @ ( produc6205719116230455971_state @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_413_snd__conv,axiom,
    ! [X1: prat,X22: set_state] :
      ( ( produc4944973370551335047_state @ ( produc9080284787853255769_state @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_414_snd__conv,axiom,
    ! [X1: nat,X22: list_char] :
      ( ( produc1900778367047502200t_char @ ( produc120197956887798346t_char @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_415_snd__conv,axiom,
    ! [X1: produc1457211279475724562t_char > prat,X22: produc1457211279475724562t_char > option_val] :
      ( ( produc2319605628138516840on_val @ ( produc74620467203698198on_val @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_416_sndI,axiom,
    ! [X: produc3142500478612311029_state,Y: option_state,Z2: option_state] :
      ( ( X
        = ( produc9160152616361873709_state @ Y @ Z2 ) )
     => ( ( produc9117690093182453595_state @ X )
        = Z2 ) ) ).

% sndI
thf(fact_417_sndI,axiom,
    ! [X: produc4844402304972151915_state,Y: prat,Z2: state] :
      ( ( X
        = ( produc6205719116230455971_state @ Y @ Z2 ) )
     => ( ( produc8138835347214057169_state @ X )
        = Z2 ) ) ).

% sndI
thf(fact_418_sndI,axiom,
    ! [X: produc6251377953716854561_state,Y: prat,Z2: set_state] :
      ( ( X
        = ( produc9080284787853255769_state @ Y @ Z2 ) )
     => ( ( produc4944973370551335047_state @ X )
        = Z2 ) ) ).

% sndI
thf(fact_419_sndI,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat,Z2: list_char] :
      ( ( X
        = ( produc120197956887798346t_char @ Y @ Z2 ) )
     => ( ( produc1900778367047502200t_char @ X )
        = Z2 ) ) ).

% sndI
thf(fact_420_sndI,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat,Z2: produc1457211279475724562t_char > option_val] :
      ( ( X
        = ( produc74620467203698198on_val @ Y @ Z2 ) )
     => ( ( produc2319605628138516840on_val @ X )
        = Z2 ) ) ).

% sndI
thf(fact_421_eq__snd__iff,axiom,
    ! [B: option_state,P: produc3142500478612311029_state] :
      ( ( B
        = ( produc9117690093182453595_state @ P ) )
      = ( ? [A3: option_state] :
            ( P
            = ( produc9160152616361873709_state @ A3 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_422_eq__snd__iff,axiom,
    ! [B: state,P: produc4844402304972151915_state] :
      ( ( B
        = ( produc8138835347214057169_state @ P ) )
      = ( ? [A3: prat] :
            ( P
            = ( produc6205719116230455971_state @ A3 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_423_eq__snd__iff,axiom,
    ! [B: set_state,P: produc6251377953716854561_state] :
      ( ( B
        = ( produc4944973370551335047_state @ P ) )
      = ( ? [A3: prat] :
            ( P
            = ( produc9080284787853255769_state @ A3 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_424_eq__snd__iff,axiom,
    ! [B: list_char,P: produc1457211279475724562t_char] :
      ( ( B
        = ( produc1900778367047502200t_char @ P ) )
      = ( ? [A3: nat] :
            ( P
            = ( produc120197956887798346t_char @ A3 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_425_eq__snd__iff,axiom,
    ! [B: produc1457211279475724562t_char > option_val,P: produc9003781588162623004on_val] :
      ( ( B
        = ( produc2319605628138516840on_val @ P ) )
      = ( ? [A3: produc1457211279475724562t_char > prat] :
            ( P
            = ( produc74620467203698198on_val @ A3 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_426_prod__eq__iff,axiom,
    ( ( ^ [Y4: produc1457211279475724562t_char,Z: produc1457211279475724562t_char] : ( Y4 = Z ) )
    = ( ^ [S4: produc1457211279475724562t_char,T: produc1457211279475724562t_char] :
          ( ( ( produc6204653154488278070t_char @ S4 )
            = ( produc6204653154488278070t_char @ T ) )
          & ( ( produc1900778367047502200t_char @ S4 )
            = ( produc1900778367047502200t_char @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_427_prod__eq__iff,axiom,
    ( ( ^ [Y4: produc9003781588162623004on_val,Z: produc9003781588162623004on_val] : ( Y4 = Z ) )
    = ( ^ [S4: produc9003781588162623004on_val,T: produc9003781588162623004on_val] :
          ( ( ( produc5239619271231976746on_val @ S4 )
            = ( produc5239619271231976746on_val @ T ) )
          & ( ( produc2319605628138516840on_val @ S4 )
            = ( produc2319605628138516840on_val @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_428_prod__eqI,axiom,
    ! [P: produc1457211279475724562t_char,Q2: produc1457211279475724562t_char] :
      ( ( ( produc6204653154488278070t_char @ P )
        = ( produc6204653154488278070t_char @ Q2 ) )
     => ( ( ( produc1900778367047502200t_char @ P )
          = ( produc1900778367047502200t_char @ Q2 ) )
       => ( P = Q2 ) ) ) ).

% prod_eqI
thf(fact_429_prod__eqI,axiom,
    ! [P: produc9003781588162623004on_val,Q2: produc9003781588162623004on_val] :
      ( ( ( produc5239619271231976746on_val @ P )
        = ( produc5239619271231976746on_val @ Q2 ) )
     => ( ( ( produc2319605628138516840on_val @ P )
          = ( produc2319605628138516840on_val @ Q2 ) )
       => ( P = Q2 ) ) ) ).

% prod_eqI
thf(fact_430_prod_Oexpand,axiom,
    ! [Prod: produc1457211279475724562t_char,Prod2: produc1457211279475724562t_char] :
      ( ( ( ( produc6204653154488278070t_char @ Prod )
          = ( produc6204653154488278070t_char @ Prod2 ) )
        & ( ( produc1900778367047502200t_char @ Prod )
          = ( produc1900778367047502200t_char @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_431_prod_Oexpand,axiom,
    ! [Prod: produc9003781588162623004on_val,Prod2: produc9003781588162623004on_val] :
      ( ( ( ( produc5239619271231976746on_val @ Prod )
          = ( produc5239619271231976746on_val @ Prod2 ) )
        & ( ( produc2319605628138516840on_val @ Prod )
          = ( produc2319605628138516840on_val @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_432_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3142500478612311029_state] :
      ( Prod
      = ( produc9160152616361873709_state @ ( produc3900939990612242713_state @ Prod ) @ ( produc9117690093182453595_state @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_433_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4844402304972151915_state] :
      ( Prod
      = ( produc6205719116230455971_state @ ( produc6030790797199838863_state @ Prod ) @ ( produc8138835347214057169_state @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_434_prod_Oexhaust__sel,axiom,
    ! [Prod: produc6251377953716854561_state] :
      ( Prod
      = ( produc9080284787853255769_state @ ( produc7279835715735703621_state @ Prod ) @ ( produc4944973370551335047_state @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_435_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1457211279475724562t_char] :
      ( Prod
      = ( produc120197956887798346t_char @ ( produc6204653154488278070t_char @ Prod ) @ ( produc1900778367047502200t_char @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_436_prod_Oexhaust__sel,axiom,
    ! [Prod: produc9003781588162623004on_val] :
      ( Prod
      = ( produc74620467203698198on_val @ ( produc5239619271231976746on_val @ Prod ) @ ( produc2319605628138516840on_val @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_437_surjective__pairing,axiom,
    ! [T4: produc3142500478612311029_state] :
      ( T4
      = ( produc9160152616361873709_state @ ( produc3900939990612242713_state @ T4 ) @ ( produc9117690093182453595_state @ T4 ) ) ) ).

% surjective_pairing
thf(fact_438_surjective__pairing,axiom,
    ! [T4: produc4844402304972151915_state] :
      ( T4
      = ( produc6205719116230455971_state @ ( produc6030790797199838863_state @ T4 ) @ ( produc8138835347214057169_state @ T4 ) ) ) ).

% surjective_pairing
thf(fact_439_surjective__pairing,axiom,
    ! [T4: produc6251377953716854561_state] :
      ( T4
      = ( produc9080284787853255769_state @ ( produc7279835715735703621_state @ T4 ) @ ( produc4944973370551335047_state @ T4 ) ) ) ).

% surjective_pairing
thf(fact_440_surjective__pairing,axiom,
    ! [T4: produc1457211279475724562t_char] :
      ( T4
      = ( produc120197956887798346t_char @ ( produc6204653154488278070t_char @ T4 ) @ ( produc1900778367047502200t_char @ T4 ) ) ) ).

% surjective_pairing
thf(fact_441_surjective__pairing,axiom,
    ! [T4: produc9003781588162623004on_val] :
      ( T4
      = ( produc74620467203698198on_val @ ( produc5239619271231976746on_val @ T4 ) @ ( produc2319605628138516840on_val @ T4 ) ) ) ).

% surjective_pairing
thf(fact_442_get__h_Osimps,axiom,
    ( get_h
    = ( ^ [A3: state] : ( produc2319605628138516840on_val @ ( rep_state @ A3 ) ) ) ) ).

% get_h.simps
thf(fact_443_get__h_Oelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X )
        = Y )
     => ( Y
        = ( produc2319605628138516840on_val @ ( rep_state @ X ) ) ) ) ).

% get_h.elims
thf(fact_444_get__pre_I1_J,axiom,
    ( get_h
    = ( ^ [X3: state] : ( produc2319605628138516840on_val @ ( rep_state @ X3 ) ) ) ) ).

% get_pre(1)
thf(fact_445_compatibleI__old,axiom,
    ! [Phi2: produc9003781588162623004on_val,Phi4: produc9003781588162623004on_val] :
      ( ! [Hl3: produc1457211279475724562t_char,X2: val,Y3: val] :
          ( ( ( ( produc2319605628138516840on_val @ Phi2 @ Hl3 )
              = ( some_val @ X2 ) )
            & ( ( produc2319605628138516840on_val @ Phi4 @ Hl3 )
              = ( some_val @ Y3 ) ) )
         => ( X2 = Y3 ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( produc5239619271231976746on_val @ Phi2 ) @ ( produc5239619271231976746on_val @ Phi4 ) ) )
       => ( compatible @ Phi2 @ Phi4 ) ) ) ).

% compatibleI_old
thf(fact_446_PartialSA_Opackage__rhs__connectionI,axiom,
    ! [Phi2: state,F: state,Phi4: state,F5: state,S2: set_Pr4231240917283394591_state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state] :
      ( ( ( plus @ Phi2 @ F )
        = ( plus @ Phi4 @ F5 ) )
     => ( ( stable @ F5 )
       => ( ( defined @ Phi2 @ F )
         => ( ( greater @ F5 @ F )
           => ( ! [A7: state,U: state,T3: state > state] :
                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
                 => ? [Au2: state] :
                      ( ( ( some_state @ Au2 )
                        = ( plus @ A7 @ U ) )
                      & ( ( defined @ Au2 @ ( minus @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                       => ? [A9: state,U4: state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A9 @ ( produc8632743443909064678_state @ U4 @ T3 ) ) @ S3 )
                            & ( greater @ ( core @ A9 ) @ ( core @ A7 ) )
                            & ( ( plus @ Au2 @ ( minus @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                              = ( plus @ A9 @ U4 ) )
                            & ( greater @ U4 @ U )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A5 @ A9 @ U4 @ U ) ) ) ) )
             => ( packag2054414653763826108_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connectionI
thf(fact_447_get__h_Opelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X )
        = Y )
     => ( ( accp_state @ get_h_rel @ X )
       => ~ ( ( Y
              = ( produc2319605628138516840on_val @ ( rep_state @ X ) ) )
           => ~ ( accp_state @ get_h_rel @ X ) ) ) ) ).

% get_h.pelims
thf(fact_448_exI__realizer,axiom,
    ! [P4: option_state > option_state > $o,Y: option_state,X: option_state] :
      ( ( P4 @ Y @ X )
     => ( P4 @ ( produc9117690093182453595_state @ ( produc9160152616361873709_state @ X @ Y ) ) @ ( produc3900939990612242713_state @ ( produc9160152616361873709_state @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_449_exI__realizer,axiom,
    ! [P4: state > prat > $o,Y: state,X: prat] :
      ( ( P4 @ Y @ X )
     => ( P4 @ ( produc8138835347214057169_state @ ( produc6205719116230455971_state @ X @ Y ) ) @ ( produc6030790797199838863_state @ ( produc6205719116230455971_state @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_450_exI__realizer,axiom,
    ! [P4: set_state > prat > $o,Y: set_state,X: prat] :
      ( ( P4 @ Y @ X )
     => ( P4 @ ( produc4944973370551335047_state @ ( produc9080284787853255769_state @ X @ Y ) ) @ ( produc7279835715735703621_state @ ( produc9080284787853255769_state @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_451_exI__realizer,axiom,
    ! [P4: list_char > nat > $o,Y: list_char,X: nat] :
      ( ( P4 @ Y @ X )
     => ( P4 @ ( produc1900778367047502200t_char @ ( produc120197956887798346t_char @ X @ Y ) ) @ ( produc6204653154488278070t_char @ ( produc120197956887798346t_char @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_452_exI__realizer,axiom,
    ! [P4: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > $o,Y: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char > prat] :
      ( ( P4 @ Y @ X )
     => ( P4 @ ( produc2319605628138516840on_val @ ( produc74620467203698198on_val @ X @ Y ) ) @ ( produc5239619271231976746on_val @ ( produc74620467203698198on_val @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_453_conjI__realizer,axiom,
    ! [P4: option_state > $o,P: option_state,Q: option_state > $o,Q2: option_state] :
      ( ( P4 @ P )
     => ( ( Q @ Q2 )
       => ( ( P4 @ ( produc3900939990612242713_state @ ( produc9160152616361873709_state @ P @ Q2 ) ) )
          & ( Q @ ( produc9117690093182453595_state @ ( produc9160152616361873709_state @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_454_conjI__realizer,axiom,
    ! [P4: prat > $o,P: prat,Q: state > $o,Q2: state] :
      ( ( P4 @ P )
     => ( ( Q @ Q2 )
       => ( ( P4 @ ( produc6030790797199838863_state @ ( produc6205719116230455971_state @ P @ Q2 ) ) )
          & ( Q @ ( produc8138835347214057169_state @ ( produc6205719116230455971_state @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_455_conjI__realizer,axiom,
    ! [P4: prat > $o,P: prat,Q: set_state > $o,Q2: set_state] :
      ( ( P4 @ P )
     => ( ( Q @ Q2 )
       => ( ( P4 @ ( produc7279835715735703621_state @ ( produc9080284787853255769_state @ P @ Q2 ) ) )
          & ( Q @ ( produc4944973370551335047_state @ ( produc9080284787853255769_state @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_456_conjI__realizer,axiom,
    ! [P4: nat > $o,P: nat,Q: list_char > $o,Q2: list_char] :
      ( ( P4 @ P )
     => ( ( Q @ Q2 )
       => ( ( P4 @ ( produc6204653154488278070t_char @ ( produc120197956887798346t_char @ P @ Q2 ) ) )
          & ( Q @ ( produc1900778367047502200t_char @ ( produc120197956887798346t_char @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_457_conjI__realizer,axiom,
    ! [P4: ( produc1457211279475724562t_char > prat ) > $o,P: produc1457211279475724562t_char > prat,Q: ( produc1457211279475724562t_char > option_val ) > $o,Q2: produc1457211279475724562t_char > option_val] :
      ( ( P4 @ P )
     => ( ( Q @ Q2 )
       => ( ( P4 @ ( produc5239619271231976746on_val @ ( produc74620467203698198on_val @ P @ Q2 ) ) )
          & ( Q @ ( produc2319605628138516840on_val @ ( produc74620467203698198on_val @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_458_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P4: option_state > option_state > $o,X: option_state,Y: option_state,A: produc3142500478612311029_state] :
      ( ( P4 @ X @ Y )
     => ( ( A
          = ( produc9160152616361873709_state @ X @ Y ) )
       => ( P4 @ ( produc3900939990612242713_state @ A ) @ ( produc9117690093182453595_state @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_459_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P4: prat > state > $o,X: prat,Y: state,A: produc4844402304972151915_state] :
      ( ( P4 @ X @ Y )
     => ( ( A
          = ( produc6205719116230455971_state @ X @ Y ) )
       => ( P4 @ ( produc6030790797199838863_state @ A ) @ ( produc8138835347214057169_state @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_460_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P4: prat > set_state > $o,X: prat,Y: set_state,A: produc6251377953716854561_state] :
      ( ( P4 @ X @ Y )
     => ( ( A
          = ( produc9080284787853255769_state @ X @ Y ) )
       => ( P4 @ ( produc7279835715735703621_state @ A ) @ ( produc4944973370551335047_state @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_461_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P4: nat > list_char > $o,X: nat,Y: list_char,A: produc1457211279475724562t_char] :
      ( ( P4 @ X @ Y )
     => ( ( A
          = ( produc120197956887798346t_char @ X @ Y ) )
       => ( P4 @ ( produc6204653154488278070t_char @ A ) @ ( produc1900778367047502200t_char @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_462_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,X: produc1457211279475724562t_char > prat,Y: produc1457211279475724562t_char > option_val,A: produc9003781588162623004on_val] :
      ( ( P4 @ X @ Y )
     => ( ( A
          = ( produc74620467203698198on_val @ X @ Y ) )
       => ( P4 @ ( produc5239619271231976746on_val @ A ) @ ( produc2319605628138516840on_val @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_463_PartialSA_Opackage__satI,axiom,
    ! [Pc: state > $o,A6: state,U5: state,U2: state,A5: aassertion_state] :
      ( ( ( Pc @ ( core @ A6 ) )
       => ? [X5: state] :
            ( ( ( some_state @ X5 )
              = ( plus @ ( core @ A6 ) @ ( minus @ U5 @ U2 ) ) )
            & ( package_sat_state @ plus @ A5 @ X5 ) ) )
     => ( packag8070727096299822599_state @ plus @ core @ Pc @ A5 @ A6 @ U5 @ U2 ) ) ).

% PartialSA.package_satI
thf(fact_464_PartialSA_Opackage__sat__def,axiom,
    ! [Pc: state > $o,A5: aassertion_state,A6: state,U5: state,U2: state] :
      ( ( packag8070727096299822599_state @ plus @ core @ Pc @ A5 @ A6 @ U5 @ U2 )
      = ( ( Pc @ ( core @ A6 ) )
       => ? [X3: state] :
            ( ( ( some_state @ X3 )
              = ( plus @ ( core @ A6 ) @ ( minus @ U5 @ U2 ) ) )
            & ( package_sat_state @ plus @ A5 @ X3 ) ) ) ) ).

% PartialSA.package_sat_def
thf(fact_465_PartialSA_Ois__footprint__standard__def,axiom,
    ! [W: state,A5: aassertion_state,B4: aassertion_state] :
      ( ( packag7096211993527611489_state @ plus @ W @ A5 @ B4 )
      = ( ! [A3: state,B2: state] :
            ( ( ( package_sat_state @ plus @ A5 @ A3 )
              & ( ( some_state @ B2 )
                = ( plus @ A3 @ W ) ) )
           => ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.is_footprint_standard_def
thf(fact_466_PartialSA_Ois__footprint__general__def,axiom,
    ! [W: state,R3: state > state > state,A5: aassertion_state,B4: aassertion_state] :
      ( ( packag6192661653625646554_state @ plus @ W @ R3 @ A5 @ B4 )
      = ( ! [A3: state,B2: state] :
            ( ( ( package_sat_state @ plus @ A5 @ A3 )
              & ( ( some_state @ B2 )
                = ( plus @ A3 @ ( R3 @ A3 @ W ) ) ) )
           => ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.is_footprint_general_def
thf(fact_467_PartialSA_Ois__footprint__standardI,axiom,
    ! [A5: aassertion_state,W: state,B4: aassertion_state] :
      ( ! [A7: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A5 @ A7 )
            & ( ( some_state @ B6 )
              = ( plus @ A7 @ W ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag7096211993527611489_state @ plus @ W @ A5 @ B4 ) ) ).

% PartialSA.is_footprint_standardI
thf(fact_468_PartialSA_Ois__footprint__generalI,axiom,
    ! [A5: aassertion_state,R3: state > state > state,W: state,B4: aassertion_state] :
      ( ! [A7: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A5 @ A7 )
            & ( ( some_state @ B6 )
              = ( plus @ A7 @ ( R3 @ A7 @ W ) ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag6192661653625646554_state @ plus @ W @ R3 @ A5 @ B4 ) ) ).

% PartialSA.is_footprint_generalI
thf(fact_469_PartialSA_Owf__assertion__and__the,axiom,
    ! [A: state,B: state,A5: aassertion_state] :
      ( ( defined @ ( core @ A ) @ B )
     => ( ( package_sat_state @ plus @ A5 @ B )
       => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
         => ( package_sat_state @ plus @ A5 @ ( the_state @ ( plus @ ( core @ A ) @ B ) ) ) ) ) ) ).

% PartialSA.wf_assertion_and_the
thf(fact_470_prod_Oswap__def,axiom,
    ( produc8425362190318354125_state
    = ( ^ [P2: produc3142500478612311029_state] : ( produc9160152616361873709_state @ ( produc9117690093182453595_state @ P2 ) @ ( produc3900939990612242713_state @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_471_prod_Oswap__def,axiom,
    ( produc6343331096166649923e_prat
    = ( ^ [P2: produc7334356684927367531e_prat] : ( produc6205719116230455971_state @ ( produc7795413381861543633e_prat @ P2 ) @ ( produc5687368831847325327e_prat @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_472_prod_Oswap__def,axiom,
    ( produc7016766326345971705e_prat
    = ( ^ [P2: produc2654212508281724193e_prat] : ( produc9080284787853255769_state @ ( produc1175801883329052295e_prat @ P2 ) @ ( produc3510664228513420869e_prat @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_473_prod_Oswap__def,axiom,
    ( produc4410195085741832554ar_nat
    = ( ^ [P2: produc7606469099237612818ar_nat] : ( produc120197956887798346t_char @ ( produc1259554233722553080ar_nat @ P2 ) @ ( produc5563429021163328950ar_nat @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_474_prod_Oswap__def,axiom,
    ( produc5819413633627552064r_prat
    = ( ^ [P2: produc7776263825685906734r_prat] : ( produc74620467203698198on_val @ ( produc4142415063207305778r_prat @ P2 ) @ ( produc7062428706300765684r_prat @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_475_prod_Oswap__def,axiom,
    ( produc5051419219066781674t_char
    = ( ^ [P2: produc1457211279475724562t_char] : ( produc8702345860417625034ar_nat @ ( produc1900778367047502200t_char @ P2 ) @ ( produc6204653154488278070t_char @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_476_prod_Oswap__def,axiom,
    ( produc3996604198558763126on_val
    = ( ^ [P2: produc9003781588162623004on_val] : ( produc1897429902272487136r_prat @ ( produc2319605628138516840on_val @ P2 ) @ ( produc5239619271231976746on_val @ P2 ) ) ) ) ).

% prod.swap_def
thf(fact_477_swap__simp,axiom,
    ! [X: state,Y: prat] :
      ( ( produc6343331096166649923e_prat @ ( produc5862297150877942435e_prat @ X @ Y ) )
      = ( produc6205719116230455971_state @ Y @ X ) ) ).

% swap_simp
thf(fact_478_swap__simp,axiom,
    ! [X: set_state,Y: prat] :
      ( ( produc7016766326345971705e_prat @ ( produc5311113300630973017e_prat @ X @ Y ) )
      = ( produc9080284787853255769_state @ Y @ X ) ) ).

% swap_simp
thf(fact_479_swap__simp,axiom,
    ! [X: list_char,Y: nat] :
      ( ( produc4410195085741832554ar_nat @ ( produc8702345860417625034ar_nat @ X @ Y ) )
      = ( produc120197956887798346t_char @ Y @ X ) ) ).

% swap_simp
thf(fact_480_swap__simp,axiom,
    ! [X: produc1457211279475724562t_char > option_val,Y: produc1457211279475724562t_char > prat] :
      ( ( produc5819413633627552064r_prat @ ( produc1897429902272487136r_prat @ X @ Y ) )
      = ( produc74620467203698198on_val @ Y @ X ) ) ).

% swap_simp
thf(fact_481_swap__simp,axiom,
    ! [X: option_state,Y: option_state] :
      ( ( produc8425362190318354125_state @ ( produc9160152616361873709_state @ X @ Y ) )
      = ( produc9160152616361873709_state @ Y @ X ) ) ).

% swap_simp
thf(fact_482_swap__simp,axiom,
    ! [X: prat,Y: state] :
      ( ( produc6686753061519163459_state @ ( produc6205719116230455971_state @ X @ Y ) )
      = ( produc5862297150877942435e_prat @ Y @ X ) ) ).

% swap_simp
thf(fact_483_swap__simp,axiom,
    ! [X: prat,Y: set_state] :
      ( ( produc1562565776713478649_state @ ( produc9080284787853255769_state @ X @ Y ) )
      = ( produc5311113300630973017e_prat @ Y @ X ) ) ).

% swap_simp
thf(fact_484_swap__simp,axiom,
    ! [X: nat,Y: list_char] :
      ( ( produc5051419219066781674t_char @ ( produc120197956887798346t_char @ X @ Y ) )
      = ( produc8702345860417625034ar_nat @ Y @ X ) ) ).

% swap_simp
thf(fact_485_swap__simp,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: produc1457211279475724562t_char > option_val] :
      ( ( produc3996604198558763126on_val @ ( produc74620467203698198on_val @ X @ Y ) )
      = ( produc1897429902272487136r_prat @ Y @ X ) ) ).

% swap_simp
thf(fact_486_snd__swap,axiom,
    ! [X: produc1457211279475724562t_char] :
      ( ( produc1259554233722553080ar_nat @ ( produc5051419219066781674t_char @ X ) )
      = ( produc6204653154488278070t_char @ X ) ) ).

% snd_swap
thf(fact_487_snd__swap,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( produc4142415063207305778r_prat @ ( produc3996604198558763126on_val @ X ) )
      = ( produc5239619271231976746on_val @ X ) ) ).

% snd_swap
thf(fact_488_snd__swap,axiom,
    ! [X: produc7776263825685906734r_prat] :
      ( ( produc2319605628138516840on_val @ ( produc5819413633627552064r_prat @ X ) )
      = ( produc7062428706300765684r_prat @ X ) ) ).

% snd_swap
thf(fact_489_fst__swap,axiom,
    ! [X: produc7606469099237612818ar_nat] :
      ( ( produc6204653154488278070t_char @ ( produc4410195085741832554ar_nat @ X ) )
      = ( produc1259554233722553080ar_nat @ X ) ) ).

% fst_swap
thf(fact_490_fst__swap,axiom,
    ! [X: produc7776263825685906734r_prat] :
      ( ( produc5239619271231976746on_val @ ( produc5819413633627552064r_prat @ X ) )
      = ( produc4142415063207305778r_prat @ X ) ) ).

% fst_swap
thf(fact_491_fst__swap,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( produc7062428706300765684r_prat @ ( produc3996604198558763126on_val @ X ) )
      = ( produc2319605628138516840on_val @ X ) ) ).

% fst_swap
thf(fact_492_PartialSA_Owf__assertion__sat__larger__pure,axiom,
    ! [A5: aassertion_state,Phi2: state,Phi4: state,R2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ A5 )
     => ( ( package_sat_state @ plus @ A5 @ Phi2 )
       => ( ( ( some_state @ Phi4 )
            = ( plus @ Phi2 @ R2 ) )
         => ( ( sep_pure_state @ plus @ R2 )
           => ( package_sat_state @ plus @ A5 @ Phi4 ) ) ) ) ) ).

% PartialSA.wf_assertion_sat_larger_pure
thf(fact_493_PartialSA_Osat__star__exists__bigger,axiom,
    ! [A5: aassertion_state,B4: aassertion_state,Phi2: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ A5 @ B4 ) @ Phi2 )
     => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
       => ( ( packag7298478212905792770_state @ plus @ core @ B4 )
         => ? [A7: state,B6: state] :
              ( ( greater @ ( core @ A7 ) @ ( core @ Phi2 ) )
              & ( greater @ ( core @ B6 ) @ ( core @ Phi2 ) )
              & ( ( some_state @ Phi2 )
                = ( plus @ A7 @ B6 ) )
              & ( package_sat_state @ plus @ A5 @ A7 )
              & ( package_sat_state @ plus @ B4 @ B6 ) ) ) ) ) ).

% PartialSA.sat_star_exists_bigger
thf(fact_494_PartialSA_Opackage__rhs__proof,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( stable @ F )
             => ( ( defined @ Phi2 @ F )
               => ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
                  & ( packag3877571396724326311_state @ plus @ core @ unit @ S3 @ F5 ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs_proof
thf(fact_495_add__states_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa )
        = Y )
     => ( ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ X @ Xa ) )
       => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
             => ! [Pi4: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
                  ( ( Xa
                    = ( produc74620467203698198on_val @ Pi4 @ H3 ) )
                 => ( ( Y
                      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi2 @ Pi4 ) @ ( map_ad2908576761495157028ar_val @ H2 @ H3 ) ) )
                   => ~ ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi2 @ H2 ) @ ( produc74620467203698198on_val @ Pi4 @ H3 ) ) ) ) ) ) ) ) ).

% add_states.pelims
thf(fact_496_add__states_Osimps,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val,Pi5: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
      ( ( add_states @ ( produc74620467203698198on_val @ Pi3 @ H ) @ ( produc74620467203698198on_val @ Pi5 @ H6 ) )
      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi3 @ Pi5 ) @ ( map_ad2908576761495157028ar_val @ H @ H6 ) ) ) ).

% add_states.simps
thf(fact_497_add__states_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa )
        = Y )
     => ~ ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
           => ! [Pi4: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
                ( ( Xa
                  = ( produc74620467203698198on_val @ Pi4 @ H3 ) )
               => ( Y
                 != ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi2 @ Pi4 ) @ ( map_ad2908576761495157028ar_val @ H2 @ H3 ) ) ) ) ) ) ).

% add_states.elims
thf(fact_498_compatible__heaps__sum,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A @ B )
     => ( ( compatible_heaps @ A @ C )
       => ( compatible_heaps @ A @ ( map_ad2908576761495157028ar_val @ B @ C ) ) ) ) ).

% compatible_heaps_sum
thf(fact_499_compatible__heaps__comm,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A @ B )
     => ( ( map_ad2908576761495157028ar_val @ A @ B )
        = ( map_ad2908576761495157028ar_val @ B @ A ) ) ) ).

% compatible_heaps_comm
thf(fact_500_PartialSA_Opackage__rhs_Ointros_I1_J,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state,Ba: aassertion_state,Phi6: state,F6: state,S5: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F5 @ S3 @ Pc @ Ba @ Phi6 @ F6 @ S5 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ ( aStar_state @ A5 @ Ba ) @ Phi6 @ F6 @ S5 ) ) ) ).

% PartialSA.package_rhs.intros(1)
thf(fact_501_PartialSA_OAStar,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state,B4: aassertion_state,Phi6: state,F6: state,S5: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F5 @ S3 @ Pc @ B4 @ Phi6 @ F6 @ S5 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ ( aStar_state @ A5 @ B4 ) @ Phi6 @ F6 @ S5 ) ) ) ).

% PartialSA.AStar
thf(fact_502_larger__heap__plus,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ A @ C )
       => ( larger1532547405891354081ar_val @ A @ ( map_ad2908576761495157028ar_val @ B @ C ) ) ) ) ).

% larger_heap_plus
thf(fact_503_PartialSA_Omono__pure__cond__def,axiom,
    ! [B: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ B )
      = ( ! [Phi: state] :
            ( ( B @ Phi )
            = ( B @ ( core @ Phi ) ) )
        & ! [Phi5: state,Phi: state,R: state] :
            ( ( ( sep_pure_state @ plus @ R )
              & ( ( some_state @ Phi5 )
                = ( plus @ Phi @ R ) )
              & ~ ( B @ Phi ) )
           => ~ ( B @ Phi5 ) ) ) ) ).

% PartialSA.mono_pure_cond_def
thf(fact_504_PartialSA_Omono__pure__condI,axiom,
    ! [B: state > $o] :
      ( ! [Phi3: state] :
          ( ( B @ Phi3 )
          = ( B @ ( core @ Phi3 ) ) )
     => ( ! [Phi3: state,Phi7: state,R4: state] :
            ( ( ( sep_pure_state @ plus @ R4 )
              & ( ( some_state @ Phi7 )
                = ( plus @ Phi3 @ R4 ) )
              & ~ ( B @ Phi3 ) )
           => ~ ( B @ Phi7 ) )
       => ( packag6595153354952283300_state @ plus @ core @ B ) ) ) ).

% PartialSA.mono_pure_condI
thf(fact_505_empty__heap__neutral,axiom,
    ! [A: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ A @ empty_7512026568161686585ar_val )
      = A ) ).

% empty_heap_neutral
thf(fact_506_PartialSA_Opure__stable,axiom,
    ! [A: state,B: state,C: state] :
      ( ( sep_pure_state @ plus @ A )
     => ( ( sep_pure_state @ plus @ B )
       => ( ( ( some_state @ C )
            = ( plus @ A @ B ) )
         => ( sep_pure_state @ plus @ C ) ) ) ) ).

% PartialSA.pure_stable
thf(fact_507_PartialSA_Opure__def,axiom,
    ! [A: state] :
      ( ( sep_pure_state @ plus @ A )
      = ( ( some_state @ A )
        = ( plus @ A @ A ) ) ) ).

% PartialSA.pure_def
thf(fact_508_PartialSA_Opure__smaller,axiom,
    ! [A: state,B: state] :
      ( ( sep_pure_state @ plus @ A )
     => ( ( greater @ A @ B )
       => ( sep_pure_state @ plus @ B ) ) ) ).

% PartialSA.pure_smaller
thf(fact_509_larger__heaps__sum__ineq,axiom,
    ! [A6: produc1457211279475724562t_char > option_val,A: produc1457211279475724562t_char > option_val,B5: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A6 @ A )
     => ( ( larger1532547405891354081ar_val @ B5 @ B )
       => ( ( compatible_heaps @ A6 @ B5 )
         => ( larger1532547405891354081ar_val @ ( map_ad2908576761495157028ar_val @ A6 @ B5 ) @ ( map_ad2908576761495157028ar_val @ A @ B ) ) ) ) ) ).

% larger_heaps_sum_ineq
thf(fact_510_PartialSA_Osat_Osimps_I1_J,axiom,
    ! [Aa2: aassertion_state,B4: aassertion_state,Phi2: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ Aa2 @ B4 ) @ Phi2 )
      = ( ? [A3: state,B2: state] :
            ( ( ( some_state @ Phi2 )
              = ( plus @ A3 @ B2 ) )
            & ( package_sat_state @ plus @ Aa2 @ A3 )
            & ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.sat.simps(1)
thf(fact_511_PartialSA_Owf__assertion_Osimps_I1_J,axiom,
    ! [Aa2: aassertion_state,B4: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aStar_state @ Aa2 @ B4 ) )
      = ( ( packag7298478212905792770_state @ plus @ core @ Aa2 )
        & ( packag7298478212905792770_state @ plus @ core @ B4 ) ) ) ).

% PartialSA.wf_assertion.simps(1)
thf(fact_512_plus__charact_I2_J,axiom,
    ! [A: state,B: state,X: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ X ) )
     => ( ( get_h @ X )
        = ( map_ad2908576761495157028ar_val @ ( get_h @ A ) @ ( get_h @ B ) ) ) ) ).

% plus_charact(2)
thf(fact_513_PartialSA_Osmaller__pure__sum__smaller,axiom,
    ! [Y: state,A: state,B: state,X: state] :
      ( ( greater @ Y @ A )
     => ( ( greater @ Y @ B )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( ( sep_pure_state @ plus @ B )
           => ( greater @ Y @ X ) ) ) ) ) ).

% PartialSA.smaller_pure_sum_smaller
thf(fact_514_PartialSA_Ogeneral__completeness,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state,A5: aassertion_state,Phi2: state,Phi4: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ! [X2: state] :
              ( ( ( some_state @ X2 )
                = ( plus @ A7 @ ( T3 @ F ) ) )
             => ( package_sat_state @ plus @ A5 @ X2 ) ) )
     => ( ( ( some_state @ Phi2 )
          = ( plus @ Phi4 @ F ) )
       => ( ( stable @ F )
         => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ unit )
           => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
             => ? [X_1: set_Pr4231240917283394591_state] :
                  ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ unit @ S2
                  @ ^ [Uu3: state] : $true
                  @ A5
                  @ Phi4
                  @ F
                  @ X_1 ) ) ) ) ) ) ).

% PartialSA.general_completeness
thf(fact_515_PartialSA_Omono__pure__cond__conj,axiom,
    ! [Pc: state > $o,B: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ Pc )
     => ( ( packag6595153354952283300_state @ plus @ core @ B )
       => ( packag6595153354952283300_state @ plus @ core @ ( packag1330488657391168505_state @ Pc @ B ) ) ) ) ).

% PartialSA.mono_pure_cond_conj
thf(fact_516_PartialSA_Omono__pruner__def,axiom,
    ! [P: state > $o] :
      ( ( packag2456304381420842418_state @ plus @ P )
      = ( ! [Phi5: state,Phi: state,R: state] :
            ( ( ( sep_pure_state @ plus @ R )
              & ( P @ Phi )
              & ( ( some_state @ Phi5 )
                = ( plus @ Phi @ R ) ) )
           => ( P @ Phi5 ) ) ) ) ).

% PartialSA.mono_pruner_def
thf(fact_517_PartialSA_Omax__projection__prop__pure__core,axiom,
    sep_ma8214210560313151521_state @ plus @ ( sep_pure_state @ plus ) @ core ).

% PartialSA.max_projection_prop_pure_core
thf(fact_518_PartialSA_Owf__assertion_Osimps_I2_J,axiom,
    ! [B: state > $o,Aa2: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aImp_state @ B @ Aa2 ) )
      = ( ( packag6595153354952283300_state @ plus @ core @ B )
        & ( packag7298478212905792770_state @ plus @ core @ Aa2 ) ) ) ).

% PartialSA.wf_assertion.simps(2)
thf(fact_519_subset__CollectI,axiom,
    ! [B4: set_Pr2391701600042252046_state,A5: set_Pr2391701600042252046_state,Q: produc3882902684156697774_state > $o,P4: produc3882902684156697774_state > $o] :
      ( ( ord_le6483787752022044334_state @ B4 @ A5 )
     => ( ! [X2: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X2 @ B4 )
           => ( ( Q @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le6483787752022044334_state
          @ ( collec394671971739345689_state
            @ ^ [X3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X3 @ B4 )
                & ( Q @ X3 ) ) )
          @ ( collec394671971739345689_state
            @ ^ [X3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_520_subset__CollectI,axiom,
    ! [B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state,Q: produc7272280185086996969_state > $o,P4: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ B4 @ A5 )
     => ( ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ B4 )
           => ( ( Q @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le4032880777312351359_state
          @ ( collec906845016635587262_state
            @ ^ [X3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X3 @ B4 )
                & ( Q @ X3 ) ) )
          @ ( collec906845016635587262_state
            @ ^ [X3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_521_subset__CollectI,axiom,
    ! [B4: set_Pr7649655576376376530on_val,A5: set_Pr7649655576376376530on_val,Q: produc9003781588162623004on_val > $o,P4: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ B4 @ A5 )
     => ( ! [X2: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X2 @ B4 )
           => ( ( Q @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le6900622908513426738on_val
          @ ( collec7475294502966882545on_val
            @ ^ [X3: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X3 @ B4 )
                & ( Q @ X3 ) ) )
          @ ( collec7475294502966882545on_val
            @ ^ [X3: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_522_subset__CollectI,axiom,
    ! [B4: set_state,A5: set_state,Q: state > $o,P4: state > $o] :
      ( ( ord_le2494988322063910608_state @ B4 @ A5 )
     => ( ! [X2: state] :
            ( ( member_state @ X2 @ B4 )
           => ( ( Q @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le2494988322063910608_state
          @ ( collect_state
            @ ^ [X3: state] :
                ( ( member_state @ X3 @ B4 )
                & ( Q @ X3 ) ) )
          @ ( collect_state
            @ ^ [X3: state] :
                ( ( member_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_523_subset__Collect__iff,axiom,
    ! [B4: set_Pr2391701600042252046_state,A5: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
      ( ( ord_le6483787752022044334_state @ B4 @ A5 )
     => ( ( ord_le6483787752022044334_state @ B4
          @ ( collec394671971739345689_state
            @ ^ [X3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) )
        = ( ! [X3: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X3 @ B4 )
             => ( P4 @ X3 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_524_subset__Collect__iff,axiom,
    ! [B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ B4 @ A5 )
     => ( ( ord_le4032880777312351359_state @ B4
          @ ( collec906845016635587262_state
            @ ^ [X3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) )
        = ( ! [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ B4 )
             => ( P4 @ X3 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_525_subset__Collect__iff,axiom,
    ! [B4: set_Pr7649655576376376530on_val,A5: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ B4 @ A5 )
     => ( ( ord_le6900622908513426738on_val @ B4
          @ ( collec7475294502966882545on_val
            @ ^ [X3: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) )
        = ( ! [X3: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ X3 @ B4 )
             => ( P4 @ X3 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_526_subset__Collect__iff,axiom,
    ! [B4: set_state,A5: set_state,P4: state > $o] :
      ( ( ord_le2494988322063910608_state @ B4 @ A5 )
     => ( ( ord_le2494988322063910608_state @ B4
          @ ( collect_state
            @ ^ [X3: state] :
                ( ( member_state @ X3 @ A5 )
                & ( P4 @ X3 ) ) ) )
        = ( ! [X3: state] :
              ( ( member_state @ X3 @ B4 )
             => ( P4 @ X3 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_527_pred__subset__eq,axiom,
    ! [R3: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le7281427340513060550tate_o
        @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ R3 )
        @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ S2 ) )
      = ( ord_le4032880777312351359_state @ R3 @ S2 ) ) ).

% pred_subset_eq
thf(fact_528_pred__subset__eq,axiom,
    ! [R3: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le6140313152057869779_val_o
        @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ R3 )
        @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R3 @ S2 ) ) ).

% pred_subset_eq
thf(fact_529_pred__subset__eq,axiom,
    ! [R3: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le8077393285996101039tate_o
        @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ R3 )
        @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ S2 ) )
      = ( ord_le6483787752022044334_state @ R3 @ S2 ) ) ).

% pred_subset_eq
thf(fact_530_pred__subset__eq,axiom,
    ! [R3: set_state,S2: set_state] :
      ( ( ord_less_eq_state_o
        @ ^ [X3: state] : ( member_state @ X3 @ R3 )
        @ ^ [X3: state] : ( member_state @ X3 @ S2 ) )
      = ( ord_le2494988322063910608_state @ R3 @ S2 ) ) ).

% pred_subset_eq
thf(fact_531_PartialSA_Obool__conj__def,axiom,
    ( packag1330488657391168505_state
    = ( ^ [A3: state > $o,B2: state > $o,X3: state] :
          ( ( A3 @ X3 )
          & ( B2 @ X3 ) ) ) ) ).

% PartialSA.bool_conj_def
thf(fact_532_less__eq__set__def,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
          ( ord_le7281427340513060550tate_o
          @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ A4 )
          @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_533_less__eq__set__def,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,B3: set_Pr7649655576376376530on_val] :
          ( ord_le6140313152057869779_val_o
          @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ A4 )
          @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_534_less__eq__set__def,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A4: set_Pr2391701600042252046_state,B3: set_Pr2391701600042252046_state] :
          ( ord_le8077393285996101039tate_o
          @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ A4 )
          @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_535_less__eq__set__def,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A4: set_state,B3: set_state] :
          ( ord_less_eq_state_o
          @ ^ [X3: state] : ( member_state @ X3 @ A4 )
          @ ^ [X3: state] : ( member_state @ X3 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_536_Collect__subset,axiom,
    ! [A5: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ A5 )
            & ( P4 @ X3 ) ) )
      @ A5 ) ).

% Collect_subset
thf(fact_537_Collect__subset,axiom,
    ! [A5: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ A5 )
            & ( P4 @ X3 ) ) )
      @ A5 ) ).

% Collect_subset
thf(fact_538_Collect__subset,axiom,
    ! [A5: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ A5 )
            & ( P4 @ X3 ) ) )
      @ A5 ) ).

% Collect_subset
thf(fact_539_Collect__subset,axiom,
    ! [A5: set_state,P4: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ A5 )
            & ( P4 @ X3 ) ) )
      @ A5 ) ).

% Collect_subset
thf(fact_540_pred__subset__eq2,axiom,
    ! [R3: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le6704609105599929480tate_o
        @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le4032880777312351359_state @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_541_pred__subset__eq2,axiom,
    ! [R3: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le1106678366802930969tate_o
        @ ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le6483787752022044334_state @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_542_pred__subset__eq2,axiom,
    ! [R3: set_Pr1688445902015331925_state,S2: set_Pr1688445902015331925_state] :
      ( ( ord_le2052508915978315794tate_o
        @ ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le6423325748750870005_state @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_543_pred__subset__eq2,axiom,
    ! [R3: set_Pr6039890582625207499_state,S2: set_Pr6039890582625207499_state] :
      ( ( ord_le9040380983013460636tate_o
        @ ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le262197048489888875_state @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_544_pred__subset__eq2,axiom,
    ! [R3: set_Pr6847263425858009217_state,S2: set_Pr6847263425858009217_state] :
      ( ( ord_le8830457724327557734tate_o
        @ ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le5761494056910127137_state @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_545_pred__subset__eq2,axiom,
    ! [R3: set_Pr2507339680178222706t_char,S2: set_Pr2507339680178222706t_char] :
      ( ( ord_le2712619360209801397char_o
        @ ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le6315511645215477266t_char @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_546_pred__subset__eq2,axiom,
    ! [R3: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le3852884270828607079_val_o
        @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R3 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_547_pred__equals__eq2,axiom,
    ! [R3: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ( ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_548_pred__equals__eq2,axiom,
    ! [R3: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ( ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_549_pred__equals__eq2,axiom,
    ! [R3: set_Pr1688445902015331925_state,S2: set_Pr1688445902015331925_state] :
      ( ( ( ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_550_pred__equals__eq2,axiom,
    ! [R3: set_Pr6039890582625207499_state,S2: set_Pr6039890582625207499_state] :
      ( ( ( ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_551_pred__equals__eq2,axiom,
    ! [R3: set_Pr6847263425858009217_state,S2: set_Pr6847263425858009217_state] :
      ( ( ( ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_552_pred__equals__eq2,axiom,
    ! [R3: set_Pr2507339680178222706t_char,S2: set_Pr2507339680178222706t_char] :
      ( ( ( ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_553_pred__equals__eq2,axiom,
    ! [R3: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ( ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ R3 ) )
        = ( ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ S2 ) ) )
      = ( R3 = S2 ) ) ).

% pred_equals_eq2
thf(fact_554_PartialSA_Ompp__prop,axiom,
    ! [P4: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( P4 @ ( F @ X ) ) ) ).

% PartialSA.mpp_prop
thf(fact_555_PartialSA_Ompp__invo,axiom,
    ! [P4: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( ( F @ ( F @ X ) )
        = ( F @ X ) ) ) ).

% PartialSA.mpp_invo
thf(fact_556_PartialSA_Osat_Osimps_I2_J,axiom,
    ! [B: state > $o,Aa2: aassertion_state,Phi2: state] :
      ( ( package_sat_state @ plus @ ( aImp_state @ B @ Aa2 ) @ Phi2 )
      = ( ( B @ Phi2 )
       => ( package_sat_state @ plus @ Aa2 @ Phi2 ) ) ) ).

% PartialSA.sat.simps(2)
thf(fact_557_PartialSA_OAImp,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,B: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ ( packag1330488657391168505_state @ Pc @ B ) @ A5 @ Phi4 @ F5 @ S3 )
     => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ ( aImp_state @ B @ A5 ) @ Phi4 @ F5 @ S3 ) ) ).

% PartialSA.AImp
thf(fact_558_PartialSA_Omax__projection__propE_I3_J,axiom,
    ! [P4: state > $o,F: state > state,P: state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( ( ( P4 @ P )
          & ( greater @ X @ P ) )
       => ( greater @ ( F @ X ) @ P ) ) ) ).

% PartialSA.max_projection_propE(3)
thf(fact_559_PartialSA_OmppI,axiom,
    ! [P4: state > $o,F: state > state,A: state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( ( greater @ A @ X )
       => ( ( P4 @ X )
         => ( ( greater @ X @ ( F @ A ) )
           => ( X
              = ( F @ A ) ) ) ) ) ) ).

% PartialSA.mppI
thf(fact_560_PartialSA_Ompp__mono,axiom,
    ! [P4: state > $o,F: state > state,A: state,B: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( ( greater @ A @ B )
       => ( greater @ ( F @ A ) @ ( F @ B ) ) ) ) ).

% PartialSA.mpp_mono
thf(fact_561_PartialSA_Ompp__smaller,axiom,
    ! [P4: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( greater @ X @ ( F @ X ) ) ) ).

% PartialSA.mpp_smaller
thf(fact_562_PartialSA_Omax__projection__propI,axiom,
    ! [F: state > state,P4: state > $o] :
      ( ! [X2: state] : ( greater @ X2 @ ( F @ X2 ) )
     => ( ! [X2: state] : ( P4 @ ( F @ X2 ) )
       => ( ! [X2: state,P3: state] :
              ( ( ( P4 @ P3 )
                & ( greater @ X2 @ P3 ) )
             => ( greater @ ( F @ X2 ) @ P3 ) )
         => ( sep_ma8214210560313151521_state @ plus @ P4 @ F ) ) ) ) ).

% PartialSA.max_projection_propI
thf(fact_563_PartialSA_Omax__projection__prop__def,axiom,
    ! [P4: state > $o,F: state > state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
      = ( ! [X3: state] :
            ( ( greater @ X3 @ ( F @ X3 ) )
            & ( P4 @ ( F @ X3 ) )
            & ! [P2: state] :
                ( ( ( P4 @ P2 )
                  & ( greater @ X3 @ P2 ) )
               => ( greater @ ( F @ X3 ) @ P2 ) ) ) ) ) ).

% PartialSA.max_projection_prop_def
thf(fact_564_PartialSA_Ompp__compatible,axiom,
    ! [P4: state > $o,F: state > state,A: state,B: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P4 @ F )
     => ( ( defined @ A @ B )
       => ( defined @ ( F @ A ) @ ( F @ B ) ) ) ) ).

% PartialSA.mpp_compatible
thf(fact_565_PartialSA_Ocompleteness,axiom,
    ! [B4: aassertion_state,W: state,R3: state > state > state,A5: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag6192661653625646554_state @ plus @ W @ R3 @ A5 @ B4 ) )
       => ( ( ( some_state @ Sigma )
            = ( plus @ Sigma2 @ W ) )
         => ( ! [A7: state] :
                ( ( package_sat_state @ plus @ A5 @ A7 )
               => ( packag4817583915586052229_state @ plus @ unit @ ( R3 @ A7 ) ) )
           => ? [X_1: set_Pr4231240917283394591_state] :
                ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ unit @ ( R3 @ A3 ) ) ) )
                      & ( package_sat_state @ plus @ A5 @ A3 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% PartialSA.completeness
thf(fact_566_PartialSA_Osoundness,axiom,
    ! [B4: aassertion_state,A5: aassertion_state,S2: set_state,R3: state > state > state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A7: state] :
            ( ( package_sat_state @ plus @ A5 @ A7 )
           => ( member_state @ A7 @ S2 ) )
       => ( ! [A7: state] :
              ( ( member_state @ A7 @ S2 )
             => ( packag4817583915586052229_state @ plus @ unit @ ( R3 @ A7 ) ) )
         => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ unit @ ( R3 @ A3 ) ) ) )
                    & ( member_state @ A3 @ S2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ B4 ) )
                | ( packag4152378406607043437_state @ plus @ S3 ) )
             => ( ( stable @ W )
                & ( ( some_state @ Sigma )
                  = ( plus @ Sigma2 @ W ) )
                & ( packag6192661653625646554_state @ plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ).

% PartialSA.soundness
thf(fact_567_PartialSA_Ominus__def,axiom,
    ( minus
    = ( ^ [B2: state,A3: state] :
          ( fun_TH8221542053827138557_state @ B2
          @ ^ [X3: state] :
              ( ( ( some_state @ B2 )
                = ( plus @ A3 @ X3 ) )
              & ( greater @ X3 @ ( core @ B2 ) ) ) ) ) ) ).

% PartialSA.minus_def
thf(fact_568_PartialSA_Owf__assertion_Oelims_I3_J,axiom,
    ! [X: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( ( packag7298478212905792770_state @ plus @ core @ A10 )
              & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(3)
thf(fact_569_PartialSA_Owf__assertion_Oelims_I2_J,axiom,
    ! [X: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                  & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(2)
thf(fact_570_PartialSA_Osat_Osimps_I3_J,axiom,
    ! [A5: state > $o,Phi2: state] :
      ( ( package_sat_state @ plus @ ( aSem_state @ A5 ) @ Phi2 )
      = ( A5 @ Phi2 ) ) ).

% PartialSA.sat.simps(3)
thf(fact_571_PartialSA_Owf__assertion_Ocases,axiom,
    ! [X: aassertion_state] :
      ( ! [A10: aassertion_state,B8: aassertion_state] :
          ( X
         != ( aStar_state @ A10 @ B8 ) )
     => ( ! [B6: state > $o,A10: aassertion_state] :
            ( X
           != ( aImp_state @ B6 @ A10 ) )
       => ~ ! [A10: state > $o] :
              ( X
             != ( aSem_state @ A10 ) ) ) ) ).

% PartialSA.wf_assertion.cases
thf(fact_572_PartialSA_Osat_Ocases,axiom,
    ! [X: produc2756261550280135502_state] :
      ( ! [A10: aassertion_state,B8: aassertion_state,Phi3: state] :
          ( X
         != ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Phi3 ) )
     => ( ! [B6: state > $o,A10: aassertion_state,Phi3: state] :
            ( X
           != ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Phi3 ) )
       => ~ ! [A10: state > $o,Phi3: state] :
              ( X
             != ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Phi3 ) ) ) ) ).

% PartialSA.sat.cases
thf(fact_573_PartialSA_Oadd__set__def,axiom,
    ( add_set
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi: state,A3: state,B2: state] :
              ( ( Uu3 = Phi )
              & ( member_state @ A3 @ A4 )
              & ( member_state @ B2 @ B3 )
              & ( ( some_state @ Phi )
                = ( plus @ A3 @ B2 ) ) ) ) ) ) ).

% PartialSA.add_set_def
thf(fact_574_PartialSA_Owf__assertion_Osimps_I3_J,axiom,
    ! [A5: state > $o] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aSem_state @ A5 ) )
      = ( packag2456304381420842418_state @ plus @ A5 ) ) ).

% PartialSA.wf_assertion.simps(3)
thf(fact_575_PartialSA_Osat_Oelims_I1_J,axiom,
    ! [X: aassertion_state,Xa: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X @ Xa )
        = Y )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( Y
              = ( ~ ? [A3: state,B2: state] :
                      ( ( ( some_state @ Xa )
                        = ( plus @ A3 @ B2 ) )
                      & ( package_sat_state @ plus @ A10 @ A3 )
                      & ( package_sat_state @ plus @ B8 @ B2 ) ) ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( Y
                = ( ~ ( ( B6 @ Xa )
                     => ( package_sat_state @ plus @ A10 @ Xa ) ) ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( Y
                  = ( ~ ( A10 @ Xa ) ) ) ) ) ) ) ).

% PartialSA.sat.elims(1)
thf(fact_576_PartialSA_Osat_Oelims_I2_J,axiom,
    ! [X: aassertion_state,Xa: state] :
      ( ( package_sat_state @ plus @ X @ Xa )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ~ ? [A7: state,B6: state] :
                  ( ( ( some_state @ Xa )
                    = ( plus @ A7 @ B6 ) )
                  & ( package_sat_state @ plus @ A10 @ A7 )
                  & ( package_sat_state @ plus @ B8 @ B6 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( ( B6 @ Xa )
                 => ( package_sat_state @ plus @ A10 @ Xa ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ~ ( A10 @ Xa ) ) ) ) ) ).

% PartialSA.sat.elims(2)
thf(fact_577_PartialSA_Osat_Oelims_I3_J,axiom,
    ! [X: aassertion_state,Xa: state] :
      ( ~ ( package_sat_state @ plus @ X @ Xa )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ? [A11: state,B9: state] :
                ( ( ( some_state @ Xa )
                  = ( plus @ A11 @ B9 ) )
                & ( package_sat_state @ plus @ A10 @ A11 )
                & ( package_sat_state @ plus @ B8 @ B9 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( ( B6 @ Xa )
               => ( package_sat_state @ plus @ A10 @ Xa ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( A10 @ Xa ) ) ) ) ) ).

% PartialSA.sat.elims(3)
thf(fact_578_PartialSA_Owf__assertion_Oelims_I1_J,axiom,
    ! [X: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X )
        = Y )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( Y
              = ( ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( Y
                = ( ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( Y
                  = ( ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(1)
thf(fact_579_PartialSA_Osoundness__paper,axiom,
    ! [B4: aassertion_state,A5: aassertion_state,S2: set_state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A7: state] :
            ( ( package_sat_state @ plus @ A5 @ A7 )
           => ( member_state @ A7 @ S2 ) )
       => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A3: state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ unit @ id_state ) ) )
                  & ( member_state @ A3 @ S2 ) ) )
            @ ^ [Uu3: state] : $true
            @ B4
            @ Sigma2
            @ W
            @ S3 )
         => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ B4 ) )
              | ( packag4152378406607043437_state @ plus @ S3 ) )
           => ( ( stable @ W )
              & ( ( some_state @ Sigma )
                = ( plus @ Sigma2 @ W ) )
              & ( packag7096211993527611489_state @ plus @ W @ A5 @ B4 ) ) ) ) ) ) ).

% PartialSA.soundness_paper
thf(fact_580_PartialSA_Ocompleteness__paper,axiom,
    ! [B4: aassertion_state,W: state,A5: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag7096211993527611489_state @ plus @ W @ A5 @ B4 ) )
       => ( ( ( some_state @ Sigma )
            = ( plus @ Sigma2 @ W ) )
         => ? [X_1: set_Pr4231240917283394591_state] :
              ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ unit @ id_state ) ) )
                    & ( package_sat_state @ plus @ A5 @ A3 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ X_1 ) ) ) ) ).

% PartialSA.completeness_paper
thf(fact_581_PartialSA_Owf__assertion_Opelims_I1_J,axiom,
    ! [X: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X )
        = Y )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( Y
                  = ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
               => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( Y
                    = ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
                 => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( Y
                      = ( packag2456304381420842418_state @ plus @ A10 ) )
                   => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(1)
thf(fact_582_PartialSA_Owf__assertion_Opelims_I2_J,axiom,
    ! [X: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
               => ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                 => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                   => ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(2)
thf(fact_583_PartialSA_Owf__assertion_Opelims_I3_J,axiom,
    ! [X: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
               => ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                  & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                 => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                    & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                   => ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(3)
thf(fact_584_accp__subset,axiom,
    ! [R1: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,R22: produc1317171644805857433on_val > produc1317171644805857433on_val > $o] :
      ( ( ord_le2319172193063290574_val_o @ R1 @ R22 )
     => ( ord_le8528861841627966596_val_o @ ( accp_P6797916352740768290on_val @ R22 ) @ ( accp_P6797916352740768290on_val @ R1 ) ) ) ).

% accp_subset
thf(fact_585_accp__subset,axiom,
    ! [R1: produc4844402304972151915_state > produc4844402304972151915_state > $o,R22: produc4844402304972151915_state > produc4844402304972151915_state > $o] :
      ( ( ord_le2599682012455951694tate_o @ R1 @ R22 )
     => ( ord_le5681876185599785522tate_o @ ( accp_P6233459008282737652_state @ R22 ) @ ( accp_P6233459008282737652_state @ R1 ) ) ) ).

% accp_subset
thf(fact_586_accp__subset,axiom,
    ! [R1: produc6251377953716854561_state > produc6251377953716854561_state > $o,R22: produc6251377953716854561_state > produc6251377953716854561_state > $o] :
      ( ( ord_le249087669307848398tate_o @ R1 @ R22 )
     => ( ord_le8699832056682887676tate_o @ ( accp_P6554740477754186410_state @ R22 ) @ ( accp_P6554740477754186410_state @ R1 ) ) ) ).

% accp_subset
thf(fact_587_accp__subset,axiom,
    ! [R1: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,R22: produc9003781588162623004on_val > produc9003781588162623004on_val > $o] :
      ( ( ord_le616650860478780142_val_o @ R1 @ R22 )
     => ( ord_le6140313152057869779_val_o @ ( accp_P4405556307444930259on_val @ R22 ) @ ( accp_P4405556307444930259on_val @ R1 ) ) ) ).

% accp_subset
thf(fact_588_accp__subset,axiom,
    ! [R1: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,R22: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le6723339807950303054prat_o @ R1 @ R22 )
     => ( ord_le2830794348966088778prat_o @ ( accp_P4765339447491148764r_prat @ R22 ) @ ( accp_P4765339447491148764r_prat @ R1 ) ) ) ).

% accp_subset
thf(fact_589_PartialSA_OAddFromOutside,axiom,
    ! [Phi2: state,Phi4: state,M: state,F5: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi6: state,F6: state,S5: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( ( some_state @ Phi2 )
        = ( plus @ Phi4 @ M ) )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F5 @ S3 @ Pc @ A5 @ Phi6 @ F6 @ S5 )
       => ( ( stable @ M )
         => ( ( ( some_state @ F5 )
              = ( plus @ F @ M ) )
           => ( ( S3
                = ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state,U6: state,T5: state > state,R: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                      & ( ( some_state @ R )
                        = ( plus @ A3 @ ( minus @ ( T5 @ F5 ) @ ( T5 @ F ) ) ) )
                      & ( defined @ R @ U6 ) ) ) )
             => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi6 @ F6 @ S5 ) ) ) ) ) ) ).

% PartialSA.AddFromOutside
thf(fact_590_PartialSA_Osat_Opelims_I1_J,axiom,
    ! [X: aassertion_state,Xa: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X @ Xa )
        = Y )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( Y
                  = ( ? [A3: state,B2: state] :
                        ( ( ( some_state @ Xa )
                          = ( plus @ A3 @ B2 ) )
                        & ( package_sat_state @ plus @ A10 @ A3 )
                        & ( package_sat_state @ plus @ B8 @ B2 ) ) ) )
               => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( Y
                    = ( ( B6 @ Xa )
                     => ( package_sat_state @ plus @ A10 @ Xa ) ) )
                 => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( Y
                      = ( A10 @ Xa ) )
                   => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(1)
thf(fact_591_PartialSA_Osat_Opelims_I2_J,axiom,
    ! [X: aassertion_state,Xa: state] :
      ( ( package_sat_state @ plus @ X @ Xa )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) )
               => ~ ? [A7: state,B6: state] :
                      ( ( ( some_state @ Xa )
                        = ( plus @ A7 @ B6 ) )
                      & ( package_sat_state @ plus @ A10 @ A7 )
                      & ( package_sat_state @ plus @ B8 @ B6 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) )
                 => ~ ( ( B6 @ Xa )
                     => ( package_sat_state @ plus @ A10 @ Xa ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) )
                   => ~ ( A10 @ Xa ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(2)
thf(fact_592_PartialSA_Osat_Opelims_I3_J,axiom,
    ! [X: aassertion_state,Xa: state] :
      ( ~ ( package_sat_state @ plus @ X @ Xa )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) )
               => ? [A11: state,B9: state] :
                    ( ( ( some_state @ Xa )
                      = ( plus @ A11 @ B9 ) )
                    & ( package_sat_state @ plus @ A10 @ A11 )
                    & ( package_sat_state @ plus @ B8 @ B9 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) )
                 => ( ( B6 @ Xa )
                   => ( package_sat_state @ plus @ A10 @ Xa ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) )
                   => ( A10 @ Xa ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(3)
thf(fact_593_accp__induct__rule,axiom,
    ! [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,A: produc1317171644805857433on_val,P4: produc1317171644805857433on_val > $o] :
      ( ( accp_P6797916352740768290on_val @ R2 @ A )
     => ( ! [X2: produc1317171644805857433on_val] :
            ( ( accp_P6797916352740768290on_val @ R2 @ X2 )
           => ( ! [Y7: produc1317171644805857433on_val] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct_rule
thf(fact_594_accp__induct__rule,axiom,
    ! [R2: produc4844402304972151915_state > produc4844402304972151915_state > $o,A: produc4844402304972151915_state,P4: produc4844402304972151915_state > $o] :
      ( ( accp_P6233459008282737652_state @ R2 @ A )
     => ( ! [X2: produc4844402304972151915_state] :
            ( ( accp_P6233459008282737652_state @ R2 @ X2 )
           => ( ! [Y7: produc4844402304972151915_state] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct_rule
thf(fact_595_accp__induct__rule,axiom,
    ! [R2: produc6251377953716854561_state > produc6251377953716854561_state > $o,A: produc6251377953716854561_state,P4: produc6251377953716854561_state > $o] :
      ( ( accp_P6554740477754186410_state @ R2 @ A )
     => ( ! [X2: produc6251377953716854561_state] :
            ( ( accp_P6554740477754186410_state @ R2 @ X2 )
           => ( ! [Y7: produc6251377953716854561_state] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct_rule
thf(fact_596_accp__induct__rule,axiom,
    ! [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,A: produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( accp_P4405556307444930259on_val @ R2 @ A )
     => ( ! [X2: produc9003781588162623004on_val] :
            ( ( accp_P4405556307444930259on_val @ R2 @ X2 )
           => ( ! [Y7: produc9003781588162623004on_val] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct_rule
thf(fact_597_accp__induct__rule,axiom,
    ! [R2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,A: produc1457211279475724562t_char > prat,P4: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( accp_P4765339447491148764r_prat @ R2 @ A )
     => ( ! [X2: produc1457211279475724562t_char > prat] :
            ( ( accp_P4765339447491148764r_prat @ R2 @ X2 )
           => ( ! [Y7: produc1457211279475724562t_char > prat] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct_rule
thf(fact_598_not__accp__down,axiom,
    ! [R3: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,X: produc1317171644805857433on_val] :
      ( ~ ( accp_P6797916352740768290on_val @ R3 @ X )
     => ~ ! [Z3: produc1317171644805857433on_val] :
            ( ( R3 @ Z3 @ X )
           => ( accp_P6797916352740768290on_val @ R3 @ Z3 ) ) ) ).

% not_accp_down
thf(fact_599_not__accp__down,axiom,
    ! [R3: produc4844402304972151915_state > produc4844402304972151915_state > $o,X: produc4844402304972151915_state] :
      ( ~ ( accp_P6233459008282737652_state @ R3 @ X )
     => ~ ! [Z3: produc4844402304972151915_state] :
            ( ( R3 @ Z3 @ X )
           => ( accp_P6233459008282737652_state @ R3 @ Z3 ) ) ) ).

% not_accp_down
thf(fact_600_not__accp__down,axiom,
    ! [R3: produc6251377953716854561_state > produc6251377953716854561_state > $o,X: produc6251377953716854561_state] :
      ( ~ ( accp_P6554740477754186410_state @ R3 @ X )
     => ~ ! [Z3: produc6251377953716854561_state] :
            ( ( R3 @ Z3 @ X )
           => ( accp_P6554740477754186410_state @ R3 @ Z3 ) ) ) ).

% not_accp_down
thf(fact_601_not__accp__down,axiom,
    ! [R3: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,X: produc9003781588162623004on_val] :
      ( ~ ( accp_P4405556307444930259on_val @ R3 @ X )
     => ~ ! [Z3: produc9003781588162623004on_val] :
            ( ( R3 @ Z3 @ X )
           => ( accp_P4405556307444930259on_val @ R3 @ Z3 ) ) ) ).

% not_accp_down
thf(fact_602_not__accp__down,axiom,
    ! [R3: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,X: produc1457211279475724562t_char > prat] :
      ( ~ ( accp_P4765339447491148764r_prat @ R3 @ X )
     => ~ ! [Z3: produc1457211279475724562t_char > prat] :
            ( ( R3 @ Z3 @ X )
           => ( accp_P4765339447491148764r_prat @ R3 @ Z3 ) ) ) ).

% not_accp_down
thf(fact_603_accp__downward,axiom,
    ! [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,B: produc1317171644805857433on_val,A: produc1317171644805857433on_val] :
      ( ( accp_P6797916352740768290on_val @ R2 @ B )
     => ( ( R2 @ A @ B )
       => ( accp_P6797916352740768290on_val @ R2 @ A ) ) ) ).

% accp_downward
thf(fact_604_accp__downward,axiom,
    ! [R2: produc4844402304972151915_state > produc4844402304972151915_state > $o,B: produc4844402304972151915_state,A: produc4844402304972151915_state] :
      ( ( accp_P6233459008282737652_state @ R2 @ B )
     => ( ( R2 @ A @ B )
       => ( accp_P6233459008282737652_state @ R2 @ A ) ) ) ).

% accp_downward
thf(fact_605_accp__downward,axiom,
    ! [R2: produc6251377953716854561_state > produc6251377953716854561_state > $o,B: produc6251377953716854561_state,A: produc6251377953716854561_state] :
      ( ( accp_P6554740477754186410_state @ R2 @ B )
     => ( ( R2 @ A @ B )
       => ( accp_P6554740477754186410_state @ R2 @ A ) ) ) ).

% accp_downward
thf(fact_606_accp__downward,axiom,
    ! [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,B: produc9003781588162623004on_val,A: produc9003781588162623004on_val] :
      ( ( accp_P4405556307444930259on_val @ R2 @ B )
     => ( ( R2 @ A @ B )
       => ( accp_P4405556307444930259on_val @ R2 @ A ) ) ) ).

% accp_downward
thf(fact_607_accp__downward,axiom,
    ! [R2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,B: produc1457211279475724562t_char > prat,A: produc1457211279475724562t_char > prat] :
      ( ( accp_P4765339447491148764r_prat @ R2 @ B )
     => ( ( R2 @ A @ B )
       => ( accp_P4765339447491148764r_prat @ R2 @ A ) ) ) ).

% accp_downward
thf(fact_608_accp__induct,axiom,
    ! [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,A: produc1317171644805857433on_val,P4: produc1317171644805857433on_val > $o] :
      ( ( accp_P6797916352740768290on_val @ R2 @ A )
     => ( ! [X2: produc1317171644805857433on_val] :
            ( ( accp_P6797916352740768290on_val @ R2 @ X2 )
           => ( ! [Y7: produc1317171644805857433on_val] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct
thf(fact_609_accp__induct,axiom,
    ! [R2: produc4844402304972151915_state > produc4844402304972151915_state > $o,A: produc4844402304972151915_state,P4: produc4844402304972151915_state > $o] :
      ( ( accp_P6233459008282737652_state @ R2 @ A )
     => ( ! [X2: produc4844402304972151915_state] :
            ( ( accp_P6233459008282737652_state @ R2 @ X2 )
           => ( ! [Y7: produc4844402304972151915_state] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct
thf(fact_610_accp__induct,axiom,
    ! [R2: produc6251377953716854561_state > produc6251377953716854561_state > $o,A: produc6251377953716854561_state,P4: produc6251377953716854561_state > $o] :
      ( ( accp_P6554740477754186410_state @ R2 @ A )
     => ( ! [X2: produc6251377953716854561_state] :
            ( ( accp_P6554740477754186410_state @ R2 @ X2 )
           => ( ! [Y7: produc6251377953716854561_state] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct
thf(fact_611_accp__induct,axiom,
    ! [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,A: produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( accp_P4405556307444930259on_val @ R2 @ A )
     => ( ! [X2: produc9003781588162623004on_val] :
            ( ( accp_P4405556307444930259on_val @ R2 @ X2 )
           => ( ! [Y7: produc9003781588162623004on_val] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct
thf(fact_612_accp__induct,axiom,
    ! [R2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,A: produc1457211279475724562t_char > prat,P4: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( accp_P4765339447491148764r_prat @ R2 @ A )
     => ( ! [X2: produc1457211279475724562t_char > prat] :
            ( ( accp_P4765339447491148764r_prat @ R2 @ X2 )
           => ( ! [Y7: produc1457211279475724562t_char > prat] :
                  ( ( R2 @ Y7 @ X2 )
                 => ( P4 @ Y7 ) )
             => ( P4 @ X2 ) ) )
       => ( P4 @ A ) ) ) ).

% accp_induct
thf(fact_613_accpI,axiom,
    ! [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,X: produc1317171644805857433on_val] :
      ( ! [Y3: produc1317171644805857433on_val] :
          ( ( R2 @ Y3 @ X )
         => ( accp_P6797916352740768290on_val @ R2 @ Y3 ) )
     => ( accp_P6797916352740768290on_val @ R2 @ X ) ) ).

% accpI
thf(fact_614_accpI,axiom,
    ! [R2: produc4844402304972151915_state > produc4844402304972151915_state > $o,X: produc4844402304972151915_state] :
      ( ! [Y3: produc4844402304972151915_state] :
          ( ( R2 @ Y3 @ X )
         => ( accp_P6233459008282737652_state @ R2 @ Y3 ) )
     => ( accp_P6233459008282737652_state @ R2 @ X ) ) ).

% accpI
thf(fact_615_accpI,axiom,
    ! [R2: produc6251377953716854561_state > produc6251377953716854561_state > $o,X: produc6251377953716854561_state] :
      ( ! [Y3: produc6251377953716854561_state] :
          ( ( R2 @ Y3 @ X )
         => ( accp_P6554740477754186410_state @ R2 @ Y3 ) )
     => ( accp_P6554740477754186410_state @ R2 @ X ) ) ).

% accpI
thf(fact_616_accpI,axiom,
    ! [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,X: produc9003781588162623004on_val] :
      ( ! [Y3: produc9003781588162623004on_val] :
          ( ( R2 @ Y3 @ X )
         => ( accp_P4405556307444930259on_val @ R2 @ Y3 ) )
     => ( accp_P4405556307444930259on_val @ R2 @ X ) ) ).

% accpI
thf(fact_617_accpI,axiom,
    ! [R2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,X: produc1457211279475724562t_char > prat] :
      ( ! [Y3: produc1457211279475724562t_char > prat] :
          ( ( R2 @ Y3 @ X )
         => ( accp_P4765339447491148764r_prat @ R2 @ Y3 ) )
     => ( accp_P4765339447491148764r_prat @ R2 @ X ) ) ).

% accpI
thf(fact_618_accp_Osimps,axiom,
    ( accp_P6797916352740768290on_val
    = ( ^ [R: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,A3: produc1317171644805857433on_val] :
        ? [X3: produc1317171644805857433on_val] :
          ( ( A3 = X3 )
          & ! [Y5: produc1317171644805857433on_val] :
              ( ( R @ Y5 @ X3 )
             => ( accp_P6797916352740768290on_val @ R @ Y5 ) ) ) ) ) ).

% accp.simps
thf(fact_619_accp_Osimps,axiom,
    ( accp_P6233459008282737652_state
    = ( ^ [R: produc4844402304972151915_state > produc4844402304972151915_state > $o,A3: produc4844402304972151915_state] :
        ? [X3: produc4844402304972151915_state] :
          ( ( A3 = X3 )
          & ! [Y5: produc4844402304972151915_state] :
              ( ( R @ Y5 @ X3 )
             => ( accp_P6233459008282737652_state @ R @ Y5 ) ) ) ) ) ).

% accp.simps
thf(fact_620_accp_Osimps,axiom,
    ( accp_P6554740477754186410_state
    = ( ^ [R: produc6251377953716854561_state > produc6251377953716854561_state > $o,A3: produc6251377953716854561_state] :
        ? [X3: produc6251377953716854561_state] :
          ( ( A3 = X3 )
          & ! [Y5: produc6251377953716854561_state] :
              ( ( R @ Y5 @ X3 )
             => ( accp_P6554740477754186410_state @ R @ Y5 ) ) ) ) ) ).

% accp.simps
thf(fact_621_accp_Osimps,axiom,
    ( accp_P4405556307444930259on_val
    = ( ^ [R: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,A3: produc9003781588162623004on_val] :
        ? [X3: produc9003781588162623004on_val] :
          ( ( A3 = X3 )
          & ! [Y5: produc9003781588162623004on_val] :
              ( ( R @ Y5 @ X3 )
             => ( accp_P4405556307444930259on_val @ R @ Y5 ) ) ) ) ) ).

% accp.simps
thf(fact_622_accp_Osimps,axiom,
    ( accp_P4765339447491148764r_prat
    = ( ^ [R: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,A3: produc1457211279475724562t_char > prat] :
        ? [X3: produc1457211279475724562t_char > prat] :
          ( ( A3 = X3 )
          & ! [Y5: produc1457211279475724562t_char > prat] :
              ( ( R @ Y5 @ X3 )
             => ( accp_P4765339447491148764r_prat @ R @ Y5 ) ) ) ) ) ).

% accp.simps
thf(fact_623_accp_Ocases,axiom,
    ! [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,A: produc1317171644805857433on_val] :
      ( ( accp_P6797916352740768290on_val @ R2 @ A )
     => ! [Y7: produc1317171644805857433on_val] :
          ( ( R2 @ Y7 @ A )
         => ( accp_P6797916352740768290on_val @ R2 @ Y7 ) ) ) ).

% accp.cases
thf(fact_624_accp_Ocases,axiom,
    ! [R2: produc4844402304972151915_state > produc4844402304972151915_state > $o,A: produc4844402304972151915_state] :
      ( ( accp_P6233459008282737652_state @ R2 @ A )
     => ! [Y7: produc4844402304972151915_state] :
          ( ( R2 @ Y7 @ A )
         => ( accp_P6233459008282737652_state @ R2 @ Y7 ) ) ) ).

% accp.cases
thf(fact_625_accp_Ocases,axiom,
    ! [R2: produc6251377953716854561_state > produc6251377953716854561_state > $o,A: produc6251377953716854561_state] :
      ( ( accp_P6554740477754186410_state @ R2 @ A )
     => ! [Y7: produc6251377953716854561_state] :
          ( ( R2 @ Y7 @ A )
         => ( accp_P6554740477754186410_state @ R2 @ Y7 ) ) ) ).

% accp.cases
thf(fact_626_accp_Ocases,axiom,
    ! [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,A: produc9003781588162623004on_val] :
      ( ( accp_P4405556307444930259on_val @ R2 @ A )
     => ! [Y7: produc9003781588162623004on_val] :
          ( ( R2 @ Y7 @ A )
         => ( accp_P4405556307444930259on_val @ R2 @ Y7 ) ) ) ).

% accp.cases
thf(fact_627_accp_Ocases,axiom,
    ! [R2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,A: produc1457211279475724562t_char > prat] :
      ( ( accp_P4765339447491148764r_prat @ R2 @ A )
     => ! [Y7: produc1457211279475724562t_char > prat] :
          ( ( R2 @ Y7 @ A )
         => ( accp_P4765339447491148764r_prat @ R2 @ Y7 ) ) ) ).

% accp.cases
thf(fact_628_accp__subset__induct,axiom,
    ! [D2: produc1317171644805857433on_val > $o,R3: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,X: produc1317171644805857433on_val,P4: produc1317171644805857433on_val > $o] :
      ( ( ord_le8528861841627966596_val_o @ D2 @ ( accp_P6797916352740768290on_val @ R3 ) )
     => ( ! [X2: produc1317171644805857433on_val,Z3: produc1317171644805857433on_val] :
            ( ( D2 @ X2 )
           => ( ( R3 @ Z3 @ X2 )
             => ( D2 @ Z3 ) ) )
       => ( ( D2 @ X )
         => ( ! [X2: produc1317171644805857433on_val] :
                ( ( D2 @ X2 )
               => ( ! [Z4: produc1317171644805857433on_val] :
                      ( ( R3 @ Z4 @ X2 )
                     => ( P4 @ Z4 ) )
                 => ( P4 @ X2 ) ) )
           => ( P4 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_629_accp__subset__induct,axiom,
    ! [D2: produc4844402304972151915_state > $o,R3: produc4844402304972151915_state > produc4844402304972151915_state > $o,X: produc4844402304972151915_state,P4: produc4844402304972151915_state > $o] :
      ( ( ord_le5681876185599785522tate_o @ D2 @ ( accp_P6233459008282737652_state @ R3 ) )
     => ( ! [X2: produc4844402304972151915_state,Z3: produc4844402304972151915_state] :
            ( ( D2 @ X2 )
           => ( ( R3 @ Z3 @ X2 )
             => ( D2 @ Z3 ) ) )
       => ( ( D2 @ X )
         => ( ! [X2: produc4844402304972151915_state] :
                ( ( D2 @ X2 )
               => ( ! [Z4: produc4844402304972151915_state] :
                      ( ( R3 @ Z4 @ X2 )
                     => ( P4 @ Z4 ) )
                 => ( P4 @ X2 ) ) )
           => ( P4 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_630_accp__subset__induct,axiom,
    ! [D2: produc6251377953716854561_state > $o,R3: produc6251377953716854561_state > produc6251377953716854561_state > $o,X: produc6251377953716854561_state,P4: produc6251377953716854561_state > $o] :
      ( ( ord_le8699832056682887676tate_o @ D2 @ ( accp_P6554740477754186410_state @ R3 ) )
     => ( ! [X2: produc6251377953716854561_state,Z3: produc6251377953716854561_state] :
            ( ( D2 @ X2 )
           => ( ( R3 @ Z3 @ X2 )
             => ( D2 @ Z3 ) ) )
       => ( ( D2 @ X )
         => ( ! [X2: produc6251377953716854561_state] :
                ( ( D2 @ X2 )
               => ( ! [Z4: produc6251377953716854561_state] :
                      ( ( R3 @ Z4 @ X2 )
                     => ( P4 @ Z4 ) )
                 => ( P4 @ X2 ) ) )
           => ( P4 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_631_accp__subset__induct,axiom,
    ! [D2: produc9003781588162623004on_val > $o,R3: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,X: produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( ord_le6140313152057869779_val_o @ D2 @ ( accp_P4405556307444930259on_val @ R3 ) )
     => ( ! [X2: produc9003781588162623004on_val,Z3: produc9003781588162623004on_val] :
            ( ( D2 @ X2 )
           => ( ( R3 @ Z3 @ X2 )
             => ( D2 @ Z3 ) ) )
       => ( ( D2 @ X )
         => ( ! [X2: produc9003781588162623004on_val] :
                ( ( D2 @ X2 )
               => ( ! [Z4: produc9003781588162623004on_val] :
                      ( ( R3 @ Z4 @ X2 )
                     => ( P4 @ Z4 ) )
                 => ( P4 @ X2 ) ) )
           => ( P4 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_632_accp__subset__induct,axiom,
    ! [D2: ( produc1457211279475724562t_char > prat ) > $o,R3: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,X: produc1457211279475724562t_char > prat,P4: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le2830794348966088778prat_o @ D2 @ ( accp_P4765339447491148764r_prat @ R3 ) )
     => ( ! [X2: produc1457211279475724562t_char > prat,Z3: produc1457211279475724562t_char > prat] :
            ( ( D2 @ X2 )
           => ( ( R3 @ Z3 @ X2 )
             => ( D2 @ Z3 ) ) )
       => ( ( D2 @ X )
         => ( ! [X2: produc1457211279475724562t_char > prat] :
                ( ( D2 @ X2 )
               => ( ! [Z4: produc1457211279475724562t_char > prat] :
                      ( ( R3 @ Z4 @ X2 )
                     => ( P4 @ Z4 ) )
                 => ( P4 @ X2 ) ) )
           => ( P4 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_633_PartialSA_Opackage__rhs_Osimps,axiom,
    ! [A12: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
      = ( ? [Phi: state,F3: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,A4: aassertion_state,Phi5: state,F7: state,S7: set_Pr4231240917283394591_state,B3: aassertion_state,Phi8: state,F8: state,S8: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi )
            & ( A22 = F3 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aStar_state @ A4 @ B3 ) )
            & ( A62 = Phi8 )
            & ( A72 = F8 )
            & ( A82 = S8 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F3 @ S6 @ Pc2 @ A4 @ Phi5 @ F7 @ S7 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi5 @ F7 @ S7 @ Pc2 @ B3 @ Phi8 @ F8 @ S8 ) )
        | ? [Phi: state,F3: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,B2: state > $o,A4: aassertion_state,Phi5: state,F7: state,S7: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi )
            & ( A22 = F3 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aImp_state @ B2 @ A4 ) )
            & ( A62 = Phi5 )
            & ( A72 = F7 )
            & ( A82 = S7 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F3 @ S6 @ ( packag1330488657391168505_state @ Pc2 @ B2 ) @ A4 @ Phi5 @ F7 @ S7 ) )
        | ? [S6: set_Pr4231240917283394591_state,Pc2: state > $o,Witness: produc7272280185086996969_state > state,B3: state > $o,S7: set_Pr4231240917283394591_state,Phi: state,F3: state] :
            ( ( A12 = Phi )
            & ( A22 = F3 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aSem_state @ B3 ) )
            & ( A62 = Phi )
            & ( A72 = F3 )
            & ( A82 = S7 )
            & ! [X3: state,Y5: state,Z5: state > state,Aa3: state] :
                ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ ( produc8632743443909064678_state @ Y5 @ Z5 ) ) @ S6 )
               => ( ( Pc2 @ X3 )
                 => ( ( Aa3
                      = ( Witness @ ( produc5886875603596089627_state @ X3 @ ( produc8632743443909064678_state @ Y5 @ Z5 ) ) ) )
                   => ( ( greater @ X3 @ Aa3 )
                      & ( B3 @ Aa3 ) ) ) ) )
            & ( S7
              = ( sup_su3837536599209510219_state
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state,U6: state,T5: state > state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                      & ~ ( Pc2 @ A3 ) ) )
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state,U6: state,T5: state > state,B2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ ( minus @ A3 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B2 ) ) @ T5 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                      & ( Pc2 @ A3 )
                      & ( B2
                        = ( Witness @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) ) ) ) )
        | ? [Phi: state,Phi5: state,M2: state,F7: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,A4: aassertion_state,Phi8: state,F8: state,S8: set_Pr4231240917283394591_state,F3: state,S6: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi )
            & ( A22 = F3 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52 = A4 )
            & ( A62 = Phi8 )
            & ( A72 = F8 )
            & ( A82 = S8 )
            & ( ( some_state @ Phi )
              = ( plus @ Phi5 @ M2 ) )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi5 @ F7 @ S7 @ Pc2 @ A4 @ Phi8 @ F8 @ S8 )
            & ( stable @ M2 )
            & ( ( some_state @ F7 )
              = ( plus @ F3 @ M2 ) )
            & ( S7
              = ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state,U6: state,T5: state > state,R: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                    & ( ( some_state @ R )
                      = ( plus @ A3 @ ( minus @ ( T5 @ F7 ) @ ( T5 @ F3 ) ) ) )
                    & ( defined @ R @ U6 ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.simps
thf(fact_634_PartialSA_Opackage__rhs_Ocases,axiom,
    ! [A12: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
     => ( ! [A10: aassertion_state,Phi7: state,F9: state,S9: set_Pr4231240917283394591_state,B8: aassertion_state] :
            ( ( A52
              = ( aStar_state @ A10 @ B8 ) )
           => ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A22 @ A32 @ A42 @ A10 @ Phi7 @ F9 @ S9 )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ Phi7 @ F9 @ S9 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( A52
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A22 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
         => ( ! [Witness2: produc7272280185086996969_state > state,B8: state > $o] :
                ( ( A52
                  = ( aSem_state @ B8 ) )
               => ( ( A62 = A12 )
                 => ( ( A72 = A22 )
                   => ( ! [A11: state,U7: state,T6: state > state] :
                          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) @ A32 )
                         => ( ( A42 @ A11 )
                           => ( ( greater @ A11 @ ( Witness2 @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) ) )
                              & ( B8 @ ( Witness2 @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) ) ) ) ) )
                     => ( A82
                       != ( sup_su3837536599209510219_state
                          @ ( collec906845016635587262_state
                            @ ^ [Uu3: produc7272280185086996969_state] :
                              ? [A3: state,U6: state,T5: state > state] :
                                ( ( Uu3
                                  = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                                & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                & ~ ( A42 @ A3 ) ) )
                          @ ( collec906845016635587262_state
                            @ ^ [Uu3: produc7272280185086996969_state] :
                              ? [A3: state,U6: state,T5: state > state] :
                                ( ( Uu3
                                  = ( produc5886875603596089627_state @ ( minus @ A3 @ ( Witness2 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ ( Witness2 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) @ T5 ) ) )
                                & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                & ( A42 @ A3 ) ) ) ) ) ) ) ) )
           => ~ ! [Phi7: state,M3: state] :
                  ( ( ( some_state @ A12 )
                    = ( plus @ Phi7 @ M3 ) )
                 => ! [F9: state,S9: set_Pr4231240917283394591_state] :
                      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi7 @ F9 @ S9 @ A42 @ A52 @ A62 @ A72 @ A82 )
                     => ( ( stable @ M3 )
                       => ( ( ( some_state @ F9 )
                            = ( plus @ A22 @ M3 ) )
                         => ( S9
                           != ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A3: state,U6: state,T5: state > state,R: state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                  & ( ( some_state @ R )
                                    = ( plus @ A3 @ ( minus @ ( T5 @ F9 ) @ ( T5 @ A22 ) ) ) )
                                  & ( defined @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.cases
thf(fact_635_PartialSA_OASem,axiom,
    ! [S2: set_Pr4231240917283394591_state,Pc: state > $o,Witness3: produc7272280185086996969_state > state,B4: state > $o,S3: set_Pr4231240917283394591_state,Phi2: state,F: state] :
      ( ! [A7: state,U: state,T3: state > state,B6: state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( Pc @ A7 )
           => ( ( B6
                = ( Witness3 @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) ) )
             => ( ( greater @ A7 @ B6 )
                & ( B4 @ B6 ) ) ) ) )
     => ( ( S3
          = ( sup_su3837536599209510219_state
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A3: state,U6: state,T5: state > state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                  & ~ ( Pc @ A3 ) ) )
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A3: state,U6: state,T5: state > state,B2: state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ ( minus @ A3 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B2 ) ) @ T5 ) ) )
                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                  & ( Pc @ A3 )
                  & ( B2
                    = ( Witness3 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) ) ) )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ ( aSem_state @ B4 ) @ Phi2 @ F @ S3 ) ) ) ).

% PartialSA.ASem
thf(fact_636_package__logic_Osoundness,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Unit: produc7272280185086996969_state,Stable: produc7272280185086996969_state > $o,B4: aasser7019605857572776418_state,A5: aasser7019605857572776418_state,S2: set_Pr4231240917283394591_state,R3: produc7272280185086996969_state > produc7272280185086996969_state > produc7272280185086996969_state,Sigma: produc7272280185086996969_state,Sigma2: produc7272280185086996969_state,W: produc7272280185086996969_state,S3: set_Pr3289333603297600445_state] :
      ( ( packag2204431621656667814_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6254535061403973169_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A5 @ A7 )
             => ( member7461423308196221312_state @ A7 @ S2 ) )
         => ( ! [A7: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ A7 @ S2 )
               => ( packag3884151059541177780_state @ Plus @ Unit @ ( R3 @ A7 ) ) )
           => ( ( packag3630742828623380589_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec7677102015826254172_state
                  @ ^ [Uu3: produc3057782296003698823_state] :
                    ? [A3: produc7272280185086996969_state] :
                      ( ( Uu3
                        = ( produc1904032489304825401_state @ A3 @ ( produc7648782313880683123_state @ Unit @ ( R3 @ A3 ) ) ) )
                      & ( member7461423308196221312_state @ A3 @ S2 ) ) )
                @ ^ [Uu3: produc7272280185086996969_state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1160585701684337059_state @ Plus @ ( packag4865960244449834244_state @ Plus @ B4 ) )
                  | ( packag3875795242785447337_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P6297086604321900740_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag7261830501500456713_state @ Plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_637_package__logic_Osoundness,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Unit: produc9003781588162623004on_val,Stable: produc9003781588162623004on_val > $o,B4: aasser1163550960519286933on_val,A5: aasser1163550960519286933on_val,S2: set_Pr7649655576376376530on_val,R3: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val,Sigma: produc9003781588162623004on_val,Sigma2: produc9003781588162623004on_val,W: produc9003781588162623004on_val,S3: set_Pr1565700067222966883on_val] :
      ( ( packag4549880205214723289on_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5541956234368469604on_val @ Plus @ Core @ B4 )
       => ( ! [A7: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A5 @ A7 )
             => ( member2879030624002546611on_val @ A7 @ S2 ) )
         => ( ! [A7: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ A7 @ S2 )
               => ( packag5955012701910386663on_val @ Plus @ Unit @ ( R3 @ A7 ) ) )
           => ( ( packag6843733491101478048on_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec3787697688312515330on_val
                  @ ^ [Uu3: produc217507841372899885on_val] :
                    ? [A3: produc9003781588162623004on_val] :
                      ( ( Uu3
                        = ( produc6985948203474072671on_val @ A3 @ ( produc6949276712527400972on_val @ Unit @ ( R3 @ A3 ) ) ) )
                      & ( member2879030624002546611on_val @ A3 @ S2 ) ) )
                @ ^ [Uu3: produc9003781588162623004on_val] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1465513459401564630on_val @ Plus @ ( packag3677137384183703351on_val @ Plus @ B4 ) )
                  | ( packag161099568566171125on_val @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P2581650809551911671on_val @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag8228529196479615804on_val @ Plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_638_package__logic_Osoundness,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Unit: produc3882902684156697774_state,Stable: produc3882902684156697774_state > $o,B4: aasser3179708585289803787_state,A5: aasser3179708585289803787_state,S2: set_Pr2391701600042252046_state,R3: produc3882902684156697774_state > produc3882902684156697774_state > produc3882902684156697774_state,Sigma: produc3882902684156697774_state,Sigma2: produc3882902684156697774_state,W: produc3882902684156697774_state,S3: set_Pr5308428015838290133_state] :
      ( ( packag9124413901382861105_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8517968027831007846_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A5 @ A7 )
             => ( member6715010751053357271_state @ A7 @ S2 ) )
         => ( ! [A7: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ A7 @ S2 )
               => ( packag5827594511758291363_state @ Plus @ Unit @ ( R3 @ A7 ) ) )
           => ( ( packag4061699384143886122_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec6806307004801468532_state
                  @ ^ [Uu3: produc6455357576889117855_state] :
                    ? [A3: produc3882902684156697774_state] :
                      ( ( Uu3
                        = ( produc5427679348311974809_state @ A3 @ ( produc3987245858496418492_state @ Unit @ ( R3 @ A3 ) ) ) )
                      & ( member6715010751053357271_state @ A3 @ S2 ) ) )
                @ ^ [Uu3: produc3882902684156697774_state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1930333982449825652_state @ Plus @ ( packag2518615827549365843_state @ Plus @ B4 ) )
                  | ( packag1386629450763126729_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P5383513176685068947_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag4438072966337169294_state @ Plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_639_package__logic_Osoundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A5: aassertion_val,S2: set_val,R3: val > val > val,Sigma: val,Sigma2: val,W: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ! [A7: val] :
              ( ( package_sat_val @ Plus @ A5 @ A7 )
             => ( member_val @ A7 @ S2 ) )
         => ( ! [A7: val] :
                ( ( member_val @ A7 @ S2 )
               => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R3 @ A7 ) ) )
           => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A3: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ Unit @ ( R3 @ A3 ) ) ) )
                      & ( member_val @ A3 @ S2 ) ) )
                @ ^ [Uu3: val] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ B4 ) )
                  | ( packag3202507263771882441al_val @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_val @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag4897621287243763553al_val @ Plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_640_package__logic_Osoundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A5: aassertion_state,S2: set_state,R3: state > state > state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ! [A7: state] :
              ( ( package_sat_state @ Plus @ A5 @ A7 )
             => ( member_state @ A7 @ S2 ) )
         => ( ! [A7: state] :
                ( ( member_state @ A7 @ S2 )
               => ( packag4817583915586052229_state @ Plus @ Unit @ ( R3 @ A7 ) ) )
           => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ Unit @ ( R3 @ A3 ) ) ) )
                      & ( member_state @ A3 @ S2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ B4 ) )
                  | ( packag4152378406607043437_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag6192661653625646554_state @ Plus @ W @ R3 @ A5 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_641_Un__iff,axiom,
    ! [C: state,A5: set_state,B4: set_state] :
      ( ( member_state @ C @ ( sup_sup_set_state @ A5 @ B4 ) )
      = ( ( member_state @ C @ A5 )
        | ( member_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_642_Un__iff,axiom,
    ! [C: produc9003781588162623004on_val,A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A5 @ B4 ) )
      = ( ( member2879030624002546611on_val @ C @ A5 )
        | ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_643_Un__iff,axiom,
    ! [C: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A5 @ B4 ) )
      = ( ( member6715010751053357271_state @ C @ A5 )
        | ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_644_Un__iff,axiom,
    ! [C: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
      = ( ( member7461423308196221312_state @ C @ A5 )
        | ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_645_UnCI,axiom,
    ! [C: state,B4: set_state,A5: set_state] :
      ( ( ~ ( member_state @ C @ B4 )
       => ( member_state @ C @ A5 ) )
     => ( member_state @ C @ ( sup_sup_set_state @ A5 @ B4 ) ) ) ).

% UnCI
thf(fact_646_UnCI,axiom,
    ! [C: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,A5: set_Pr7649655576376376530on_val] :
      ( ( ~ ( member2879030624002546611on_val @ C @ B4 )
       => ( member2879030624002546611on_val @ C @ A5 ) )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A5 @ B4 ) ) ) ).

% UnCI
thf(fact_647_UnCI,axiom,
    ! [C: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,A5: set_Pr2391701600042252046_state] :
      ( ( ~ ( member6715010751053357271_state @ C @ B4 )
       => ( member6715010751053357271_state @ C @ A5 ) )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A5 @ B4 ) ) ) ).

% UnCI
thf(fact_648_UnCI,axiom,
    ! [C: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state] :
      ( ( ~ ( member7461423308196221312_state @ C @ B4 )
       => ( member7461423308196221312_state @ C @ A5 ) )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ) ).

% UnCI
thf(fact_649_Un__subset__iff,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A5 @ B4 ) @ C2 )
      = ( ( ord_le4032880777312351359_state @ A5 @ C2 )
        & ( ord_le4032880777312351359_state @ B4 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_650_Un__subset__iff,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A5 @ B4 ) @ C2 )
      = ( ( ord_le2494988322063910608_state @ A5 @ C2 )
        & ( ord_le2494988322063910608_state @ B4 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_651_Collect__disj__eq,axiom,
    ! [P4: state > $o,Q: state > $o] :
      ( ( collect_state
        @ ^ [X3: state] :
            ( ( P4 @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_state @ ( collect_state @ P4 ) @ ( collect_state @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_652_Collect__disj__eq,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [X3: produc9003781588162623004on_val] :
            ( ( P4 @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_su7506060154676209150on_val @ ( collec7475294502966882545on_val @ P4 ) @ ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_653_Collect__disj__eq,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( P4 @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_su3837536599209510219_state @ ( collec906845016635587262_state @ P4 ) @ ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_654_Un__def,axiom,
    ( sup_su1984960714304006370_state
    = ( ^ [A4: set_Pr2391701600042252046_state,B3: set_Pr2391701600042252046_state] :
          ( collec394671971739345689_state
          @ ^ [X3: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X3 @ A4 )
              | ( member6715010751053357271_state @ X3 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_655_Un__def,axiom,
    ( sup_sup_set_state
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ^ [X3: state] :
              ( ( member_state @ X3 @ A4 )
              | ( member_state @ X3 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_656_Un__def,axiom,
    ( sup_su7506060154676209150on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,B3: set_Pr7649655576376376530on_val] :
          ( collec7475294502966882545on_val
          @ ^ [X3: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ X3 @ A4 )
              | ( member2879030624002546611on_val @ X3 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_657_Un__def,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
          ( collec906845016635587262_state
          @ ^ [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ A4 )
              | ( member7461423308196221312_state @ X3 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_658_subset__Un__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A4 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_659_subset__Un__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A4: set_state,B3: set_state] :
          ( ( sup_sup_set_state @ A4 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_660_subset__UnE,axiom,
    ! [C2: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C2 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
     => ~ ! [A13: set_Pr4231240917283394591_state] :
            ( ( ord_le4032880777312351359_state @ A13 @ A5 )
           => ! [B10: set_Pr4231240917283394591_state] :
                ( ( ord_le4032880777312351359_state @ B10 @ B4 )
               => ( C2
                 != ( sup_su3837536599209510219_state @ A13 @ B10 ) ) ) ) ) ).

% subset_UnE
thf(fact_661_subset__UnE,axiom,
    ! [C2: set_state,A5: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ C2 @ ( sup_sup_set_state @ A5 @ B4 ) )
     => ~ ! [A13: set_state] :
            ( ( ord_le2494988322063910608_state @ A13 @ A5 )
           => ! [B10: set_state] :
                ( ( ord_le2494988322063910608_state @ B10 @ B4 )
               => ( C2
                 != ( sup_sup_set_state @ A13 @ B10 ) ) ) ) ) ).

% subset_UnE
thf(fact_662_Un__absorb2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B4 @ A5 )
     => ( ( sup_su3837536599209510219_state @ A5 @ B4 )
        = A5 ) ) ).

% Un_absorb2
thf(fact_663_Un__absorb2,axiom,
    ! [B4: set_state,A5: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ A5 )
     => ( ( sup_sup_set_state @ A5 @ B4 )
        = A5 ) ) ).

% Un_absorb2
thf(fact_664_Un__absorb1,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ B4 )
     => ( ( sup_su3837536599209510219_state @ A5 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_665_Un__absorb1,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ( sup_sup_set_state @ A5 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_666_Un__upper2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ B4 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ).

% Un_upper2
thf(fact_667_Un__upper2,axiom,
    ! [B4: set_state,A5: set_state] : ( ord_le2494988322063910608_state @ B4 @ ( sup_sup_set_state @ A5 @ B4 ) ) ).

% Un_upper2
thf(fact_668_Un__upper1,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ A5 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ).

% Un_upper1
thf(fact_669_Un__upper1,axiom,
    ! [A5: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ A5 @ ( sup_sup_set_state @ A5 @ B4 ) ) ).

% Un_upper1
thf(fact_670_Un__least,axiom,
    ! [A5: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ C2 )
     => ( ( ord_le4032880777312351359_state @ B4 @ C2 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A5 @ B4 ) @ C2 ) ) ) ).

% Un_least
thf(fact_671_Un__least,axiom,
    ! [A5: set_state,C2: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ C2 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C2 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A5 @ B4 ) @ C2 ) ) ) ).

% Un_least
thf(fact_672_Un__mono,axiom,
    ! [A5: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,D2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ C2 )
     => ( ( ord_le4032880777312351359_state @ B4 @ D2 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A5 @ B4 ) @ ( sup_su3837536599209510219_state @ C2 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_673_Un__mono,axiom,
    ! [A5: set_state,C2: set_state,B4: set_state,D2: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ C2 )
     => ( ( ord_le2494988322063910608_state @ B4 @ D2 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A5 @ B4 ) @ ( sup_sup_set_state @ C2 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_674_Un__left__commute,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A5 @ ( sup_su3837536599209510219_state @ B4 @ C2 ) )
      = ( sup_su3837536599209510219_state @ B4 @ ( sup_su3837536599209510219_state @ A5 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_675_Un__left__absorb,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A5 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
      = ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ).

% Un_left_absorb
thf(fact_676_Un__commute,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] : ( sup_su3837536599209510219_state @ B3 @ A4 ) ) ) ).

% Un_commute
thf(fact_677_Un__absorb,axiom,
    ! [A5: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A5 @ A5 )
      = A5 ) ).

% Un_absorb
thf(fact_678_Un__assoc,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ ( sup_su3837536599209510219_state @ A5 @ B4 ) @ C2 )
      = ( sup_su3837536599209510219_state @ A5 @ ( sup_su3837536599209510219_state @ B4 @ C2 ) ) ) ).

% Un_assoc
thf(fact_679_ball__Un,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
           => ( P4 @ X3 ) ) )
      = ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ A5 )
           => ( P4 @ X3 ) )
        & ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ B4 )
           => ( P4 @ X3 ) ) ) ) ).

% ball_Un
thf(fact_680_bex__Un,axiom,
    ! [A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ( ? [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
            & ( P4 @ X3 ) ) )
      = ( ? [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ A5 )
            & ( P4 @ X3 ) )
        | ? [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ B4 )
            & ( P4 @ X3 ) ) ) ) ).

% bex_Un
thf(fact_681_UnI2,axiom,
    ! [C: state,B4: set_state,A5: set_state] :
      ( ( member_state @ C @ B4 )
     => ( member_state @ C @ ( sup_sup_set_state @ A5 @ B4 ) ) ) ).

% UnI2
thf(fact_682_UnI2,axiom,
    ! [C: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,A5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ B4 )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A5 @ B4 ) ) ) ).

% UnI2
thf(fact_683_UnI2,axiom,
    ! [C: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,A5: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ B4 )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A5 @ B4 ) ) ) ).

% UnI2
thf(fact_684_UnI2,axiom,
    ! [C: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,A5: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ B4 )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ) ).

% UnI2
thf(fact_685_UnI1,axiom,
    ! [C: state,A5: set_state,B4: set_state] :
      ( ( member_state @ C @ A5 )
     => ( member_state @ C @ ( sup_sup_set_state @ A5 @ B4 ) ) ) ).

% UnI1
thf(fact_686_UnI1,axiom,
    ! [C: produc9003781588162623004on_val,A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ A5 )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A5 @ B4 ) ) ) ).

% UnI1
thf(fact_687_UnI1,axiom,
    ! [C: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ A5 )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A5 @ B4 ) ) ) ).

% UnI1
thf(fact_688_UnI1,axiom,
    ! [C: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ A5 )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A5 @ B4 ) ) ) ).

% UnI1
thf(fact_689_UnE,axiom,
    ! [C: state,A5: set_state,B4: set_state] :
      ( ( member_state @ C @ ( sup_sup_set_state @ A5 @ B4 ) )
     => ( ~ ( member_state @ C @ A5 )
       => ( member_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_690_UnE,axiom,
    ! [C: produc9003781588162623004on_val,A5: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A5 @ B4 ) )
     => ( ~ ( member2879030624002546611on_val @ C @ A5 )
       => ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% UnE
thf(fact_691_UnE,axiom,
    ! [C: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A5 @ B4 ) )
     => ( ~ ( member6715010751053357271_state @ C @ A5 )
       => ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_692_UnE,axiom,
    ! [C: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
     => ( ~ ( member7461423308196221312_state @ C @ A5 )
       => ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_693_Rep__state__induct,axiom,
    ! [Y: produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ Y
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi )
              & ( valid_state @ Phi ) ) ) )
     => ( ! [X2: state] : ( P4 @ ( rep_state @ X2 ) )
       => ( P4 @ Y ) ) ) ).

% Rep_state_induct
thf(fact_694_Rep__state__cases,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ Y @ ( collec7475294502966882545on_val @ valid_state ) )
     => ~ ! [X2: state] :
            ( Y
           != ( rep_state @ X2 ) ) ) ).

% Rep_state_cases
thf(fact_695_Rep__state,axiom,
    ! [X: state] :
      ( member2879030624002546611on_val @ ( rep_state @ X )
      @ ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [Phi: produc9003781588162623004on_val] :
            ( ( Uu3 = Phi )
            & ( valid_state @ Phi ) ) ) ) ).

% Rep_state
thf(fact_696_Abs__state__inject,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ X
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi )
              & ( valid_state @ Phi ) ) ) )
     => ( ( member2879030624002546611on_val @ Y
          @ ( collec7475294502966882545on_val
            @ ^ [Uu3: produc9003781588162623004on_val] :
              ? [Phi: produc9003781588162623004on_val] :
                ( ( Uu3 = Phi )
                & ( valid_state @ Phi ) ) ) )
       => ( ( ( abs_state @ X )
            = ( abs_state @ Y ) )
          = ( X = Y ) ) ) ) ).

% Abs_state_inject
thf(fact_697_Abs__state__induct,axiom,
    ! [P4: state > $o,X: state] :
      ( ! [Y3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ Y3
            @ ( collec7475294502966882545on_val
              @ ^ [Uu3: produc9003781588162623004on_val] :
                ? [Phi: produc9003781588162623004on_val] :
                  ( ( Uu3 = Phi )
                  & ( valid_state @ Phi ) ) ) )
         => ( P4 @ ( abs_state @ Y3 ) ) )
     => ( P4 @ X ) ) ).

% Abs_state_induct
thf(fact_698_Abs__state__cases,axiom,
    ! [X: state] :
      ~ ! [Y3: produc9003781588162623004on_val] :
          ( ( X
            = ( abs_state @ Y3 ) )
         => ~ ( member2879030624002546611on_val @ Y3 @ ( collec7475294502966882545on_val @ valid_state ) ) ) ).

% Abs_state_cases
thf(fact_699_package__logic_Osat_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: produc2756261550280135502_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A10: aassertion_state,B8: aassertion_state,Phi3: state] :
            ( X
           != ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Phi3 ) )
       => ( ! [B6: state > $o,A10: aassertion_state,Phi3: state] :
              ( X
             != ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Phi3 ) )
         => ~ ! [A10: state > $o,Phi3: state] :
                ( X
               != ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Phi3 ) ) ) ) ) ).

% package_logic.sat.cases
thf(fact_700_Abs__state__inverse,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ Y
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi )
              & ( valid_state @ Phi ) ) ) )
     => ( ( rep_state @ ( abs_state @ Y ) )
        = Y ) ) ).

% Abs_state_inverse
thf(fact_701_PartialSA_Opackage__logic__axioms,axiom,
    package_logic_state @ plus @ core @ unit @ stable ).

% PartialSA.package_logic_axioms
thf(fact_702_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,S2: set_Pr4723104092121316667al_val,F: val,A5: aassertion_val,Phi2: val,Phi4: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: val,U: val,T3: val > val] :
            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A7 @ ( produc303288909735261391al_val @ U @ T3 ) ) @ S2 )
           => ! [X2: val] :
                ( ( ( some_val @ X2 )
                  = ( Plus @ A7 @ ( T3 @ F ) ) )
               => ( package_sat_val @ Plus @ A5 @ X2 ) ) )
       => ( ( ( some_val @ Phi2 )
            = ( Plus @ Phi4 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag7517340229427718612et_val @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag5732365195153136185on_val @ Plus @ Core @ A5 )
               => ? [X_1: set_Pr4723104092121316667al_val] :
                    ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ Unit @ S2
                    @ ^ [Uu3: val] : $true
                    @ A5
                    @ Phi4
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_703_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state,A5: aassertion_state,Phi2: state,Phi4: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ! [X2: state] :
                ( ( ( some_state @ X2 )
                  = ( Plus @ A7 @ ( T3 @ F ) ) )
               => ( package_sat_state @ Plus @ A5 @ X2 ) ) )
       => ( ( ( some_state @ Phi2 )
            = ( Plus @ Phi4 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag7298478212905792770_state @ Plus @ Core @ A5 )
               => ? [X_1: set_Pr4231240917283394591_state] :
                    ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ Unit @ S2
                    @ ^ [Uu3: state] : $true
                    @ A5
                    @ Phi4
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_704_package__logic_Osat_Opelims_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa: val,Y: $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_val @ Plus @ X @ Xa )
          = Y )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( Y
                    = ( ? [A3: val,B2: val] :
                          ( ( ( some_val @ Xa )
                            = ( Plus @ A3 @ B2 ) )
                          & ( package_sat_val @ Plus @ A10 @ A3 )
                          & ( package_sat_val @ Plus @ B8 @ B2 ) ) ) )
                 => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( Y
                      = ( ( B6 @ Xa )
                       => ( package_sat_val @ Plus @ A10 @ Xa ) ) )
                   => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( Y
                        = ( A10 @ Xa ) )
                     => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa ) ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(1)
thf(fact_705_package__logic_Osat_Opelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa: state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_state @ Plus @ X @ Xa )
          = Y )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( Y
                    = ( ? [A3: state,B2: state] :
                          ( ( ( some_state @ Xa )
                            = ( Plus @ A3 @ B2 ) )
                          & ( package_sat_state @ Plus @ A10 @ A3 )
                          & ( package_sat_state @ Plus @ B8 @ B2 ) ) ) )
                 => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( Y
                      = ( ( B6 @ Xa )
                       => ( package_sat_state @ Plus @ A10 @ Xa ) ) )
                   => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( Y
                        = ( A10 @ Xa ) )
                     => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(1)
thf(fact_706_package__logic_Osat_Opelims_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ X @ Xa )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa ) )
                 => ~ ? [A7: val,B6: val] :
                        ( ( ( some_val @ Xa )
                          = ( Plus @ A7 @ B6 ) )
                        & ( package_sat_val @ Plus @ A10 @ A7 )
                        & ( package_sat_val @ Plus @ B8 @ B6 ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa ) )
                   => ~ ( ( B6 @ Xa )
                       => ( package_sat_val @ Plus @ A10 @ Xa ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa ) )
                     => ~ ( A10 @ Xa ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(2)
thf(fact_707_package__logic_Osat_Opelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ X @ Xa )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) )
                 => ~ ? [A7: state,B6: state] :
                        ( ( ( some_state @ Xa )
                          = ( Plus @ A7 @ B6 ) )
                        & ( package_sat_state @ Plus @ A10 @ A7 )
                        & ( package_sat_state @ Plus @ B8 @ B6 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) )
                   => ~ ( ( B6 @ Xa )
                       => ( package_sat_state @ Plus @ A10 @ Xa ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) )
                     => ~ ( A10 @ Xa ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(2)
thf(fact_708_package__logic_Osat_Opelims_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_val @ Plus @ X @ Xa )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa ) )
                 => ? [A11: val,B9: val] :
                      ( ( ( some_val @ Xa )
                        = ( Plus @ A11 @ B9 ) )
                      & ( package_sat_val @ Plus @ A10 @ A11 )
                      & ( package_sat_val @ Plus @ B8 @ B9 ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa ) )
                   => ( ( B6 @ Xa )
                     => ( package_sat_val @ Plus @ A10 @ Xa ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa ) )
                     => ( A10 @ Xa ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(3)
thf(fact_709_package__logic_Osat_Opelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_state @ Plus @ X @ Xa )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa ) )
                 => ? [A11: state,B9: state] :
                      ( ( ( some_state @ Xa )
                        = ( Plus @ A11 @ B9 ) )
                      & ( package_sat_state @ Plus @ A10 @ A11 )
                      & ( package_sat_state @ Plus @ B8 @ B9 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa ) )
                   => ( ( B6 @ Xa )
                     => ( package_sat_state @ Plus @ A10 @ Xa ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa ) )
                     => ( A10 @ Xa ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(3)
thf(fact_710_package__logic_Owf__assertion_Opelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( packag7298478212905792770_state @ Plus @ Core @ X )
       => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
                 => ( ( packag7298478212905792770_state @ Plus @ Core @ A10 )
                    & ( packag7298478212905792770_state @ Plus @ Core @ B8 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                   => ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                      & ( packag7298478212905792770_state @ Plus @ Core @ A10 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                     => ( packag2456304381420842418_state @ Plus @ A10 ) ) ) ) ) ) ) ) ).

% package_logic.wf_assertion.pelims(3)
thf(fact_711_package__logic_Owf__assertion_Opelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ X )
       => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
                 => ~ ( ( packag7298478212905792770_state @ Plus @ Core @ A10 )
                      & ( packag7298478212905792770_state @ Plus @ Core @ B8 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                   => ~ ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                        & ( packag7298478212905792770_state @ Plus @ Core @ A10 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                     => ~ ( packag2456304381420842418_state @ Plus @ A10 ) ) ) ) ) ) ) ) ).

% package_logic.wf_assertion.pelims(2)
thf(fact_712_package__logic_Owf__assertion_Opelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( packag7298478212905792770_state @ Plus @ Core @ X )
          = Y )
       => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( Y
                    = ( ( packag7298478212905792770_state @ Plus @ Core @ A10 )
                      & ( packag7298478212905792770_state @ Plus @ Core @ B8 ) ) )
                 => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( Y
                      = ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                        & ( packag7298478212905792770_state @ Plus @ Core @ A10 ) ) )
                   => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( Y
                        = ( packag2456304381420842418_state @ Plus @ A10 ) )
                     => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) ) ) ) ) ) ) ) ) ).

% package_logic.wf_assertion.pelims(1)
thf(fact_713_scaled__def,axiom,
    ( scaled
    = ( ^ [Phi: state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [P2: prat] :
              ( ( Uu3
                = ( multiply @ P2 @ Phi ) )
              & ( ppos @ P2 )
              & ( pgte @ pwrite @ P2 ) ) ) ) ) ).

% scaled_def
thf(fact_714_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,A5: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag685230357167683994rd_val @ Plus @ W @ A5 @ B4 ) )
         => ( ( ( some_val @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ? [X_1: set_Pr4723104092121316667al_val] :
                ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A3: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ Unit @ id_val ) ) )
                      & ( package_sat_val @ Plus @ A5 @ A3 ) ) )
                @ ^ [Uu3: val] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_715_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,A5: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag7096211993527611489_state @ Plus @ W @ A5 @ B4 ) )
         => ( ( ( some_state @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ? [X_1: set_Pr4231240917283394591_state] :
                ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ Unit @ id_state ) ) )
                      & ( package_sat_state @ Plus @ A5 @ A3 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_716_package__logic_Ocompleteness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,R3: val > val > val,A5: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag4897621287243763553al_val @ Plus @ W @ R3 @ A5 @ B4 ) )
         => ( ( ( some_val @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A7: val] :
                  ( ( package_sat_val @ Plus @ A5 @ A7 )
                 => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R3 @ A7 ) ) )
             => ? [X_1: set_Pr4723104092121316667al_val] :
                  ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                  @ ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A3: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ Unit @ ( R3 @ A3 ) ) ) )
                        & ( package_sat_val @ Plus @ A5 @ A3 ) ) )
                  @ ^ [Uu3: val] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_717_package__logic_Ocompleteness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,R3: state > state > state,A5: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag6192661653625646554_state @ Plus @ W @ R3 @ A5 @ B4 ) )
         => ( ( ( some_state @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A7: state] :
                  ( ( package_sat_state @ Plus @ A5 @ A7 )
                 => ( packag4817583915586052229_state @ Plus @ Unit @ ( R3 @ A7 ) ) )
             => ? [X_1: set_Pr4231240917283394591_state] :
                  ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                  @ ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A3: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ Unit @ ( R3 @ A3 ) ) ) )
                        & ( package_sat_state @ Plus @ A5 @ A3 ) ) )
                  @ ^ [Uu3: state] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_718_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Unit: produc7272280185086996969_state,Stable: produc7272280185086996969_state > $o,B4: aasser7019605857572776418_state,A5: aasser7019605857572776418_state,S2: set_Pr4231240917283394591_state,Sigma: produc7272280185086996969_state,Sigma2: produc7272280185086996969_state,W: produc7272280185086996969_state,S3: set_Pr3289333603297600445_state] :
      ( ( packag2204431621656667814_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6254535061403973169_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A5 @ A7 )
             => ( member7461423308196221312_state @ A7 @ S2 ) )
         => ( ( packag3630742828623380589_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec7677102015826254172_state
                @ ^ [Uu3: produc3057782296003698823_state] :
                  ? [A3: produc7272280185086996969_state] :
                    ( ( Uu3
                      = ( produc1904032489304825401_state @ A3 @ ( produc7648782313880683123_state @ Unit @ id_Pro2933125508726022968_state ) ) )
                    & ( member7461423308196221312_state @ A3 @ S2 ) ) )
              @ ^ [Uu3: produc7272280185086996969_state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1160585701684337059_state @ Plus @ ( packag4865960244449834244_state @ Plus @ B4 ) )
                | ( packag3875795242785447337_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P6297086604321900740_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag8077625386405451152_state @ Plus @ W @ A5 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_719_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Unit: produc9003781588162623004on_val,Stable: produc9003781588162623004on_val > $o,B4: aasser1163550960519286933on_val,A5: aasser1163550960519286933on_val,S2: set_Pr7649655576376376530on_val,Sigma: produc9003781588162623004on_val,Sigma2: produc9003781588162623004on_val,W: produc9003781588162623004on_val,S3: set_Pr1565700067222966883on_val] :
      ( ( packag4549880205214723289on_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5541956234368469604on_val @ Plus @ Core @ B4 )
       => ( ! [A7: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A5 @ A7 )
             => ( member2879030624002546611on_val @ A7 @ S2 ) )
         => ( ( packag6843733491101478048on_val @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec3787697688312515330on_val
                @ ^ [Uu3: produc217507841372899885on_val] :
                  ? [A3: produc9003781588162623004on_val] :
                    ( ( Uu3
                      = ( produc6985948203474072671on_val @ A3 @ ( produc6949276712527400972on_val @ Unit @ id_Pro1402184692240358763on_val ) ) )
                    & ( member2879030624002546611on_val @ A3 @ S2 ) ) )
              @ ^ [Uu3: produc9003781588162623004on_val] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1465513459401564630on_val @ Plus @ ( packag3677137384183703351on_val @ Plus @ B4 ) )
                | ( packag161099568566171125on_val @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P2581650809551911671on_val @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag6258220590826782659on_val @ Plus @ W @ A5 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_720_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Unit: produc3882902684156697774_state,Stable: produc3882902684156697774_state > $o,B4: aasser3179708585289803787_state,A5: aasser3179708585289803787_state,S2: set_Pr2391701600042252046_state,Sigma: produc3882902684156697774_state,Sigma2: produc3882902684156697774_state,W: produc3882902684156697774_state,S3: set_Pr5308428015838290133_state] :
      ( ( packag9124413901382861105_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8517968027831007846_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A5 @ A7 )
             => ( member6715010751053357271_state @ A7 @ S2 ) )
         => ( ( packag4061699384143886122_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec6806307004801468532_state
                @ ^ [Uu3: produc6455357576889117855_state] :
                  ? [A3: produc3882902684156697774_state] :
                    ( ( Uu3
                      = ( produc5427679348311974809_state @ A3 @ ( produc3987245858496418492_state @ Unit @ id_Pro689249233197853983_state ) ) )
                    & ( member6715010751053357271_state @ A3 @ S2 ) ) )
              @ ^ [Uu3: produc3882902684156697774_state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1930333982449825652_state @ Plus @ ( packag2518615827549365843_state @ Plus @ B4 ) )
                | ( packag1386629450763126729_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P5383513176685068947_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag3130788337556013255_state @ Plus @ W @ A5 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_721_package__logic_Osoundness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A5: aassertion_val,S2: set_val,Sigma: val,Sigma2: val,W: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ! [A7: val] :
              ( ( package_sat_val @ Plus @ A5 @ A7 )
             => ( member_val @ A7 @ S2 ) )
         => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec8300311316619386842al_val
                @ ^ [Uu3: produc2072440392815185925al_val] :
                  ? [A3: val] :
                    ( ( Uu3
                      = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ Unit @ id_val ) ) )
                    & ( member_val @ A3 @ S2 ) ) )
              @ ^ [Uu3: val] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ B4 ) )
                | ( packag3202507263771882441al_val @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_val @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag685230357167683994rd_val @ Plus @ W @ A5 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_722_package__logic_Osoundness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A5: aassertion_state,S2: set_state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ! [A7: state] :
              ( ( package_sat_state @ Plus @ A5 @ A7 )
             => ( member_state @ A7 @ S2 ) )
         => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ Unit @ id_state ) ) )
                    & ( member_state @ A3 @ S2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ B4 ) )
                | ( packag4152378406607043437_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag7096211993527611489_state @ Plus @ W @ A5 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_723_le__sup__iff,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ X @ Y ) @ Z2 )
      = ( ( ord_le4032880777312351359_state @ X @ Z2 )
        & ( ord_le4032880777312351359_state @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_724_le__sup__iff,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X @ Y ) @ Z2 )
      = ( ( ord_le2494988322063910608_state @ X @ Z2 )
        & ( ord_le2494988322063910608_state @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_725_sup_Obounded__iff,axiom,
    ! [B: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A )
      = ( ( ord_le4032880777312351359_state @ B @ A )
        & ( ord_le4032880777312351359_state @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_726_sup_Obounded__iff,axiom,
    ! [B: set_state,C: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A )
      = ( ( ord_le2494988322063910608_state @ B @ A )
        & ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_727_PartialSA_Ogeneral__soundness,axiom,
    ! [Phi2: state,S2: set_Pr2391701600042252046_state,A5: aassertion_state,Phi4: state,F: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ unit
        @ ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [A3: state,T5: state > state] :
              ( ( Uu3
                = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ unit @ T5 ) ) )
              & ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A3 @ T5 ) @ S2 ) ) )
        @ ^ [Uu3: state] : $true
        @ A5
        @ Phi4
        @ F
        @ S3 )
     => ( ! [A7: state,T3: state > state] :
            ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A7 @ T3 ) @ S2 )
           => ( packag4817583915586052229_state @ plus @ unit @ T3 ) )
       => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
         => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ A5 ) )
              | ( packag4152378406607043437_state @ plus @ S3 ) )
           => ( ( ( some_state @ Phi2 )
                = ( plus @ Phi4 @ F ) )
              & ( stable @ F )
              & ! [X5: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ X5 @ S2 )
                 => ( produc3645877548210629341tate_o
                    @ ^ [A3: state,T5: state > state] :
                        ( ( defined @ A3 @ ( T5 @ F ) )
                       => ( package_sat_state @ plus @ A5 @ ( the_state @ ( plus @ A3 @ ( T5 @ F ) ) ) ) )
                    @ X5 ) ) ) ) ) ) ) ).

% PartialSA.general_soundness
thf(fact_728_PartialSA_Ounder__def,axiom,
    ! [A5: set_state,Omega2: state] :
      ( ( sep_under_state @ plus @ A5 @ Omega2 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Omega3: state] :
            ( ( Uu3 = Omega3 )
            & ( member_state @ Omega3 @ A5 )
            & ( greater @ Omega2 @ Omega3 ) ) ) ) ).

% PartialSA.under_def
thf(fact_729_split__part,axiom,
    ! [P4: $o,Q: state > ( state > state ) > $o] :
      ( ( produc3645877548210629341tate_o
        @ ^ [A3: state,B2: state > state] :
            ( P4
            & ( Q @ A3 @ B2 ) ) )
      = ( ^ [Ab2: produc3882902684156697774_state] :
            ( P4
            & ( produc3645877548210629341tate_o @ Q @ Ab2 ) ) ) ) ).

% split_part
thf(fact_730_split__part,axiom,
    ! [P4: $o,Q: state > produc3882902684156697774_state > $o] :
      ( ( produc1745419677418529872tate_o
        @ ^ [A3: state,B2: produc3882902684156697774_state] :
            ( P4
            & ( Q @ A3 @ B2 ) ) )
      = ( ^ [Ab2: produc7272280185086996969_state] :
            ( P4
            & ( produc1745419677418529872tate_o @ Q @ Ab2 ) ) ) ) ).

% split_part
thf(fact_731_case__prod__conv,axiom,
    ! [F: state > ( state > state ) > $o,A: state,B: state > state] :
      ( ( produc3645877548210629341tate_o @ F @ ( produc8632743443909064678_state @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_732_case__prod__conv,axiom,
    ! [F: state > produc3882902684156697774_state > $o,A: state,B: produc3882902684156697774_state] :
      ( ( produc1745419677418529872tate_o @ F @ ( produc5886875603596089627_state @ A @ B ) )
      = ( F @ A @ B ) ) ).

% case_prod_conv
thf(fact_733_case__prodI2,axiom,
    ! [P: produc3142500478612311029_state,C: option_state > option_state > $o] :
      ( ! [A7: option_state,B6: option_state] :
          ( ( P
            = ( produc9160152616361873709_state @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc6082990154846732246tate_o @ C @ P ) ) ).

% case_prodI2
thf(fact_734_case__prodI2,axiom,
    ! [P: produc4844402304972151915_state,C: prat > state > $o] :
      ( ! [A7: prat,B6: state] :
          ( ( P
            = ( produc6205719116230455971_state @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc1228703470279370976tate_o @ C @ P ) ) ).

% case_prodI2
thf(fact_735_case__prodI2,axiom,
    ! [P: produc6251377953716854561_state,C: prat > set_state > $o] :
      ( ! [A7: prat,B6: set_state] :
          ( ( P
            = ( produc9080284787853255769_state @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc7925652287191295402tate_o @ C @ P ) ) ).

% case_prodI2
thf(fact_736_case__prodI2,axiom,
    ! [P: produc1457211279475724562t_char,C: nat > list_char > $o] :
      ( ! [A7: nat,B6: list_char] :
          ( ( P
            = ( produc120197956887798346t_char @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc8526122873445342073char_o @ C @ P ) ) ).

% case_prodI2
thf(fact_737_case__prodI2,axiom,
    ! [P: produc9003781588162623004on_val,C: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ! [A7: produc1457211279475724562t_char > prat,B6: produc1457211279475724562t_char > option_val] :
          ( ( P
            = ( produc74620467203698198on_val @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc5248837549992124053_val_o @ C @ P ) ) ).

% case_prodI2
thf(fact_738_case__prodI2,axiom,
    ! [P: produc3882902684156697774_state,C: state > ( state > state ) > $o] :
      ( ! [A7: state,B6: state > state] :
          ( ( P
            = ( produc8632743443909064678_state @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc3645877548210629341tate_o @ C @ P ) ) ).

% case_prodI2
thf(fact_739_case__prodI2,axiom,
    ! [P: produc7272280185086996969_state,C: state > produc3882902684156697774_state > $o] :
      ( ! [A7: state,B6: produc3882902684156697774_state] :
          ( ( P
            = ( produc5886875603596089627_state @ A7 @ B6 ) )
         => ( C @ A7 @ B6 ) )
     => ( produc1745419677418529872tate_o @ C @ P ) ) ).

% case_prodI2
thf(fact_740_case__prodI,axiom,
    ! [F: option_state > option_state > $o,A: option_state,B: option_state] :
      ( ( F @ A @ B )
     => ( produc6082990154846732246tate_o @ F @ ( produc9160152616361873709_state @ A @ B ) ) ) ).

% case_prodI
thf(fact_741_case__prodI,axiom,
    ! [F: prat > state > $o,A: prat,B: state] :
      ( ( F @ A @ B )
     => ( produc1228703470279370976tate_o @ F @ ( produc6205719116230455971_state @ A @ B ) ) ) ).

% case_prodI
thf(fact_742_case__prodI,axiom,
    ! [F: prat > set_state > $o,A: prat,B: set_state] :
      ( ( F @ A @ B )
     => ( produc7925652287191295402tate_o @ F @ ( produc9080284787853255769_state @ A @ B ) ) ) ).

% case_prodI
thf(fact_743_case__prodI,axiom,
    ! [F: nat > list_char > $o,A: nat,B: list_char] :
      ( ( F @ A @ B )
     => ( produc8526122873445342073char_o @ F @ ( produc120197956887798346t_char @ A @ B ) ) ) ).

% case_prodI
thf(fact_744_case__prodI,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val] :
      ( ( F @ A @ B )
     => ( produc5248837549992124053_val_o @ F @ ( produc74620467203698198on_val @ A @ B ) ) ) ).

% case_prodI
thf(fact_745_case__prodI,axiom,
    ! [F: state > ( state > state ) > $o,A: state,B: state > state] :
      ( ( F @ A @ B )
     => ( produc3645877548210629341tate_o @ F @ ( produc8632743443909064678_state @ A @ B ) ) ) ).

% case_prodI
thf(fact_746_case__prodI,axiom,
    ! [F: state > produc3882902684156697774_state > $o,A: state,B: produc3882902684156697774_state] :
      ( ( F @ A @ B )
     => ( produc1745419677418529872tate_o @ F @ ( produc5886875603596089627_state @ A @ B ) ) ) ).

% case_prodI
thf(fact_747_case__swap,axiom,
    ! [F: state > ( state > state ) > $o,P: produc3882902684156697774_state] :
      ( ( produc7947965470134731869tate_o
        @ ^ [Y5: state > state,X3: state] : ( F @ X3 @ Y5 )
        @ ( produc6438927260845192582_state @ P ) )
      = ( produc3645877548210629341tate_o @ F @ P ) ) ).

% case_swap
thf(fact_748_case__swap,axiom,
    ! [F: state > produc3882902684156697774_state > $o,P: produc7272280185086996969_state] :
      ( ( produc2011331576729698010tate_o
        @ ^ [Y5: produc3882902684156697774_state,X3: state] : ( F @ X3 @ Y5 )
        @ ( produc6564544480275723131_state @ P ) )
      = ( produc1745419677418529872tate_o @ F @ P ) ) ).

% case_swap
thf(fact_749_case__swap,axiom,
    ! [F: ( state > state ) > state > $o,P: produc5876769945872133550_state] :
      ( ( produc3645877548210629341tate_o
        @ ^ [Y5: state,X3: state > state] : ( F @ X3 @ Y5 )
        @ ( produc2543546466205187078_state @ P ) )
      = ( produc7947965470134731869tate_o @ F @ P ) ) ).

% case_swap
thf(fact_750_case__swap,axiom,
    ! [F: produc3882902684156697774_state > state > $o,P: produc1357540302793366807_state] :
      ( ( produc1745419677418529872tate_o
        @ ^ [Y5: state,X3: produc3882902684156697774_state] : ( F @ X3 @ Y5 )
        @ ( produc8011752947996305265_state @ P ) )
      = ( produc2011331576729698010tate_o @ F @ P ) ) ).

% case_swap
thf(fact_751_old_Oprod_Ocase,axiom,
    ! [F: state > ( state > state ) > $o,X1: state,X22: state > state] :
      ( ( produc3645877548210629341tate_o @ F @ ( produc8632743443909064678_state @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_752_old_Oprod_Ocase,axiom,
    ! [F: state > produc3882902684156697774_state > $o,X1: state,X22: produc3882902684156697774_state] :
      ( ( produc1745419677418529872tate_o @ F @ ( produc5886875603596089627_state @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_753_Ball__def,axiom,
    ( ball_state
    = ( ^ [A4: set_state,P5: state > $o] :
        ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( P5 @ X3 ) ) ) ) ).

% Ball_def
thf(fact_754_Ball__def,axiom,
    ( ball_P7403102246598991807_state
    = ( ^ [A4: set_Pr4231240917283394591_state,P5: produc7272280185086996969_state > $o] :
        ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( P5 @ X3 ) ) ) ) ).

% Ball_def
thf(fact_755_Ball__def,axiom,
    ( ball_P2871712132005019634on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,P5: produc9003781588162623004on_val > $o] :
        ! [X3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X3 @ A4 )
         => ( P5 @ X3 ) ) ) ) ).

% Ball_def
thf(fact_756_Ball__def,axiom,
    ( ball_P1066487999220904024_state
    = ( ^ [A4: set_Pr2391701600042252046_state,P5: produc3882902684156697774_state > $o] :
        ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( P5 @ X3 ) ) ) ) ).

% Ball_def
thf(fact_757_Ball__Collect,axiom,
    ( ball_P7403102246598991807_state
    = ( ^ [A4: set_Pr4231240917283394591_state,P5: produc7272280185086996969_state > $o] : ( ord_le4032880777312351359_state @ A4 @ ( collec906845016635587262_state @ P5 ) ) ) ) ).

% Ball_Collect
thf(fact_758_Ball__Collect,axiom,
    ( ball_P2871712132005019634on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,P5: produc9003781588162623004on_val > $o] : ( ord_le6900622908513426738on_val @ A4 @ ( collec7475294502966882545on_val @ P5 ) ) ) ) ).

% Ball_Collect
thf(fact_759_Ball__Collect,axiom,
    ( ball_state
    = ( ^ [A4: set_state,P5: state > $o] : ( ord_le2494988322063910608_state @ A4 @ ( collect_state @ P5 ) ) ) ) ).

% Ball_Collect
thf(fact_760_prod_Ocase__distrib,axiom,
    ! [H: $o > $o,F: state > ( state > state ) > $o,Prod: produc3882902684156697774_state] :
      ( ( H @ ( produc3645877548210629341tate_o @ F @ Prod ) )
      = ( produc3645877548210629341tate_o
        @ ^ [X12: state,X23: state > state] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_761_prod_Ocase__distrib,axiom,
    ! [H: $o > $o,F: state > produc3882902684156697774_state > $o,Prod: produc7272280185086996969_state] :
      ( ( H @ ( produc1745419677418529872tate_o @ F @ Prod ) )
      = ( produc1745419677418529872tate_o
        @ ^ [X12: state,X23: produc3882902684156697774_state] : ( H @ ( F @ X12 @ X23 ) )
        @ Prod ) ) ).

% prod.case_distrib
thf(fact_762_prod_Odisc__eq__case,axiom,
    ! [Prod: produc3882902684156697774_state] :
      ( produc3645877548210629341tate_o
      @ ^ [Uu3: state,Uv3: state > state] : $true
      @ Prod ) ).

% prod.disc_eq_case
thf(fact_763_prod_Odisc__eq__case,axiom,
    ! [Prod: produc7272280185086996969_state] :
      ( produc1745419677418529872tate_o
      @ ^ [Uu3: state,Uv3: produc3882902684156697774_state] : $true
      @ Prod ) ).

% prod.disc_eq_case
thf(fact_764_case__prodE,axiom,
    ! [C: option_state > option_state > $o,P: produc3142500478612311029_state] :
      ( ( produc6082990154846732246tate_o @ C @ P )
     => ~ ! [X2: option_state,Y3: option_state] :
            ( ( P
              = ( produc9160152616361873709_state @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_765_case__prodE,axiom,
    ! [C: prat > state > $o,P: produc4844402304972151915_state] :
      ( ( produc1228703470279370976tate_o @ C @ P )
     => ~ ! [X2: prat,Y3: state] :
            ( ( P
              = ( produc6205719116230455971_state @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_766_case__prodE,axiom,
    ! [C: prat > set_state > $o,P: produc6251377953716854561_state] :
      ( ( produc7925652287191295402tate_o @ C @ P )
     => ~ ! [X2: prat,Y3: set_state] :
            ( ( P
              = ( produc9080284787853255769_state @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_767_case__prodE,axiom,
    ! [C: nat > list_char > $o,P: produc1457211279475724562t_char] :
      ( ( produc8526122873445342073char_o @ C @ P )
     => ~ ! [X2: nat,Y3: list_char] :
            ( ( P
              = ( produc120197956887798346t_char @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_768_case__prodE,axiom,
    ! [C: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,P: produc9003781588162623004on_val] :
      ( ( produc5248837549992124053_val_o @ C @ P )
     => ~ ! [X2: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
            ( ( P
              = ( produc74620467203698198on_val @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_769_case__prodE,axiom,
    ! [C: state > ( state > state ) > $o,P: produc3882902684156697774_state] :
      ( ( produc3645877548210629341tate_o @ C @ P )
     => ~ ! [X2: state,Y3: state > state] :
            ( ( P
              = ( produc8632743443909064678_state @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_770_case__prodE,axiom,
    ! [C: state > produc3882902684156697774_state > $o,P: produc7272280185086996969_state] :
      ( ( produc1745419677418529872tate_o @ C @ P )
     => ~ ! [X2: state,Y3: produc3882902684156697774_state] :
            ( ( P
              = ( produc5886875603596089627_state @ X2 @ Y3 ) )
           => ~ ( C @ X2 @ Y3 ) ) ) ).

% case_prodE
thf(fact_771_case__prodD,axiom,
    ! [F: option_state > option_state > $o,A: option_state,B: option_state] :
      ( ( produc6082990154846732246tate_o @ F @ ( produc9160152616361873709_state @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_772_case__prodD,axiom,
    ! [F: prat > state > $o,A: prat,B: state] :
      ( ( produc1228703470279370976tate_o @ F @ ( produc6205719116230455971_state @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_773_case__prodD,axiom,
    ! [F: prat > set_state > $o,A: prat,B: set_state] :
      ( ( produc7925652287191295402tate_o @ F @ ( produc9080284787853255769_state @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_774_case__prodD,axiom,
    ! [F: nat > list_char > $o,A: nat,B: list_char] :
      ( ( produc8526122873445342073char_o @ F @ ( produc120197956887798346t_char @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_775_case__prodD,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val] :
      ( ( produc5248837549992124053_val_o @ F @ ( produc74620467203698198on_val @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_776_case__prodD,axiom,
    ! [F: state > ( state > state ) > $o,A: state,B: state > state] :
      ( ( produc3645877548210629341tate_o @ F @ ( produc8632743443909064678_state @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_777_case__prodD,axiom,
    ! [F: state > produc3882902684156697774_state > $o,A: state,B: produc3882902684156697774_state] :
      ( ( produc1745419677418529872tate_o @ F @ ( produc5886875603596089627_state @ A @ B ) )
     => ( F @ A @ B ) ) ).

% case_prodD
thf(fact_778_sup__set__def,axiom,
    ( sup_su1984960714304006370_state
    = ( ^ [A4: set_Pr2391701600042252046_state,B3: set_Pr2391701600042252046_state] :
          ( collec394671971739345689_state
          @ ( sup_su1130956725435522171tate_o
            @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ A4 )
            @ ^ [X3: produc3882902684156697774_state] : ( member6715010751053357271_state @ X3 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_779_sup__set__def,axiom,
    ( sup_sup_set_state
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ( sup_sup_state_o
            @ ^ [X3: state] : ( member_state @ X3 @ A4 )
            @ ^ [X3: state] : ( member_state @ X3 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_780_sup__set__def,axiom,
    ( sup_su7506060154676209150on_val
    = ( ^ [A4: set_Pr7649655576376376530on_val,B3: set_Pr7649655576376376530on_val] :
          ( collec7475294502966882545on_val
          @ ( sup_su3200866414790943751_val_o
            @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ A4 )
            @ ^ [X3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X3 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_781_sup__set__def,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A4: set_Pr4231240917283394591_state,B3: set_Pr4231240917283394591_state] :
          ( collec906845016635587262_state
          @ ( sup_su4345871077856951546tate_o
            @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ A4 )
            @ ^ [X3: produc7272280185086996969_state] : ( member7461423308196221312_state @ X3 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_782_cond__case__prod__eta,axiom,
    ! [F: state > ( state > state ) > $o,G: produc3882902684156697774_state > $o] :
      ( ! [X2: state,Y3: state > state] :
          ( ( F @ X2 @ Y3 )
          = ( G @ ( produc8632743443909064678_state @ X2 @ Y3 ) ) )
     => ( ( produc3645877548210629341tate_o @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_783_cond__case__prod__eta,axiom,
    ! [F: state > produc3882902684156697774_state > $o,G: produc7272280185086996969_state > $o] :
      ( ! [X2: state,Y3: produc3882902684156697774_state] :
          ( ( F @ X2 @ Y3 )
          = ( G @ ( produc5886875603596089627_state @ X2 @ Y3 ) ) )
     => ( ( produc1745419677418529872tate_o @ F )
        = G ) ) ).

% cond_case_prod_eta
thf(fact_784_case__prod__eta,axiom,
    ! [F: produc3882902684156697774_state > $o] :
      ( ( produc3645877548210629341tate_o
        @ ^ [X3: state,Y5: state > state] : ( F @ ( produc8632743443909064678_state @ X3 @ Y5 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_785_case__prod__eta,axiom,
    ! [F: produc7272280185086996969_state > $o] :
      ( ( produc1745419677418529872tate_o
        @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( F @ ( produc5886875603596089627_state @ X3 @ Y5 ) ) )
      = F ) ).

% case_prod_eta
thf(fact_786_case__prodE2,axiom,
    ! [Q: $o > $o,P4: state > ( state > state ) > $o,Z2: produc3882902684156697774_state] :
      ( ( Q @ ( produc3645877548210629341tate_o @ P4 @ Z2 ) )
     => ~ ! [X2: state,Y3: state > state] :
            ( ( Z2
              = ( produc8632743443909064678_state @ X2 @ Y3 ) )
           => ~ ( Q @ ( P4 @ X2 @ Y3 ) ) ) ) ).

% case_prodE2
thf(fact_787_case__prodE2,axiom,
    ! [Q: $o > $o,P4: state > produc3882902684156697774_state > $o,Z2: produc7272280185086996969_state] :
      ( ( Q @ ( produc1745419677418529872tate_o @ P4 @ Z2 ) )
     => ~ ! [X2: state,Y3: produc3882902684156697774_state] :
            ( ( Z2
              = ( produc5886875603596089627_state @ X2 @ Y3 ) )
           => ~ ( Q @ ( P4 @ X2 @ Y3 ) ) ) ) ).

% case_prodE2
thf(fact_788_fst__def,axiom,
    ( produc6204653154488278070t_char
    = ( produc9163108120003956271ar_nat
      @ ^ [X12: nat,X23: list_char] : X12 ) ) ).

% fst_def
thf(fact_789_fst__def,axiom,
    ( produc5239619271231976746on_val
    = ( produc5787256515117077072r_prat
      @ ^ [X12: produc1457211279475724562t_char > prat,X23: produc1457211279475724562t_char > option_val] : X12 ) ) ).

% fst_def
thf(fact_790_snd__def,axiom,
    ( produc2319605628138516840on_val
    = ( produc985966260317727453on_val
      @ ^ [X12: produc1457211279475724562t_char > prat,X23: produc1457211279475724562t_char > option_val] : X23 ) ) ).

% snd_def
thf(fact_791_Product__Type_OCollect__case__prodD,axiom,
    ! [X: produc1457211279475724562t_char,A5: nat > list_char > $o] :
      ( ( member484235747325421115t_char @ X @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ A5 ) ) )
     => ( A5 @ ( produc6204653154488278070t_char @ X ) @ ( produc1900778367047502200t_char @ X ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_792_Product__Type_OCollect__case__prodD,axiom,
    ! [X: produc9003781588162623004on_val,A5: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( member2879030624002546611on_val @ X @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ A5 ) ) )
     => ( A5 @ ( produc5239619271231976746on_val @ X ) @ ( produc2319605628138516840on_val @ X ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_793_Product__Type_OCollect__case__prodD,axiom,
    ! [X: produc3882902684156697774_state,A5: state > ( state > state ) > $o] :
      ( ( member6715010751053357271_state @ X @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ A5 ) ) )
     => ( A5 @ ( produc7095885521192019410_state @ X ) @ ( produc1734700239402139924_state @ X ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_794_Product__Type_OCollect__case__prodD,axiom,
    ! [X: produc7272280185086996969_state,A5: state > produc3882902684156697774_state > $o] :
      ( ( member7461423308196221312_state @ X @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ A5 ) ) )
     => ( A5 @ ( produc848024588167747631_state @ X ) @ ( produc6310399636379773037_state @ X ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_795_Collect__case__prod__mono,axiom,
    ! [A5: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,B4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( ord_le3852884270828607079_val_o @ A5 @ B4 )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ A5 ) ) @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_796_Collect__case__prod__mono,axiom,
    ! [A5: state > ( state > state ) > $o,B4: state > ( state > state ) > $o] :
      ( ( ord_le1106678366802930969tate_o @ A5 @ B4 )
     => ( ord_le6483787752022044334_state @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ A5 ) ) @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_797_Collect__case__prod__mono,axiom,
    ! [A5: state > produc3882902684156697774_state > $o,B4: state > produc3882902684156697774_state > $o] :
      ( ( ord_le6704609105599929480tate_o @ A5 @ B4 )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ A5 ) ) @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_798_case__prod__beta,axiom,
    ( produc3645877548210629341tate_o
    = ( ^ [F3: state > ( state > state ) > $o,P2: produc3882902684156697774_state] : ( F3 @ ( produc7095885521192019410_state @ P2 ) @ ( produc1734700239402139924_state @ P2 ) ) ) ) ).

% case_prod_beta
thf(fact_799_case__prod__beta,axiom,
    ( produc1745419677418529872tate_o
    = ( ^ [F3: state > produc3882902684156697774_state > $o,P2: produc7272280185086996969_state] : ( F3 @ ( produc848024588167747631_state @ P2 ) @ ( produc6310399636379773037_state @ P2 ) ) ) ) ).

% case_prod_beta
thf(fact_800_split__beta,axiom,
    ( produc3645877548210629341tate_o
    = ( ^ [F3: state > ( state > state ) > $o,Prod3: produc3882902684156697774_state] : ( F3 @ ( produc7095885521192019410_state @ Prod3 ) @ ( produc1734700239402139924_state @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_801_split__beta,axiom,
    ( produc1745419677418529872tate_o
    = ( ^ [F3: state > produc3882902684156697774_state > $o,Prod3: produc7272280185086996969_state] : ( F3 @ ( produc848024588167747631_state @ Prod3 ) @ ( produc6310399636379773037_state @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_802_internal__case__prod__def,axiom,
    produc1225464857956169863tate_o = produc3645877548210629341tate_o ).

% internal_case_prod_def
thf(fact_803_internal__case__prod__def,axiom,
    produc3899216655821101094tate_o = produc1745419677418529872tate_o ).

% internal_case_prod_def
thf(fact_804_sup__Un__eq2,axiom,
    ! [R3: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( sup_su1108609720783396685tate_o
        @ ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y5 ) @ ( sup_su1984960714304006370_state @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_805_sup__Un__eq2,axiom,
    ! [R3: set_Pr1688445902015331925_state,S2: set_Pr1688445902015331925_state] :
      ( ( sup_su2989194110892726342tate_o
        @ ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y5 ) @ ( sup_su5006661989123481129_state @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_806_sup__Un__eq2,axiom,
    ! [R3: set_Pr6039890582625207499_state,S2: set_Pr6039890582625207499_state] :
      ( ( sup_sup_prat_state_o
        @ ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y5 ) @ ( sup_su1826719071296284831_state @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_807_sup__Un__eq2,axiom,
    ! [R3: set_Pr6847263425858009217_state,S2: set_Pr6847263425858009217_state] :
      ( ( sup_su7614437069348798106tate_o
        @ ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y5 ) @ ( sup_su5611131606495579221_state @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_808_sup__Un__eq2,axiom,
    ! [R3: set_Pr2507339680178222706t_char,S2: set_Pr2507339680178222706t_char] :
      ( ( sup_su1536542383718553321char_o
        @ ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y5 ) @ ( sup_su7899656352754981958t_char @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_809_sup__Un__eq2,axiom,
    ! [R3: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( sup_su4175861339346331443_val_o
        @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y5 ) @ ( sup_su7506060154676209150on_val @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_810_sup__Un__eq2,axiom,
    ! [R3: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( sup_su1162340662190093652tate_o
        @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ R3 )
        @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ S2 ) )
      = ( ^ [X3: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y5 ) @ ( sup_su3837536599209510219_state @ R3 @ S2 ) ) ) ) ).

% sup_Un_eq2
thf(fact_811_case__prod__unfold,axiom,
    ( produc3645877548210629341tate_o
    = ( ^ [C3: state > ( state > state ) > $o,P2: produc3882902684156697774_state] : ( C3 @ ( produc7095885521192019410_state @ P2 ) @ ( produc1734700239402139924_state @ P2 ) ) ) ) ).

% case_prod_unfold
thf(fact_812_case__prod__unfold,axiom,
    ( produc1745419677418529872tate_o
    = ( ^ [C3: state > produc3882902684156697774_state > $o,P2: produc7272280185086996969_state] : ( C3 @ ( produc848024588167747631_state @ P2 ) @ ( produc6310399636379773037_state @ P2 ) ) ) ) ).

% case_prod_unfold
thf(fact_813_case__prod__beta_H,axiom,
    ( produc3645877548210629341tate_o
    = ( ^ [F3: state > ( state > state ) > $o,X3: produc3882902684156697774_state] : ( F3 @ ( produc7095885521192019410_state @ X3 ) @ ( produc1734700239402139924_state @ X3 ) ) ) ) ).

% case_prod_beta'
thf(fact_814_case__prod__beta_H,axiom,
    ( produc1745419677418529872tate_o
    = ( ^ [F3: state > produc3882902684156697774_state > $o,X3: produc7272280185086996969_state] : ( F3 @ ( produc848024588167747631_state @ X3 ) @ ( produc6310399636379773037_state @ X3 ) ) ) ) ).

% case_prod_beta'
thf(fact_815_prod_Osplit__sel__asm,axiom,
    ! [P4: $o > $o,F: state > ( state > state ) > $o,Prod: produc3882902684156697774_state] :
      ( ( P4 @ ( produc3645877548210629341tate_o @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc8632743443909064678_state @ ( produc7095885521192019410_state @ Prod ) @ ( produc1734700239402139924_state @ Prod ) ) )
            & ~ ( P4 @ ( F @ ( produc7095885521192019410_state @ Prod ) @ ( produc1734700239402139924_state @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_816_prod_Osplit__sel__asm,axiom,
    ! [P4: $o > $o,F: state > produc3882902684156697774_state > $o,Prod: produc7272280185086996969_state] :
      ( ( P4 @ ( produc1745419677418529872tate_o @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc5886875603596089627_state @ ( produc848024588167747631_state @ Prod ) @ ( produc6310399636379773037_state @ Prod ) ) )
            & ~ ( P4 @ ( F @ ( produc848024588167747631_state @ Prod ) @ ( produc6310399636379773037_state @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_817_prod_Osplit__sel,axiom,
    ! [P4: $o > $o,F: state > ( state > state ) > $o,Prod: produc3882902684156697774_state] :
      ( ( P4 @ ( produc3645877548210629341tate_o @ F @ Prod ) )
      = ( ( Prod
          = ( produc8632743443909064678_state @ ( produc7095885521192019410_state @ Prod ) @ ( produc1734700239402139924_state @ Prod ) ) )
       => ( P4 @ ( F @ ( produc7095885521192019410_state @ Prod ) @ ( produc1734700239402139924_state @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_818_prod_Osplit__sel,axiom,
    ! [P4: $o > $o,F: state > produc3882902684156697774_state > $o,Prod: produc7272280185086996969_state] :
      ( ( P4 @ ( produc1745419677418529872tate_o @ F @ Prod ) )
      = ( ( Prod
          = ( produc5886875603596089627_state @ ( produc848024588167747631_state @ Prod ) @ ( produc6310399636379773037_state @ Prod ) ) )
       => ( P4 @ ( F @ ( produc848024588167747631_state @ Prod ) @ ( produc6310399636379773037_state @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_819_sup_OcoboundedI2,axiom,
    ! [C: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ B )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_820_sup_OcoboundedI2,axiom,
    ! [C: set_state,B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ B )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_821_sup_OcoboundedI1,axiom,
    ! [C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ A )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_822_sup_OcoboundedI1,axiom,
    ! [C: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ A )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_823_sup_Oabsorb__iff2,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A3: set_Pr4231240917283394591_state,B2: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A3 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_824_sup_Oabsorb__iff2,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A3: set_state,B2: set_state] :
          ( ( sup_sup_set_state @ A3 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_825_sup_Oabsorb__iff1,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [B2: set_Pr4231240917283394591_state,A3: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A3 @ B2 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_826_sup_Oabsorb__iff1,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [B2: set_state,A3: set_state] :
          ( ( sup_sup_set_state @ A3 @ B2 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_827_sup_Ocobounded2,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ B @ ( sup_su3837536599209510219_state @ A @ B ) ) ).

% sup.cobounded2
thf(fact_828_sup_Ocobounded2,axiom,
    ! [B: set_state,A: set_state] : ( ord_le2494988322063910608_state @ B @ ( sup_sup_set_state @ A @ B ) ) ).

% sup.cobounded2
thf(fact_829_sup_Ocobounded1,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ A @ ( sup_su3837536599209510219_state @ A @ B ) ) ).

% sup.cobounded1
thf(fact_830_sup_Ocobounded1,axiom,
    ! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ A @ ( sup_sup_set_state @ A @ B ) ) ).

% sup.cobounded1
thf(fact_831_sup_Oorder__iff,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [B2: set_Pr4231240917283394591_state,A3: set_Pr4231240917283394591_state] :
          ( A3
          = ( sup_su3837536599209510219_state @ A3 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_832_sup_Oorder__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [B2: set_state,A3: set_state] :
          ( A3
          = ( sup_sup_set_state @ A3 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_833_sup_OboundedI,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( ( ord_le4032880777312351359_state @ C @ A )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_834_sup_OboundedI,axiom,
    ! [B: set_state,A: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ C @ A )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_835_sup_OboundedE,axiom,
    ! [B: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A )
     => ~ ( ( ord_le4032880777312351359_state @ B @ A )
         => ~ ( ord_le4032880777312351359_state @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_836_sup_OboundedE,axiom,
    ! [B: set_state,C: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A )
     => ~ ( ( ord_le2494988322063910608_state @ B @ A )
         => ~ ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_837_sup__absorb2,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ Y )
     => ( ( sup_su3837536599209510219_state @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_838_sup__absorb2,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( sup_sup_set_state @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_839_sup__absorb1,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ Y @ X )
     => ( ( sup_su3837536599209510219_state @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_840_sup__absorb1,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( sup_sup_set_state @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_841_sup_Oabsorb2,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ B )
     => ( ( sup_su3837536599209510219_state @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_842_sup_Oabsorb2,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( sup_sup_set_state @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_843_sup_Oabsorb1,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( ( sup_su3837536599209510219_state @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_844_sup_Oabsorb1,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( sup_sup_set_state @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_845_sup__unique,axiom,
    ! [F: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] :
      ( ! [X2: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X2 @ ( F @ X2 @ Y3 ) )
     => ( ! [X2: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y3 @ ( F @ X2 @ Y3 ) )
       => ( ! [X2: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state,Z3: set_Pr4231240917283394591_state] :
              ( ( ord_le4032880777312351359_state @ Y3 @ X2 )
             => ( ( ord_le4032880777312351359_state @ Z3 @ X2 )
               => ( ord_le4032880777312351359_state @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
         => ( ( sup_su3837536599209510219_state @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_846_sup__unique,axiom,
    ! [F: set_state > set_state > set_state,X: set_state,Y: set_state] :
      ( ! [X2: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ X2 @ ( F @ X2 @ Y3 ) )
     => ( ! [X2: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ Y3 @ ( F @ X2 @ Y3 ) )
       => ( ! [X2: set_state,Y3: set_state,Z3: set_state] :
              ( ( ord_le2494988322063910608_state @ Y3 @ X2 )
             => ( ( ord_le2494988322063910608_state @ Z3 @ X2 )
               => ( ord_le2494988322063910608_state @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
         => ( ( sup_sup_set_state @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_847_sup_OorderI,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( A
        = ( sup_su3837536599209510219_state @ A @ B ) )
     => ( ord_le4032880777312351359_state @ B @ A ) ) ).

% sup.orderI
thf(fact_848_sup_OorderI,axiom,
    ! [A: set_state,B: set_state] :
      ( ( A
        = ( sup_sup_set_state @ A @ B ) )
     => ( ord_le2494988322063910608_state @ B @ A ) ) ).

% sup.orderI
thf(fact_849_sup_OorderE,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( A
        = ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.orderE
thf(fact_850_sup_OorderE,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( A
        = ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.orderE
thf(fact_851_le__iff__sup,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [X3: set_Pr4231240917283394591_state,Y5: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ X3 @ Y5 )
          = Y5 ) ) ) ).

% le_iff_sup
thf(fact_852_le__iff__sup,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [X3: set_state,Y5: set_state] :
          ( ( sup_sup_set_state @ X3 @ Y5 )
          = Y5 ) ) ) ).

% le_iff_sup
thf(fact_853_sup__least,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ Y @ X )
     => ( ( ord_le4032880777312351359_state @ Z2 @ X )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_854_sup__least,axiom,
    ! [Y: set_state,X: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( ord_le2494988322063910608_state @ Z2 @ X )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_855_sup__mono,axiom,
    ! [A: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,D: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ C )
     => ( ( ord_le4032880777312351359_state @ B @ D )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ ( sup_su3837536599209510219_state @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_856_sup__mono,axiom,
    ! [A: set_state,C: set_state,B: set_state,D: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ C )
     => ( ( ord_le2494988322063910608_state @ B @ D )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ ( sup_sup_set_state @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_857_sup_Omono,axiom,
    ! [C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,D: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ A )
     => ( ( ord_le4032880777312351359_state @ D @ B )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ C @ D ) @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_858_sup_Omono,axiom,
    ! [C: set_state,A: set_state,D: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ A )
     => ( ( ord_le2494988322063910608_state @ D @ B )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ C @ D ) @ ( sup_sup_set_state @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_859_le__supI2,axiom,
    ! [X: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ B )
     => ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% le_supI2
thf(fact_860_le__supI2,axiom,
    ! [X: set_state,B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ B )
     => ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ A @ B ) ) ) ).

% le_supI2
thf(fact_861_le__supI1,axiom,
    ! [X: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ A )
     => ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% le_supI1
thf(fact_862_le__supI1,axiom,
    ! [X: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ A )
     => ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ A @ B ) ) ) ).

% le_supI1
thf(fact_863_sup__ge2,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% sup_ge2
thf(fact_864_sup__ge2,axiom,
    ! [Y: set_state,X: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X @ Y ) ) ).

% sup_ge2
thf(fact_865_sup__ge1,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% sup_ge1
thf(fact_866_sup__ge1,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ X @ Y ) ) ).

% sup_ge1
thf(fact_867_le__supI,axiom,
    ! [A: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ X )
     => ( ( ord_le4032880777312351359_state @ B @ X )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_868_le__supI,axiom,
    ! [A: set_state,X: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ X )
     => ( ( ord_le2494988322063910608_state @ B @ X )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_869_le__supE,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ X )
     => ~ ( ( ord_le4032880777312351359_state @ A @ X )
         => ~ ( ord_le4032880777312351359_state @ B @ X ) ) ) ).

% le_supE
thf(fact_870_le__supE,axiom,
    ! [A: set_state,B: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ X )
     => ~ ( ( ord_le2494988322063910608_state @ A @ X )
         => ~ ( ord_le2494988322063910608_state @ B @ X ) ) ) ).

% le_supE
thf(fact_871_inf__sup__ord_I3_J,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_872_inf__sup__ord_I3_J,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_873_inf__sup__ord_I4_J,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_874_inf__sup__ord_I4_J,axiom,
    ! [Y: set_state,X: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_875_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi2: val,S2: set_Pr6546617632949187467al_val,A5: aassertion_val,Phi4: val,F: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ Unit
          @ ( collec8300311316619386842al_val
            @ ^ [Uu3: produc2072440392815185925al_val] :
              ? [A3: val,T5: val > val] :
                ( ( Uu3
                  = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ Unit @ T5 ) ) )
                & ( member331055627401653996al_val @ ( produc303288909735261391al_val @ A3 @ T5 ) @ S2 ) ) )
          @ ^ [Uu3: val] : $true
          @ A5
          @ Phi4
          @ F
          @ S3 )
       => ( ! [A7: val,T3: val > val] :
              ( ( member331055627401653996al_val @ ( produc303288909735261391al_val @ A7 @ T3 ) @ S2 )
             => ( packag4175576287423129206er_val @ Plus @ Unit @ T3 ) )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ A5 )
           => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ A5 ) )
                | ( packag3202507263771882441al_val @ Plus @ S3 ) )
             => ( ( ( some_val @ Phi2 )
                  = ( Plus @ Phi4 @ F ) )
                & ( Stable @ F )
                & ! [X5: produc5503543764249810261al_val] :
                    ( ( member331055627401653996al_val @ X5 @ S2 )
                   => ( produc7666680587469814684_val_o
                      @ ^ [A3: val,T5: val > val] :
                          ( ( sep_defined_val @ Plus @ A3 @ ( T5 @ F ) )
                         => ( package_sat_val @ Plus @ A5 @ ( the_val @ ( Plus @ A3 @ ( T5 @ F ) ) ) ) )
                      @ X5 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_876_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi2: state,S2: set_Pr2391701600042252046_state,A5: aassertion_state,Phi4: state,F: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ Unit
          @ ( collec906845016635587262_state
            @ ^ [Uu3: produc7272280185086996969_state] :
              ? [A3: state,T5: state > state] :
                ( ( Uu3
                  = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ Unit @ T5 ) ) )
                & ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A3 @ T5 ) @ S2 ) ) )
          @ ^ [Uu3: state] : $true
          @ A5
          @ Phi4
          @ F
          @ S3 )
       => ( ! [A7: state,T3: state > state] :
              ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A7 @ T3 ) @ S2 )
             => ( packag4817583915586052229_state @ Plus @ Unit @ T3 ) )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A5 )
           => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ A5 ) )
                | ( packag4152378406607043437_state @ Plus @ S3 ) )
             => ( ( ( some_state @ Phi2 )
                  = ( Plus @ Phi4 @ F ) )
                & ( Stable @ F )
                & ! [X5: produc3882902684156697774_state] :
                    ( ( member6715010751053357271_state @ X5 @ S2 )
                   => ( produc3645877548210629341tate_o
                      @ ^ [A3: state,T5: state > state] :
                          ( ( sep_defined_state @ Plus @ A3 @ ( T5 @ F ) )
                         => ( package_sat_state @ Plus @ A5 @ ( the_state @ ( Plus @ A3 @ ( T5 @ F ) ) ) ) )
                      @ X5 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_877_PartialSA_Ocompleteness__aux,axiom,
    ! [S2: set_Pr4231240917283394591_state,F1: state > state > ( state > state ) > state,F22: state > state > ( state > state ) > state,Pc: state > $o,A5: aassertion_state,F: state,Phi2: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( greater @ ( core @ ( F1 @ A7 @ U @ T3 ) ) @ ( core @ A7 ) )
            & ( ( some_state @ A7 )
              = ( plus @ ( F1 @ A7 @ U @ T3 ) @ ( F22 @ A7 @ U @ T3 ) ) )
            & ( ( Pc @ ( core @ A7 ) )
             => ( package_sat_state @ plus @ A5 @ ( the_state @ ( plus @ ( core @ A7 ) @ ( F1 @ A7 @ U @ T3 ) ) ) ) ) ) )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A5 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( ( stable @ F )
                & ( defined @ Phi2 @ F ) )
             => ? [S9: set_Pr4231240917283394591_state] :
                  ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi2 @ F @ S9 )
                  & ! [X5: produc7272280185086996969_state] :
                      ( ( member7461423308196221312_state @ X5 @ S9 )
                     => ( produc1745419677418529872tate_o
                        @ ^ [A14: state] :
                            ( produc3645877548210629341tate_o
                            @ ^ [U8: state,T5: state > state] :
                              ? [A3: state,U6: state] :
                                ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                                & ( greater @ A14 @ ( F22 @ A3 @ U6 @ T5 ) )
                                & ( ( core @ A14 )
                                  = ( core @ A3 ) ) ) )
                        @ X5 ) ) ) ) ) ) ) ) ).

% PartialSA.completeness_aux
thf(fact_878_image2__def,axiom,
    ( bNF_Gr1645861816300964896_state
    = ( ^ [A4: set_state,F3: state > prat,G2: state > state] :
          ( collec9096564466166568534_state
          @ ^ [Uu3: produc4844402304972151915_state] :
            ? [A3: state] :
              ( ( Uu3
                = ( produc6205719116230455971_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_879_image2__def,axiom,
    ( bNF_Gr8363538844033681878_state
    = ( ^ [A4: set_state,F3: state > prat,G2: state > set_state] :
          ( collec5094083866753559820_state
          @ ^ [Uu3: produc6251377953716854561_state] :
            ? [A3: state] :
              ( ( Uu3
                = ( produc9080284787853255769_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_880_image2__def,axiom,
    ( bNF_Gr71701291235176519t_char
    = ( ^ [A4: set_state,F3: state > nat,G2: state > list_char] :
          ( collec2458894688891239037t_char
          @ ^ [Uu3: produc1457211279475724562t_char] :
            ? [A3: state] :
              ( ( Uu3
                = ( produc120197956887798346t_char @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_881_image2__def,axiom,
    ( bNF_Gr8144397171961131434_state
    = ( ^ [A4: set_state,F3: state > option_state,G2: state > option_state] :
          ( collec8144523193623705312_state
          @ ^ [Uu3: produc3142500478612311029_state] :
            ? [A3: state] :
              ( ( Uu3
                = ( produc9160152616361873709_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_882_image2__def,axiom,
    ( bNF_Gr947463461346416350_state
    = ( ^ [A4: set_state,F3: state > state,G2: state > produc3882902684156697774_state] :
          ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [A3: state] :
              ( ( Uu3
                = ( produc5886875603596089627_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_883_image2__def,axiom,
    ( bNF_Gr5432878666621363808_state
    = ( ^ [A4: set_Pr2391701600042252046_state,F3: produc3882902684156697774_state > prat,G2: produc3882902684156697774_state > state] :
          ( collec9096564466166568534_state
          @ ^ [Uu3: produc4844402304972151915_state] :
            ? [A3: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc6205719116230455971_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member6715010751053357271_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_884_image2__def,axiom,
    ( bNF_Gr6818451474134737942_state
    = ( ^ [A4: set_Pr2391701600042252046_state,F3: produc3882902684156697774_state > prat,G2: produc3882902684156697774_state > set_state] :
          ( collec5094083866753559820_state
          @ ^ [Uu3: produc6251377953716854561_state] :
            ? [A3: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc9080284787853255769_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member6715010751053357271_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_885_image2__def,axiom,
    ( bNF_Gr5554302884217825927t_char
    = ( ^ [A4: set_Pr2391701600042252046_state,F3: produc3882902684156697774_state > nat,G2: produc3882902684156697774_state > list_char] :
          ( collec2458894688891239037t_char
          @ ^ [Uu3: produc1457211279475724562t_char] :
            ? [A3: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc120197956887798346t_char @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member6715010751053357271_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_886_image2__def,axiom,
    ( bNF_Gr4913868530397957098_state
    = ( ^ [A4: set_Pr2391701600042252046_state,F3: produc3882902684156697774_state > option_state,G2: produc3882902684156697774_state > option_state] :
          ( collec8144523193623705312_state
          @ ^ [Uu3: produc3142500478612311029_state] :
            ? [A3: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc9160152616361873709_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member6715010751053357271_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_887_image2__def,axiom,
    ( bNF_Gr2250442185837678927_state
    = ( ^ [A4: set_Pr4231240917283394591_state,F3: produc7272280185086996969_state > prat,G2: produc7272280185086996969_state > state] :
          ( collec9096564466166568534_state
          @ ^ [Uu3: produc4844402304972151915_state] :
            ? [A3: produc7272280185086996969_state] :
              ( ( Uu3
                = ( produc6205719116230455971_state @ ( F3 @ A3 ) @ ( G2 @ A3 ) ) )
              & ( member7461423308196221312_state @ A3 @ A4 ) ) ) ) ) ).

% image2_def
thf(fact_888_PartialSA_Opackage__rhs__connection__def,axiom,
    ! [Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
      = ( ( greater @ F5 @ F )
        & ( defined @ Phi2 @ F )
        & ( ( plus @ Phi2 @ F )
          = ( plus @ Phi4 @ F5 ) )
        & ( stable @ F5 )
        & ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A3: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,T5: state > state] :
                    ? [Au3: state] :
                      ( ( ( some_state @ Au3 )
                        = ( plus @ A3 @ U6 ) )
                      & ( ( defined @ Au3 @ ( minus @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                       => ? [A14: state,U8: state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A14 @ ( produc8632743443909064678_state @ U8 @ T5 ) ) @ S3 )
                            & ( greater @ ( core @ A14 ) @ ( core @ A3 ) )
                            & ( ( plus @ Au3 @ ( minus @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                              = ( plus @ A14 @ U8 ) )
                            & ( greater @ U8 @ U6 )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A5 @ A14 @ U8 @ U6 ) ) ) ) )
              @ X3 ) ) ) ) ).

% PartialSA.package_rhs_connection_def
thf(fact_889_case__prod__Pair,axiom,
    ( ( produc803252138055838771_state @ produc9160152616361873709_state )
    = id_Pro8715877757508063718_state ) ).

% case_prod_Pair
thf(fact_890_case__prod__Pair,axiom,
    ( ( produc1922103714420728243_state @ produc6205719116230455971_state )
    = id_Pro5916511905602125660_state ) ).

% case_prod_Pair
thf(fact_891_case__prod__Pair,axiom,
    ( ( produc897481912382009139_state @ produc9080284787853255769_state )
    = id_Pro8860473219607035410_state ) ).

% case_prod_Pair
thf(fact_892_case__prod__Pair,axiom,
    ( ( produc4071494739252518515t_char @ produc120197956887798346t_char )
    = id_Pro6264179822262827651t_char ) ).

% case_prod_Pair
thf(fact_893_case__prod__Pair,axiom,
    ( ( produc4192255817509754207on_val @ produc74620467203698198on_val )
    = id_Pro1402184692240358763on_val ) ).

% case_prod_Pair
thf(fact_894_mem__case__prodI,axiom,
    ! [Z2: state,C: prat > state > set_state,A: prat,B: state] :
      ( ( member_state @ Z2 @ ( C @ A @ B ) )
     => ( member_state @ Z2 @ ( produc2825319096956678952_state @ C @ ( produc6205719116230455971_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_895_mem__case__prodI,axiom,
    ! [Z2: state,C: prat > set_state > set_state,A: prat,B: set_state] :
      ( ( member_state @ Z2 @ ( C @ A @ B ) )
     => ( member_state @ Z2 @ ( produc5034060725774254814_state @ C @ ( produc9080284787853255769_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_896_mem__case__prodI,axiom,
    ! [Z2: state,C: nat > list_char > set_state,A: nat,B: list_char] :
      ( ( member_state @ Z2 @ ( C @ A @ B ) )
     => ( member_state @ Z2 @ ( produc7881066356751411151_state @ C @ ( produc120197956887798346t_char @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_897_mem__case__prodI,axiom,
    ! [Z2: state,C: option_state > option_state > set_state,A: option_state,B: option_state] :
      ( ( member_state @ Z2 @ ( C @ A @ B ) )
     => ( member_state @ Z2 @ ( produc3424155258940669874_state @ C @ ( produc9160152616361873709_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_898_mem__case__prodI,axiom,
    ! [Z2: produc3882902684156697774_state,C: prat > state > set_Pr2391701600042252046_state,A: prat,B: state] :
      ( ( member6715010751053357271_state @ Z2 @ ( C @ A @ B ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc4369308447073708118_state @ C @ ( produc6205719116230455971_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_899_mem__case__prodI,axiom,
    ! [Z2: produc3882902684156697774_state,C: prat > set_state > set_Pr2391701600042252046_state,A: prat,B: set_state] :
      ( ( member6715010751053357271_state @ Z2 @ ( C @ A @ B ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc9043967962556017184_state @ C @ ( produc9080284787853255769_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_900_mem__case__prodI,axiom,
    ! [Z2: produc3882902684156697774_state,C: nat > list_char > set_Pr2391701600042252046_state,A: nat,B: list_char] :
      ( ( member6715010751053357271_state @ Z2 @ ( C @ A @ B ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc3312000583120074607_state @ C @ ( produc120197956887798346t_char @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_901_mem__case__prodI,axiom,
    ! [Z2: produc3882902684156697774_state,C: option_state > option_state > set_Pr2391701600042252046_state,A: option_state,B: option_state] :
      ( ( member6715010751053357271_state @ Z2 @ ( C @ A @ B ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc2209043727768083020_state @ C @ ( produc9160152616361873709_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_902_mem__case__prodI,axiom,
    ! [Z2: produc7272280185086996969_state,C: prat > state > set_Pr4231240917283394591_state,A: prat,B: state] :
      ( ( member7461423308196221312_state @ Z2 @ ( C @ A @ B ) )
     => ( member7461423308196221312_state @ Z2 @ ( produc569869127943504087_state @ C @ ( produc6205719116230455971_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_903_mem__case__prodI,axiom,
    ! [Z2: produc7272280185086996969_state,C: prat > set_state > set_Pr4231240917283394591_state,A: prat,B: set_state] :
      ( ( member7461423308196221312_state @ Z2 @ ( C @ A @ B ) )
     => ( member7461423308196221312_state @ Z2 @ ( produc7793558081207154829_state @ C @ ( produc9080284787853255769_state @ A @ B ) ) ) ) ).

% mem_case_prodI
thf(fact_904_mem__case__prodI2,axiom,
    ! [P: produc4844402304972151915_state,Z2: state,C: prat > state > set_state] :
      ( ! [A7: prat,B6: state] :
          ( ( P
            = ( produc6205719116230455971_state @ A7 @ B6 ) )
         => ( member_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member_state @ Z2 @ ( produc2825319096956678952_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_905_mem__case__prodI2,axiom,
    ! [P: produc6251377953716854561_state,Z2: state,C: prat > set_state > set_state] :
      ( ! [A7: prat,B6: set_state] :
          ( ( P
            = ( produc9080284787853255769_state @ A7 @ B6 ) )
         => ( member_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member_state @ Z2 @ ( produc5034060725774254814_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_906_mem__case__prodI2,axiom,
    ! [P: produc1457211279475724562t_char,Z2: state,C: nat > list_char > set_state] :
      ( ! [A7: nat,B6: list_char] :
          ( ( P
            = ( produc120197956887798346t_char @ A7 @ B6 ) )
         => ( member_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member_state @ Z2 @ ( produc7881066356751411151_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_907_mem__case__prodI2,axiom,
    ! [P: produc3142500478612311029_state,Z2: state,C: option_state > option_state > set_state] :
      ( ! [A7: option_state,B6: option_state] :
          ( ( P
            = ( produc9160152616361873709_state @ A7 @ B6 ) )
         => ( member_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member_state @ Z2 @ ( produc3424155258940669874_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_908_mem__case__prodI2,axiom,
    ! [P: produc4844402304972151915_state,Z2: produc3882902684156697774_state,C: prat > state > set_Pr2391701600042252046_state] :
      ( ! [A7: prat,B6: state] :
          ( ( P
            = ( produc6205719116230455971_state @ A7 @ B6 ) )
         => ( member6715010751053357271_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc4369308447073708118_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_909_mem__case__prodI2,axiom,
    ! [P: produc6251377953716854561_state,Z2: produc3882902684156697774_state,C: prat > set_state > set_Pr2391701600042252046_state] :
      ( ! [A7: prat,B6: set_state] :
          ( ( P
            = ( produc9080284787853255769_state @ A7 @ B6 ) )
         => ( member6715010751053357271_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc9043967962556017184_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_910_mem__case__prodI2,axiom,
    ! [P: produc1457211279475724562t_char,Z2: produc3882902684156697774_state,C: nat > list_char > set_Pr2391701600042252046_state] :
      ( ! [A7: nat,B6: list_char] :
          ( ( P
            = ( produc120197956887798346t_char @ A7 @ B6 ) )
         => ( member6715010751053357271_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc3312000583120074607_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_911_mem__case__prodI2,axiom,
    ! [P: produc3142500478612311029_state,Z2: produc3882902684156697774_state,C: option_state > option_state > set_Pr2391701600042252046_state] :
      ( ! [A7: option_state,B6: option_state] :
          ( ( P
            = ( produc9160152616361873709_state @ A7 @ B6 ) )
         => ( member6715010751053357271_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member6715010751053357271_state @ Z2 @ ( produc2209043727768083020_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_912_mem__case__prodI2,axiom,
    ! [P: produc4844402304972151915_state,Z2: produc7272280185086996969_state,C: prat > state > set_Pr4231240917283394591_state] :
      ( ! [A7: prat,B6: state] :
          ( ( P
            = ( produc6205719116230455971_state @ A7 @ B6 ) )
         => ( member7461423308196221312_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member7461423308196221312_state @ Z2 @ ( produc569869127943504087_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_913_mem__case__prodI2,axiom,
    ! [P: produc6251377953716854561_state,Z2: produc7272280185086996969_state,C: prat > set_state > set_Pr4231240917283394591_state] :
      ( ! [A7: prat,B6: set_state] :
          ( ( P
            = ( produc9080284787853255769_state @ A7 @ B6 ) )
         => ( member7461423308196221312_state @ Z2 @ ( C @ A7 @ B6 ) ) )
     => ( member7461423308196221312_state @ Z2 @ ( produc7793558081207154829_state @ C @ P ) ) ) ).

% mem_case_prodI2
thf(fact_914_mem__case__prodE,axiom,
    ! [Z2: state,C: prat > state > set_state,P: produc4844402304972151915_state] :
      ( ( member_state @ Z2 @ ( produc2825319096956678952_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: state] :
            ( ( P
              = ( produc6205719116230455971_state @ X2 @ Y3 ) )
           => ~ ( member_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_915_mem__case__prodE,axiom,
    ! [Z2: state,C: prat > set_state > set_state,P: produc6251377953716854561_state] :
      ( ( member_state @ Z2 @ ( produc5034060725774254814_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: set_state] :
            ( ( P
              = ( produc9080284787853255769_state @ X2 @ Y3 ) )
           => ~ ( member_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_916_mem__case__prodE,axiom,
    ! [Z2: state,C: nat > list_char > set_state,P: produc1457211279475724562t_char] :
      ( ( member_state @ Z2 @ ( produc7881066356751411151_state @ C @ P ) )
     => ~ ! [X2: nat,Y3: list_char] :
            ( ( P
              = ( produc120197956887798346t_char @ X2 @ Y3 ) )
           => ~ ( member_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_917_mem__case__prodE,axiom,
    ! [Z2: state,C: option_state > option_state > set_state,P: produc3142500478612311029_state] :
      ( ( member_state @ Z2 @ ( produc3424155258940669874_state @ C @ P ) )
     => ~ ! [X2: option_state,Y3: option_state] :
            ( ( P
              = ( produc9160152616361873709_state @ X2 @ Y3 ) )
           => ~ ( member_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_918_mem__case__prodE,axiom,
    ! [Z2: produc3882902684156697774_state,C: prat > state > set_Pr2391701600042252046_state,P: produc4844402304972151915_state] :
      ( ( member6715010751053357271_state @ Z2 @ ( produc4369308447073708118_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: state] :
            ( ( P
              = ( produc6205719116230455971_state @ X2 @ Y3 ) )
           => ~ ( member6715010751053357271_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_919_mem__case__prodE,axiom,
    ! [Z2: produc3882902684156697774_state,C: prat > set_state > set_Pr2391701600042252046_state,P: produc6251377953716854561_state] :
      ( ( member6715010751053357271_state @ Z2 @ ( produc9043967962556017184_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: set_state] :
            ( ( P
              = ( produc9080284787853255769_state @ X2 @ Y3 ) )
           => ~ ( member6715010751053357271_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_920_mem__case__prodE,axiom,
    ! [Z2: produc3882902684156697774_state,C: nat > list_char > set_Pr2391701600042252046_state,P: produc1457211279475724562t_char] :
      ( ( member6715010751053357271_state @ Z2 @ ( produc3312000583120074607_state @ C @ P ) )
     => ~ ! [X2: nat,Y3: list_char] :
            ( ( P
              = ( produc120197956887798346t_char @ X2 @ Y3 ) )
           => ~ ( member6715010751053357271_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_921_mem__case__prodE,axiom,
    ! [Z2: produc3882902684156697774_state,C: option_state > option_state > set_Pr2391701600042252046_state,P: produc3142500478612311029_state] :
      ( ( member6715010751053357271_state @ Z2 @ ( produc2209043727768083020_state @ C @ P ) )
     => ~ ! [X2: option_state,Y3: option_state] :
            ( ( P
              = ( produc9160152616361873709_state @ X2 @ Y3 ) )
           => ~ ( member6715010751053357271_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_922_mem__case__prodE,axiom,
    ! [Z2: produc7272280185086996969_state,C: prat > state > set_Pr4231240917283394591_state,P: produc4844402304972151915_state] :
      ( ( member7461423308196221312_state @ Z2 @ ( produc569869127943504087_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: state] :
            ( ( P
              = ( produc6205719116230455971_state @ X2 @ Y3 ) )
           => ~ ( member7461423308196221312_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_923_mem__case__prodE,axiom,
    ! [Z2: produc7272280185086996969_state,C: prat > set_state > set_Pr4231240917283394591_state,P: produc6251377953716854561_state] :
      ( ( member7461423308196221312_state @ Z2 @ ( produc7793558081207154829_state @ C @ P ) )
     => ~ ! [X2: prat,Y3: set_state] :
            ( ( P
              = ( produc9080284787853255769_state @ X2 @ Y3 ) )
           => ~ ( member7461423308196221312_state @ Z2 @ ( C @ X2 @ Y3 ) ) ) ) ).

% mem_case_prodE
thf(fact_924_defined__def,axiom,
    ( defined
    = ( sep_defined_state @ plus ) ) ).

% defined_def
thf(fact_925_image2__eqI,axiom,
    ! [B: prat,F: state > prat,X: state,C: state,G: state > state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ B @ C ) @ ( bNF_Gr1645861816300964896_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_926_image2__eqI,axiom,
    ! [B: prat,F: state > prat,X: state,C: set_state,G: state > set_state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ B @ C ) @ ( bNF_Gr8363538844033681878_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_927_image2__eqI,axiom,
    ! [B: nat,F: state > nat,X: state,C: list_char,G: state > list_char,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ B @ C ) @ ( bNF_Gr71701291235176519t_char @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_928_image2__eqI,axiom,
    ! [B: state,F: state > state,X: state,C: state > state,G: state > state > state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ B @ C ) @ ( bNF_Gr7364880804673765603_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_929_image2__eqI,axiom,
    ! [B: option_state,F: state > option_state,X: state,C: option_state,G: state > option_state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ B @ C ) @ ( bNF_Gr8144397171961131434_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_930_image2__eqI,axiom,
    ! [B: state,F: state > state,X: state,C: produc3882902684156697774_state,G: state > produc3882902684156697774_state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member_state @ X @ A5 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ B @ C ) @ ( bNF_Gr947463461346416350_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_931_image2__eqI,axiom,
    ! [B: prat,F: produc3882902684156697774_state > prat,X: produc3882902684156697774_state,C: state,G: produc3882902684156697774_state > state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member6715010751053357271_state @ X @ A5 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ B @ C ) @ ( bNF_Gr5432878666621363808_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_932_image2__eqI,axiom,
    ! [B: prat,F: produc3882902684156697774_state > prat,X: produc3882902684156697774_state,C: set_state,G: produc3882902684156697774_state > set_state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member6715010751053357271_state @ X @ A5 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ B @ C ) @ ( bNF_Gr6818451474134737942_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_933_image2__eqI,axiom,
    ! [B: nat,F: produc3882902684156697774_state > nat,X: produc3882902684156697774_state,C: list_char,G: produc3882902684156697774_state > list_char,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member6715010751053357271_state @ X @ A5 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ B @ C ) @ ( bNF_Gr5554302884217825927t_char @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_934_image2__eqI,axiom,
    ! [B: state,F: produc3882902684156697774_state > state,X: produc3882902684156697774_state,C: state > state,G: produc3882902684156697774_state > state > state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( C
          = ( G @ X ) )
       => ( ( member6715010751053357271_state @ X @ A5 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ B @ C ) @ ( bNF_Gr5413576055295359779_state @ A5 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_935_same__fst__def,axiom,
    ( same_f3145481655561538747_state
    = ( ^ [P5: state > $o,R5: state > set_Pr5527899070135025255_state] :
          ( collec2083760461196787346_state
          @ ( produc7167296152490707052tate_o
            @ ( produc8588859638187112394tate_o
              @ ^ [X6: state,Y8: state > state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [X3: state,Y5: state > state] :
                      ( ( X6 = X3 )
                      & ( P5 @ X3 )
                      & ( member6978531283771894448_state @ ( produc5362444129537099455_state @ Y8 @ Y5 ) @ ( R5 @ X3 ) ) ) ) ) ) ) ) ) ).

% same_fst_def
thf(fact_936_same__fst__def,axiom,
    ( same_f8765775015391913222_state
    = ( ^ [P5: state > $o,R5: state > set_Pr4846723933414538759_state] :
          ( collec4625684881440051358_state
          @ ( produc3133855996611560728tate_o
            @ ( produc6466221716036377566tate_o
              @ ^ [X6: state,Y8: produc3882902684156697774_state] :
                  ( produc1745419677418529872tate_o
                  @ ^ [X3: state,Y5: produc3882902684156697774_state] :
                      ( ( X6 = X3 )
                      & ( P5 @ X3 )
                      & ( member3801449062345016400_state @ ( produc2343482328048119831_state @ Y8 @ Y5 ) @ ( R5 @ X3 ) ) ) ) ) ) ) ) ) ).

% same_fst_def
thf(fact_937_PartialSA_Ovalid__package__set__def,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
      = ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A3: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,T5: state > state] :
                      ( ( defined @ A3 @ U6 )
                      & ( greater @ ( core @ A3 ) @ ( core @ U6 ) )
                      & ( packag4817583915586052229_state @ plus @ unit @ T5 )
                      & ( greater @ A3 @ ( core @ ( T5 @ F ) ) ) ) )
              @ X3 ) ) ) ) ).

% PartialSA.valid_package_set_def
thf(fact_938_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr523392378426063460_state] :
      ( ( packag9013619817833129428_state @ plus @ S2 )
      = ( ! [X3: produc4357056439811976324_state] :
            ( ( member5752234768399382829_state @ X3 @ S2 )
           => ( produc8801812494870056711tate_o
              @ ^ [A3: state] :
                  ( produc1745419677418529872tate_o
                  @ ^ [U6: state,P2: produc3882902684156697774_state] : ( sep_pure_state @ plus @ A3 ) )
              @ X3 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_939_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr4231240917283394591_state] :
      ( ( packag4152378406607043437_state @ plus @ S2 )
      = ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A3: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,P2: state > state] : ( sep_pure_state @ plus @ A3 ) )
              @ X3 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_940_package__logic_Ocompleteness__aux,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,S2: set_Pr4723104092121316667al_val,F1: val > val > ( val > val ) > val,F22: val > val > ( val > val ) > val,Pc: val > $o,A5: aassertion_val,F: val,Phi2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: val,U: val,T3: val > val] :
            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A7 @ ( produc303288909735261391al_val @ U @ T3 ) ) @ S2 )
           => ( ( sep_greater_val @ Plus @ ( Core @ ( F1 @ A7 @ U @ T3 ) ) @ ( Core @ A7 ) )
              & ( ( some_val @ A7 )
                = ( Plus @ ( F1 @ A7 @ U @ T3 ) @ ( F22 @ A7 @ U @ T3 ) ) )
              & ( ( Pc @ ( Core @ A7 ) )
               => ( package_sat_val @ Plus @ A5 @ ( the_val @ ( Plus @ ( Core @ A7 ) @ ( F1 @ A7 @ U @ T3 ) ) ) ) ) ) )
       => ( ( packag7517340229427718612et_val @ Plus @ Core @ Unit @ S2 @ F )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ A5 )
           => ( ( packag6714868506247462167nd_val @ Plus @ Core @ Pc )
             => ( ( ( Stable @ F )
                  & ( sep_defined_val @ Plus @ Phi2 @ F ) )
               => ? [S9: set_Pr4723104092121316667al_val] :
                    ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi2 @ F @ S9 )
                    & ! [X5: produc2072440392815185925al_val] :
                        ( ( member5640714103519202460al_val @ X5 @ S9 )
                       => ( produc6995717860488419308_val_o
                          @ ^ [A14: val] :
                              ( produc7666680587469814684_val_o
                              @ ^ [U8: val,T5: val > val] :
                                ? [A3: val,U6: val] :
                                  ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ S2 )
                                  & ( sep_greater_val @ Plus @ A14 @ ( F22 @ A3 @ U6 @ T5 ) )
                                  & ( ( Core @ A14 )
                                    = ( Core @ A3 ) ) ) )
                          @ X5 ) ) ) ) ) ) ) ) ) ).

% package_logic.completeness_aux
thf(fact_941_package__logic_Ocompleteness__aux,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F1: state > state > ( state > state ) > state,F22: state > state > ( state > state ) > state,Pc: state > $o,A5: aassertion_state,F: state,Phi2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ( ( sep_greater_state @ Plus @ ( Core @ ( F1 @ A7 @ U @ T3 ) ) @ ( Core @ A7 ) )
              & ( ( some_state @ A7 )
                = ( Plus @ ( F1 @ A7 @ U @ T3 ) @ ( F22 @ A7 @ U @ T3 ) ) )
              & ( ( Pc @ ( Core @ A7 ) )
               => ( package_sat_state @ Plus @ A5 @ ( the_state @ ( Plus @ ( Core @ A7 ) @ ( F1 @ A7 @ U @ T3 ) ) ) ) ) ) )
       => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A5 )
           => ( ( packag6595153354952283300_state @ Plus @ Core @ Pc )
             => ( ( ( Stable @ F )
                  & ( sep_defined_state @ Plus @ Phi2 @ F ) )
               => ? [S9: set_Pr4231240917283394591_state] :
                    ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi2 @ F @ S9 )
                    & ! [X5: produc7272280185086996969_state] :
                        ( ( member7461423308196221312_state @ X5 @ S9 )
                       => ( produc1745419677418529872tate_o
                          @ ^ [A14: state] :
                              ( produc3645877548210629341tate_o
                              @ ^ [U8: state,T5: state > state] :
                                ? [A3: state,U6: state] :
                                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                                  & ( sep_greater_state @ Plus @ A14 @ ( F22 @ A3 @ U6 @ T5 ) )
                                  & ( ( Core @ A14 )
                                    = ( Core @ A3 ) ) ) )
                          @ X5 ) ) ) ) ) ) ) ) ) ).

% package_logic.completeness_aux
thf(fact_942_package__logic_OAddFromOutside,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi2: val,Phi4: val,M: val,F5: val,S3: set_Pr4723104092121316667al_val,Pc: val > $o,A5: aassertion_val,Phi6: val,F6: val,S5: set_Pr4723104092121316667al_val,F: val,S2: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ Phi2 )
          = ( Plus @ Phi4 @ M ) )
       => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi4 @ F5 @ S3 @ Pc @ A5 @ Phi6 @ F6 @ S5 )
         => ( ( Stable @ M )
           => ( ( ( some_val @ F5 )
                = ( Plus @ F @ M ) )
             => ( ( S3
                  = ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A3: val,U6: val,T5: val > val,R: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T5 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ S2 )
                        & ( ( some_val @ R )
                          = ( Plus @ A3 @ ( sep_minus_val @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) ) )
                        & ( sep_defined_val @ Plus @ R @ U6 ) ) ) )
               => ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi6 @ F6 @ S5 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_943_package__logic_OAddFromOutside,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi2: state,Phi4: state,M: state,F5: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi6: state,F6: state,S5: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ Phi2 )
          = ( Plus @ Phi4 @ M ) )
       => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi4 @ F5 @ S3 @ Pc @ A5 @ Phi6 @ F6 @ S5 )
         => ( ( Stable @ M )
           => ( ( ( some_state @ F5 )
                = ( Plus @ F @ M ) )
             => ( ( S3
                  = ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A3: state,U6: state,T5: state > state,R: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                        & ( ( some_state @ R )
                          = ( Plus @ A3 @ ( sep_minus_state @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) ) )
                        & ( sep_defined_state @ Plus @ R @ U6 ) ) ) )
               => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi6 @ F6 @ S5 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_944_package__logic_Opackage__rhs_Osimps,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A12: val,A22: val,A32: set_Pr4723104092121316667al_val,A42: val > $o,A52: aassertion_val,A62: val,A72: val,A82: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
        = ( ? [Phi: val,F3: val,S6: set_Pr4723104092121316667al_val,Pc2: val > $o,A4: aassertion_val,Phi5: val,F7: val,S7: set_Pr4723104092121316667al_val,B3: aassertion_val,Phi8: val,F8: val,S8: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aStar_val @ A4 @ B3 ) )
              & ( A62 = Phi8 )
              & ( A72 = F8 )
              & ( A82 = S8 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ F3 @ S6 @ Pc2 @ A4 @ Phi5 @ F7 @ S7 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi5 @ F7 @ S7 @ Pc2 @ B3 @ Phi8 @ F8 @ S8 ) )
          | ? [Phi: val,F3: val,S6: set_Pr4723104092121316667al_val,Pc2: val > $o,B2: val > $o,A4: aassertion_val,Phi5: val,F7: val,S7: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aImp_val @ B2 @ A4 ) )
              & ( A62 = Phi5 )
              & ( A72 = F7 )
              & ( A82 = S7 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ F3 @ S6 @ ( packag6750194596558674946nj_val @ Pc2 @ B2 ) @ A4 @ Phi5 @ F7 @ S7 ) )
          | ? [S6: set_Pr4723104092121316667al_val,Pc2: val > $o,Witness: produc2072440392815185925al_val > val,B3: val > $o,S7: set_Pr4723104092121316667al_val,Phi: val,F3: val] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aSem_val @ B3 ) )
              & ( A62 = Phi )
              & ( A72 = F3 )
              & ( A82 = S7 )
              & ! [X3: val,Y5: val,Z5: val > val,Aa3: val] :
                  ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ X3 @ ( produc303288909735261391al_val @ Y5 @ Z5 ) ) @ S6 )
                 => ( ( Pc2 @ X3 )
                   => ( ( Aa3
                        = ( Witness @ ( produc7187740677493149823al_val @ X3 @ ( produc303288909735261391al_val @ Y5 @ Z5 ) ) ) )
                     => ( ( sep_greater_val @ Plus @ X3 @ Aa3 )
                        & ( B3 @ Aa3 ) ) ) ) )
              & ( S7
                = ( sup_su4800132526891881063al_val
                  @ ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A3: val,U6: val,T5: val > val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ S6 )
                        & ~ ( Pc2 @ A3 ) ) )
                  @ ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A3: val,U6: val,T5: val > val,B2: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ ( sep_minus_val @ Plus @ Core @ A3 @ B2 ) @ ( produc303288909735261391al_val @ ( the_val @ ( Plus @ U6 @ B2 ) ) @ T5 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ S6 )
                        & ( Pc2 @ A3 )
                        & ( B2
                          = ( Witness @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) ) ) ) ) ) ) )
          | ? [Phi: val,Phi5: val,M2: val,F7: val,S7: set_Pr4723104092121316667al_val,Pc2: val > $o,A4: aassertion_val,Phi8: val,F8: val,S8: set_Pr4723104092121316667al_val,F3: val,S6: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52 = A4 )
              & ( A62 = Phi8 )
              & ( A72 = F8 )
              & ( A82 = S8 )
              & ( ( some_val @ Phi )
                = ( Plus @ Phi5 @ M2 ) )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi5 @ F7 @ S7 @ Pc2 @ A4 @ Phi8 @ F8 @ S8 )
              & ( Stable @ M2 )
              & ( ( some_val @ F7 )
                = ( Plus @ F3 @ M2 ) )
              & ( S7
                = ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A3: val,U6: val,T5: val > val,R: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T5 ) ) )
                      & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ S6 )
                      & ( ( some_val @ R )
                        = ( Plus @ A3 @ ( sep_minus_val @ Plus @ Core @ ( T5 @ F7 ) @ ( T5 @ F3 ) ) ) )
                      & ( sep_defined_val @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.simps
thf(fact_945_package__logic_Opackage__rhs_Osimps,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A12: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
        = ( ? [Phi: state,F3: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,A4: aassertion_state,Phi5: state,F7: state,S7: set_Pr4231240917283394591_state,B3: aassertion_state,Phi8: state,F8: state,S8: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aStar_state @ A4 @ B3 ) )
              & ( A62 = Phi8 )
              & ( A72 = F8 )
              & ( A82 = S8 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F3 @ S6 @ Pc2 @ A4 @ Phi5 @ F7 @ S7 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi5 @ F7 @ S7 @ Pc2 @ B3 @ Phi8 @ F8 @ S8 ) )
          | ? [Phi: state,F3: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,B2: state > $o,A4: aassertion_state,Phi5: state,F7: state,S7: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aImp_state @ B2 @ A4 ) )
              & ( A62 = Phi5 )
              & ( A72 = F7 )
              & ( A82 = S7 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F3 @ S6 @ ( packag1330488657391168505_state @ Pc2 @ B2 ) @ A4 @ Phi5 @ F7 @ S7 ) )
          | ? [S6: set_Pr4231240917283394591_state,Pc2: state > $o,Witness: produc7272280185086996969_state > state,B3: state > $o,S7: set_Pr4231240917283394591_state,Phi: state,F3: state] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aSem_state @ B3 ) )
              & ( A62 = Phi )
              & ( A72 = F3 )
              & ( A82 = S7 )
              & ! [X3: state,Y5: state,Z5: state > state,Aa3: state] :
                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ ( produc8632743443909064678_state @ Y5 @ Z5 ) ) @ S6 )
                 => ( ( Pc2 @ X3 )
                   => ( ( Aa3
                        = ( Witness @ ( produc5886875603596089627_state @ X3 @ ( produc8632743443909064678_state @ Y5 @ Z5 ) ) ) )
                     => ( ( sep_greater_state @ Plus @ X3 @ Aa3 )
                        & ( B3 @ Aa3 ) ) ) ) )
              & ( S7
                = ( sup_su3837536599209510219_state
                  @ ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A3: state,U6: state,T5: state > state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                        & ~ ( Pc2 @ A3 ) ) )
                  @ ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A3: state,U6: state,T5: state > state,B2: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ ( sep_minus_state @ Plus @ Core @ A3 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( Plus @ U6 @ B2 ) ) @ T5 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                        & ( Pc2 @ A3 )
                        & ( B2
                          = ( Witness @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) ) ) ) )
          | ? [Phi: state,Phi5: state,M2: state,F7: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,A4: aassertion_state,Phi8: state,F8: state,S8: set_Pr4231240917283394591_state,F3: state,S6: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi )
              & ( A22 = F3 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52 = A4 )
              & ( A62 = Phi8 )
              & ( A72 = F8 )
              & ( A82 = S8 )
              & ( ( some_state @ Phi )
                = ( Plus @ Phi5 @ M2 ) )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi5 @ F7 @ S7 @ Pc2 @ A4 @ Phi8 @ F8 @ S8 )
              & ( Stable @ M2 )
              & ( ( some_state @ F7 )
                = ( Plus @ F3 @ M2 ) )
              & ( S7
                = ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A3: state,U6: state,T5: state > state,R: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S6 )
                      & ( ( some_state @ R )
                        = ( Plus @ A3 @ ( sep_minus_state @ Plus @ Core @ ( T5 @ F7 ) @ ( T5 @ F3 ) ) ) )
                      & ( sep_defined_state @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.simps
thf(fact_946_greater__def,axiom,
    ( greater
    = ( sep_greater_state @ plus ) ) ).

% greater_def
thf(fact_947_minus__def,axiom,
    ( minus
    = ( sep_minus_state @ plus @ core ) ) ).

% minus_def
thf(fact_948_package__logic_Opackage__rhs__connection__instantiate,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi2: val,F: val,S2: set_Pr4723104092121316667al_val,Pc: val > $o,A5: aassertion_val,Phi4: val,F5: val,S3: set_Pr4723104092121316667al_val,A: val,U2: val,T2: val > val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
       => ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A @ ( produc303288909735261391al_val @ U2 @ T2 ) ) @ S2 )
         => ~ ! [Au: val] :
                ( ( ( some_val @ Au )
                  = ( Plus @ A @ U2 ) )
               => ~ ( ( sep_defined_val @ Plus @ Au @ ( sep_minus_val @ Plus @ Core @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                   => ? [A8: val,U3: val] :
                        ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A8 @ ( produc303288909735261391al_val @ U3 @ T2 ) ) @ S3 )
                        & ( sep_greater_val @ Plus @ ( Core @ A8 ) @ ( Core @ A ) )
                        & ( ( Plus @ Au @ ( sep_minus_val @ Plus @ Core @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                          = ( Plus @ A8 @ U3 ) )
                        & ( sep_greater_val @ Plus @ U3 @ U2 )
                        & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A5 @ A8 @ U3 @ U2 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connection_instantiate
thf(fact_949_package__logic_Opackage__rhs__connection__instantiate,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state,A: state,U2: state,T2: state > state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
       => ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ ( produc8632743443909064678_state @ U2 @ T2 ) ) @ S2 )
         => ~ ! [Au: state] :
                ( ( ( some_state @ Au )
                  = ( Plus @ A @ U2 ) )
               => ~ ( ( sep_defined_state @ Plus @ Au @ ( sep_minus_state @ Plus @ Core @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                   => ? [A8: state,U3: state] :
                        ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A8 @ ( produc8632743443909064678_state @ U3 @ T2 ) ) @ S3 )
                        & ( sep_greater_state @ Plus @ ( Core @ A8 ) @ ( Core @ A ) )
                        & ( ( Plus @ Au @ ( sep_minus_state @ Plus @ Core @ ( T2 @ F5 ) @ ( T2 @ F ) ) )
                          = ( Plus @ A8 @ U3 ) )
                        & ( sep_greater_state @ Plus @ U3 @ U2 )
                        & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A5 @ A8 @ U3 @ U2 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connection_instantiate
thf(fact_950_package__logic_Opackage__rhs__connectionI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi2: val,F: val,Phi4: val,F5: val,S2: set_Pr4723104092121316667al_val,S3: set_Pr4723104092121316667al_val,Pc: val > $o,A5: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Plus @ Phi2 @ F )
          = ( Plus @ Phi4 @ F5 ) )
       => ( ( Stable @ F5 )
         => ( ( sep_defined_val @ Plus @ Phi2 @ F )
           => ( ( sep_greater_val @ Plus @ F5 @ F )
             => ( ! [A7: val,U: val,T3: val > val] :
                    ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A7 @ ( produc303288909735261391al_val @ U @ T3 ) ) @ S2 )
                   => ? [Au2: val] :
                        ( ( ( some_val @ Au2 )
                          = ( Plus @ A7 @ U ) )
                        & ( ( sep_defined_val @ Plus @ Au2 @ ( sep_minus_val @ Plus @ Core @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                         => ? [A9: val,U4: val] :
                              ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A9 @ ( produc303288909735261391al_val @ U4 @ T3 ) ) @ S3 )
                              & ( sep_greater_val @ Plus @ ( Core @ A9 ) @ ( Core @ A7 ) )
                              & ( ( Plus @ Au2 @ ( sep_minus_val @ Plus @ Core @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                                = ( Plus @ A9 @ U4 ) )
                              & ( sep_greater_val @ Plus @ U4 @ U )
                              & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A5 @ A9 @ U4 @ U ) ) ) ) )
               => ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connectionI
thf(fact_951_package__logic_Opackage__rhs__connectionI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi2: state,F: state,Phi4: state,F5: state,S2: set_Pr4231240917283394591_state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Plus @ Phi2 @ F )
          = ( Plus @ Phi4 @ F5 ) )
       => ( ( Stable @ F5 )
         => ( ( sep_defined_state @ Plus @ Phi2 @ F )
           => ( ( sep_greater_state @ Plus @ F5 @ F )
             => ( ! [A7: state,U: state,T3: state > state] :
                    ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
                   => ? [Au2: state] :
                        ( ( ( some_state @ Au2 )
                          = ( Plus @ A7 @ U ) )
                        & ( ( sep_defined_state @ Plus @ Au2 @ ( sep_minus_state @ Plus @ Core @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                         => ? [A9: state,U4: state] :
                              ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A9 @ ( produc8632743443909064678_state @ U4 @ T3 ) ) @ S3 )
                              & ( sep_greater_state @ Plus @ ( Core @ A9 ) @ ( Core @ A7 ) )
                              & ( ( Plus @ Au2 @ ( sep_minus_state @ Plus @ Core @ ( T3 @ F5 ) @ ( T3 @ F ) ) )
                                = ( Plus @ A9 @ U4 ) )
                              & ( sep_greater_state @ Plus @ U4 @ U )
                              & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A5 @ A9 @ U4 @ U ) ) ) ) )
               => ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connectionI
thf(fact_952_package__logic_OASem,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,Pc: state > $o,Witness3: produc7272280185086996969_state > state,B4: state > $o,S3: set_Pr4231240917283394591_state,Phi2: state,F: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state,B6: state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ( ( Pc @ A7 )
             => ( ( B6
                  = ( Witness3 @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) ) )
               => ( ( sep_greater_state @ Plus @ A7 @ B6 )
                  & ( B4 @ B6 ) ) ) ) )
       => ( ( S3
            = ( sup_su3837536599209510219_state
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state,U6: state,T5: state > state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                    & ~ ( Pc @ A3 ) ) )
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A3: state,U6: state,T5: state > state,B2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ ( sep_minus_state @ Plus @ Core @ A3 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( Plus @ U6 @ B2 ) ) @ T5 ) ) )
                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ S2 )
                    & ( Pc @ A3 )
                    & ( B2
                      = ( Witness3 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) ) ) )
         => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ ( aSem_state @ B4 ) @ Phi2 @ F @ S3 ) ) ) ) ).

% package_logic.ASem
thf(fact_953_package__logic_Ovalid__package__setI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ( ( sep_defined_state @ Plus @ A7 @ U )
              & ( sep_greater_state @ Plus @ ( Core @ A7 ) @ ( Core @ U ) )
              & ( packag4817583915586052229_state @ Plus @ Unit @ T3 )
              & ( sep_greater_state @ Plus @ A7 @ ( Core @ ( T3 @ F ) ) ) ) )
       => ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F ) ) ) ).

% package_logic.valid_package_setI
thf(fact_954_package__logic_Opackage__rhs__connection__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi2: val,F: val,S2: set_Pr4723104092121316667al_val,Pc: val > $o,A5: aassertion_val,Phi4: val,F5: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
        = ( ( sep_greater_val @ Plus @ F5 @ F )
          & ( sep_defined_val @ Plus @ Phi2 @ F )
          & ( ( Plus @ Phi2 @ F )
            = ( Plus @ Phi4 @ F5 ) )
          & ( Stable @ F5 )
          & ! [X3: produc2072440392815185925al_val] :
              ( ( member5640714103519202460al_val @ X3 @ S2 )
             => ( produc6995717860488419308_val_o
                @ ^ [A3: val] :
                    ( produc7666680587469814684_val_o
                    @ ^ [U6: val,T5: val > val] :
                      ? [Au3: val] :
                        ( ( ( some_val @ Au3 )
                          = ( Plus @ A3 @ U6 ) )
                        & ( ( sep_defined_val @ Plus @ Au3 @ ( sep_minus_val @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                         => ? [A14: val,U8: val] :
                              ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A14 @ ( produc303288909735261391al_val @ U8 @ T5 ) ) @ S3 )
                              & ( sep_greater_val @ Plus @ ( Core @ A14 ) @ ( Core @ A3 ) )
                              & ( ( Plus @ Au3 @ ( sep_minus_val @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                                = ( Plus @ A14 @ U8 ) )
                              & ( sep_greater_val @ Plus @ U8 @ U6 )
                              & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A5 @ A14 @ U8 @ U6 ) ) ) ) )
                @ X3 ) ) ) ) ) ).

% package_logic.package_rhs_connection_def
thf(fact_955_package__logic_Opackage__rhs__connection__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi2: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A5: aassertion_state,Phi4: state,F5: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi2 @ F @ S2 @ Pc @ A5 @ Phi4 @ F5 @ S3 )
        = ( ( sep_greater_state @ Plus @ F5 @ F )
          & ( sep_defined_state @ Plus @ Phi2 @ F )
          & ( ( Plus @ Phi2 @ F )
            = ( Plus @ Phi4 @ F5 ) )
          & ( Stable @ F5 )
          & ! [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ S2 )
             => ( produc1745419677418529872tate_o
                @ ^ [A3: state] :
                    ( produc3645877548210629341tate_o
                    @ ^ [U6: state,T5: state > state] :
                      ? [Au3: state] :
                        ( ( ( some_state @ Au3 )
                          = ( Plus @ A3 @ U6 ) )
                        & ( ( sep_defined_state @ Plus @ Au3 @ ( sep_minus_state @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                         => ? [A14: state,U8: state] :
                              ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A14 @ ( produc8632743443909064678_state @ U8 @ T5 ) ) @ S3 )
                              & ( sep_greater_state @ Plus @ ( Core @ A14 ) @ ( Core @ A3 ) )
                              & ( ( Plus @ Au3 @ ( sep_minus_state @ Plus @ Core @ ( T5 @ F5 ) @ ( T5 @ F ) ) )
                                = ( Plus @ A14 @ U8 ) )
                              & ( sep_greater_state @ Plus @ U8 @ U6 )
                              & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A5 @ A14 @ U8 @ U6 ) ) ) ) )
                @ X3 ) ) ) ) ) ).

% package_logic.package_rhs_connection_def
thf(fact_956_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A12: val,A22: val,A32: set_Pr4723104092121316667al_val,A42: val > $o,A52: aassertion_val,A62: val,A72: val,A82: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A10: aassertion_val,Phi7: val,F9: val,S9: set_Pr4723104092121316667al_val,B8: aassertion_val] :
              ( ( A52
                = ( aStar_val @ A10 @ B8 ) )
             => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A10 @ Phi7 @ F9 @ S9 )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi7 @ F9 @ S9 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: val > $o,A10: aassertion_val] :
                ( ( A52
                  = ( aImp_val @ B6 @ A10 ) )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ ( packag6750194596558674946nj_val @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness2: produc2072440392815185925al_val > val,B8: val > $o] :
                  ( ( A52
                    = ( aSem_val @ B8 ) )
                 => ( ( A62 = A12 )
                   => ( ( A72 = A22 )
                     => ( ! [A11: val,U7: val,T6: val > val] :
                            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A11 @ ( produc303288909735261391al_val @ U7 @ T6 ) ) @ A32 )
                           => ( ( A42 @ A11 )
                             => ( ( sep_greater_val @ Plus @ A11 @ ( Witness2 @ ( produc7187740677493149823al_val @ A11 @ ( produc303288909735261391al_val @ U7 @ T6 ) ) ) )
                                & ( B8 @ ( Witness2 @ ( produc7187740677493149823al_val @ A11 @ ( produc303288909735261391al_val @ U7 @ T6 ) ) ) ) ) ) )
                       => ( A82
                         != ( sup_su4800132526891881063al_val
                            @ ( collec8300311316619386842al_val
                              @ ^ [Uu3: produc2072440392815185925al_val] :
                                ? [A3: val,U6: val,T5: val > val] :
                                  ( ( Uu3
                                    = ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) )
                                  & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ A32 )
                                  & ~ ( A42 @ A3 ) ) )
                            @ ( collec8300311316619386842al_val
                              @ ^ [Uu3: produc2072440392815185925al_val] :
                                ? [A3: val,U6: val,T5: val > val] :
                                  ( ( Uu3
                                    = ( produc7187740677493149823al_val @ ( sep_minus_val @ Plus @ Core @ A3 @ ( Witness2 @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) ) ) @ ( produc303288909735261391al_val @ ( the_val @ ( Plus @ U6 @ ( Witness2 @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) ) ) ) @ T5 ) ) )
                                  & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ A32 )
                                  & ( A42 @ A3 ) ) ) ) ) ) ) ) )
             => ~ ! [Phi7: val,M3: val] :
                    ( ( ( some_val @ A12 )
                      = ( Plus @ Phi7 @ M3 ) )
                   => ! [F9: val,S9: set_Pr4723104092121316667al_val] :
                        ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi7 @ F9 @ S9 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M3 )
                         => ( ( ( some_val @ F9 )
                              = ( Plus @ A22 @ M3 ) )
                           => ( S9
                             != ( collec8300311316619386842al_val
                                @ ^ [Uu3: produc2072440392815185925al_val] :
                                  ? [A3: val,U6: val,T5: val > val,R: val] :
                                    ( ( Uu3
                                      = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T5 ) ) )
                                    & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A3 @ ( produc303288909735261391al_val @ U6 @ T5 ) ) @ A32 )
                                    & ( ( some_val @ R )
                                      = ( Plus @ A3 @ ( sep_minus_val @ Plus @ Core @ ( T5 @ F9 ) @ ( T5 @ A22 ) ) ) )
                                    & ( sep_defined_val @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_957_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A12: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A10: aassertion_state,Phi7: state,F9: state,S9: set_Pr4231240917283394591_state,B8: aassertion_state] :
              ( ( A52
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ A42 @ A10 @ Phi7 @ F9 @ S9 )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi7 @ F9 @ S9 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( A52
                  = ( aImp_state @ B6 @ A10 ) )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A22 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness2: produc7272280185086996969_state > state,B8: state > $o] :
                  ( ( A52
                    = ( aSem_state @ B8 ) )
                 => ( ( A62 = A12 )
                   => ( ( A72 = A22 )
                     => ( ! [A11: state,U7: state,T6: state > state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) @ A32 )
                           => ( ( A42 @ A11 )
                             => ( ( sep_greater_state @ Plus @ A11 @ ( Witness2 @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) ) )
                                & ( B8 @ ( Witness2 @ ( produc5886875603596089627_state @ A11 @ ( produc8632743443909064678_state @ U7 @ T6 ) ) ) ) ) ) )
                       => ( A82
                         != ( sup_su3837536599209510219_state
                            @ ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A3: state,U6: state,T5: state > state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                  & ~ ( A42 @ A3 ) ) )
                            @ ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A3: state,U6: state,T5: state > state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ ( sep_minus_state @ Plus @ Core @ A3 @ ( Witness2 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) @ ( produc8632743443909064678_state @ ( the_state @ ( Plus @ U6 @ ( Witness2 @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) ) ) ) @ T5 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                  & ( A42 @ A3 ) ) ) ) ) ) ) ) )
             => ~ ! [Phi7: state,M3: state] :
                    ( ( ( some_state @ A12 )
                      = ( Plus @ Phi7 @ M3 ) )
                   => ! [F9: state,S9: set_Pr4231240917283394591_state] :
                        ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi7 @ F9 @ S9 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M3 )
                         => ( ( ( some_state @ F9 )
                              = ( Plus @ A22 @ M3 ) )
                           => ( S9
                             != ( collec906845016635587262_state
                                @ ^ [Uu3: produc7272280185086996969_state] :
                                  ? [A3: state,U6: state,T5: state > state,R: state] :
                                    ( ( Uu3
                                      = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T5 ) ) )
                                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U6 @ T5 ) ) @ A32 )
                                    & ( ( some_state @ R )
                                      = ( Plus @ A3 @ ( sep_minus_state @ Plus @ Core @ ( T5 @ F9 ) @ ( T5 @ A22 ) ) ) )
                                    & ( sep_defined_state @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_958_lex__prod__def,axiom,
    ( lex_pr8336311929016760645_state
    = ( ^ [Ra: set_Pr1688445902015331925_state,Rb: set_Pr1688445902015331925_state] :
          ( collec6784228404298526930_state
          @ ( produc1935756327278076076tate_o
            @ ( produc5315882979514849802tate_o
              @ ^ [A3: option_state,B2: option_state] :
                  ( produc6082990154846732246tate_o
                  @ ^ [A14: option_state,B11: option_state] :
                      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A3 @ A14 ) @ Ra )
                      | ( ( A3 = A14 )
                        & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ B2 @ B11 ) @ Rb ) ) ) ) ) ) ) ) ) ).

% lex_prod_def
thf(fact_959_lex__prod__def,axiom,
    ( lex_pr4041356198452583422_state
    = ( ^ [Ra: set_Pr1785066336555260981_state,Rb: set_Pr5527899070135025255_state] :
          ( collec2083760461196787346_state
          @ ( produc7167296152490707052tate_o
            @ ( produc8588859638187112394tate_o
              @ ^ [A3: state,B2: state > state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [A14: state,B11: state > state] :
                      ( ( member753036827967488894_state @ ( produc544653723139640077_state @ A3 @ A14 ) @ Ra )
                      | ( ( A3 = A14 )
                        & ( member6978531283771894448_state @ ( produc5362444129537099455_state @ B2 @ B11 ) @ Rb ) ) ) ) ) ) ) ) ) ).

% lex_prod_def
thf(fact_960_lex__prod__def,axiom,
    ( lex_pr7268379037978345219_state
    = ( ^ [Ra: set_Pr1785066336555260981_state,Rb: set_Pr4846723933414538759_state] :
          ( collec4625684881440051358_state
          @ ( produc3133855996611560728tate_o
            @ ( produc6466221716036377566tate_o
              @ ^ [A3: state,B2: produc3882902684156697774_state] :
                  ( produc1745419677418529872tate_o
                  @ ^ [A14: state,B11: produc3882902684156697774_state] :
                      ( ( member753036827967488894_state @ ( produc544653723139640077_state @ A3 @ A14 ) @ Ra )
                      | ( ( A3 = A14 )
                        & ( member3801449062345016400_state @ ( produc2343482328048119831_state @ B2 @ B11 ) @ Rb ) ) ) ) ) ) ) ) ) ).

% lex_prod_def
thf(fact_961_case__prod__Pair__iden,axiom,
    ! [P: produc3142500478612311029_state] :
      ( ( produc803252138055838771_state @ produc9160152616361873709_state @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_962_case__prod__Pair__iden,axiom,
    ! [P: produc4844402304972151915_state] :
      ( ( produc1922103714420728243_state @ produc6205719116230455971_state @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_963_case__prod__Pair__iden,axiom,
    ! [P: produc6251377953716854561_state] :
      ( ( produc897481912382009139_state @ produc9080284787853255769_state @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_964_case__prod__Pair__iden,axiom,
    ! [P: produc1457211279475724562t_char] :
      ( ( produc4071494739252518515t_char @ produc120197956887798346t_char @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_965_case__prod__Pair__iden,axiom,
    ! [P: produc9003781588162623004on_val] :
      ( ( produc4192255817509754207on_val @ produc74620467203698198on_val @ P )
      = P ) ).

% case_prod_Pair_iden
thf(fact_966_split__cong,axiom,
    ! [Q2: produc3882902684156697774_state,F: state > ( state > state ) > $o,G: state > ( state > state ) > $o,P: produc3882902684156697774_state] :
      ( ! [X2: state,Y3: state > state] :
          ( ( ( produc8632743443909064678_state @ X2 @ Y3 )
            = Q2 )
         => ( ( F @ X2 @ Y3 )
            = ( G @ X2 @ Y3 ) ) )
     => ( ( P = Q2 )
       => ( ( produc3645877548210629341tate_o @ F @ P )
          = ( produc3645877548210629341tate_o @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_967_split__cong,axiom,
    ! [Q2: produc7272280185086996969_state,F: state > produc3882902684156697774_state > $o,G: state > produc3882902684156697774_state > $o,P: produc7272280185086996969_state] :
      ( ! [X2: state,Y3: produc3882902684156697774_state] :
          ( ( ( produc5886875603596089627_state @ X2 @ Y3 )
            = Q2 )
         => ( ( F @ X2 @ Y3 )
            = ( G @ X2 @ Y3 ) ) )
     => ( ( P = Q2 )
       => ( ( produc1745419677418529872tate_o @ F @ P )
          = ( produc1745419677418529872tate_o @ G @ Q2 ) ) ) ) ).

% split_cong
thf(fact_968_in__lex__prod,axiom,
    ! [A: option_state,B: option_state,A6: option_state,B5: option_state,R2: set_Pr1688445902015331925_state,S: set_Pr1688445902015331925_state] :
      ( ( member2361837818702807184_state @ ( produc2397313312270560215_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc9160152616361873709_state @ A6 @ B5 ) ) @ ( lex_pr8336311929016760645_state @ R2 @ S ) )
      = ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ A6 ) @ R2 )
        | ( ( A = A6 )
          & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ B @ B5 ) @ S ) ) ) ) ).

% in_lex_prod
thf(fact_969_in__lex__prod,axiom,
    ! [A: prat,B: state,A6: prat,B5: state,R2: set_Pr3298805672376727137t_prat,S: set_Pr1785066336555260981_state] :
      ( ( member14790466581074960_state @ ( produc8801277691740291671_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc6205719116230455971_state @ A6 @ B5 ) ) @ ( lex_prod_prat_state @ R2 @ S ) )
      = ( ( member5208769068039259050t_prat @ ( produc7183142570155660857t_prat @ A @ A6 ) @ R2 )
        | ( ( A = A6 )
          & ( member753036827967488894_state @ ( produc544653723139640077_state @ B @ B5 ) @ S ) ) ) ) ).

% in_lex_prod
thf(fact_970_in__lex__prod,axiom,
    ! [A: prat,B: set_state,A6: prat,B5: set_state,R2: set_Pr3298805672376727137t_prat,S: set_Pr5618112136499017889_state] :
      ( ( member647386464819295632_state @ ( produc516693425924439767_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc9080284787853255769_state @ A6 @ B5 ) ) @ ( lex_pr1787351029354341489_state @ R2 @ S ) )
      = ( ( member5208769068039259050t_prat @ ( produc7183142570155660857t_prat @ A @ A6 ) @ R2 )
        | ( ( A = A6 )
          & ( member1976142906092959210_state @ ( produc1834047914073684089_state @ B @ B5 ) @ S ) ) ) ) ).

% in_lex_prod
thf(fact_971_in__lex__prod,axiom,
    ! [A: nat,B: list_char,A6: nat,B5: list_char,R2: set_Pr1261947904930325089at_nat,S: set_Pr4480099295215233283t_char] :
      ( ( member151853725258021968t_char @ ( produc8192741843292627479t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc120197956887798346t_char @ A6 @ B5 ) ) @ ( lex_pr1681056561245511266t_char @ R2 @ S ) )
      = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A6 ) @ R2 )
        | ( ( A = A6 )
          & ( member6023471406134104908t_char @ ( produc1606739095562851931t_char @ B @ B5 ) @ S ) ) ) ) ).

% in_lex_prod
thf(fact_972_in__lex__prod,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val,A6: produc1457211279475724562t_char > prat,B5: produc1457211279475724562t_char > option_val,R2: set_Pr1685704261205283783r_prat,S: set_Pr4698884584343881589on_val] :
      ( ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ A @ B ) @ ( produc74620467203698198on_val @ A6 @ B5 ) ) @ ( lex_pr8780192377291449342on_val @ R2 @ S ) )
      = ( ( member1381939458143960592r_prat @ ( produc1164665353665699927r_prat @ A @ A6 ) @ R2 )
        | ( ( A = A6 )
          & ( member5502714215428086462on_val @ ( produc8008623296994167373on_val @ B @ B5 ) @ S ) ) ) ) ).

% in_lex_prod
thf(fact_973_PartialSA_Oupper__closure__def,axiom,
    ! [A5: set_state] :
      ( ( sep_up1246176804924251236_state @ plus @ A5 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Phi5: state,Phi: state] :
            ( ( Uu3 = Phi5 )
            & ( greater @ Phi5 @ Phi )
            & ( member_state @ Phi @ A5 ) ) ) ) ).

% PartialSA.upper_closure_def
thf(fact_974_cwand__def,axiom,
    ( cwand
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A3: state,X3: state] :
                  ( ( ( member_state @ A3 @ A4 )
                    & ( ( some_state @ X3 )
                      = ( plus @ ( r @ A3 @ W2 ) @ A3 ) ) )
                 => ( member_state @ X3 @ B3 ) ) ) ) ) ) ).

% cwand_def
thf(fact_975_type__definition__state,axiom,
    ( type_d7385716227342696708on_val @ rep_state @ abs_state
    @ ( collec7475294502966882545on_val
      @ ^ [Uu3: produc9003781588162623004on_val] :
        ? [Phi: produc9003781588162623004on_val] :
          ( ( Uu3 = Phi )
          & ( valid_state @ Phi ) ) ) ) ).

% type_definition_state
thf(fact_976_wand__def,axiom,
    ( wand
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A3: state,X3: state] :
                  ( ( ( member_state @ A3 @ A4 )
                    & ( ( some_state @ X3 )
                      = ( plus @ W2 @ A3 ) ) )
                 => ( member_state @ X3 @ B3 ) ) ) ) ) ) ).

% wand_def
thf(fact_977_relImage__def,axiom,
    ( bNF_Gr63754628658600314_state
    = ( ^ [R5: set_Pr1688445902015331925_state,F3: option_state > option_state] :
          ( collec8144523193623705312_state
          @ ^ [Uu3: produc3142500478612311029_state] :
            ? [A15: option_state,A23: option_state] :
              ( ( Uu3
                = ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A15 @ A23 ) @ R5 ) ) ) ) ) ).

% relImage_def
thf(fact_978_multiply__sem__assertion_Oelims,axiom,
    ! [X: prat,Xa: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X @ Xa )
        = Y )
     => ( Y
        = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X ) @ Xa ) ) ) ) ).

% multiply_sem_assertion.elims
thf(fact_979_multiply__sem__assertion_Osimps,axiom,
    ( multip8064567061438756306ertion
    = ( ^ [P2: prat,P5: set_state] : ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ P2 ) @ P5 ) ) ) ) ).

% multiply_sem_assertion.simps
thf(fact_980_image__eqI,axiom,
    ! [B: state,F: state > state,X: state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_state @ X @ A5 )
       => ( member_state @ B @ ( image_state_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_981_image__eqI,axiom,
    ! [B: produc3882902684156697774_state,F: state > produc3882902684156697774_state,X: state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_state @ X @ A5 )
       => ( member6715010751053357271_state @ B @ ( image_5311902671526399277_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_982_image__eqI,axiom,
    ! [B: state,F: produc3882902684156697774_state > state,X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member6715010751053357271_state @ X @ A5 )
       => ( member_state @ B @ ( image_6759111139246981411_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_983_image__eqI,axiom,
    ! [B: produc7272280185086996969_state,F: state > produc7272280185086996969_state,X: state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_state @ X @ A5 )
       => ( member7461423308196221312_state @ B @ ( image_632992669292831658_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_984_image__eqI,axiom,
    ! [B: state,F: produc7272280185086996969_state > state,X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member7461423308196221312_state @ X @ A5 )
       => ( member_state @ B @ ( image_2710133271811360426_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_985_image__eqI,axiom,
    ! [B: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state,X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member6715010751053357271_state @ X @ A5 )
       => ( member6715010751053357271_state @ B @ ( image_508898238547643525_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_986_image__eqI,axiom,
    ! [B: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state,X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member7461423308196221312_state @ X @ A5 )
       => ( member6715010751053357271_state @ B @ ( image_7466395622266389182_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_987_image__eqI,axiom,
    ! [B: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state,X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member6715010751053357271_state @ X @ A5 )
       => ( member7461423308196221312_state @ B @ ( image_4364510454419742290_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_988_image__eqI,axiom,
    ! [B: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state,X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member7461423308196221312_state @ X @ A5 )
       => ( member7461423308196221312_state @ B @ ( image_3064086290059306969_state @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_989_image__eqI,axiom,
    ! [B: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val,X: state,A5: set_state] :
      ( ( B
        = ( F @ X ) )
     => ( ( member_state @ X @ A5 )
       => ( member2879030624002546611on_val @ B @ ( image_4772210114854293981on_val @ F @ A5 ) ) ) ) ).

% image_eqI
thf(fact_990_image__ident,axiom,
    ! [Y9: set_state] :
      ( ( image_state_state
        @ ^ [X3: state] : X3
        @ Y9 )
      = Y9 ) ).

% image_ident
thf(fact_991_image__Un,axiom,
    ! [F: state > state,A5: set_state,B4: set_state] :
      ( ( image_state_state @ F @ ( sup_sup_set_state @ A5 @ B4 ) )
      = ( sup_sup_set_state @ ( image_state_state @ F @ A5 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_Un
thf(fact_992_image__Un,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( image_3064086290059306969_state @ F @ ( sup_su3837536599209510219_state @ A5 @ B4 ) )
      = ( sup_su3837536599209510219_state @ ( image_3064086290059306969_state @ F @ A5 ) @ ( image_3064086290059306969_state @ F @ B4 ) ) ) ).

% image_Un
thf(fact_993_Compr__image__eq,axiom,
    ! [F: state > state,A5: set_state,P4: state > $o] :
      ( ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ ( image_state_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_state_state @ F
        @ ( collect_state
          @ ^ [X3: state] :
              ( ( member_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_994_Compr__image__eq,axiom,
    ! [F: state > produc3882902684156697774_state,A5: set_state,P4: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ ( image_5311902671526399277_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_5311902671526399277_state @ F
        @ ( collect_state
          @ ^ [X3: state] :
              ( ( member_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_995_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > state,A5: set_Pr2391701600042252046_state,P4: state > $o] :
      ( ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ ( image_6759111139246981411_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_6759111139246981411_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X3: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_996_Compr__image__eq,axiom,
    ! [F: state > produc7272280185086996969_state,A5: set_state,P4: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ ( image_632992669292831658_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_632992669292831658_state @ F
        @ ( collect_state
          @ ^ [X3: state] :
              ( ( member_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_997_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > state,A5: set_Pr4231240917283394591_state,P4: state > $o] :
      ( ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ ( image_2710133271811360426_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_2710133271811360426_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_998_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ ( image_508898238547643525_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_508898238547643525_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X3: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_999_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > produc3882902684156697774_state,A5: set_Pr4231240917283394591_state,P4: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ ( image_7466395622266389182_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_7466395622266389182_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1000_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > produc7272280185086996969_state,A5: set_Pr2391701600042252046_state,P4: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ ( image_4364510454419742290_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_4364510454419742290_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X3: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1001_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ ( image_3064086290059306969_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_3064086290059306969_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X3: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1002_Compr__image__eq,axiom,
    ! [F: produc9003781588162623004on_val > state,A5: set_Pr7649655576376376530on_val,P4: state > $o] :
      ( ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ ( image_1205529093420515805_state @ F @ A5 ) )
            & ( P4 @ X3 ) ) )
      = ( image_1205529093420515805_state @ F
        @ ( collec7475294502966882545on_val
          @ ^ [X3: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ X3 @ A5 )
              & ( P4 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1003_image__image,axiom,
    ! [F: state > state,G: state > state,A5: set_state] :
      ( ( image_state_state @ F @ ( image_state_state @ G @ A5 ) )
      = ( image_state_state
        @ ^ [X3: state] : ( F @ ( G @ X3 ) )
        @ A5 ) ) ).

% image_image
thf(fact_1004_imageE,axiom,
    ! [B: state,F: state > state,A5: set_state] :
      ( ( member_state @ B @ ( image_state_state @ F @ A5 ) )
     => ~ ! [X2: state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1005_imageE,axiom,
    ! [B: state,F: produc3882902684156697774_state > state,A5: set_Pr2391701600042252046_state] :
      ( ( member_state @ B @ ( image_6759111139246981411_state @ F @ A5 ) )
     => ~ ! [X2: produc3882902684156697774_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6715010751053357271_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1006_imageE,axiom,
    ! [B: produc3882902684156697774_state,F: state > produc3882902684156697774_state,A5: set_state] :
      ( ( member6715010751053357271_state @ B @ ( image_5311902671526399277_state @ F @ A5 ) )
     => ~ ! [X2: state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1007_imageE,axiom,
    ! [B: state,F: produc7272280185086996969_state > state,A5: set_Pr4231240917283394591_state] :
      ( ( member_state @ B @ ( image_2710133271811360426_state @ F @ A5 ) )
     => ~ ! [X2: produc7272280185086996969_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member7461423308196221312_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1008_imageE,axiom,
    ! [B: produc7272280185086996969_state,F: state > produc7272280185086996969_state,A5: set_state] :
      ( ( member7461423308196221312_state @ B @ ( image_632992669292831658_state @ F @ A5 ) )
     => ~ ! [X2: state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1009_imageE,axiom,
    ! [B: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state,A5: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ B @ ( image_508898238547643525_state @ F @ A5 ) )
     => ~ ! [X2: produc3882902684156697774_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6715010751053357271_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1010_imageE,axiom,
    ! [B: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state,A5: set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ B @ ( image_4364510454419742290_state @ F @ A5 ) )
     => ~ ! [X2: produc3882902684156697774_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6715010751053357271_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1011_imageE,axiom,
    ! [B: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state,A5: set_Pr4231240917283394591_state] :
      ( ( member6715010751053357271_state @ B @ ( image_7466395622266389182_state @ F @ A5 ) )
     => ~ ! [X2: produc7272280185086996969_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member7461423308196221312_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1012_imageE,axiom,
    ! [B: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state,A5: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ B @ ( image_3064086290059306969_state @ F @ A5 ) )
     => ~ ! [X2: produc7272280185086996969_state] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member7461423308196221312_state @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1013_imageE,axiom,
    ! [B: state,F: produc9003781588162623004on_val > state,A5: set_Pr7649655576376376530on_val] :
      ( ( member_state @ B @ ( image_1205529093420515805_state @ F @ A5 ) )
     => ~ ! [X2: produc9003781588162623004on_val] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member2879030624002546611on_val @ X2 @ A5 ) ) ) ).

% imageE
thf(fact_1014_image__mono,axiom,
    ! [A5: set_state,B4: set_state,F: state > state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A5 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_mono
thf(fact_1015_image__subsetI,axiom,
    ! [A5: set_state,F: state > state,B4: set_state] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ A5 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1016_image__subsetI,axiom,
    ! [A5: set_state,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ A5 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1017_image__subsetI,axiom,
    ! [A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state,B4: set_state] :
      ( ! [X2: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X2 @ A5 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_6759111139246981411_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1018_image__subsetI,axiom,
    ! [A5: set_state,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ A5 )
         => ( member7461423308196221312_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1019_image__subsetI,axiom,
    ! [A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X2 @ A5 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1020_image__subsetI,axiom,
    ! [A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X2 @ A5 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_508898238547643525_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1021_image__subsetI,axiom,
    ! [A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X2 @ A5 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1022_image__subsetI,axiom,
    ! [A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X2 @ A5 )
         => ( member7461423308196221312_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_4364510454419742290_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1023_image__subsetI,axiom,
    ! [A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X2 @ A5 )
         => ( member7461423308196221312_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1024_image__subsetI,axiom,
    ! [A5: set_state,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ A5 )
         => ( member2879030624002546611on_val @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ A5 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1025_subset__imageE,axiom,
    ! [B4: set_state,F: state > state,A5: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A5 ) )
     => ~ ! [C4: set_state] :
            ( ( ord_le2494988322063910608_state @ C4 @ A5 )
           => ( B4
             != ( image_state_state @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_1026_image__subset__iff,axiom,
    ! [F: state > state,A5: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A5 ) @ B4 )
      = ( ! [X3: state] :
            ( ( member_state @ X3 @ A5 )
           => ( member_state @ ( F @ X3 ) @ B4 ) ) ) ) ).

% image_subset_iff
thf(fact_1027_subset__image__iff,axiom,
    ! [B4: set_state,F: state > state,A5: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A5 ) )
      = ( ? [AA: set_state] :
            ( ( ord_le2494988322063910608_state @ AA @ A5 )
            & ( B4
              = ( image_state_state @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_1028_rev__image__eqI,axiom,
    ! [X: state,A5: set_state,B: state,F: state > state] :
      ( ( member_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member_state @ B @ ( image_state_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1029_rev__image__eqI,axiom,
    ! [X: state,A5: set_state,B: produc3882902684156697774_state,F: state > produc3882902684156697774_state] :
      ( ( member_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member6715010751053357271_state @ B @ ( image_5311902671526399277_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1030_rev__image__eqI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B: state,F: produc3882902684156697774_state > state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member_state @ B @ ( image_6759111139246981411_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1031_rev__image__eqI,axiom,
    ! [X: state,A5: set_state,B: produc7272280185086996969_state,F: state > produc7272280185086996969_state] :
      ( ( member_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member7461423308196221312_state @ B @ ( image_632992669292831658_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1032_rev__image__eqI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B: state,F: produc7272280185086996969_state > state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member_state @ B @ ( image_2710133271811360426_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1033_rev__image__eqI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member6715010751053357271_state @ B @ ( image_508898238547643525_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1034_rev__image__eqI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member6715010751053357271_state @ B @ ( image_7466395622266389182_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1035_rev__image__eqI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member7461423308196221312_state @ B @ ( image_4364510454419742290_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1036_rev__image__eqI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member7461423308196221312_state @ B @ ( image_3064086290059306969_state @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1037_rev__image__eqI,axiom,
    ! [X: state,A5: set_state,B: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val] :
      ( ( member_state @ X @ A5 )
     => ( ( B
          = ( F @ X ) )
       => ( member2879030624002546611on_val @ B @ ( image_4772210114854293981on_val @ F @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_1038_ball__imageD,axiom,
    ! [F: state > state,A5: set_state,P4: state > $o] :
      ( ! [X2: state] :
          ( ( member_state @ X2 @ ( image_state_state @ F @ A5 ) )
         => ( P4 @ X2 ) )
     => ! [X5: state] :
          ( ( member_state @ X5 @ A5 )
         => ( P4 @ ( F @ X5 ) ) ) ) ).

% ball_imageD
thf(fact_1039_image__cong,axiom,
    ! [M4: set_state,N: set_state,F: state > state,G: state > state] :
      ( ( M4 = N )
     => ( ! [X2: state] :
            ( ( member_state @ X2 @ N )
           => ( ( F @ X2 )
              = ( G @ X2 ) ) )
       => ( ( image_state_state @ F @ M4 )
          = ( image_state_state @ G @ N ) ) ) ) ).

% image_cong
thf(fact_1040_bex__imageD,axiom,
    ! [F: state > state,A5: set_state,P4: state > $o] :
      ( ? [X5: state] :
          ( ( member_state @ X5 @ ( image_state_state @ F @ A5 ) )
          & ( P4 @ X5 ) )
     => ? [X2: state] :
          ( ( member_state @ X2 @ A5 )
          & ( P4 @ ( F @ X2 ) ) ) ) ).

% bex_imageD
thf(fact_1041_image__iff,axiom,
    ! [Z2: state,F: state > state,A5: set_state] :
      ( ( member_state @ Z2 @ ( image_state_state @ F @ A5 ) )
      = ( ? [X3: state] :
            ( ( member_state @ X3 @ A5 )
            & ( Z2
              = ( F @ X3 ) ) ) ) ) ).

% image_iff
thf(fact_1042_imageI,axiom,
    ! [X: state,A5: set_state,F: state > state] :
      ( ( member_state @ X @ A5 )
     => ( member_state @ ( F @ X ) @ ( image_state_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1043_imageI,axiom,
    ! [X: state,A5: set_state,F: state > produc3882902684156697774_state] :
      ( ( member_state @ X @ A5 )
     => ( member6715010751053357271_state @ ( F @ X ) @ ( image_5311902671526399277_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1044_imageI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( member_state @ ( F @ X ) @ ( image_6759111139246981411_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1045_imageI,axiom,
    ! [X: state,A5: set_state,F: state > produc7272280185086996969_state] :
      ( ( member_state @ X @ A5 )
     => ( member7461423308196221312_state @ ( F @ X ) @ ( image_632992669292831658_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1046_imageI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( member_state @ ( F @ X ) @ ( image_2710133271811360426_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1047_imageI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( member6715010751053357271_state @ ( F @ X ) @ ( image_508898238547643525_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1048_imageI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc3882902684156697774_state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( member6715010751053357271_state @ ( F @ X ) @ ( image_7466395622266389182_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1049_imageI,axiom,
    ! [X: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc7272280185086996969_state] :
      ( ( member6715010751053357271_state @ X @ A5 )
     => ( member7461423308196221312_state @ ( F @ X ) @ ( image_4364510454419742290_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1050_imageI,axiom,
    ! [X: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ X @ A5 )
     => ( member7461423308196221312_state @ ( F @ X ) @ ( image_3064086290059306969_state @ F @ A5 ) ) ) ).

% imageI
thf(fact_1051_imageI,axiom,
    ! [X: state,A5: set_state,F: state > produc9003781588162623004on_val] :
      ( ( member_state @ X @ A5 )
     => ( member2879030624002546611on_val @ ( F @ X ) @ ( image_4772210114854293981on_val @ F @ A5 ) ) ) ).

% imageI
thf(fact_1052_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,P4: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_3064086290059306969_state @ F @ ( collec906845016635587262_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1053_setcompr__eq__image,axiom,
    ! [F: state > produc7272280185086996969_state,P4: state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_632992669292831658_state @ F @ ( collect_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1054_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc7272280185086996969_state,P4: produc9003781588162623004on_val > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_3204238854701872908_state @ F @ ( collec7475294502966882545on_val @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1055_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > state,P4: produc7272280185086996969_state > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_2710133271811360426_state @ F @ ( collec906845016635587262_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1056_setcompr__eq__image,axiom,
    ! [F: state > state,P4: state > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_state_state @ F @ ( collect_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1057_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > state,P4: produc9003781588162623004on_val > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_1205529093420515805_state @ F @ ( collec7475294502966882545on_val @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1058_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc9003781588162623004on_val,P4: produc7272280185086996969_state > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X3: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_3393013468800240652on_val @ F @ ( collec906845016635587262_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1059_setcompr__eq__image,axiom,
    ! [F: state > produc9003781588162623004on_val,P4: state > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_4772210114854293981on_val @ F @ ( collect_state @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1060_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc9003781588162623004on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X3: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( P4 @ X3 ) ) )
      = ( image_4170889944715819327on_val @ F @ ( collec7475294502966882545on_val @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_1061_Setcompr__eq__image,axiom,
    ! [F: state > state,A5: set_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member_state @ X3 @ A5 ) ) )
      = ( image_state_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1062_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > state,A5: set_Pr2391701600042252046_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member6715010751053357271_state @ X3 @ A5 ) ) )
      = ( image_6759111139246981411_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1063_Setcompr__eq__image,axiom,
    ! [F: state > produc7272280185086996969_state,A5: set_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member_state @ X3 @ A5 ) ) )
      = ( image_632992669292831658_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1064_Setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > state,A5: set_Pr4231240917283394591_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member7461423308196221312_state @ X3 @ A5 ) ) )
      = ( image_2710133271811360426_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1065_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > produc7272280185086996969_state,A5: set_Pr2391701600042252046_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member6715010751053357271_state @ X3 @ A5 ) ) )
      = ( image_4364510454419742290_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1066_Setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A5: set_Pr4231240917283394591_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member7461423308196221312_state @ X3 @ A5 ) ) )
      = ( image_3064086290059306969_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1067_Setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > state,A5: set_Pr7649655576376376530on_val] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X3: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member2879030624002546611on_val @ X3 @ A5 ) ) )
      = ( image_1205529093420515805_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1068_Setcompr__eq__image,axiom,
    ! [F: state > produc9003781588162623004on_val,A5: set_state] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X3: state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member_state @ X3 @ A5 ) ) )
      = ( image_4772210114854293981on_val @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1069_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > produc9003781588162623004on_val,A5: set_Pr2391701600042252046_state] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X3: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member6715010751053357271_state @ X3 @ A5 ) ) )
      = ( image_4690842878458256517on_val @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1070_Setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc7272280185086996969_state,A5: set_Pr7649655576376376530on_val] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X3: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X3 ) )
            & ( member2879030624002546611on_val @ X3 @ A5 ) ) )
      = ( image_3204238854701872908_state @ F @ A5 ) ) ).

% Setcompr_eq_image
thf(fact_1071_multiply__sem__assertion_Opelims,axiom,
    ! [X: prat,Xa: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X @ Xa )
        = Y )
     => ( ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X @ Xa ) )
       => ~ ( ( Y
              = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X ) @ Xa ) ) )
           => ~ ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X @ Xa ) ) ) ) ) ).

% multiply_sem_assertion.pelims
thf(fact_1072_image__Collect__subsetI,axiom,
    ! [P4: state > $o,F: state > state,B4: set_state] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ ( collect_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1073_image__Collect__subsetI,axiom,
    ! [P4: state > $o,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ ( collect_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1074_image__Collect__subsetI,axiom,
    ! [P4: state > $o,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
         => ( member7461423308196221312_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ ( collect_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1075_image__Collect__subsetI,axiom,
    ! [P4: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ ( collec906845016635587262_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1076_image__Collect__subsetI,axiom,
    ! [P4: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ ( collec906845016635587262_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1077_image__Collect__subsetI,axiom,
    ! [P4: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
         => ( member7461423308196221312_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ ( collec906845016635587262_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1078_image__Collect__subsetI,axiom,
    ! [P4: state > $o,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X2: state] :
          ( ( P4 @ X2 )
         => ( member2879030624002546611on_val @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ ( collect_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1079_image__Collect__subsetI,axiom,
    ! [P4: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > state,B4: set_state] :
      ( ! [X2: produc9003781588162623004on_val] :
          ( ( P4 @ X2 )
         => ( member_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_1205529093420515805_state @ F @ ( collec7475294502966882545on_val @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1080_image__Collect__subsetI,axiom,
    ! [P4: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X2: produc9003781588162623004on_val] :
          ( ( P4 @ X2 )
         => ( member6715010751053357271_state @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_4494208899119068747_state @ F @ ( collec7475294502966882545on_val @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1081_image__Collect__subsetI,axiom,
    ! [P4: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X2: produc7272280185086996969_state] :
          ( ( P4 @ X2 )
         => ( member2879030624002546611on_val @ ( F @ X2 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_3393013468800240652on_val @ F @ ( collec906845016635587262_state @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_1082_all__subset__image,axiom,
    ! [F: state > state,A5: set_state,P4: set_state > $o] :
      ( ( ! [B3: set_state] :
            ( ( ord_le2494988322063910608_state @ B3 @ ( image_state_state @ F @ A5 ) )
           => ( P4 @ B3 ) ) )
      = ( ! [B3: set_state] :
            ( ( ord_le2494988322063910608_state @ B3 @ A5 )
           => ( P4 @ ( image_state_state @ F @ B3 ) ) ) ) ) ).

% all_subset_image
thf(fact_1083_pair__in__swap__image,axiom,
    ! [Y: state,X: prat,A5: set_Pr6039890582625207499_state] :
      ( ( member8716344949261458452e_prat @ ( produc5862297150877942435e_prat @ Y @ X ) @ ( image_2830361380300980677e_prat @ produc6686753061519163459_state @ A5 ) )
      = ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1084_pair__in__swap__image,axiom,
    ! [Y: prat,X: state,A5: set_Pr8996442262779224523e_prat] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Y @ X ) @ ( image_8107462086123161541_state @ produc6343331096166649923e_prat @ A5 ) )
      = ( member8716344949261458452e_prat @ ( produc5862297150877942435e_prat @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1085_pair__in__swap__image,axiom,
    ! [Y: set_state,X: prat,A5: set_Pr6847263425858009217_state] :
      ( ( member3111753566487124938e_prat @ ( produc5311113300630973017e_prat @ Y @ X ) @ ( image_8313154324233580357e_prat @ produc1562565776713478649_state @ A5 ) )
      = ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1086_pair__in__swap__image,axiom,
    ! [Y: list_char,X: nat,A5: set_Pr2507339680178222706t_char] :
      ( ( member6633493567087309371ar_nat @ ( produc8702345860417625034ar_nat @ Y @ X ) @ ( image_652198164289537669ar_nat @ produc5051419219066781674t_char @ A5 ) )
      = ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1087_pair__in__swap__image,axiom,
    ! [Y: prat,X: set_state,A5: set_Pr6566877984550221441e_prat] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Y @ X ) @ ( image_8063195947988251461_state @ produc7016766326345971705e_prat @ A5 ) )
      = ( member3111753566487124938e_prat @ ( produc5311113300630973017e_prat @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1088_pair__in__swap__image,axiom,
    ! [Y: nat,X: list_char,A5: set_Pr8803067691650843250ar_nat] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Y @ X ) @ ( image_688197443715608197t_char @ produc4410195085741832554ar_nat @ A5 ) )
      = ( member6633493567087309371ar_nat @ ( produc8702345860417625034ar_nat @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1089_pair__in__swap__image,axiom,
    ! [Y: state > state,X: state,A5: set_Pr2391701600042252046_state] :
      ( ( member8708878012768793047_state @ ( produc4737362649269059174_state @ Y @ X ) @ ( image_2502765500263079301_state @ produc6438927260845192582_state @ A5 ) )
      = ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1090_pair__in__swap__image,axiom,
    ! [Y: state,X: state > state,A5: set_Pr2063381651806504974_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Y @ X ) @ ( image_5540908381507763077_state @ produc2543546466205187078_state @ A5 ) )
      = ( member8708878012768793047_state @ ( produc4737362649269059174_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1091_pair__in__swap__image,axiom,
    ! [Y: option_state,X: option_state,A5: set_Pr1688445902015331925_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Y @ X ) @ ( image_3543735668343923269_state @ produc8425362190318354125_state @ A5 ) )
      = ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1092_pair__in__swap__image,axiom,
    ! [Y: produc3882902684156697774_state,X: state,A5: set_Pr4231240917283394591_state] :
      ( ( member1546683425902591150_state @ ( produc7334084071316671761_state @ Y @ X ) @ ( image_6372718444620452615_state @ produc6564544480275723131_state @ A5 ) )
      = ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_1093_pair__imageI,axiom,
    ! [A: prat,B: state,A5: set_Pr6039890582625207499_state,F: prat > state > state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_6883929567913436896_state @ ( produc5191658985856023922_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1094_pair__imageI,axiom,
    ! [A: prat,B: set_state,A5: set_Pr6847263425858009217_state,F: prat > set_state > state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_1091725855630477206_state @ ( produc2626907587099862312_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1095_pair__imageI,axiom,
    ! [A: nat,B: list_char,A5: set_Pr2507339680178222706t_char,F: nat > list_char > state] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_7385172899168281479_state @ ( produc217683206301814297_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1096_pair__imageI,axiom,
    ! [A: state,B: state > state,A5: set_Pr2391701600042252046_state,F: state > ( state > state ) > state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_6759111139246981411_state @ ( produc8575939086779714485_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1097_pair__imageI,axiom,
    ! [A: option_state,B: option_state,A5: set_Pr1688445902015331925_state,F: option_state > option_state > state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_393491784373993066_state @ ( produc7211634496914305532_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1098_pair__imageI,axiom,
    ! [A: state,B: state > state,A5: set_Pr2391701600042252046_state,F: state > ( state > state ) > $o] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ A5 )
     => ( member_o @ ( F @ A @ B ) @ ( image_528283217102427119tate_o @ ( produc3645877548210629341tate_o @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1099_pair__imageI,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_Pr4231240917283394591_state,F: state > produc3882902684156697774_state > state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ A5 )
     => ( member_state @ ( F @ A @ B ) @ ( image_2710133271811360426_state @ ( produc8258182183023037954_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1100_pair__imageI,axiom,
    ! [A: prat,B: state,A5: set_Pr6039890582625207499_state,F: prat > state > produc3882902684156697774_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ A5 )
     => ( member6715010751053357271_state @ ( F @ A @ B ) @ ( image_1979208616201753608_state @ ( produc6727336724318121462_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1101_pair__imageI,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_Pr4231240917283394591_state,F: state > produc3882902684156697774_state > $o] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ A5 )
     => ( member_o @ ( F @ A @ B ) @ ( image_6262870063963634088tate_o @ ( produc1745419677418529872tate_o @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1102_pair__imageI,axiom,
    ! [A: prat,B: set_state,A5: set_Pr6847263425858009217_state,F: prat > set_state > produc3882902684156697774_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ A5 )
     => ( member6715010751053357271_state @ ( F @ A @ B ) @ ( image_7417905060788143314_state @ ( produc8936804542704588736_state @ F ) @ A5 ) ) ) ).

% pair_imageI
thf(fact_1103_multiply__sem__assertion_Ocases,axiom,
    ! [X: produc6251377953716854561_state] :
      ~ ! [P3: prat,P6: set_state] :
          ( X
         != ( produc9080284787853255769_state @ P3 @ P6 ) ) ).

% multiply_sem_assertion.cases
thf(fact_1104_ssubst__Pair__rhs,axiom,
    ! [R2: state,S: produc3882902684156697774_state,R3: set_Pr4231240917283394591_state,S10: produc3882902684156697774_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1105_ssubst__Pair__rhs,axiom,
    ! [R2: state,S: state > state,R3: set_Pr2391701600042252046_state,S10: state > state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1106_ssubst__Pair__rhs,axiom,
    ! [R2: option_state,S: option_state,R3: set_Pr1688445902015331925_state,S10: option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1107_ssubst__Pair__rhs,axiom,
    ! [R2: prat,S: state,R3: set_Pr6039890582625207499_state,S10: state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1108_ssubst__Pair__rhs,axiom,
    ! [R2: prat,S: set_state,R3: set_Pr6847263425858009217_state,S10: set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1109_ssubst__Pair__rhs,axiom,
    ! [R2: nat,S: list_char,R3: set_Pr2507339680178222706t_char,S10: list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1110_ssubst__Pair__rhs,axiom,
    ! [R2: produc1457211279475724562t_char > prat,S: produc1457211279475724562t_char > option_val,R3: set_Pr7649655576376376530on_val,S10: produc1457211279475724562t_char > option_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ R2 @ S ) @ R3 )
     => ( ( S10 = S )
       => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ R2 @ S10 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1111_Collect__split__mono__strong,axiom,
    ! [X7: set_nat,A5: set_Pr2507339680178222706t_char,Y9: set_list_char,P4: nat > list_char > $o,Q: nat > list_char > $o] :
      ( ( X7
        = ( image_3548405822317538717ar_nat @ produc6204653154488278070t_char @ A5 ) )
     => ( ( Y9
          = ( image_3034139768025083822t_char @ produc1900778367047502200t_char @ A5 ) )
       => ( ! [X2: nat] :
              ( ( member_nat @ X2 @ X7 )
             => ! [Xa2: list_char] :
                  ( ( member_list_char @ Xa2 @ Y9 )
                 => ( ( P4 @ X2 @ Xa2 )
                   => ( Q @ X2 @ Xa2 ) ) ) )
         => ( ( ord_le6315511645215477266t_char @ A5 @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ P4 ) ) )
           => ( ord_le6315511645215477266t_char @ A5 @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_1112_Collect__split__mono__strong,axiom,
    ! [X7: set_Pr3433046674199179443r_prat,A5: set_Pr7649655576376376530on_val,Y9: set_Pr1004501353197068112on_val,P4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,Q: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( X7
        = ( image_3067683418878703216r_prat @ produc5239619271231976746on_val @ A5 ) )
     => ( ( Y9
          = ( image_2330660378567450301on_val @ produc2319605628138516840on_val @ A5 ) )
       => ( ! [X2: produc1457211279475724562t_char > prat] :
              ( ( member2336342582916103932r_prat @ X2 @ X7 )
             => ! [Xa2: produc1457211279475724562t_char > option_val] :
                  ( ( member1577473829074448177on_val @ Xa2 @ Y9 )
                 => ( ( P4 @ X2 @ Xa2 )
                   => ( Q @ X2 @ Xa2 ) ) ) )
         => ( ( ord_le6900622908513426738on_val @ A5 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ P4 ) ) )
           => ( ord_le6900622908513426738on_val @ A5 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_1113_Collect__split__mono__strong,axiom,
    ! [X7: set_state,A5: set_Pr2391701600042252046_state,Y9: set_state_state,P4: state > ( state > state ) > $o,Q: state > ( state > state ) > $o] :
      ( ( X7
        = ( image_6759111139246981411_state @ produc7095885521192019410_state @ A5 ) )
     => ( ( Y9
          = ( image_6089932313839440636_state @ produc1734700239402139924_state @ A5 ) )
       => ( ! [X2: state] :
              ( ( member_state @ X2 @ X7 )
             => ! [Xa2: state > state] :
                  ( ( member_state_state @ Xa2 @ Y9 )
                 => ( ( P4 @ X2 @ Xa2 )
                   => ( Q @ X2 @ Xa2 ) ) ) )
         => ( ( ord_le6483787752022044334_state @ A5 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ P4 ) ) )
           => ( ord_le6483787752022044334_state @ A5 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_1114_Collect__split__mono__strong,axiom,
    ! [X7: set_state,A5: set_Pr4231240917283394591_state,Y9: set_Pr2391701600042252046_state,P4: state > produc3882902684156697774_state > $o,Q: state > produc3882902684156697774_state > $o] :
      ( ( X7
        = ( image_2710133271811360426_state @ produc848024588167747631_state @ A5 ) )
     => ( ( Y9
          = ( image_7466395622266389182_state @ produc6310399636379773037_state @ A5 ) )
       => ( ! [X2: state] :
              ( ( member_state @ X2 @ X7 )
             => ! [Xa2: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ Xa2 @ Y9 )
                 => ( ( P4 @ X2 @ Xa2 )
                   => ( Q @ X2 @ Xa2 ) ) ) )
         => ( ( ord_le4032880777312351359_state @ A5 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ P4 ) ) )
           => ( ord_le4032880777312351359_state @ A5 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_1115_prop__restrict,axiom,
    ! [X: produc3882902684156697774_state,Z6: set_Pr2391701600042252046_state,X7: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ X @ Z6 )
     => ( ( ord_le6483787752022044334_state @ Z6
          @ ( collec394671971739345689_state
            @ ^ [X3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X3 @ X7 )
                & ( P4 @ X3 ) ) ) )
       => ( P4 @ X ) ) ) ).

% prop_restrict
thf(fact_1116_prop__restrict,axiom,
    ! [X: produc7272280185086996969_state,Z6: set_Pr4231240917283394591_state,X7: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ( member7461423308196221312_state @ X @ Z6 )
     => ( ( ord_le4032880777312351359_state @ Z6
          @ ( collec906845016635587262_state
            @ ^ [X3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X3 @ X7 )
                & ( P4 @ X3 ) ) ) )
       => ( P4 @ X ) ) ) ).

% prop_restrict
thf(fact_1117_prop__restrict,axiom,
    ! [X: produc9003781588162623004on_val,Z6: set_Pr7649655576376376530on_val,X7: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ X @ Z6 )
     => ( ( ord_le6900622908513426738on_val @ Z6
          @ ( collec7475294502966882545on_val
            @ ^ [X3: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X3 @ X7 )
                & ( P4 @ X3 ) ) ) )
       => ( P4 @ X ) ) ) ).

% prop_restrict
thf(fact_1118_prop__restrict,axiom,
    ! [X: state,Z6: set_state,X7: set_state,P4: state > $o] :
      ( ( member_state @ X @ Z6 )
     => ( ( ord_le2494988322063910608_state @ Z6
          @ ( collect_state
            @ ^ [X3: state] :
                ( ( member_state @ X3 @ X7 )
                & ( P4 @ X3 ) ) ) )
       => ( P4 @ X ) ) ) ).

% prop_restrict
thf(fact_1119_Collect__restrict,axiom,
    ! [X7: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ X7 )
            & ( P4 @ X3 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_1120_Collect__restrict,axiom,
    ! [X7: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ X7 )
            & ( P4 @ X3 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_1121_Collect__restrict,axiom,
    ! [X7: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ X7 )
            & ( P4 @ X3 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_1122_Collect__restrict,axiom,
    ! [X7: set_state,P4: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X3: state] :
            ( ( member_state @ X3 @ X7 )
            & ( P4 @ X3 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_1123_relInvImage__def,axiom,
    ( bNF_Gr8759033791985395207_state
    = ( ^ [A4: set_state,R5: set_Pr1688445902015331925_state,F3: state > option_state] :
          ( collec7320380983431419584_state
          @ ^ [Uu3: produc8023240190789890773_state] :
            ? [A15: state,A23: state] :
              ( ( Uu3
                = ( produc544653723139640077_state @ A15 @ A23 ) )
              & ( member_state @ A15 @ A4 )
              & ( member_state @ A23 @ A4 )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) @ R5 ) ) ) ) ) ).

% relInvImage_def
thf(fact_1124_relInvImage__def,axiom,
    ( bNF_Gr5630821380644201398_state
    = ( ^ [A4: set_Pr4231240917283394591_state,R5: set_Pr1688445902015331925_state,F3: produc7272280185086996969_state > option_state] :
          ( collec4625684881440051358_state
          @ ^ [Uu3: produc1362221940583236787_state] :
            ? [A15: produc7272280185086996969_state,A23: produc7272280185086996969_state] :
              ( ( Uu3
                = ( produc2330690084503141483_state @ A15 @ A23 ) )
              & ( member7461423308196221312_state @ A15 @ A4 )
              & ( member7461423308196221312_state @ A23 @ A4 )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) @ R5 ) ) ) ) ) ).

% relInvImage_def
thf(fact_1125_relInvImage__def,axiom,
    ( bNF_Gr4364826243083562601_state
    = ( ^ [A4: set_Pr7649655576376376530on_val,R5: set_Pr1688445902015331925_state,F3: produc9003781588162623004on_val > option_state] :
          ( collec5166231387257825412on_val
          @ ^ [Uu3: produc1317171644805857433on_val] :
            ? [A15: produc9003781588162623004on_val,A23: produc9003781588162623004on_val] :
              ( ( Uu3
                = ( produc4958730763592889809on_val @ A15 @ A23 ) )
              & ( member2879030624002546611on_val @ A15 @ A4 )
              & ( member2879030624002546611on_val @ A23 @ A4 )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) @ R5 ) ) ) ) ) ).

% relInvImage_def
thf(fact_1126_relInvImage__def,axiom,
    ( bNF_Gr919661598790814775_state
    = ( ^ [A4: set_Pr2391701600042252046_state,R5: set_Pr1688445902015331925_state,F3: produc3882902684156697774_state > option_state] :
          ( collec2083760461196787346_state
          @ ^ [Uu3: produc2030649568307348519_state] :
            ? [A15: produc3882902684156697774_state,A23: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc2343482328048119831_state @ A15 @ A23 ) )
              & ( member6715010751053357271_state @ A15 @ A4 )
              & ( member6715010751053357271_state @ A23 @ A4 )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) @ R5 ) ) ) ) ) ).

% relInvImage_def
thf(fact_1127_relInvImage__def,axiom,
    ( bNF_Gr621135371174781015_state
    = ( ^ [A4: set_option_state,R5: set_Pr1688445902015331925_state,F3: option_state > option_state] :
          ( collec8144523193623705312_state
          @ ^ [Uu3: produc3142500478612311029_state] :
            ? [A15: option_state,A23: option_state] :
              ( ( Uu3
                = ( produc9160152616361873709_state @ A15 @ A23 ) )
              & ( member_option_state @ A15 @ A4 )
              & ( member_option_state @ A23 @ A4 )
              & ( member3029510603097127326_state @ ( produc9160152616361873709_state @ ( F3 @ A15 ) @ ( F3 @ A23 ) ) @ R5 ) ) ) ) ) ).

% relInvImage_def
thf(fact_1128_comp__one__def,axiom,
    ( comp_one
    = ( ^ [P2: prat] :
          ( fChoice_prat
          @ ^ [R: prat] :
              ( ( padd @ P2 @ R )
              = pwrite ) ) ) ) ).

% comp_one_def
thf(fact_1129_flip__pred,axiom,
    ! [A5: set_Pr7649655576376376530on_val,R3: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le6900622908513426738on_val @ A5 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ ( conver4900003399366114050r_prat @ R3 ) ) ) )
     => ( ord_le2122960673345045316r_prat
        @ ( image_2943372182239103057r_prat
          @ ( produc2964738055033037937r_prat
            @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( produc1897429902272487136r_prat @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec6247776740490166275r_prat @ ( produc5226666187743293259prat_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1130_flip__pred,axiom,
    ! [A5: set_Pr1688445902015331925_state,R3: option_state > option_state > $o] :
      ( ( ord_le6423325748750870005_state @ A5 @ ( collec8144523193623705312_state @ ( produc6082990154846732246tate_o @ ( conver5693912221178358411_state @ R3 ) ) ) )
     => ( ord_le6423325748750870005_state
        @ ( image_3543735668343923269_state
          @ ( produc803252138055838771_state
            @ ^ [X3: option_state,Y5: option_state] : ( produc9160152616361873709_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec8144523193623705312_state @ ( produc6082990154846732246tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1131_flip__pred,axiom,
    ! [A5: set_Pr8996442262779224523e_prat,R3: prat > state > $o] :
      ( ( ord_le3218748728643905899e_prat @ A5 @ ( collec2363146809267008342e_prat @ ( produc5248533930912372960prat_o @ ( conversep_prat_state @ R3 ) ) ) )
     => ( ord_le262197048489888875_state
        @ ( image_8107462086123161541_state
          @ ( produc772268595108696499_state
            @ ^ [X3: state,Y5: prat] : ( produc6205719116230455971_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec9096564466166568534_state @ ( produc1228703470279370976tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1132_flip__pred,axiom,
    ! [A5: set_Pr6566877984550221441e_prat,R3: prat > set_state > $o] :
      ( ( ord_le5481108615602339361e_prat @ A5 @ ( collec1496918421318429452e_prat @ ( produc6803115863956348842prat_o @ ( conver7791356076405787575_state @ R3 ) ) ) )
     => ( ord_le5761494056910127137_state
        @ ( image_8063195947988251461_state
          @ ( produc4505194488364329267_state
            @ ^ [X3: set_state,Y5: prat] : ( produc9080284787853255769_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec5094083866753559820_state @ ( produc7925652287191295402tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1133_flip__pred,axiom,
    ! [A5: set_Pr8803067691650843250ar_nat,R3: nat > list_char > $o] :
      ( ( ord_le3387867619833322002ar_nat @ A5 @ ( collec8608152508653127293ar_nat @ ( produc2492928673396900345_nat_o @ ( conver4209408378539545768t_char @ R3 ) ) ) )
     => ( ord_le6315511645215477266t_char
        @ ( image_688197443715608197t_char
          @ ( produc6166083679720228083t_char
            @ ^ [X3: list_char,Y5: nat] : ( produc120197956887798346t_char @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1134_flip__pred,axiom,
    ! [A5: set_Pr2871993341207995108r_prat,R3: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( ord_le2122960673345045316r_prat @ A5 @ ( collec6247776740490166275r_prat @ ( produc5226666187743293259prat_o @ ( conver3077193964297325112on_val @ R3 ) ) ) )
     => ( ord_le6900622908513426738on_val
        @ ( image_1698057272686278225on_val
          @ ( produc4110721796449090601on_val
            @ ^ [X3: produc1457211279475724562t_char > option_val,Y5: produc1457211279475724562t_char > prat] : ( produc74620467203698198on_val @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1135_flip__pred,axiom,
    ! [A5: set_Pr2063381651806504974_state,R3: state > ( state > state ) > $o] :
      ( ( ord_le6155467803786297262_state @ A5 @ ( collec2388539233454781465_state @ ( produc7947965470134731869tate_o @ ( conver5193656574937193540_state @ R3 ) ) ) )
     => ( ord_le6483787752022044334_state
        @ ( image_5540908381507763077_state
          @ ( produc3696886681956174835_state
            @ ^ [X3: state > state,Y5: state] : ( produc8632743443909064678_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1136_flip__pred,axiom,
    ! [A5: set_Pr4366116562226448461_state,R3: state > produc3882902684156697774_state > $o] :
      ( ( ord_le4167756422255405229_state @ A5 @ ( collec4215477171196732908_state @ ( produc2011331576729698010tate_o @ ( conver7967167495199203645_state @ R3 ) ) ) )
     => ( ord_le4032880777312351359_state
        @ ( image_726267498729412871_state
          @ ( produc5156651381015392551_state
            @ ^ [X3: produc3882902684156697774_state,Y5: state] : ( produc5886875603596089627_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1137_flip__pred,axiom,
    ! [A5: set_Pr2391701600042252046_state,R3: ( state > state ) > state > $o] :
      ( ( ord_le6483787752022044334_state @ A5 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ ( conver1298275780297188036_state @ R3 ) ) ) )
     => ( ord_le6155467803786297262_state
        @ ( image_2502765500263079301_state
          @ ( produc7521540169313256307_state
            @ ^ [X3: state,Y5: state > state] : ( produc4737362649269059174_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec2388539233454781465_state @ ( produc7947965470134731869tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1138_flip__pred,axiom,
    ! [A5: set_Pr4231240917283394591_state,R3: produc3882902684156697774_state > state > $o] :
      ( ( ord_le4032880777312351359_state @ A5 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ ( conver191003926065009971_state @ R3 ) ) ) )
     => ( ord_le4167756422255405229_state
        @ ( image_6372718444620452615_state
          @ ( produc6605482068524530271_state
            @ ^ [X3: state,Y5: produc3882902684156697774_state] : ( produc7334084071316671761_state @ Y5 @ X3 ) )
          @ A5 )
        @ ( collec4215477171196732908_state @ ( produc2011331576729698010tate_o @ R3 ) ) ) ) ).

% flip_pred
thf(fact_1139_relImage__relInvImage,axiom,
    ! [R3: set_Pr1785066336555260981_state,F: state > state,A5: set_state] :
      ( ( ord_le2777189432094499797_state @ R3
        @ ( produc4572292869282958142_state @ ( image_state_state @ F @ A5 )
          @ ^ [Uu3: state] : ( image_state_state @ F @ A5 ) ) )
     => ( ( bNF_Gr6805951496242791002_state @ ( bNF_Gr4114592414835599415_state @ A5 @ R3 @ F ) @ F )
        = R3 ) ) ).

% relImage_relInvImage
thf(fact_1140_conj__subset__def,axiom,
    ! [A5: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ A5
        @ ( collec906845016635587262_state
          @ ^ [X3: produc7272280185086996969_state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 ) ) ) )
      = ( ( ord_le4032880777312351359_state @ A5 @ ( collec906845016635587262_state @ P4 ) )
        & ( ord_le4032880777312351359_state @ A5 @ ( collec906845016635587262_state @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_1141_conj__subset__def,axiom,
    ! [A5: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ A5
        @ ( collec7475294502966882545on_val
          @ ^ [X3: produc9003781588162623004on_val] :
              ( ( P4 @ X3 )
              & ( Q @ X3 ) ) ) )
      = ( ( ord_le6900622908513426738on_val @ A5 @ ( collec7475294502966882545on_val @ P4 ) )
        & ( ord_le6900622908513426738on_val @ A5 @ ( collec7475294502966882545on_val @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_1142_conj__subset__def,axiom,
    ! [A5: set_state,P4: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ A5
        @ ( collect_state
          @ ^ [X3: state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 ) ) ) )
      = ( ( ord_le2494988322063910608_state @ A5 @ ( collect_state @ P4 ) )
        & ( ord_le2494988322063910608_state @ A5 @ ( collect_state @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_1143_mem__Sigma__iff,axiom,
    ! [A: state,B: state,A5: set_state,B4: state > set_state] :
      ( ( member753036827967488894_state @ ( produc544653723139640077_state @ A @ B ) @ ( produc4572292869282958142_state @ A5 @ B4 ) )
      = ( ( member_state @ A @ A5 )
        & ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1144_mem__Sigma__iff,axiom,
    ! [A: prat,B: state,A5: set_prat,B4: prat > set_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc1658785944879207636_state @ A5 @ B4 ) )
      = ( ( member_prat @ A @ A5 )
        & ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1145_mem__Sigma__iff,axiom,
    ! [A: prat,B: set_state,A5: set_prat,B4: prat > set_set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc4653271056321233546_state @ A5 @ B4 ) )
      = ( ( member_prat @ A @ A5 )
        & ( member_set_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1146_mem__Sigma__iff,axiom,
    ! [A: nat,B: list_char,A5: set_nat,B4: nat > set_list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc6030673636645808891t_char @ A5 @ B4 ) )
      = ( ( member_nat @ A @ A5 )
        & ( member_list_char @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1147_mem__Sigma__iff,axiom,
    ! [A: state,B: state > state,A5: set_state,B4: state > set_state_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ ( produc6646226935541082007_state @ A5 @ B4 ) )
      = ( ( member_state @ A @ A5 )
        & ( member_state_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1148_mem__Sigma__iff,axiom,
    ! [A: option_state,B: option_state,A5: set_option_state,B4: option_state > set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc7708045757989049950_state @ A5 @ B4 ) )
      = ( ( member_option_state @ A @ A5 )
        & ( member_option_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1149_mem__Sigma__iff,axiom,
    ! [A: produc3882902684156697774_state,B: state,A5: set_Pr2391701600042252046_state,B4: produc3882902684156697774_state > set_state] :
      ( ( member1546683425902591150_state @ ( produc7334084071316671761_state @ A @ B ) @ ( produc4278832915810242336_state @ A5 @ B4 ) )
      = ( ( member6715010751053357271_state @ A @ A5 )
        & ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1150_mem__Sigma__iff,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ ( produc2831624448089660202_state @ A5 @ B4 ) )
      = ( ( member_state @ A @ A5 )
        & ( member6715010751053357271_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1151_mem__Sigma__iff,axiom,
    ! [A: state,B: produc7272280185086996969_state,A5: set_state,B4: state > set_Pr4231240917283394591_state] :
      ( ( member5752234768399382829_state @ ( produc5194695453622026300_state @ A @ B ) @ ( produc8552965988182875245_state @ A5 @ B4 ) )
      = ( ( member_state @ A @ A5 )
        & ( member7461423308196221312_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1152_mem__Sigma__iff,axiom,
    ! [A: produc7272280185086996969_state,B: state,A5: set_Pr4231240917283394591_state,B4: produc7272280185086996969_state > set_state] :
      ( ( member5722111062937351085_state @ ( produc7271836056140555068_state @ A @ B ) @ ( produc1406734553846628205_state @ A5 @ B4 ) )
      = ( ( member7461423308196221312_state @ A @ A5 )
        & ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1153_SigmaI,axiom,
    ! [A: state,A5: set_state,B: state,B4: state > set_state] :
      ( ( member_state @ A @ A5 )
     => ( ( member_state @ B @ ( B4 @ A ) )
       => ( member753036827967488894_state @ ( produc544653723139640077_state @ A @ B ) @ ( produc4572292869282958142_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1154_SigmaI,axiom,
    ! [A: prat,A5: set_prat,B: state,B4: prat > set_state] :
      ( ( member_prat @ A @ A5 )
     => ( ( member_state @ B @ ( B4 @ A ) )
       => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc1658785944879207636_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1155_SigmaI,axiom,
    ! [A: prat,A5: set_prat,B: set_state,B4: prat > set_set_state] :
      ( ( member_prat @ A @ A5 )
     => ( ( member_set_state @ B @ ( B4 @ A ) )
       => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc4653271056321233546_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1156_SigmaI,axiom,
    ! [A: nat,A5: set_nat,B: list_char,B4: nat > set_list_char] :
      ( ( member_nat @ A @ A5 )
     => ( ( member_list_char @ B @ ( B4 @ A ) )
       => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc6030673636645808891t_char @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1157_SigmaI,axiom,
    ! [A: state,A5: set_state,B: state > state,B4: state > set_state_state] :
      ( ( member_state @ A @ A5 )
     => ( ( member_state_state @ B @ ( B4 @ A ) )
       => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ ( produc6646226935541082007_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1158_SigmaI,axiom,
    ! [A: option_state,A5: set_option_state,B: option_state,B4: option_state > set_option_state] :
      ( ( member_option_state @ A @ A5 )
     => ( ( member_option_state @ B @ ( B4 @ A ) )
       => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc7708045757989049950_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1159_SigmaI,axiom,
    ! [A: state,A5: set_state,B: produc3882902684156697774_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member_state @ A @ A5 )
     => ( ( member6715010751053357271_state @ B @ ( B4 @ A ) )
       => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ ( produc2831624448089660202_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1160_SigmaI,axiom,
    ! [A: produc3882902684156697774_state,A5: set_Pr2391701600042252046_state,B: state,B4: produc3882902684156697774_state > set_state] :
      ( ( member6715010751053357271_state @ A @ A5 )
     => ( ( member_state @ B @ ( B4 @ A ) )
       => ( member1546683425902591150_state @ ( produc7334084071316671761_state @ A @ B ) @ ( produc4278832915810242336_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1161_SigmaI,axiom,
    ! [A: state,A5: set_state,B: produc7272280185086996969_state,B4: state > set_Pr4231240917283394591_state] :
      ( ( member_state @ A @ A5 )
     => ( ( member7461423308196221312_state @ B @ ( B4 @ A ) )
       => ( member5752234768399382829_state @ ( produc5194695453622026300_state @ A @ B ) @ ( produc8552965988182875245_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1162_SigmaI,axiom,
    ! [A: produc7272280185086996969_state,A5: set_Pr4231240917283394591_state,B: state,B4: produc7272280185086996969_state > set_state] :
      ( ( member7461423308196221312_state @ A @ A5 )
     => ( ( member_state @ B @ ( B4 @ A ) )
       => ( member5722111062937351085_state @ ( produc7271836056140555068_state @ A @ B ) @ ( produc1406734553846628205_state @ A5 @ B4 ) ) ) ) ).

% SigmaI
thf(fact_1163_Collect__case__prod,axiom,
    ! [P4: state > $o,Q: state > $o] :
      ( ( collec7320380983431419584_state
        @ ( produc5376313899190161910tate_o
          @ ^ [A3: state,B2: state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc4572292869282958142_state @ ( collect_state @ P4 )
        @ ^ [Uu3: state] : ( collect_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1164_Collect__case__prod,axiom,
    ! [P4: state > $o,Q: ( state > state ) > $o] :
      ( ( collec394671971739345689_state
        @ ( produc3645877548210629341tate_o
          @ ^ [A3: state,B2: state > state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc6646226935541082007_state @ ( collect_state @ P4 )
        @ ^ [Uu3: state] : ( collect_state_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1165_Collect__case__prod,axiom,
    ! [P4: state > $o,Q: produc3882902684156697774_state > $o] :
      ( ( collec906845016635587262_state
        @ ( produc1745419677418529872tate_o
          @ ^ [A3: state,B2: produc3882902684156697774_state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc2831624448089660202_state @ ( collect_state @ P4 )
        @ ^ [Uu3: state] : ( collec394671971739345689_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1166_Collect__case__prod,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: state > $o] :
      ( ( collec8329173533518380783_state
        @ ( produc3925133191046228999tate_o
          @ ^ [A3: produc7272280185086996969_state,B2: state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc1406734553846628205_state @ ( collec906845016635587262_state @ P4 )
        @ ^ [Uu3: produc7272280185086996969_state] : ( collect_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1167_Collect__case__prod,axiom,
    ! [P4: state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( collec8359297238980412527_state
        @ ( produc8801812494870056711tate_o
          @ ^ [A3: state,B2: produc7272280185086996969_state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc8552965988182875245_state @ ( collect_state @ P4 )
        @ ^ [Uu3: state] : ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1168_Collect__case__prod,axiom,
    ! [P4: ( produc1457211279475724562t_char > prat ) > $o,Q: ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( collec7475294502966882545on_val
        @ ( produc5248837549992124053_val_o
          @ ^ [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc1366239611153933861on_val @ ( collec7093475260167521854r_prat @ P4 )
        @ ^ [Uu3: produc1457211279475724562t_char > prat] : ( collec8455114619259388271on_val @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1169_Collect__case__prod,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( collec4625684881440051358_state
        @ ( produc3133855996611560728tate_o
          @ ^ [A3: produc7272280185086996969_state,B2: produc7272280185086996969_state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc8058815403421562012_state @ ( collec906845016635587262_state @ P4 )
        @ ^ [Uu3: produc7272280185086996969_state] : ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1170_Collect__case__prod,axiom,
    ! [P4: state > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( collec4277618271863934242on_val
        @ ( produc3402325802329673236_val_o
          @ ^ [A3: state,B2: produc9003781588162623004on_val] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc4123186969287248032on_val @ ( collect_state @ P4 )
        @ ^ [Uu3: state] : ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1171_Collect__case__prod,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: state > $o] :
      ( ( collec7689951075418334754_state
        @ ( produc8998596806100491796tate_o
          @ ^ [A3: produc9003781588162623004on_val,B2: state] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc556505947853469856_state @ ( collec7475294502966882545on_val @ P4 )
        @ ^ [Uu3: produc9003781588162623004on_val] : ( collect_state @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1172_Collect__case__prod,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( collec7485704936941981521on_val
        @ ( produc7822554240239717925_val_o
          @ ^ [A3: produc7272280185086996969_state,B2: produc9003781588162623004on_val] :
              ( ( P4 @ A3 )
              & ( Q @ B2 ) ) ) )
      = ( produc2280571527155128015on_val @ ( collec906845016635587262_state @ P4 )
        @ ^ [Uu3: produc7272280185086996969_state] : ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_case_prod
thf(fact_1173_Collect__case__prod__Sigma,axiom,
    ! [P4: state > $o,Q: state > state > $o] :
      ( ( collec7320380983431419584_state
        @ ( produc5376313899190161910tate_o
          @ ^ [X3: state,Y5: state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc4572292869282958142_state @ ( collect_state @ P4 )
        @ ^ [X3: state] : ( collect_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1174_Collect__case__prod__Sigma,axiom,
    ! [P4: state > $o,Q: state > ( state > state ) > $o] :
      ( ( collec394671971739345689_state
        @ ( produc3645877548210629341tate_o
          @ ^ [X3: state,Y5: state > state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc6646226935541082007_state @ ( collect_state @ P4 )
        @ ^ [X3: state] : ( collect_state_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1175_Collect__case__prod__Sigma,axiom,
    ! [P4: state > $o,Q: state > produc3882902684156697774_state > $o] :
      ( ( collec906845016635587262_state
        @ ( produc1745419677418529872tate_o
          @ ^ [X3: state,Y5: produc3882902684156697774_state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc2831624448089660202_state @ ( collect_state @ P4 )
        @ ^ [X3: state] : ( collec394671971739345689_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1176_Collect__case__prod__Sigma,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > state > $o] :
      ( ( collec8329173533518380783_state
        @ ( produc3925133191046228999tate_o
          @ ^ [X3: produc7272280185086996969_state,Y5: state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc1406734553846628205_state @ ( collec906845016635587262_state @ P4 )
        @ ^ [X3: produc7272280185086996969_state] : ( collect_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1177_Collect__case__prod__Sigma,axiom,
    ! [P4: state > $o,Q: state > produc7272280185086996969_state > $o] :
      ( ( collec8359297238980412527_state
        @ ( produc8801812494870056711tate_o
          @ ^ [X3: state,Y5: produc7272280185086996969_state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc8552965988182875245_state @ ( collect_state @ P4 )
        @ ^ [X3: state] : ( collec906845016635587262_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1178_Collect__case__prod__Sigma,axiom,
    ! [P4: ( produc1457211279475724562t_char > prat ) > $o,Q: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( collec7475294502966882545on_val
        @ ( produc5248837549992124053_val_o
          @ ^ [X3: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc1366239611153933861on_val @ ( collec7093475260167521854r_prat @ P4 )
        @ ^ [X3: produc1457211279475724562t_char > prat] : ( collec8455114619259388271on_val @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1179_Collect__case__prod__Sigma,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > produc7272280185086996969_state > $o] :
      ( ( collec4625684881440051358_state
        @ ( produc3133855996611560728tate_o
          @ ^ [X3: produc7272280185086996969_state,Y5: produc7272280185086996969_state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc8058815403421562012_state @ ( collec906845016635587262_state @ P4 )
        @ ^ [X3: produc7272280185086996969_state] : ( collec906845016635587262_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1180_Collect__case__prod__Sigma,axiom,
    ! [P4: state > $o,Q: state > produc9003781588162623004on_val > $o] :
      ( ( collec4277618271863934242on_val
        @ ( produc3402325802329673236_val_o
          @ ^ [X3: state,Y5: produc9003781588162623004on_val] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc4123186969287248032on_val @ ( collect_state @ P4 )
        @ ^ [X3: state] : ( collec7475294502966882545on_val @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1181_Collect__case__prod__Sigma,axiom,
    ! [P4: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > state > $o] :
      ( ( collec7689951075418334754_state
        @ ( produc8998596806100491796tate_o
          @ ^ [X3: produc9003781588162623004on_val,Y5: state] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc556505947853469856_state @ ( collec7475294502966882545on_val @ P4 )
        @ ^ [X3: produc9003781588162623004on_val] : ( collect_state @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1182_Collect__case__prod__Sigma,axiom,
    ! [P4: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > produc9003781588162623004on_val > $o] :
      ( ( collec7485704936941981521on_val
        @ ( produc7822554240239717925_val_o
          @ ^ [X3: produc7272280185086996969_state,Y5: produc9003781588162623004on_val] :
              ( ( P4 @ X3 )
              & ( Q @ X3 @ Y5 ) ) ) )
      = ( produc2280571527155128015on_val @ ( collec906845016635587262_state @ P4 )
        @ ^ [X3: produc7272280185086996969_state] : ( collec7475294502966882545on_val @ ( Q @ X3 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_1183_SigmaE,axiom,
    ! [C: produc8023240190789890773_state,A5: set_state,B4: state > set_state] :
      ( ( member753036827967488894_state @ C @ ( produc4572292869282958142_state @ A5 @ B4 ) )
     => ~ ! [X2: state] :
            ( ( member_state @ X2 @ A5 )
           => ! [Y3: state] :
                ( ( member_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc544653723139640077_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1184_SigmaE,axiom,
    ! [C: produc4844402304972151915_state,A5: set_prat,B4: prat > set_state] :
      ( ( member6226390569306242836_state @ C @ ( produc1658785944879207636_state @ A5 @ B4 ) )
     => ~ ! [X2: prat] :
            ( ( member_prat @ X2 @ A5 )
           => ! [Y3: state] :
                ( ( member_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc6205719116230455971_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1185_SigmaE,axiom,
    ! [C: produc6251377953716854561_state,A5: set_prat,B4: prat > set_set_state] :
      ( ( member6708919011922255306_state @ C @ ( produc4653271056321233546_state @ A5 @ B4 ) )
     => ~ ! [X2: prat] :
            ( ( member_prat @ X2 @ A5 )
           => ! [Y3: set_state] :
                ( ( member_set_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc9080284787853255769_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1186_SigmaE,axiom,
    ! [C: produc1457211279475724562t_char,A5: set_nat,B4: nat > set_list_char] :
      ( ( member484235747325421115t_char @ C @ ( produc6030673636645808891t_char @ A5 @ B4 ) )
     => ~ ! [X2: nat] :
            ( ( member_nat @ X2 @ A5 )
           => ! [Y3: list_char] :
                ( ( member_list_char @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc120197956887798346t_char @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1187_SigmaE,axiom,
    ! [C: produc3882902684156697774_state,A5: set_state,B4: state > set_state_state] :
      ( ( member6715010751053357271_state @ C @ ( produc6646226935541082007_state @ A5 @ B4 ) )
     => ~ ! [X2: state] :
            ( ( member_state @ X2 @ A5 )
           => ! [Y3: state > state] :
                ( ( member_state_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc8632743443909064678_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1188_SigmaE,axiom,
    ! [C: produc3142500478612311029_state,A5: set_option_state,B4: option_state > set_option_state] :
      ( ( member3029510603097127326_state @ C @ ( produc7708045757989049950_state @ A5 @ B4 ) )
     => ~ ! [X2: option_state] :
            ( ( member_option_state @ X2 @ A5 )
           => ! [Y3: option_state] :
                ( ( member_option_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc9160152616361873709_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1189_SigmaE,axiom,
    ! [C: produc1357540302793366807_state,A5: set_Pr2391701600042252046_state,B4: produc3882902684156697774_state > set_state] :
      ( ( member1546683425902591150_state @ C @ ( produc4278832915810242336_state @ A5 @ B4 ) )
     => ~ ! [X2: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X2 @ A5 )
           => ! [Y3: state] :
                ( ( member_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc7334084071316671761_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1190_SigmaE,axiom,
    ! [C: produc7272280185086996969_state,A5: set_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ C @ ( produc2831624448089660202_state @ A5 @ B4 ) )
     => ~ ! [X2: state] :
            ( ( member_state @ X2 @ A5 )
           => ! [Y3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc5886875603596089627_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1191_SigmaE,axiom,
    ! [C: produc4357056439811976324_state,A5: set_state,B4: state > set_Pr4231240917283394591_state] :
      ( ( member5752234768399382829_state @ C @ ( produc8552965988182875245_state @ A5 @ B4 ) )
     => ~ ! [X2: state] :
            ( ( member_state @ X2 @ A5 )
           => ! [Y3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc5194695453622026300_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1192_SigmaE,axiom,
    ! [C: produc4326932734349944580_state,A5: set_Pr4231240917283394591_state,B4: produc7272280185086996969_state > set_state] :
      ( ( member5722111062937351085_state @ C @ ( produc1406734553846628205_state @ A5 @ B4 ) )
     => ~ ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ A5 )
           => ! [Y3: state] :
                ( ( member_state @ Y3 @ ( B4 @ X2 ) )
               => ( C
                 != ( produc7271836056140555068_state @ X2 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_1193_SigmaD1,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ ( produc2831624448089660202_state @ A5 @ B4 ) )
     => ( member_state @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1194_SigmaD1,axiom,
    ! [A: state,B: state > state,A5: set_state,B4: state > set_state_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ ( produc6646226935541082007_state @ A5 @ B4 ) )
     => ( member_state @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1195_SigmaD1,axiom,
    ! [A: option_state,B: option_state,A5: set_option_state,B4: option_state > set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc7708045757989049950_state @ A5 @ B4 ) )
     => ( member_option_state @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1196_SigmaD1,axiom,
    ! [A: prat,B: state,A5: set_prat,B4: prat > set_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc1658785944879207636_state @ A5 @ B4 ) )
     => ( member_prat @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1197_SigmaD1,axiom,
    ! [A: prat,B: set_state,A5: set_prat,B4: prat > set_set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc4653271056321233546_state @ A5 @ B4 ) )
     => ( member_prat @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1198_SigmaD1,axiom,
    ! [A: nat,B: list_char,A5: set_nat,B4: nat > set_list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc6030673636645808891t_char @ A5 @ B4 ) )
     => ( member_nat @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1199_SigmaD1,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val,A5: set_Pr3433046674199179443r_prat,B4: ( produc1457211279475724562t_char > prat ) > set_Pr1004501353197068112on_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ A @ B ) @ ( produc1366239611153933861on_val @ A5 @ B4 ) )
     => ( member2336342582916103932r_prat @ A @ A5 ) ) ).

% SigmaD1
thf(fact_1200_SigmaD2,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ ( produc2831624448089660202_state @ A5 @ B4 ) )
     => ( member6715010751053357271_state @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1201_SigmaD2,axiom,
    ! [A: state,B: state > state,A5: set_state,B4: state > set_state_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ ( produc6646226935541082007_state @ A5 @ B4 ) )
     => ( member_state_state @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1202_SigmaD2,axiom,
    ! [A: option_state,B: option_state,A5: set_option_state,B4: option_state > set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc7708045757989049950_state @ A5 @ B4 ) )
     => ( member_option_state @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1203_SigmaD2,axiom,
    ! [A: prat,B: state,A5: set_prat,B4: prat > set_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc1658785944879207636_state @ A5 @ B4 ) )
     => ( member_state @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1204_SigmaD2,axiom,
    ! [A: prat,B: set_state,A5: set_prat,B4: prat > set_set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc4653271056321233546_state @ A5 @ B4 ) )
     => ( member_set_state @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1205_SigmaD2,axiom,
    ! [A: nat,B: list_char,A5: set_nat,B4: nat > set_list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc6030673636645808891t_char @ A5 @ B4 ) )
     => ( member_list_char @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1206_SigmaD2,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > option_val,A5: set_Pr3433046674199179443r_prat,B4: ( produc1457211279475724562t_char > prat ) > set_Pr1004501353197068112on_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ A @ B ) @ ( produc1366239611153933861on_val @ A5 @ B4 ) )
     => ( member1577473829074448177on_val @ B @ ( B4 @ A ) ) ) ).

% SigmaD2
thf(fact_1207_SigmaE2,axiom,
    ! [A: state,B: state,A5: set_state,B4: state > set_state] :
      ( ( member753036827967488894_state @ ( produc544653723139640077_state @ A @ B ) @ ( produc4572292869282958142_state @ A5 @ B4 ) )
     => ~ ( ( member_state @ A @ A5 )
         => ~ ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1208_SigmaE2,axiom,
    ! [A: prat,B: state,A5: set_prat,B4: prat > set_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ A @ B ) @ ( produc1658785944879207636_state @ A5 @ B4 ) )
     => ~ ( ( member_prat @ A @ A5 )
         => ~ ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1209_SigmaE2,axiom,
    ! [A: prat,B: set_state,A5: set_prat,B4: prat > set_set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ A @ B ) @ ( produc4653271056321233546_state @ A5 @ B4 ) )
     => ~ ( ( member_prat @ A @ A5 )
         => ~ ( member_set_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1210_SigmaE2,axiom,
    ! [A: nat,B: list_char,A5: set_nat,B4: nat > set_list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ A @ B ) @ ( produc6030673636645808891t_char @ A5 @ B4 ) )
     => ~ ( ( member_nat @ A @ A5 )
         => ~ ( member_list_char @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1211_SigmaE2,axiom,
    ! [A: state,B: state > state,A5: set_state,B4: state > set_state_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A @ B ) @ ( produc6646226935541082007_state @ A5 @ B4 ) )
     => ~ ( ( member_state @ A @ A5 )
         => ~ ( member_state_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1212_SigmaE2,axiom,
    ! [A: option_state,B: option_state,A5: set_option_state,B4: option_state > set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ A @ B ) @ ( produc7708045757989049950_state @ A5 @ B4 ) )
     => ~ ( ( member_option_state @ A @ A5 )
         => ~ ( member_option_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1213_SigmaE2,axiom,
    ! [A: produc3882902684156697774_state,B: state,A5: set_Pr2391701600042252046_state,B4: produc3882902684156697774_state > set_state] :
      ( ( member1546683425902591150_state @ ( produc7334084071316671761_state @ A @ B ) @ ( produc4278832915810242336_state @ A5 @ B4 ) )
     => ~ ( ( member6715010751053357271_state @ A @ A5 )
         => ~ ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1214_SigmaE2,axiom,
    ! [A: state,B: produc3882902684156697774_state,A5: set_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ B ) @ ( produc2831624448089660202_state @ A5 @ B4 ) )
     => ~ ( ( member_state @ A @ A5 )
         => ~ ( member6715010751053357271_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1215_SigmaE2,axiom,
    ! [A: state,B: produc7272280185086996969_state,A5: set_state,B4: state > set_Pr4231240917283394591_state] :
      ( ( member5752234768399382829_state @ ( produc5194695453622026300_state @ A @ B ) @ ( produc8552965988182875245_state @ A5 @ B4 ) )
     => ~ ( ( member_state @ A @ A5 )
         => ~ ( member7461423308196221312_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1216_SigmaE2,axiom,
    ! [A: produc7272280185086996969_state,B: state,A5: set_Pr4231240917283394591_state,B4: produc7272280185086996969_state > set_state] :
      ( ( member5722111062937351085_state @ ( produc7271836056140555068_state @ A @ B ) @ ( produc1406734553846628205_state @ A5 @ B4 ) )
     => ~ ( ( member7461423308196221312_state @ A @ A5 )
         => ~ ( member_state @ B @ ( B4 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1217_Sigma__mono,axiom,
    ! [A5: set_Pr4231240917283394591_state,C2: set_Pr4231240917283394591_state,B4: produc7272280185086996969_state > set_state,D2: produc7272280185086996969_state > set_state] :
      ( ( ord_le4032880777312351359_state @ A5 @ C2 )
     => ( ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ A5 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X2 ) @ ( D2 @ X2 ) ) )
       => ( ord_le9131031735280434308_state @ ( produc1406734553846628205_state @ A5 @ B4 ) @ ( produc1406734553846628205_state @ C2 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_1218_Sigma__mono,axiom,
    ! [A5: set_Pr7649655576376376530on_val,C2: set_Pr7649655576376376530on_val,B4: produc9003781588162623004on_val > set_state,D2: produc9003781588162623004on_val > set_state] :
      ( ( ord_le6900622908513426738on_val @ A5 @ C2 )
     => ( ! [X2: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X2 @ A5 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X2 ) @ ( D2 @ X2 ) ) )
       => ( ord_le801108382804549175_state @ ( produc556505947853469856_state @ A5 @ B4 ) @ ( produc556505947853469856_state @ C2 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_1219_Sigma__mono,axiom,
    ! [A5: set_Pr2391701600042252046_state,C2: set_Pr2391701600042252046_state,B4: produc3882902684156697774_state > set_state,D2: produc3882902684156697774_state > set_state] :
      ( ( ord_le6483787752022044334_state @ A5 @ C2 )
     => ( ! [X2: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X2 @ A5 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X2 ) @ ( D2 @ X2 ) ) )
       => ( ord_le4167756422255405229_state @ ( produc4278832915810242336_state @ A5 @ B4 ) @ ( produc4278832915810242336_state @ C2 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_1220_Sigma__mono,axiom,
    ! [A5: set_state,C2: set_state,B4: state > set_state,D2: state > set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ C2 )
     => ( ! [X2: state] :
            ( ( member_state @ X2 @ A5 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X2 ) @ ( D2 @ X2 ) ) )
       => ( ord_le2777189432094499797_state @ ( produc4572292869282958142_state @ A5 @ B4 ) @ ( produc4572292869282958142_state @ C2 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_1221_Sigma__Un__distrib1,axiom,
    ! [I2: set_state,J2: set_state,C2: state > set_Pr2391701600042252046_state] :
      ( ( produc2831624448089660202_state @ ( sup_sup_set_state @ I2 @ J2 ) @ C2 )
      = ( sup_su3837536599209510219_state @ ( produc2831624448089660202_state @ I2 @ C2 ) @ ( produc2831624448089660202_state @ J2 @ C2 ) ) ) ).

% Sigma_Un_distrib1
thf(fact_1222_Times__subset__cancel2,axiom,
    ! [X: state,C2: set_state,A5: set_state,B4: set_state] :
      ( ( member_state @ X @ C2 )
     => ( ( ord_le2777189432094499797_state
          @ ( produc4572292869282958142_state @ A5
            @ ^ [Uu3: state] : C2 )
          @ ( produc4572292869282958142_state @ B4
            @ ^ [Uu3: state] : C2 ) )
        = ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1223_Times__subset__cancel2,axiom,
    ! [X: produc7272280185086996969_state,C2: set_Pr4231240917283394591_state,A5: set_state,B4: set_state] :
      ( ( member7461423308196221312_state @ X @ C2 )
     => ( ( ord_le6305643028697367044_state
          @ ( produc8552965988182875245_state @ A5
            @ ^ [Uu3: state] : C2 )
          @ ( produc8552965988182875245_state @ B4
            @ ^ [Uu3: state] : C2 ) )
        = ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1224_Times__subset__cancel2,axiom,
    ! [X: produc9003781588162623004on_val,C2: set_Pr7649655576376376530on_val,A5: set_state,B4: set_state] :
      ( ( member2879030624002546611on_val @ X @ C2 )
     => ( ( ord_le2093392236560368951on_val
          @ ( produc4123186969287248032on_val @ A5
            @ ^ [Uu3: state] : C2 )
          @ ( produc4123186969287248032on_val @ B4
            @ ^ [Uu3: state] : C2 ) )
        = ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1225_Times__subset__cancel2,axiom,
    ! [X: produc3882902684156697774_state,C2: set_Pr2391701600042252046_state,A5: set_state,B4: set_state] :
      ( ( member6715010751053357271_state @ X @ C2 )
     => ( ( ord_le4032880777312351359_state
          @ ( produc2831624448089660202_state @ A5
            @ ^ [Uu3: state] : C2 )
          @ ( produc2831624448089660202_state @ B4
            @ ^ [Uu3: state] : C2 ) )
        = ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1226_mem__Times__iff,axiom,
    ! [X: produc8023240190789890773_state,A5: set_state,B4: set_state] :
      ( ( member753036827967488894_state @ X
        @ ( produc4572292869282958142_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( ( member_state @ ( produc6071883272770572025_state @ X ) @ A5 )
        & ( member_state @ ( produc992860721336220475_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1227_mem__Times__iff,axiom,
    ! [X: produc1457211279475724562t_char,A5: set_nat,B4: set_list_char] :
      ( ( member484235747325421115t_char @ X
        @ ( produc6030673636645808891t_char @ A5
          @ ^ [Uu3: nat] : B4 ) )
      = ( ( member_nat @ ( produc6204653154488278070t_char @ X ) @ A5 )
        & ( member_list_char @ ( produc1900778367047502200t_char @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1228_mem__Times__iff,axiom,
    ! [X: produc3882902684156697774_state,A5: set_state,B4: set_state_state] :
      ( ( member6715010751053357271_state @ X
        @ ( produc6646226935541082007_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( ( member_state @ ( produc7095885521192019410_state @ X ) @ A5 )
        & ( member_state_state @ ( produc1734700239402139924_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1229_mem__Times__iff,axiom,
    ! [X: produc1357540302793366807_state,A5: set_Pr2391701600042252046_state,B4: set_state] :
      ( ( member1546683425902591150_state @ X
        @ ( produc4278832915810242336_state @ A5
          @ ^ [Uu3: produc3882902684156697774_state] : B4 ) )
      = ( ( member6715010751053357271_state @ ( produc2295233055888329765_state @ X ) @ A5 )
        & ( member_state @ ( produc7757608104100355171_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1230_mem__Times__iff,axiom,
    ! [X: produc7272280185086996969_state,A5: set_state,B4: set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ X
        @ ( produc2831624448089660202_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( ( member_state @ ( produc848024588167747631_state @ X ) @ A5 )
        & ( member6715010751053357271_state @ ( produc6310399636379773037_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1231_mem__Times__iff,axiom,
    ! [X: produc4357056439811976324_state,A5: set_state,B4: set_Pr4231240917283394591_state] :
      ( ( member5752234768399382829_state @ X
        @ ( produc8552965988182875245_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( ( member_state @ ( produc9028042817728042024_state @ X ) @ A5 )
        & ( member7461423308196221312_state @ ( produc8002322135157487722_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1232_mem__Times__iff,axiom,
    ! [X: produc4326932734349944580_state,A5: set_Pr4231240917283394591_state,B4: set_state] :
      ( ( member5722111062937351085_state @ X
        @ ( produc1406734553846628205_state @ A5
          @ ^ [Uu3: produc7272280185086996969_state] : B4 ) )
      = ( ( member7461423308196221312_state @ ( produc1881811383391794984_state @ X ) @ A5 )
        & ( member_state @ ( produc856090700821240682_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1233_mem__Times__iff,axiom,
    ! [X: produc2030649568307348519_state,A5: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member3801449062345016400_state @ X
        @ ( produc5372175771586804680_state @ A5
          @ ^ [Uu3: produc3882902684156697774_state] : B4 ) )
      = ( ( member6715010751053357271_state @ ( produc528253918903283203_state @ X ) @ A5 )
        & ( member6715010751053357271_state @ ( produc1543742031010890053_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1234_mem__Times__iff,axiom,
    ! [X: produc2932130718683550586_state,A5: set_Pr4231240917283394591_state,B4: set_Pr2391701600042252046_state] :
      ( ( member3497469645994473233_state @ X
        @ ( produc7282391691264310459_state @ A5
          @ ^ [Uu3: produc7272280185086996969_state] : B4 ) )
      = ( ( member7461423308196221312_state @ ( produc3617983543337321920_state @ X ) @ A5 )
        & ( member6715010751053357271_state @ ( produc3196213569639636478_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1235_mem__Times__iff,axiom,
    ! [X: produc3798933545658027718_state,A5: set_Pr2391701600042252046_state,B4: set_Pr4231240917283394591_state] :
      ( ( member4364272472968950365_state @ X
        @ ( produc4180506523417663567_state @ A5
          @ ^ [Uu3: produc3882902684156697774_state] : B4 ) )
      = ( ( member6715010751053357271_state @ ( produc516098375490675028_state @ X ) @ A5 )
        & ( member7461423308196221312_state @ ( produc94328401792989586_state @ X ) @ B4 ) ) ) ).

% mem_Times_iff
thf(fact_1236_Sigma__Un__distrib2,axiom,
    ! [I2: set_state,A5: state > set_Pr2391701600042252046_state,B4: state > set_Pr2391701600042252046_state] :
      ( ( produc2831624448089660202_state @ I2
        @ ^ [I: state] : ( sup_su1984960714304006370_state @ ( A5 @ I ) @ ( B4 @ I ) ) )
      = ( sup_su3837536599209510219_state @ ( produc2831624448089660202_state @ I2 @ A5 ) @ ( produc2831624448089660202_state @ I2 @ B4 ) ) ) ).

% Sigma_Un_distrib2
thf(fact_1237_Times__Un__distrib1,axiom,
    ! [A5: set_state,B4: set_state,C2: set_Pr2391701600042252046_state] :
      ( ( produc2831624448089660202_state @ ( sup_sup_set_state @ A5 @ B4 )
        @ ^ [Uu3: state] : C2 )
      = ( sup_su3837536599209510219_state
        @ ( produc2831624448089660202_state @ A5
          @ ^ [Uu3: state] : C2 )
        @ ( produc2831624448089660202_state @ B4
          @ ^ [Uu3: state] : C2 ) ) ) ).

% Times_Un_distrib1
thf(fact_1238_swap__product,axiom,
    ! [A5: set_option_state,B4: set_option_state] :
      ( ( image_3543735668343923269_state
        @ ( produc803252138055838771_state
          @ ^ [I: option_state,J: option_state] : ( produc9160152616361873709_state @ J @ I ) )
        @ ( produc7708045757989049950_state @ A5
          @ ^ [Uu3: option_state] : B4 ) )
      = ( produc7708045757989049950_state @ B4
        @ ^ [Uu3: option_state] : A5 ) ) ).

% swap_product
thf(fact_1239_swap__product,axiom,
    ! [A5: set_state,B4: set_prat] :
      ( ( image_8107462086123161541_state
        @ ( produc772268595108696499_state
          @ ^ [I: state,J: prat] : ( produc6205719116230455971_state @ J @ I ) )
        @ ( produc1315363979526694100e_prat @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( produc1658785944879207636_state @ B4
        @ ^ [Uu3: prat] : A5 ) ) ).

% swap_product
thf(fact_1240_swap__product,axiom,
    ! [A5: set_set_state,B4: set_prat] :
      ( ( image_8063195947988251461_state
        @ ( produc4505194488364329267_state
          @ ^ [I: set_state,J: prat] : ( produc9080284787853255769_state @ J @ I ) )
        @ ( produc884099569098950794e_prat @ A5
          @ ^ [Uu3: set_state] : B4 ) )
      = ( produc4653271056321233546_state @ B4
        @ ^ [Uu3: prat] : A5 ) ) ).

% swap_product
thf(fact_1241_swap__product,axiom,
    ! [A5: set_list_char,B4: set_nat] :
      ( ( image_688197443715608197t_char
        @ ( produc6166083679720228083t_char
          @ ^ [I: list_char,J: nat] : ( produc120197956887798346t_char @ J @ I ) )
        @ ( produc5389449503320859771ar_nat @ A5
          @ ^ [Uu3: list_char] : B4 ) )
      = ( produc6030673636645808891t_char @ B4
        @ ^ [Uu3: nat] : A5 ) ) ).

% swap_product
thf(fact_1242_swap__product,axiom,
    ! [A5: set_Pr1004501353197068112on_val,B4: set_Pr3433046674199179443r_prat] :
      ( ( image_1698057272686278225on_val
        @ ( produc4110721796449090601on_val
          @ ^ [I: produc1457211279475724562t_char > option_val,J: produc1457211279475724562t_char > prat] : ( produc74620467203698198on_val @ J @ I ) )
        @ ( produc3189049046222722799r_prat @ A5
          @ ^ [Uu3: produc1457211279475724562t_char > option_val] : B4 ) )
      = ( produc1366239611153933861on_val @ B4
        @ ^ [Uu3: produc1457211279475724562t_char > prat] : A5 ) ) ).

% swap_product
thf(fact_1243_subset__fst__snd,axiom,
    ! [A5: set_Pr2507339680178222706t_char] :
      ( ord_le6315511645215477266t_char @ A5
      @ ( produc6030673636645808891t_char @ ( image_3548405822317538717ar_nat @ produc6204653154488278070t_char @ A5 )
        @ ^ [Uu3: nat] : ( image_3034139768025083822t_char @ produc1900778367047502200t_char @ A5 ) ) ) ).

% subset_fst_snd
thf(fact_1244_subset__fst__snd,axiom,
    ! [A5: set_Pr7649655576376376530on_val] :
      ( ord_le6900622908513426738on_val @ A5
      @ ( produc1366239611153933861on_val @ ( image_3067683418878703216r_prat @ produc5239619271231976746on_val @ A5 )
        @ ^ [Uu3: produc1457211279475724562t_char > prat] : ( image_2330660378567450301on_val @ produc2319605628138516840on_val @ A5 ) ) ) ).

% subset_fst_snd
thf(fact_1245_image__paired__Times,axiom,
    ! [F: state > state,G: state > state,A5: set_state,B4: set_state] :
      ( ( image_1391693815708851269_state
        @ ( produc4988896184150421299_state
          @ ^ [X3: state,Y5: state] : ( produc544653723139640077_state @ ( F @ X3 ) @ ( G @ Y5 ) ) )
        @ ( produc4572292869282958142_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( produc4572292869282958142_state @ ( image_state_state @ F @ A5 )
        @ ^ [Uu3: state] : ( image_state_state @ G @ B4 ) ) ) ).

% image_paired_Times
thf(fact_1246_Gr__incl,axiom,
    ! [A5: set_state,F: state > state,B4: set_state] :
      ( ( ord_le2777189432094499797_state @ ( bNF_Gr_state_state @ A5 @ F )
        @ ( produc4572292869282958142_state @ A5
          @ ^ [Uu3: state] : B4 ) )
      = ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A5 ) @ B4 ) ) ).

% Gr_incl
thf(fact_1247_member__product,axiom,
    ! [X: produc7272280185086996969_state,A5: set_state,B4: set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ X @ ( produc3518108405486217632_state @ A5 @ B4 ) )
      = ( member7461423308196221312_state @ X
        @ ( produc2831624448089660202_state @ A5
          @ ^ [Uu3: state] : B4 ) ) ) ).

% member_product
thf(fact_1248_member__product,axiom,
    ! [X: produc9003781588162623004on_val,A5: set_Pr3433046674199179443r_prat,B4: set_Pr1004501353197068112on_val] :
      ( ( member2879030624002546611on_val @ X @ ( produc747609993485717659on_val @ A5 @ B4 ) )
      = ( member2879030624002546611on_val @ X
        @ ( produc1366239611153933861on_val @ A5
          @ ^ [Uu3: produc1457211279475724562t_char > prat] : B4 ) ) ) ).

% member_product
thf(fact_1249_member__product,axiom,
    ! [X: produc3882902684156697774_state,A5: set_state,B4: set_state_state] :
      ( ( member6715010751053357271_state @ X @ ( produc7466003549325918881_state @ A5 @ B4 ) )
      = ( member6715010751053357271_state @ X
        @ ( produc6646226935541082007_state @ A5
          @ ^ [Uu3: state] : B4 ) ) ) ).

% member_product
thf(fact_1250_GrD2,axiom,
    ! [X: produc1457211279475724562t_char > prat,Fx: produc1457211279475724562t_char > option_val,A5: set_Pr3433046674199179443r_prat,F: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > option_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X @ Fx ) @ ( bNF_Gr7520394057480975179on_val @ A5 @ F ) )
     => ( ( F @ X )
        = Fx ) ) ).

% GrD2
thf(fact_1251_PartialSA_Oempty__set__sum,axiom,
    ! [A5: set_state] :
      ( ( add_set @ bot_bot_set_state @ A5 )
      = bot_bot_set_state ) ).

% PartialSA.empty_set_sum
thf(fact_1252_wand__equiv__def,axiom,
    ( wand
    = ( ^ [A4: set_state,B3: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi: state] :
              ( ( Uu3 = Phi )
              & ( ord_le2494988322063910608_state @ ( add_set @ A4 @ ( insert_state @ Phi @ bot_bot_set_state ) ) @ B3 ) ) ) ) ) ).

% wand_equiv_def
thf(fact_1253_PartialSA_Osum__then__singleton,axiom,
    ! [A: state,B: state,C: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ C ) )
      = ( ( insert_state @ A @ bot_bot_set_state )
        = ( add_set @ ( insert_state @ B @ bot_bot_set_state ) @ ( insert_state @ C @ bot_bot_set_state ) ) ) ) ).

% PartialSA.sum_then_singleton
thf(fact_1254_PartialSA_Osetify__def,axiom,
    ( sep_setify_state
    = ( ^ [P5: state > $o,A4: set_state] :
        ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( P5 @ X3 ) ) ) ) ).

% PartialSA.setify_def
thf(fact_1255_PartialSA_Osetify__sum,axiom,
    ! [P4: state > $o,A5: set_state,B4: set_state] :
      ( ( sep_setify_state @ P4 @ ( add_set @ A5 @ B4 ) )
      = ( ! [X3: state] :
            ( ( member_state @ X3 @ A5 )
           => ( sep_setify_state @ P4 @ ( add_set @ ( insert_state @ X3 @ bot_bot_set_state ) @ B4 ) ) ) ) ) ).

% PartialSA.setify_sum
thf(fact_1256_PartialSA_Omono__prop__set,axiom,
    ! [A5: set_state,B4: set_state,P4: state > $o] :
      ( ( greater_set @ A5 @ B4 )
     => ( ( sep_setify_state @ P4 @ B4 )
       => ( ( sep_mono_prop_state @ plus @ P4 )
         => ( sep_setify_state @ P4 @ A5 ) ) ) ) ).

% PartialSA.mono_prop_set
thf(fact_1257_PartialSA_Olarger__set__refl,axiom,
    ! [A5: set_state] : ( greater_set @ A5 @ A5 ) ).

% PartialSA.larger_set_refl
thf(fact_1258_PartialSA_Osucc__set__trans,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( greater_set @ A5 @ B4 )
     => ( ( greater_set @ B4 @ C2 )
       => ( greater_set @ A5 @ C2 ) ) ) ).

% PartialSA.succ_set_trans
thf(fact_1259_PartialSA_Ogreater__set__def,axiom,
    ( greater_set
    = ( ^ [A4: set_state,B3: set_state] :
        ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ? [Y5: state] :
              ( ( member_state @ Y5 @ B3 )
              & ( greater @ X3 @ Y5 ) ) ) ) ) ).

% PartialSA.greater_set_def
thf(fact_1260_PartialSA_Ogreater__setI,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ! [A7: state] :
          ( ( member_state @ A7 @ A5 )
         => ? [X5: state] :
              ( ( member_state @ X5 @ B4 )
              & ( greater @ A7 @ X5 ) ) )
     => ( greater_set @ A5 @ B4 ) ) ).

% PartialSA.greater_setI
thf(fact_1261_PartialSA_Obigger__set,axiom,
    ! [A16: set_state,A5: set_state,B4: set_state] :
      ( ( greater_set @ A16 @ A5 )
     => ( greater_set @ ( add_set @ A16 @ B4 ) @ ( add_set @ A5 @ B4 ) ) ) ).

% PartialSA.bigger_set
thf(fact_1262_PartialSA_Osub__bigger,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A5 @ B4 )
     => ( greater_set @ A5 @ B4 ) ) ).

% PartialSA.sub_bigger
thf(fact_1263_PartialSA_Obigger__singleton,axiom,
    ! [Phi4: state,Phi2: state] :
      ( ( greater @ Phi4 @ Phi2 )
     => ( greater_set @ ( insert_state @ Phi4 @ bot_bot_set_state ) @ ( insert_state @ Phi2 @ bot_bot_set_state ) ) ) ).

% PartialSA.bigger_singleton
thf(fact_1264_PartialSA_Omono__prop__set__equiv,axiom,
    ! [P4: state > $o,A5: set_state,B4: set_state] :
      ( ( sep_mono_prop_state @ plus @ P4 )
     => ( ( sep_equiv_state @ plus @ A5 @ B4 )
       => ( ( sep_setify_state @ P4 @ A5 )
          = ( sep_setify_state @ P4 @ B4 ) ) ) ) ).

% PartialSA.mono_prop_set_equiv
thf(fact_1265_PartialSA_Oequiv__stable__sum,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( sep_equiv_state @ plus @ A5 @ B4 )
     => ( sep_equiv_state @ plus @ ( add_set @ A5 @ C2 ) @ ( add_set @ B4 @ C2 ) ) ) ).

% PartialSA.equiv_stable_sum
thf(fact_1266_PartialSA_Oequiv__def,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( sep_equiv_state @ plus @ A5 @ B4 )
      = ( ( greater_set @ A5 @ B4 )
        & ( greater_set @ B4 @ A5 ) ) ) ).

% PartialSA.equiv_def
thf(fact_1267_PartialSA_OequivI,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( greater_set @ A5 @ B4 )
     => ( ( greater_set @ B4 @ A5 )
       => ( sep_equiv_state @ plus @ A5 @ B4 ) ) ) ).

% PartialSA.equivI
thf(fact_1268_PartialSA_Oequiv__up__closed__subset,axiom,
    ! [A5: set_state,B4: set_state,C2: set_state] :
      ( ( sep_up_closed_state @ plus @ A5 )
     => ( ( sep_equiv_state @ plus @ B4 @ C2 )
       => ( ( ord_le2494988322063910608_state @ B4 @ A5 )
          = ( ord_le2494988322063910608_state @ C2 @ A5 ) ) ) ) ).

% PartialSA.equiv_up_closed_subset
thf(fact_1269_PartialSA_Oup__closedI,axiom,
    ! [A5: set_state] :
      ( ! [Phi7: state,Phi3: state] :
          ( ( ( greater @ Phi7 @ Phi3 )
            & ( member_state @ Phi3 @ A5 ) )
         => ( member_state @ Phi7 @ A5 ) )
     => ( sep_up_closed_state @ plus @ A5 ) ) ).

% PartialSA.up_closedI
thf(fact_1270_PartialSA_Oup__closed__def,axiom,
    ! [A5: set_state] :
      ( ( sep_up_closed_state @ plus @ A5 )
      = ( ! [Phi5: state] :
            ( ? [X3: state] :
                ( ( member_state @ X3 @ A5 )
                & ( greater @ Phi5 @ X3 ) )
           => ( member_state @ Phi5 @ A5 ) ) ) ) ).

% PartialSA.up_closed_def
thf(fact_1271_PartialSA_Oup__closed__sum,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A5 )
     => ( sep_up_closed_state @ plus @ ( add_set @ A5 @ B4 ) ) ) ).

% PartialSA.up_closed_sum
thf(fact_1272_PartialSA_Oup__close__equiv,axiom,
    ! [A5: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A5 )
     => ( ( sep_up_closed_state @ plus @ B4 )
       => ( ( sep_equiv_state @ plus @ A5 @ B4 )
          = ( A5 = B4 ) ) ) ) ).

% PartialSA.up_close_equiv
thf(fact_1273_PartialSA_Oupper__closure__up__closed,axiom,
    ! [A5: set_state] : ( sep_up_closed_state @ plus @ ( sep_up1246176804924251236_state @ plus @ A5 ) ) ).

% PartialSA.upper_closure_up_closed
thf(fact_1274_PartialSA_Oup__closed__bigger__subset,axiom,
    ! [B4: set_state,A5: set_state] :
      ( ( sep_up_closed_state @ plus @ B4 )
     => ( ( greater_set @ A5 @ B4 )
       => ( ord_le2494988322063910608_state @ A5 @ B4 ) ) ) ).

% PartialSA.up_closed_bigger_subset

% Helper facts (8)
thf(help_If_2_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y: prat] :
      ( ( if_prat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y: prat] :
      ( ( if_prat @ $true @ X @ Y )
      = X ) ).

thf(help_fChoice_1_1_fChoice_001t__PosRat__Oprat_T,axiom,
    ! [P4: prat > $o] :
      ( ( P4 @ ( fChoice_prat @ P4 ) )
      = ( ? [X8: prat] : ( P4 @ X8 ) ) ) ).

thf(help_If_2_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ( if_state @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ( if_state @ $true @ X @ Y )
      = X ) ).

thf(help_If_3_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [P4: $o] :
      ( ( P4 = $true )
      | ( P4 = $false ) ) ).

thf(help_If_2_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X: option_state,Y: option_state] :
      ( ( if_option_state @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X: option_state,Y: option_state] :
      ( ( if_option_state @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( pgte @ pwrite @ a2 )
    & ( pgte @ pwrite @ b2 ) ) ).

%------------------------------------------------------------------------------