%------------------------------------------------------------------------------
% 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/0002_PartialHeapSA/prob_00339_011977__7308534_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1736 ( 748 unt; 448 typ;   0 def)
%            Number of atoms       : 3055 (2082 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 9496 ( 485   ~;  53   |; 193   &;7742   @)
%                                         (   0 <=>;1023  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :   38 (  37 usr)
%            Number of type conns  : 2657 (2657   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  414 ( 411 usr;  36 con; 0-4 aty)
%            Number of variables   : 3391 ( 188   ^;3114   !;  89   ?;3391   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 09:08:37.077
%------------------------------------------------------------------------------
% Could-be-implicit typings (37)
thf(ty_n_t__Set__Oset_It__Option__Ooption_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_J,type,
    set_op7951517479864145599on_val: $tType ).

thf(ty_n_t__Option__Ooption_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,
    option2092740943492073951on_val: $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_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__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__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_J,type,
    set_op6240181410663953058on_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__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__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__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__Set__Oset_It__Option__Ooption_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_J,type,
    set_op8153969091884965280on_val: $tType ).

thf(ty_n_t__Option__Ooption_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,
    option5747939881698552298on_val: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J_J,type,
    set_op1110311134966800505r_prat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Mask__Oval_J_J,type,
    list_P375024181684815772ar_val: $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__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Mask__Oval_J_J,type,
    set_Pr7730668076155855478ar_val: $tType ).

thf(ty_n_t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    option3572569098863364761r_prat: $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__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__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    set_op9137726805559506488t_char: $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__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    option2736423997234022232t_char: $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__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    set_op9003753404445127824_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__Set__Oset_It__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J_J,type,
    set_op1974636978870893421on_val: $tType ).

thf(ty_n_t__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    option_option_state: $tType ).

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

thf(ty_n_t__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J,type,
    option_option_val: $tType ).

thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Mask__Oval_J_J,type,
    set_option_val: $tType ).

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

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

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

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

% Explicit typings (411)
thf(sy_c_Finite__Set_Ofinite_001t__Mask__Oval,type,
    finite_finite_val: set_val > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Mask__Oval_J,type,
    finite4212117559080419824on_val: set_option_val > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    finite3180955649987104801_state: set_option_state > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__PartialHeapSA__Ostate,type,
    finite_finite_state: set_state > $o ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Mask__Oval_001t__Mask__Oval,type,
    comp_val_val_val: ( val > val ) > ( val > val ) > val > val ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_v5381271067920388324on_val: ( val > val ) > ( option_val > val ) > option_val > val ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    comp_val_val_state: ( val > val ) > ( state > val ) > state > val ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    comp_v7980881360141566424al_val: ( val > option_val ) > ( val > val ) > val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    comp_v2440280314650358435_state: ( val > option_val ) > ( state > val ) > state > option_val ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    comp_v1148607367049806487te_val: ( val > option_state ) > ( val > val ) > val > option_state ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    comp_v956742881576431396_state: ( val > option_state ) > ( state > val ) > state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__PartialHeapSA__Ostate_001t__Mask__Oval,type,
    comp_val_state_val: ( val > state ) > ( val > val ) > val > state ).

thf(sy_c_Fun_Ocomp_001t__Mask__Oval_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    comp_val_state_state: ( val > state ) > ( state > val ) > state > state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_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_001t__Option__Ooption_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_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    comp_o1785488210378369114r_prat: ( option5747939881698552298on_val > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_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_001t__Option__Ooption_It__Mask__Oval_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    comp_o5748106371294530457r_prat: ( option5747939881698552298on_val > option_val ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_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_001t__Option__Ooption_It__Mask__Oval_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o3878402015218311000t_char: ( option5747939881698552298on_val > option_val ) > ( produc1457211279475724562t_char > option5747939881698552298on_val ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_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_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    comp_o6942933442099041594r_prat: ( option5747939881698552298on_val > option_state ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval_001t__Mask__Oval,type,
    comp_o5604524432708427236al_val: ( option_val > val ) > ( val > option_val ) > val > val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o5868975259454090282on_val: ( option_val > val ) > ( option_val > option_val ) > option_val > val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_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_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    comp_o1018635247228614211r_prat: ( option_val > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option_val ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o7664117635472112386t_char: ( option_val > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option5747939881698552298on_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    comp_o8468585551675268382al_val: ( option_val > option_val ) > ( val > option_val ) > val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o1349245612712103012on_val: ( option_val > option_val ) > ( option_val > option_val ) > option_val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o4299076027095827629_state: ( option_val > option_val ) > ( option_state > option_val ) > option_state > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    comp_o3129965315624761309_state: ( option_val > option_val ) > ( state > option_val ) > state > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o7206986085106588079t_char: ( option_val > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    comp_o1838292368024209361te_val: ( option_val > option_state ) > ( val > option_val ) > val > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o1688524877211496087on_val: ( option_val > option_state ) > ( option_val > option_val ) > option_val > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o9000648883196993210_state: ( option_val > option_state ) > ( option_state > option_val ) > option_state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    comp_o8110046981998356842_state: ( option_val > option_state ) > ( state > option_val ) > state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o1559856024338158690t_char: ( option_val > option_state ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__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_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o5741203133494854784t_char: ( option_val > option8887860577033306220on_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option8887860577033306220on_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Mask__Oval_J_001t__PosRat__Oprat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o4096340722787922972t_char: ( option_val > prat ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > prat ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o5089890310235258666on_val: ( option_option_val > option_val ) > ( option_val > option_option_val ) > option_val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o4730161381108774995_state: ( option_option_state > option_state ) > ( option_state > option_option_state ) > option_state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_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_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    comp_o9034235373990032058r_prat: ( option_state > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option_state ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    comp_o1385090485725692007al_val: ( option_state > option_val ) > ( val > option_state ) > val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o2128577701018291757on_val: ( option_state > option_val ) > ( option_val > option_state ) > option_val > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o2122277431643274148_state: ( option_state > option_val ) > ( option_state > option_state ) > option_state > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    comp_o6956270512087543124_state: ( option_state > option_val ) > ( state > option_state ) > state > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_o5861356331151617272t_char: ( option_state > option_val ) > ( produc1457211279475724562t_char > option_state ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    comp_o5664597564486991176te_val: ( option_state > option_state ) > ( val > option_state ) > val > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    comp_o8735098318613718414on_val: ( option_state > option_state ) > ( option_val > option_state ) > option_val > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o1977787000485117699_state: ( option_state > option_state ) > ( option_state > option_state ) > option_state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    comp_o8889379070304545587_state: ( option_state > option_state ) > ( state > option_state ) > state > option_state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_o2210334810017003187_state: ( option_state > state ) > ( option_state > option_state ) > option_state > state ).

thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    comp_o4916166309651032803_state: ( option_state > state ) > ( state > option_state ) > state > state ).

thf(sy_c_Fun_Ocomp_001t__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_001t__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_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,
    comp_o7026769649805512793on_val: ( option8887860577033306220on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > option8887860577033306220on_val ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Mask__Oval_001t__Mask__Oval,type,
    comp_state_val_val: ( state > val ) > ( val > state ) > val > val ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    comp_state_val_state: ( state > val ) > ( state > state ) > state > val ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    comp_s256881845002425239al_val: ( state > option_val ) > ( val > state ) > val > option_val ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    comp_s6403480550475472420_state: ( state > option_val ) > ( state > state ) > state > option_val ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    comp_s5111807602874920472te_val: ( state > option_state ) > ( val > state ) > val > option_state ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    comp_s2749706468613731939_state: ( state > option_state ) > ( state > state ) > state > option_state ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__Mask__Oval,type,
    comp_state_state_val: ( state > state ) > ( val > state ) > val > state ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    comp_s5294034245180965347_state: ( state > state ) > ( option_state > state ) > option_state > state ).

thf(sy_c_Fun_Ocomp_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    comp_s3787957668927766035_state: ( state > state ) > ( state > state ) > state > state ).

thf(sy_c_Fun_Ocomp_001t__PosRat__Oprat_001t__Option__Ooption_It__Mask__Oval_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_p7839051931923448766t_char: ( prat > option_val ) > ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ocomp_001t__PosRat__Oprat_001t__PosRat__Oprat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_p2042986060831646413t_char: ( prat > prat ) > ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Mask__Oval_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    comp_P7186816004269530362t_char: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > produc1457211279475724562t_char ) > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ofun__upd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_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,
    fun_up1601731230164360576on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ofun__upd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up5104302054361798705on_val: ( ( produc1457211279475724562t_char > prat ) > option_val ) > ( produc1457211279475724562t_char > prat ) > option_val > ( produc1457211279475724562t_char > prat ) > option_val ).

thf(sy_c_Fun_Ofun__upd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up1585067318606691488_state: ( ( produc1457211279475724562t_char > prat ) > option_state ) > ( produc1457211279475724562t_char > prat ) > option_state > ( produc1457211279475724562t_char > prat ) > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__Mask__Oval_001t__Mask__Oval,type,
    fun_upd_val_val: ( val > val ) > val > val > val > val ).

thf(sy_c_Fun_Ofun__upd_001t__Mask__Oval_001t__Option__Ooption_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,
    fun_up8940424251277849774on_val: ( val > option5747939881698552298on_val ) > val > option5747939881698552298on_val > val > option5747939881698552298on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up735531404784515971on_val: ( val > option_val ) > val > option_val > val > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Mask__Oval_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up7100790768922270414_state: ( val > option_state ) > val > option_state > val > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    fun_up3335141697005694071al_val: ( option_val > val ) > option_val > val > option_val > val ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up8761876891205509693on_val: ( option_val > option_val ) > option_val > option_val > option_val > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up2039547756584784788_state: ( option_val > option_state ) > option_val > option_state > option_val > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    fun_up6339919150111145272te_val: ( option_state > val ) > option_state > val > option_state > val ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_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,
    fun_up3115773442321631859on_val: ( option_state > option5747939881698552298on_val ) > option_state > option5747939881698552298on_val > option_state > option5747939881698552298on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up8652368643555229054on_val: ( option_state > option_val ) > option_state > option_val > option_state > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up6517640620910344979_state: ( option_state > option_state ) > option_state > option_state > option_state > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up8843634000204221123_state: ( state > option_state ) > state > option_state > state > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    fun_upd_state_state: ( state > state ) > state > state > state > state ).

thf(sy_c_Fun_Ofun__upd_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__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,
    fun_up273046073882939271on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > option8887860577033306220on_val > produc9003781588162623004on_val > option8887860577033306220on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_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,
    fun_up7235018766041795647on_val: ( produc1457211279475724562t_char > option5747939881698552298on_val ) > produc1457211279475724562t_char > option5747939881698552298on_val > produc1457211279475724562t_char > option5747939881698552298on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up5735975307950539954on_val: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up6995552760743215839_state: ( produc1457211279475724562t_char > option_state ) > produc1457211279475724562t_char > option_state > produc1457211279475724562t_char > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__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,
    fun_up4210561521004557121on_val: ( produc1457211279475724562t_char > option8887860577033306220on_val ) > produc1457211279475724562t_char > option8887860577033306220on_val > produc1457211279475724562t_char > option8887860577033306220on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__PosRat__Oprat,type,
    fun_up829850848796697765r_prat: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat > produc1457211279475724562t_char > prat ).

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_Oinj__on_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    inj_on4074814566786472055on_val: ( val > option_val ) > set_val > $o ).

thf(sy_c_Fun_Oinj__on_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    inj_on3577428053172332983_state: ( state > option_state ) > set_state > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    inj_on4474484569326248358on_val: ( produc1457211279475724562t_char > option_val ) > set_Pr2507339680178222706t_char > $o ).

thf(sy_c_Fun_Ooverride__on_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_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,
    overri3784772535335278463on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > set_Pr3433046674199179443r_prat > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ooverride__on_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__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,
    overri6608491219596025288on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr7649655576376376530on_val > produc9003781588162623004on_val > option8887860577033306220on_val ).

thf(sy_c_Fun_Ooverride__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    overri6326584771168529523on_val: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > set_Pr2507339680178222706t_char > produc1457211279475724562t_char > option_val ).

thf(sy_c_Fun_Ooverride__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__PosRat__Oprat,type,
    overri4208557840210724900r_prat: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > set_Pr2507339680178222706t_char > produc1457211279475724562t_char > prat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__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,
    minus_7863043754688659098r_prat: set_Pr3433046674199179443r_prat > set_Pr3433046674199179443r_prat > set_Pr3433046674199179443r_prat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Mask__Oval_J,type,
    minus_minus_set_val: set_val > set_val > set_val ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Option__Ooption_It__Mask__Oval_J_J,type,
    minus_3256168188512067470on_val: set_option_val > set_option_val > set_option_val ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    minus_7537472381646091673_state: set_option_state > set_option_state > set_option_state ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    minus_3933957440811877961_state: set_state > set_state > set_state ).

thf(sy_c_Groups_Ominus__class_Ominus_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,
    minus_9160195963678339755on_val: set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    minus_6181227053800976857t_char: set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Groups_Ominus__class_Ominus_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__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,
    minus_7211471524202483680on_val: set_Pr4305388979797279737on_val > set_Pr4305388979797279737on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_If_001t__Option__Ooption_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,
    if_opt6509584284076893604on_val: $o > option5747939881698552298on_val > option5747939881698552298on_val > option5747939881698552298on_val ).

thf(sy_c_If_001t__Option__Ooption_It__Mask__Oval_J,type,
    if_option_val: $o > option_val > option_val > option_val ).

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__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,
    if_opt2965748431298708774on_val: $o > option8887860577033306220on_val > option8887860577033306220on_val > option8887860577033306220on_val ).

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

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    inf_in3544766959038609504t_char: set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Mask__Oval_J,type,
    sup_sup_set_val: set_val > set_val > set_val ).

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__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__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Mask__Oval_J_J,type,
    sup_su5754804325903363146ar_val: set_Pr7730668076155855478ar_val > set_Pr7730668076155855478ar_val > set_Pr7730668076155855478ar_val ).

thf(sy_c_Map_Odom_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Mask__Oval,type,
    dom_Pr3224398758927333440at_val: ( ( produc1457211279475724562t_char > prat ) > option_val ) > set_Pr3433046674199179443r_prat ).

thf(sy_c_Map_Odom_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__PartialHeapSA__Ostate,type,
    dom_Pr2103017623604714043_state: ( ( produc1457211279475724562t_char > prat ) > option_state ) > set_Pr3433046674199179443r_prat ).

thf(sy_c_Map_Odom_001t__Mask__Oval_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,
    dom_va8931846639282357193on_val: ( val > option5747939881698552298on_val ) > set_val ).

thf(sy_c_Map_Odom_001t__Mask__Oval_001t__Mask__Oval,type,
    dom_val_val: ( val > option_val ) > set_val ).

thf(sy_c_Map_Odom_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    dom_val_state: ( val > option_state ) > set_val ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__Mask__Oval_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,
    dom_op3430095273566047759on_val: ( option_val > option5747939881698552298on_val ) > set_option_val ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    dom_option_val_val: ( option_val > option_val ) > set_option_val ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    dom_option_val_state: ( option_val > option_state ) > set_option_val ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__PartialHeapSA__Ostate_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,
    dom_op741179583939567608on_val: ( option_state > option5747939881698552298on_val ) > set_option_state ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    dom_option_state_val: ( option_state > option_val ) > set_option_state ).

thf(sy_c_Map_Odom_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    dom_op8569336450220619928_state: ( option_state > option_state ) > set_option_state ).

thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    dom_Pr8989479155164304065ar_val: ( produc1457211279475724562t_char > option_val ) > set_Pr2507339680178222706t_char ).

thf(sy_c_Map_Odom_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__PartialHeapSA__Ostate,type,
    dom_Pr24798649119601274_state: ( produc1457211279475724562t_char > option_state ) > set_Pr2507339680178222706t_char ).

thf(sy_c_Map_Ograph_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,
    graph_1288227317702120175on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > set_Pr7649655576376376530on_val ).

thf(sy_c_Map_Ograph_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,
    graph_6108330199704490680on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr4305388979797279737on_val ).

thf(sy_c_Map_Ograph_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    graph_1733029056113894637ar_val: ( produc1457211279475724562t_char > option_val ) > set_Pr7730668076155855478ar_val ).

thf(sy_c_Map_Omap__add_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,
    map_ad2898753242718228216on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Map_Omap__add_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Mask__Oval,type,
    map_ad5245944522959850275at_val: ( ( produc1457211279475724562t_char > prat ) > option_val ) > ( ( produc1457211279475724562t_char > prat ) > option_val ) > ( produc1457211279475724562t_char > prat ) > option_val ).

thf(sy_c_Map_Omap__add_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__PartialHeapSA__Ostate,type,
    map_ad5796490619809589144_state: ( ( produc1457211279475724562t_char > prat ) > option_state ) > ( ( produc1457211279475724562t_char > prat ) > option_state ) > ( produc1457211279475724562t_char > prat ) > option_state ).

thf(sy_c_Map_Omap__add_001t__Mask__Oval_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,
    map_ad4617731073159927590on_val: ( val > option5747939881698552298on_val ) > ( val > option5747939881698552298on_val ) > val > option5747939881698552298on_val ).

thf(sy_c_Map_Omap__add_001t__Mask__Oval_001t__Mask__Oval,type,
    map_add_val_val: ( val > option_val ) > ( val > option_val ) > val > option_val ).

thf(sy_c_Map_Omap__add_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    map_add_val_state: ( val > option_state ) > ( val > option_state ) > val > option_state ).

thf(sy_c_Map_Omap__add_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    map_ad2791809220819668783al_val: ( option_val > option_val ) > ( option_val > option_val ) > option_val > option_val ).

thf(sy_c_Map_Omap__add_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    map_ad1596397661948740748_state: ( option_val > option_state ) > ( option_val > option_state ) > option_val > option_state ).

thf(sy_c_Map_Omap__add_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    map_ad304724714348188800te_val: ( option_state > option_val ) > ( option_state > option_val ) > option_state > option_val ).

thf(sy_c_Map_Omap__add_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    map_ad3143451158333058555_state: ( option_state > option_state ) > ( option_state > option_state ) > option_state > option_state ).

thf(sy_c_Map_Omap__add_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,
    map_ad6375351378680859759on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > option8887860577033306220on_val ).

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_Map_Omap__le_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,
    map_le7591542393800649736on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > $o ).

thf(sy_c_Map_Omap__le_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,
    map_le1786601613863086943on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > option8887860577033306220on_val ) > $o ).

thf(sy_c_Map_Omap__le_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    map_le3432596473071271956ar_val: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_Map_Omap__of_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    map_of6844234013878170066ar_val: list_P375024181684815772ar_val > produc1457211279475724562t_char > option_val ).

thf(sy_c_Map_Oran_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,
    ran_Pr878516737976613822on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > set_Pr1004501353197068112on_val ).

thf(sy_c_Map_Oran_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,
    ran_Pr1583955956598603305on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr7649655576376376530on_val ).

thf(sy_c_Map_Oran_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    ran_Pr786515303459910110ar_val: ( produc1457211279475724562t_char > option_val ) > set_val ).

thf(sy_c_Map_Orestrict__map_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,
    restri7594233908965391805on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > set_Pr3433046674199179443r_prat > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Map_Orestrict__map_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Mask__Oval,type,
    restri9007081556893774878at_val: ( ( produc1457211279475724562t_char > prat ) > option_val ) > set_Pr3433046674199179443r_prat > ( produc1457211279475724562t_char > prat ) > option_val ).

thf(sy_c_Map_Orestrict__map_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__PartialHeapSA__Ostate,type,
    restri738375759408046301_state: ( ( produc1457211279475724562t_char > prat ) > option_state ) > set_Pr3433046674199179443r_prat > ( produc1457211279475724562t_char > prat ) > option_state ).

thf(sy_c_Map_Orestrict__map_001t__Mask__Oval_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,
    restri8187230408314553963on_val: ( val > option5747939881698552298on_val ) > set_val > val > option5747939881698552298on_val ).

thf(sy_c_Map_Orestrict__map_001t__Mask__Oval_001t__Mask__Oval,type,
    restrict_map_val_val: ( val > option_val ) > set_val > val > option_val ).

thf(sy_c_Map_Orestrict__map_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    restri6351330254082781323_state: ( val > option_state ) > set_val > val > option_state ).

thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    restri7980214582795305770al_val: ( option_val > option_val ) > set_option_val > option_val > option_val ).

thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_It__Mask__Oval_J_001t__PartialHeapSA__Ostate,type,
    restri8841944298656297681_state: ( option_val > option_state ) > set_option_val > option_val > option_state ).

thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_It__PartialHeapSA__Ostate_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,
    restri3062571084349347286on_val: ( option_state > option5747939881698552298on_val ) > set_option_state > option_state > option5747939881698552298on_val ).

thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    restri7550271351055745733te_val: ( option_state > option_val ) > set_option_state > option_state > option_val ).

thf(sy_c_Map_Orestrict__map_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    restri4758375023823916406_state: ( option_state > option_state ) > set_option_state > option_state > option_state ).

thf(sy_c_Map_Orestrict__map_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,
    restri2354629191430751338on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr7649655576376376530on_val > produc9003781588162623004on_val > option8887860577033306220on_val ).

thf(sy_c_Map_Orestrict__map_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Mask__Oval,type,
    restri4256959289591943583ar_val: ( produc1457211279475724562t_char > option_val ) > set_Pr2507339680178222706t_char > produc1457211279475724562t_char > option_val ).

thf(sy_c_Map_Orestrict__map_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__PartialHeapSA__Ostate,type,
    restri8083244519320860188_state: ( produc1457211279475724562t_char > option_state ) > set_Pr2507339680178222706t_char > produc1457211279475724562t_char > option_state ).

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_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_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_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_Ovalid__mask,type,
    valid_mask: ( produc1457211279475724562t_char > prat ) > $o ).

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

thf(sy_c_Option_Obind_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,
    bind_P4424090778364213876on_val: option5747939881698552298on_val > ( ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val ) > option5747939881698552298on_val ).

thf(sy_c_Option_Obind_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__Mask__Oval,type,
    bind_P5848121846087789735al_val: option5747939881698552298on_val > ( ( produc1457211279475724562t_char > option_val ) > option_val ) > option_val ).

thf(sy_c_Option_Obind_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__PartialHeapSA__Ostate,type,
    bind_P6102080752330912020_state: option5747939881698552298on_val > ( ( produc1457211279475724562t_char > option_val ) > option_state ) > option_state ).

thf(sy_c_Option_Obind_001t__Mask__Oval_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,
    bind_v3756559123625202269on_val: option_val > ( val > option5747939881698552298on_val ) > option5747939881698552298on_val ).

thf(sy_c_Option_Obind_001t__Mask__Oval_001t__Mask__Oval,type,
    bind_val_val: option_val > ( val > option_val ) > option_val ).

thf(sy_c_Option_Obind_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    bind_val_state: option_val > ( val > option_state ) > option_state ).

thf(sy_c_Option_Obind_001t__Mask__Oval_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,
    bind_v217880529008409823on_val: option_val > ( val > option8887860577033306220on_val ) > option8887860577033306220on_val ).

thf(sy_c_Option_Obind_001t__PartialHeapSA__Ostate_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,
    bind_s7388421589535509396on_val: option_state > ( state > option5747939881698552298on_val ) > option5747939881698552298on_val ).

thf(sy_c_Option_Obind_001t__PartialHeapSA__Ostate_001t__Mask__Oval,type,
    bind_state_val: option_state > ( state > option_val ) > option_val ).

thf(sy_c_Option_Obind_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    bind_state_state: option_state > ( state > option_state ) > option_state ).

thf(sy_c_Option_Obind_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,
    bind_s5745438296695018390on_val: option_state > ( state > option8887860577033306220on_val ) > option8887860577033306220on_val ).

thf(sy_c_Option_Obind_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__Mask__Oval,type,
    bind_P8603646205577311397al_val: option8887860577033306220on_val > ( produc9003781588162623004on_val > option_val ) > option_val ).

thf(sy_c_Option_Obind_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,
    bind_P2178757275261240214_state: option8887860577033306220on_val > ( produc9003781588162623004on_val > option_state ) > option_state ).

thf(sy_c_Option_Obind_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,
    bind_P2485767298420691192on_val: option8887860577033306220on_val > ( produc9003781588162623004on_val > option8887860577033306220on_val ) > option8887860577033306220on_val ).

thf(sy_c_Option_Ocombine__options_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,
    combin3271118981050854363on_val: ( ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val > option5747939881698552298on_val > option5747939881698552298on_val ).

thf(sy_c_Option_Ocombine__options_001t__Mask__Oval,type,
    combine_options_val: ( val > val > val ) > option_val > option_val > option_val ).

thf(sy_c_Option_Ocombine__options_001t__PartialHeapSA__Ostate,type,
    combin3633514924185701883_state: ( state > state > state ) > option_state > option_state > option_state ).

thf(sy_c_Option_Ocombine__options_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,
    combin6222804963853957469on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val ) > option8887860577033306220on_val > option8887860577033306220on_val > option8887860577033306220on_val ).

thf(sy_c_Option_Ois__none_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,
    is_non6205214127102033982on_val: option5747939881698552298on_val > $o ).

thf(sy_c_Option_Ois__none_001t__Mask__Oval,type,
    is_none_val: option_val > $o ).

thf(sy_c_Option_Ois__none_001t__PartialHeapSA__Ostate,type,
    is_none_state: option_state > $o ).

thf(sy_c_Option_Ois__none_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,
    is_non3468859156093823296on_val: option8887860577033306220on_val > $o ).

thf(sy_c_Option_Ooption_ONone_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,
    none_P1334921381875262201on_val: option5747939881698552298on_val ).

thf(sy_c_Option_Ooption_ONone_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    none_P6742040017396684084r_prat: option3572569098863364761r_prat ).

thf(sy_c_Option_Ooption_ONone_001t__Mask__Oval,type,
    none_val: option_val ).

thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_It__Mask__Oval_J,type,
    none_option_val: option_option_val ).

thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    none_option_state: option_option_state ).

thf(sy_c_Option_Ooption_ONone_001t__PartialHeapSA__Ostate,type,
    none_state: option_state ).

thf(sy_c_Option_Ooption_ONone_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,
    none_P8728355543607141243on_val: option8887860577033306220on_val ).

thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    none_P5486107665612286067t_char: option2736423997234022232t_char ).

thf(sy_c_Option_Ooption_OSome_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,
    some_P7669353234731512949on_val: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val ).

thf(sy_c_Option_Ooption_OSome_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    some_P8530153984677361336r_prat: ( produc1457211279475724562t_char > prat ) > option3572569098863364761r_prat ).

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

thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_It__Mask__Oval_J,type,
    some_option_val: option_val > option_option_val ).

thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    some_option_state: option_state > option_option_state ).

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__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    some_P6851457240968045559t_char: produc1457211279475724562t_char > option2736423997234022232t_char ).

thf(sy_c_Option_Ooption_OSome_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,
    some_P3086335783055994110on_val: produc1317171644805857433on_val > option2092740943492073951on_val ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mask__Oval_001t__Mask__Oval,type,
    case_option_val_val: val > ( val > val ) > option_val > val ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    case_o5195096591205178001on_val: val > ( option_val > val ) > option_option_val > val ).

thf(sy_c_Option_Ooption_Ocase__option_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    case_o2237019792253254865_state: state > ( option_state > state ) > option_option_state > state ).

thf(sy_c_Option_Ooption_Ocase__option_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    case_o2102410670496921089_state: state > ( state > state ) > option_state > state ).

thf(sy_c_Option_Ooption_Omap__option_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,
    map_op5506263056045291841on_val: ( ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val > option5747939881698552298on_val ).

thf(sy_c_Option_Ooption_Omap__option_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__Mask__Oval,type,
    map_op880068700720311194al_val: ( ( produc1457211279475724562t_char > option_val ) > val ) > option5747939881698552298on_val > option_val ).

thf(sy_c_Option_Ooption_Omap__option_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__PartialHeapSA__Ostate,type,
    map_op1814185762381987425_state: ( ( produc1457211279475724562t_char > option_val ) > state ) > option5747939881698552298on_val > option_state ).

thf(sy_c_Option_Ooption_Omap__option_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,
    map_op2194283413446040907r_prat: ( ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat ) > option3572569098863364761r_prat > option3572569098863364761r_prat ).

thf(sy_c_Option_Ooption_Omap__option_001t__Mask__Oval_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,
    map_op8011878015112499536on_val: ( val > produc1457211279475724562t_char > option_val ) > option_val > option5747939881698552298on_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Mask__Oval_001t__Mask__Oval,type,
    map_option_val_val: ( val > val ) > option_val > option_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    map_op5819421865013908113on_val: ( val > option_val ) > option_val > option_option_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Mask__Oval_001t__PartialHeapSA__Ostate,type,
    map_option_val_state: ( val > state ) > option_val > option_state ).

thf(sy_c_Option_Ooption_Omap__option_001t__Mask__Oval_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,
    map_op3897579098253967186on_val: ( val > produc9003781588162623004on_val ) > option_val > option8887860577033306220on_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    map_op8419032157235086213al_val: ( option_val > val ) > option_option_val > option_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    map_op2847309980797881419on_val: ( option_val > option_val ) > option_option_val > option_option_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    map_op5992293608522446881_state: ( option_state > option_state ) > option_option_state > option_option_state ).

thf(sy_c_Option_Ooption_Omap__option_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__PartialHeapSA__Ostate,type,
    map_op384739313229359441_state: ( option_state > state ) > option_option_state > option_state ).

thf(sy_c_Option_Ooption_Omap__option_001t__PartialHeapSA__Ostate_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,
    map_op3100526599586584801on_val: ( state > produc1457211279475724562t_char > option_val ) > option_state > option5747939881698552298on_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__PartialHeapSA__Ostate_001t__Mask__Oval,type,
    map_option_state_val: ( state > val ) > option_state > option_val ).

thf(sy_c_Option_Ooption_Omap__option_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    map_op2929067089796592849_state: ( state > option_state ) > option_state > option_option_state ).

thf(sy_c_Option_Ooption_Omap__option_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    map_op2726735944305651201_state: ( state > state ) > option_state > option_state ).

thf(sy_c_Option_Ooption_Omap__option_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,
    map_op2202097680607477091on_val: ( state > produc9003781588162623004on_val ) > option_state > option8887860577033306220on_val ).

thf(sy_c_Option_Ooption_Omap__option_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__Mask__Oval,type,
    map_op3059972737968092952al_val: ( produc9003781588162623004on_val > val ) > option8887860577033306220on_val > option_val ).

thf(sy_c_Option_Ooption_Omap__option_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,
    map_op7858788696028474723_state: ( produc9003781588162623004on_val > state ) > option8887860577033306220on_val > option_state ).

thf(sy_c_Option_Ooption_Omap__option_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,
    map_op7709461780610975941on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > option8887860577033306220on_val > option8887860577033306220on_val ).

thf(sy_c_Option_Ooption_Oset__option_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,
    set_op1770538635792728844on_val: option5747939881698552298on_val > set_Pr1004501353197068112on_val ).

thf(sy_c_Option_Ooption_Oset__option_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    set_op923924987228895969r_prat: option3572569098863364761r_prat > set_Pr3433046674199179443r_prat ).

thf(sy_c_Option_Ooption_Oset__option_001t__Mask__Oval,type,
    set_option_val2: option_val > set_val ).

thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_It__Mask__Oval_J,type,
    set_op911010586042427349on_val: option_option_val > set_option_val ).

thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    set_op5162993263733338108_state: option_option_state > set_option_state ).

thf(sy_c_Option_Ooption_Oset__option_001t__PartialHeapSA__Ostate,type,
    set_option_state2: option_state > set_state ).

thf(sy_c_Option_Ooption_Oset__option_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,
    set_op9004752959087400718on_val: option8887860577033306220on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Option_Ooption_Oset__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    set_op7440730737645789856t_char: option2736423997234022232t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Option_Ooption_Oset__option_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,
    set_op5043251206941365031on_val: option2092740943492073951on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_Option_Ooption_Othe_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,
    the_Pr646328391962797958on_val: option5747939881698552298on_val > produc1457211279475724562t_char > option_val ).

thf(sy_c_Option_Ooption_Othe_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    the_Pr3206600365949932263r_prat: option3572569098863364761r_prat > produc1457211279475724562t_char > prat ).

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

thf(sy_c_Option_Ooption_Othe_001t__Option__Ooption_It__Mask__Oval_J,type,
    the_option_val: option_option_val > option_val ).

thf(sy_c_Option_Ooption_Othe_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    the_option_state: option_option_state > option_state ).

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

thf(sy_c_Option_Ooption_Othe_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,
    the_Pr3639693038709580936on_val: option8887860577033306220on_val > produc9003781588162623004on_val ).

thf(sy_c_Option_Othese_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,
    these_602426935119867933on_val: set_op8153969091884965280on_val > set_Pr1004501353197068112on_val ).

thf(sy_c_Option_Othese_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    these_2482516890548509968r_prat: set_op1110311134966800505r_prat > set_Pr3433046674199179443r_prat ).

thf(sy_c_Option_Othese_001t__Mask__Oval,type,
    these_val: set_option_val > set_val ).

thf(sy_c_Option_Othese_001t__Option__Ooption_It__Mask__Oval_J,type,
    these_option_val: set_op1974636978870893421on_val > set_option_val ).

thf(sy_c_Option_Othese_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    these_option_state: set_op9003753404445127824_state > set_option_state ).

thf(sy_c_Option_Othese_001t__PartialHeapSA__Ostate,type,
    these_state: set_option_state > set_state ).

thf(sy_c_Option_Othese_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,
    these_3919539662624406175on_val: set_op6240181410663953058on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    these_2739680984639915599t_char: set_op9137726805559506488t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Option_Othese_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,
    these_4429819578991166294on_val: set_op7951517479864145599on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_Order__Relation_Olinear__order__on_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,
    order_6061556925426544295on_val: set_Pr7649655576376376530on_val > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Order__Relation_Owell__order__on_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,
    order_2579646547231075838on_val: set_Pr7649655576376376530on_val > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo3932128351999234686prat_o: ( produc1457211279475724562t_char > prat ) > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Mask__Oval_M_Eo_J,type,
    bot_bot_val_o: val > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Option__Ooption_It__Mask__Oval_J_M_Eo_J,type,
    bot_bot_option_val_o: option_val > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_Eo_J,type,
    bot_bo4453335400789057457tate_o: option_state > $o ).

thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo6370234372831922335_val_o: produc9003781588162623004on_val > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_M_Eo_J,type,
    bot_bo1808431002336377727char_o: produc1457211279475724562t_char > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__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,
    bot_bo5671083314777306084on_val: set_Pr1004501353197068112on_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__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,
    bot_bo3164680191535668511r_prat: set_Pr3433046674199179443r_prat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Mask__Oval_J,type,
    bot_bot_set_val: set_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_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_J,type,
    bot_bo832982859489559604on_val: set_op8153969091884965280on_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Mask__Oval_J_J,type,
    bot_bo5906790151302476563on_val: set_option_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J_J,type,
    bot_bo6240080102570541529on_val: set_op1974636978870893421on_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J_J,type,
    bot_bo489212050006660900_state: set_op9003753404445127824_state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    bot_bo710180891245420500_state: set_option_state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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_J,type,
    bot_bo6421125907362167606on_val: set_op6240181410663953058on_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
    bot_bo2782010437066608292t_char: set_op9137726805559506488t_char ).

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_Obot__class_Obot_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,
    bot_bo6722054719108133734on_val: set_Pr7649655576376376530on_val ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    bot_bo1414094081888755934t_char: set_Pr2507339680178222706t_char ).

thf(sy_c_Orderings_Obot__class_Obot_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__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,
    bot_bo402267660617762917on_val: set_Pr4305388979797279737on_val ).

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__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,
    ord_le7224449410216889241on_val: set_Pr4305388979797279737on_val > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Mask__Oval_J,type,
    top_top_set_val: set_val ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Mask__Oval_J_J,type,
    top_to853123400021307383on_val: set_option_val ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    top_to7666338855062656496_state: set_option_state ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    top_top_set_state: set_state ).

thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to1561438921946393474on_val: set_Pr7649655576376376530on_val ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    top_to1250346684925019074t_char: set_Pr2507339680178222706t_char ).

thf(sy_c_PackageLogic_Opackage__logic__axioms_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,
    packag6610728152020528762on_val: ( ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > option_val ) > ( ( produc1457211279475724562t_char > option_val ) > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic__axioms_001t__Mask__Oval,type,
    packag6139878888743580961ms_val: ( val > val > option_val ) > val > ( val > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic__axioms_001t__PartialHeapSA__Ostate,type,
    packag2647621270594721818_state: ( state > state > option_state ) > state > ( state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic__axioms_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,
    packag3831085842030230908on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > produc9003781588162623004on_val > ( produc9003781588162623004on_val > $o ) > $o ).

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_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,
    compat2032066794789061494on_val: option5747939881698552298on_val > option5747939881698552298on_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_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,
    compat6602494657299208312on_val: option8887860577033306220on_val > option8887860577033306220on_val > $o ).

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

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__m,type,
    get_m: state > produc1457211279475724562t_char > prat ).

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_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_PosRat_Opadd,type,
    padd: prat > prat > prat ).

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

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_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__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__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_Relation_OField_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,
    field_9010718613293825679on_val: set_Pr4305388979797279737on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Relation_Orefl__on_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,
    refl_o6679066329051764061on_val: set_Pr7649655576376376530on_val > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Relation_Otrans__on_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,
    trans_3212976107463897212on_val: set_Pr7649655576376376530on_val > set_Pr4305388979797279737on_val > $o ).

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__Mask__Oval,type,
    collect_val: ( val > $o ) > set_val ).

thf(sy_c_Set_OCollect_001t__Option__Ooption_It__Mask__Oval_J,type,
    collect_option_val: ( option_val > $o ) > set_option_val ).

thf(sy_c_Set_OCollect_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    collect_option_state: ( option_state > $o ) > set_option_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__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__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    collec2458894688891239037t_char: ( produc1457211279475724562t_char > $o ) > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_Oimage_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__Option__Ooption_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,
    image_5626594990718149899on_val: ( ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val ) > set_Pr1004501353197068112on_val > set_op8153969091884965280on_val ).

thf(sy_c_Set_Oimage_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    image_1941897556587066297on_val: ( ( produc1457211279475724562t_char > prat ) > option_val ) > set_Pr3433046674199179443r_prat > set_option_val ).

thf(sy_c_Set_Oimage_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    image_4340244011621553944_state: ( ( produc1457211279475724562t_char > prat ) > option_state ) > set_Pr3433046674199179443r_prat > set_option_state ).

thf(sy_c_Set_Oimage_001t__Mask__Oval_001t__Mask__Oval,type,
    image_val_val: ( val > val ) > set_val > set_val ).

thf(sy_c_Set_Oimage_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    image_val_option_val: ( val > option_val ) > set_val > set_option_val ).

thf(sy_c_Set_Oimage_001t__Mask__Oval_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    image_8370355904157991238_state: ( val > option_state ) > set_val > set_option_state ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    image_option_val_val: ( option_val > val ) > set_option_val > set_val ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    image_5994708315261978053on_val: ( option_val > option_val ) > set_option_val > set_option_val ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__Mask__Oval_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    image_2662813144889517580_state: ( option_val > option_state ) > set_option_val > set_option_state ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Mask__Oval,type,
    image_7609484285346866096te_val: ( option_state > val ) > set_option_state > set_val ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    image_52261995005186038on_val: ( option_state > option_val ) > set_option_state > set_option_val ).

thf(sy_c_Set_Oimage_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    image_8299601973402907291_state: ( option_state > option_state ) > set_option_state > set_option_state ).

thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    image_6076465424260689483_state: ( state > option_state ) > set_state > set_option_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__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,
    image_4416128703135814415on_val: ( produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr7649655576376376530on_val > set_op6240181410663953058on_val ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    image_4269386950610408506on_val: ( produc1457211279475724562t_char > option_val ) > set_Pr2507339680178222706t_char > set_option_val ).

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__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    image_3726312381382425221t_char: ( produc1457211279475724562t_char > produc1457211279475724562t_char ) > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_Oinsert_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,
    insert216038912599248202on_val: ( produc1457211279475724562t_char > option_val ) > set_Pr1004501353197068112on_val > set_Pr1004501353197068112on_val ).

thf(sy_c_Set_Oinsert_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    insert8113562578550770211r_prat: ( produc1457211279475724562t_char > prat ) > set_Pr3433046674199179443r_prat > set_Pr3433046674199179443r_prat ).

thf(sy_c_Set_Oinsert_001t__Mask__Oval,type,
    insert_val: val > set_val > set_val ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_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,
    insert4694516387090290714on_val: option5747939881698552298on_val > set_op8153969091884965280on_val > set_op8153969091884965280on_val ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Mask__Oval_J,type,
    insert_option_val: option_val > set_option_val > set_option_val ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J,type,
    insert7563226391266834525on_val: option_option_val > set_op1974636978870893421on_val > set_op1974636978870893421on_val ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    insert7535573567550883338_state: option_option_state > set_op9003753404445127824_state > set_op9003753404445127824_state ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    insert_option_state: option_state > set_option_state > set_option_state ).

thf(sy_c_Set_Oinsert_001t__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,
    insert751572358616671900on_val: option8887860577033306220on_val > set_op6240181410663953058on_val > set_op6240181410663953058on_val ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_J,type,
    insert213255421748673832t_char: option2736423997234022232t_char > set_op9137726805559506488t_char > set_op9137726805559506488t_char ).

thf(sy_c_Set_Oinsert_001t__Option__Ooption_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,
    insert4270431555848968111on_val: option2092740943492073951on_val > set_op7951517479864145599on_val > set_op7951517479864145599on_val ).

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

thf(sy_c_Set_Oinsert_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,
    insert3030518898131756108on_val: produc9003781588162623004on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    insert3372640069787401954t_char: produc1457211279475724562t_char > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_Oinsert_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,
    insert7062705985672971881on_val: produc1317171644805857433on_val > set_Pr4305388979797279737on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_Set_Ois__empty_001t__Mask__Oval,type,
    is_empty_val: set_val > $o ).

thf(sy_c_Set_Ois__empty_001t__Option__Ooption_It__Mask__Oval_J,type,
    is_empty_option_val: set_option_val > $o ).

thf(sy_c_Set_Ois__empty_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    is_emp7138872393943660984_state: set_option_state > $o ).

thf(sy_c_Set_Ois__empty_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,
    is_emp5364603196349043402on_val: set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    is_emp609703007689476580t_char: set_Pr2507339680178222706t_char > $o ).

thf(sy_c_Set_Ois__singleton_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    is_sin6650292796724890951r_prat: set_Pr3433046674199179443r_prat > $o ).

thf(sy_c_Set_Ois__singleton_001t__Mask__Oval,type,
    is_singleton_val: set_val > $o ).

thf(sy_c_Set_Ois__singleton_001t__Option__Ooption_It__Mask__Oval_J,type,
    is_sin5830670008703254587on_val: set_option_val > $o ).

thf(sy_c_Set_Ois__singleton_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    is_sin8559911096322084886_state: set_option_state > $o ).

thf(sy_c_Set_Ois__singleton_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,
    is_sin1022367449962840616on_val: set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    is_sin3863772449867033606t_char: set_Pr2507339680178222706t_char > $o ).

thf(sy_c_Set_Ois__singleton_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,
    is_sin7597786275116224909on_val: set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Set_Opairwise_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    pairwi5837023185793671998r_prat: ( ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o ) > set_Pr3433046674199179443r_prat > $o ).

thf(sy_c_Set_Opairwise_001t__Mask__Oval,type,
    pairwise_val: ( val > val > $o ) > set_val > $o ).

thf(sy_c_Set_Opairwise_001t__Option__Ooption_It__Mask__Oval_J,type,
    pairwise_option_val: ( option_val > option_val > $o ) > set_option_val > $o ).

thf(sy_c_Set_Opairwise_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    pairwi7845604448133876319_state: ( option_state > option_state > $o ) > set_option_state > $o ).

thf(sy_c_Set_Opairwise_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,
    pairwi3211334688826577905on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > $o ) > set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Set_Opairwise_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    pairwi421018896454539133t_char: ( produc1457211279475724562t_char > produc1457211279475724562t_char > $o ) > set_Pr2507339680178222706t_char > $o ).

thf(sy_c_Set_Opairwise_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,
    pairwi8980569249058178436on_val: ( produc1317171644805857433on_val > produc1317171644805857433on_val > $o ) > set_Pr4305388979797279737on_val > $o ).

thf(sy_c_Set_Oremove_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    remove6968564113294249144r_prat: ( produc1457211279475724562t_char > prat ) > set_Pr3433046674199179443r_prat > set_Pr3433046674199179443r_prat ).

thf(sy_c_Set_Oremove_001t__Mask__Oval,type,
    remove_val: val > set_val > set_val ).

thf(sy_c_Set_Oremove_001t__Option__Ooption_It__Mask__Oval_J,type,
    remove_option_val: option_val > set_option_val > set_option_val ).

thf(sy_c_Set_Oremove_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    remove_option_state: option_state > set_option_state > set_option_state ).

thf(sy_c_Set_Oremove_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,
    remove6046006348179432695on_val: produc9003781588162623004on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    remove1543384711646755319t_char: produc1457211279475724562t_char > set_Pr2507339680178222706t_char > set_Pr2507339680178222706t_char ).

thf(sy_c_Set_Oremove_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,
    remove5903733279999771390on_val: produc1317171644805857433on_val > set_Pr4305388979797279737on_val > set_Pr4305388979797279737on_val ).

thf(sy_c_Set_Othe__elem_001t__Mask__Oval,type,
    the_elem_val: set_val > val ).

thf(sy_c_Set_Othe__elem_001t__Option__Ooption_It__Mask__Oval_J,type,
    the_elem_option_val: set_option_val > option_val ).

thf(sy_c_Set_Othe__elem_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    the_el1618976816499768149_state: set_option_state > option_state ).

thf(sy_c_Set_Othe__elem_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,
    the_el8055350808190710247on_val: set_Pr7649655576376376530on_val > produc9003781588162623004on_val ).

thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J,type,
    the_el4510683560064399623t_char: set_Pr2507339680178222706t_char > produc1457211279475724562t_char ).

thf(sy_c_Set_Othe__elem_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,
    the_el5720079856748460558on_val: set_Pr4305388979797279737on_val > produc1317171644805857433on_val ).

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__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_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_001t__Mask__Oval,type,
    member_val: val > set_val > $o ).

thf(sy_c_member_001t__Option__Ooption_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,
    member7216203038034776961on_val: option5747939881698552298on_val > set_op8153969091884965280on_val > $o ).

thf(sy_c_member_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_J,type,
    member8024166271143588802r_prat: option3572569098863364761r_prat > set_op1110311134966800505r_prat > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Mask__Oval_J,type,
    member_option_val: option_val > set_option_val > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Option__Ooption_It__Mask__Oval_J_J,type,
    member8465289789052943542on_val: option_option_val > set_op1974636978870893421on_val > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    member1079230918592710257_state: option_option_state > set_op9003753404445127824_state > $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__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,
    member4602090469187516291on_val: option8887860577033306220on_val > set_op6240181410663953058on_val > $o ).

thf(sy_c_member_001t__PartialHeapSA__Ostate,type,
    member_state: state > set_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__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_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__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_v_a,type,
    a: state ).

thf(sy_v_ab,type,
    ab: state ).

thf(sy_v_b,type,
    b: state ).

thf(sy_v_c,type,
    c: state ).

thf(sy_v_thesis____,type,
    thesis: $o ).

% Relevant facts (1275)
thf(fact_0__092_060open_062_092_060not_062_Acompatible__heaps_A_Iget__h_Ab_J_A_Iget__h_Ac_J_092_060close_062,axiom,
    ~ ( compatible_heaps @ ( get_h @ b ) @ ( get_h @ c ) ) ).

% \<open>\<not> compatible_heaps (get_h b) (get_h c)\<close>
thf(fact_1_compatible__heapsI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H2: produc1457211279475724562t_char > option_val] :
      ( ! [Hl: produc1457211279475724562t_char,A: val,B: val] :
          ( ( ( H @ Hl )
            = ( some_val @ A ) )
         => ( ( ( H2 @ Hl )
              = ( some_val @ B ) )
           => ( A = B ) ) )
     => ( compatible_heaps @ H @ H2 ) ) ).

% compatible_heapsI
thf(fact_2_option_Oinject,axiom,
    ! [X2: produc9003781588162623004on_val,Y2: produc9003781588162623004on_val] :
      ( ( ( some_P2581650809551911671on_val @ X2 )
        = ( some_P2581650809551911671on_val @ Y2 ) )
      = ( X2 = Y2 ) ) ).

% option.inject
thf(fact_3_option_Oinject,axiom,
    ! [X2: produc1457211279475724562t_char > option_val,Y2: produc1457211279475724562t_char > option_val] :
      ( ( ( some_P7669353234731512949on_val @ X2 )
        = ( some_P7669353234731512949on_val @ Y2 ) )
      = ( X2 = Y2 ) ) ).

% option.inject
thf(fact_4_option_Oinject,axiom,
    ! [X2: val,Y2: val] :
      ( ( ( some_val @ X2 )
        = ( some_val @ Y2 ) )
      = ( X2 = Y2 ) ) ).

% option.inject
thf(fact_5_option_Oinject,axiom,
    ! [X2: state,Y2: state] :
      ( ( ( some_state @ X2 )
        = ( some_state @ Y2 ) )
      = ( X2 = Y2 ) ) ).

% option.inject
thf(fact_6_True,axiom,
    valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ b ) @ ( get_m @ c ) ) ).

% True
thf(fact_7_assms,axiom,
    ( ( ( plus @ a @ b )
      = ( some_state @ ab ) )
    & ( ( plus @ b @ c )
      = none_state ) ) ).

% assms
thf(fact_8_compatible__options_Oelims_I3_J,axiom,
    ! [X: option8887860577033306220on_val,Xa: option8887860577033306220on_val] :
      ( ~ ( compat6602494657299208312on_val @ X @ Xa )
     => ~ ! [A: produc9003781588162623004on_val] :
            ( ( X
              = ( some_P2581650809551911671on_val @ A ) )
           => ! [B: produc9003781588162623004on_val] :
                ( ( Xa
                  = ( some_P2581650809551911671on_val @ B ) )
               => ( A = B ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_9_compatible__options_Oelims_I3_J,axiom,
    ! [X: option5747939881698552298on_val,Xa: option5747939881698552298on_val] :
      ( ~ ( compat2032066794789061494on_val @ X @ Xa )
     => ~ ! [A: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( some_P7669353234731512949on_val @ A ) )
           => ! [B: produc1457211279475724562t_char > option_val] :
                ( ( Xa
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( A = B ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_10_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ~ ( compat2278460363914054422_state @ X @ Xa )
     => ~ ! [A: state] :
            ( ( X
              = ( some_state @ A ) )
           => ! [B: state] :
                ( ( Xa
                  = ( some_state @ B ) )
               => ( A = B ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_11_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X @ Xa )
     => ~ ! [A: val] :
            ( ( X
              = ( some_val @ A ) )
           => ! [B: val] :
                ( ( Xa
                  = ( some_val @ B ) )
               => ( A = B ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_12_compatible__options_Osimps_I1_J,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
      ( ( compat6602494657299208312on_val @ ( some_P2581650809551911671on_val @ A2 ) @ ( some_P2581650809551911671on_val @ B2 ) )
      = ( A2 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_13_compatible__options_Osimps_I1_J,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( compat2032066794789061494on_val @ ( some_P7669353234731512949on_val @ A2 ) @ ( some_P7669353234731512949on_val @ B2 ) )
      = ( A2 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_14_compatible__options_Osimps_I1_J,axiom,
    ! [A2: state,B2: state] :
      ( ( compat2278460363914054422_state @ ( some_state @ A2 ) @ ( some_state @ B2 ) )
      = ( A2 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_15_compatible__options_Osimps_I1_J,axiom,
    ! [A2: val,B2: val] :
      ( ( compat7209469420100717861ns_val @ ( some_val @ A2 ) @ ( some_val @ B2 ) )
      = ( A2 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_16_larger__heapI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H2: produc1457211279475724562t_char > option_val] :
      ( ! [Hl: produc1457211279475724562t_char,X3: val] :
          ( ( ( H @ Hl )
            = ( some_val @ X3 ) )
         => ( ( H2 @ Hl )
            = ( some_val @ X3 ) ) )
     => ( larger1532547405891354081ar_val @ H2 @ H ) ) ).

% larger_heapI
thf(fact_17_larger__heap__def,axiom,
    ( larger1532547405891354081ar_val
    = ( ^ [H3: produc1457211279475724562t_char > option_val,H4: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char,X4: val] :
          ( ( ( H4 @ Hl2 )
            = ( some_val @ X4 ) )
         => ( ( H3 @ Hl2 )
            = ( some_val @ X4 ) ) ) ) ) ).

% larger_heap_def
thf(fact_18_package__logic__axioms_Ointro,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Unit: produc9003781588162623004on_val,Stable: produc9003781588162623004on_val > $o] :
      ( ! [A: produc9003781588162623004on_val] :
          ( ( some_P2581650809551911671on_val @ A )
          = ( Plus @ A @ Unit ) )
     => ( ! [A: produc9003781588162623004on_val,B: produc9003781588162623004on_val,X3: produc9003781588162623004on_val] :
            ( ( Stable @ A )
           => ( ( Stable @ B )
             => ( ( ( some_P2581650809551911671on_val @ X3 )
                  = ( Plus @ A @ B ) )
               => ( Stable @ X3 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag3831085842030230908on_val @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_19_package__logic__axioms_Ointro,axiom,
    ! [Plus: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val,Unit: produc1457211279475724562t_char > option_val,Stable: ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ! [A: produc1457211279475724562t_char > option_val] :
          ( ( some_P7669353234731512949on_val @ A )
          = ( Plus @ A @ Unit ) )
     => ( ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,X3: produc1457211279475724562t_char > option_val] :
            ( ( Stable @ A )
           => ( ( Stable @ B )
             => ( ( ( some_P7669353234731512949on_val @ X3 )
                  = ( Plus @ A @ B ) )
               => ( Stable @ X3 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag6610728152020528762on_val @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_20_package__logic__axioms_Ointro,axiom,
    ! [Plus: val > val > option_val,Unit: val,Stable: val > $o] :
      ( ! [A: val] :
          ( ( some_val @ A )
          = ( Plus @ A @ Unit ) )
     => ( ! [A: val,B: val,X3: val] :
            ( ( Stable @ A )
           => ( ( Stable @ B )
             => ( ( ( some_val @ X3 )
                  = ( Plus @ A @ B ) )
               => ( Stable @ X3 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag6139878888743580961ms_val @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_21_package__logic__axioms_Ointro,axiom,
    ! [Plus: state > state > option_state,Unit: state,Stable: state > $o] :
      ( ! [A: state] :
          ( ( some_state @ A )
          = ( Plus @ A @ Unit ) )
     => ( ! [A: state,B: state,X3: state] :
            ( ( Stable @ A )
           => ( ( Stable @ B )
             => ( ( ( some_state @ X3 )
                  = ( Plus @ A @ B ) )
               => ( Stable @ X3 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag2647621270594721818_state @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_22_package__logic__axioms__def,axiom,
    ( packag3831085842030230908on_val
    = ( ^ [Plus2: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Unit2: produc9003781588162623004on_val,Stable2: produc9003781588162623004on_val > $o] :
          ( ! [A3: produc9003781588162623004on_val] :
              ( ( some_P2581650809551911671on_val @ A3 )
              = ( Plus2 @ A3 @ Unit2 ) )
          & ! [A3: produc9003781588162623004on_val,B3: produc9003781588162623004on_val,X4: produc9003781588162623004on_val] :
              ( ( Stable2 @ A3 )
             => ( ( Stable2 @ B3 )
               => ( ( ( some_P2581650809551911671on_val @ X4 )
                    = ( Plus2 @ A3 @ B3 ) )
                 => ( Stable2 @ X4 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_23_package__logic__axioms__def,axiom,
    ( packag6610728152020528762on_val
    = ( ^ [Plus2: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val,Unit2: produc1457211279475724562t_char > option_val,Stable2: ( produc1457211279475724562t_char > option_val ) > $o] :
          ( ! [A3: produc1457211279475724562t_char > option_val] :
              ( ( some_P7669353234731512949on_val @ A3 )
              = ( Plus2 @ A3 @ Unit2 ) )
          & ! [A3: produc1457211279475724562t_char > option_val,B3: produc1457211279475724562t_char > option_val,X4: produc1457211279475724562t_char > option_val] :
              ( ( Stable2 @ A3 )
             => ( ( Stable2 @ B3 )
               => ( ( ( some_P7669353234731512949on_val @ X4 )
                    = ( Plus2 @ A3 @ B3 ) )
                 => ( Stable2 @ X4 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_24_package__logic__axioms__def,axiom,
    ( packag6139878888743580961ms_val
    = ( ^ [Plus2: val > val > option_val,Unit2: val,Stable2: val > $o] :
          ( ! [A3: val] :
              ( ( some_val @ A3 )
              = ( Plus2 @ A3 @ Unit2 ) )
          & ! [A3: val,B3: val,X4: val] :
              ( ( Stable2 @ A3 )
             => ( ( Stable2 @ B3 )
               => ( ( ( some_val @ X4 )
                    = ( Plus2 @ A3 @ B3 ) )
                 => ( Stable2 @ X4 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_25_package__logic__axioms__def,axiom,
    ( packag2647621270594721818_state
    = ( ^ [Plus2: state > state > option_state,Unit2: state,Stable2: state > $o] :
          ( ! [A3: state] :
              ( ( some_state @ A3 )
              = ( Plus2 @ A3 @ Unit2 ) )
          & ! [A3: state,B3: state,X4: state] :
              ( ( Stable2 @ A3 )
             => ( ( Stable2 @ B3 )
               => ( ( ( some_state @ X4 )
                    = ( Plus2 @ A3 @ B3 ) )
                 => ( Stable2 @ X4 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_26_not__Some__eq,axiom,
    ! [X: option8887860577033306220on_val] :
      ( ( ! [Y: produc9003781588162623004on_val] :
            ( X
           != ( some_P2581650809551911671on_val @ Y ) ) )
      = ( X = none_P8728355543607141243on_val ) ) ).

% not_Some_eq
thf(fact_27_not__Some__eq,axiom,
    ! [X: option5747939881698552298on_val] :
      ( ( ! [Y: produc1457211279475724562t_char > option_val] :
            ( X
           != ( some_P7669353234731512949on_val @ Y ) ) )
      = ( X = none_P1334921381875262201on_val ) ) ).

% not_Some_eq
thf(fact_28_not__Some__eq,axiom,
    ! [X: option_val] :
      ( ( ! [Y: val] :
            ( X
           != ( some_val @ Y ) ) )
      = ( X = none_val ) ) ).

% not_Some_eq
thf(fact_29_not__Some__eq,axiom,
    ! [X: option_state] :
      ( ( ! [Y: state] :
            ( X
           != ( some_state @ Y ) ) )
      = ( X = none_state ) ) ).

% not_Some_eq
thf(fact_30_not__None__eq,axiom,
    ! [X: option8887860577033306220on_val] :
      ( ( X != none_P8728355543607141243on_val )
      = ( ? [Y: produc9003781588162623004on_val] :
            ( X
            = ( some_P2581650809551911671on_val @ Y ) ) ) ) ).

% not_None_eq
thf(fact_31_not__None__eq,axiom,
    ! [X: option5747939881698552298on_val] :
      ( ( X != none_P1334921381875262201on_val )
      = ( ? [Y: produc1457211279475724562t_char > option_val] :
            ( X
            = ( some_P7669353234731512949on_val @ Y ) ) ) ) ).

% not_None_eq
thf(fact_32_not__None__eq,axiom,
    ! [X: option_val] :
      ( ( X != none_val )
      = ( ? [Y: val] :
            ( X
            = ( some_val @ Y ) ) ) ) ).

% not_None_eq
thf(fact_33_not__None__eq,axiom,
    ! [X: option_state] :
      ( ( X != none_state )
      = ( ? [Y: state] :
            ( X
            = ( some_state @ Y ) ) ) ) ).

% not_None_eq
thf(fact_34_plus__charact_I1_J,axiom,
    ! [A2: state,B2: state,X: state] :
      ( ( ( plus @ A2 @ B2 )
        = ( some_state @ X ) )
     => ( ( get_m @ X )
        = ( add_ma6586698345353345811t_char @ ( get_m @ A2 ) @ ( get_m @ B2 ) ) ) ) ).

% plus_charact(1)
thf(fact_35_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option8887860577033306220on_val] : ( compat6602494657299208312on_val @ Uu @ none_P8728355543607141243on_val ) ).

% compatible_options.simps(3)
thf(fact_36_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option5747939881698552298on_val] : ( compat2032066794789061494on_val @ Uu @ none_P1334921381875262201on_val ) ).

% compatible_options.simps(3)
thf(fact_37_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_val] : ( compat7209469420100717861ns_val @ Uu @ none_val ) ).

% compatible_options.simps(3)
thf(fact_38_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_state] : ( compat2278460363914054422_state @ Uu @ none_state ) ).

% compatible_options.simps(3)
thf(fact_39_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option8887860577033306220on_val] : ( compat6602494657299208312on_val @ none_P8728355543607141243on_val @ Uv ) ).

% compatible_options.simps(2)
thf(fact_40_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option5747939881698552298on_val] : ( compat2032066794789061494on_val @ none_P1334921381875262201on_val @ Uv ) ).

% compatible_options.simps(2)
thf(fact_41_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_val] : ( compat7209469420100717861ns_val @ none_val @ Uv ) ).

% compatible_options.simps(2)
thf(fact_42_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_state] : ( compat2278460363914054422_state @ none_state @ Uv ) ).

% compatible_options.simps(2)
thf(fact_43_asso1,axiom,
    ! [A2: state,B2: state,Ab: state,C: state,Bc: state] :
      ( ( ( ( plus @ A2 @ B2 )
          = ( some_state @ Ab ) )
        & ( ( plus @ B2 @ C )
          = ( some_state @ Bc ) ) )
     => ( ( plus @ Ab @ C )
        = ( plus @ A2 @ Bc ) ) ) ).

% asso1
thf(fact_44_plus__ab__defined,axiom,
    ! [Phi: state,Phi2: state] :
      ( ( ( plus @ Phi @ Phi2 )
       != none_state )
      = ( ( compatible_heaps @ ( get_h @ Phi ) @ ( get_h @ Phi2 ) )
        & ( valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ Phi ) @ ( get_m @ Phi2 ) ) ) ) ) ).

% plus_ab_defined
thf(fact_45_larger__heap__comp,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A2 @ B2 )
     => ( ( compatible_heaps @ A2 @ C )
       => ( compatible_heaps @ B2 @ C ) ) ) ).

% larger_heap_comp
thf(fact_46_compatible__heaps__def,axiom,
    ( compatible_heaps
    = ( ^ [H4: produc1457211279475724562t_char > option_val,H3: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char] : ( compat7209469420100717861ns_val @ ( H4 @ Hl2 ) @ ( H3 @ Hl2 ) ) ) ) ).

% compatible_heaps_def
thf(fact_47_larger__compatible__sum__heaps,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A2 @ X )
     => ( ( larger1532547405891354081ar_val @ B2 @ Y3 )
       => ( ( compatible_heaps @ A2 @ B2 )
         => ( compatible_heaps @ X @ Y3 ) ) ) ) ).

% larger_compatible_sum_heaps
thf(fact_48_larger__heap__trans,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A2 @ B2 )
     => ( ( larger1532547405891354081ar_val @ B2 @ C )
       => ( larger1532547405891354081ar_val @ A2 @ C ) ) ) ).

% larger_heap_trans
thf(fact_49_larger__heap__refl,axiom,
    ! [H: produc1457211279475724562t_char > option_val] : ( larger1532547405891354081ar_val @ H @ H ) ).

% larger_heap_refl
thf(fact_50_larger__heap__anti,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A2 @ B2 )
     => ( ( larger1532547405891354081ar_val @ B2 @ A2 )
       => ( A2 = B2 ) ) ) ).

% larger_heap_anti
thf(fact_51_commutative,axiom,
    ( plus
    = ( ^ [A3: state,B3: state] : ( plus @ B3 @ A3 ) ) ) ).

% commutative
thf(fact_52_combine__options__cases,axiom,
    ! [X: option_val,P: option_val > option_val > $o,Y3: option_val] :
      ( ( ( X = none_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: val,B: val] :
              ( ( X
                = ( some_val @ A ) )
             => ( ( Y3
                  = ( some_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_53_combine__options__cases,axiom,
    ! [X: option_val,P: option_val > option_state > $o,Y3: option_state] :
      ( ( ( X = none_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_state )
         => ( P @ X @ Y3 ) )
       => ( ! [A: val,B: state] :
              ( ( X
                = ( some_val @ A ) )
             => ( ( Y3
                  = ( some_state @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_54_combine__options__cases,axiom,
    ! [X: option_state,P: option_state > option_val > $o,Y3: option_val] :
      ( ( ( X = none_state )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: state,B: val] :
              ( ( X
                = ( some_state @ A ) )
             => ( ( Y3
                  = ( some_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_55_combine__options__cases,axiom,
    ! [X: option_state,P: option_state > option_state > $o,Y3: option_state] :
      ( ( ( X = none_state )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_state )
         => ( P @ X @ Y3 ) )
       => ( ! [A: state,B: state] :
              ( ( X
                = ( some_state @ A ) )
             => ( ( Y3
                  = ( some_state @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_56_combine__options__cases,axiom,
    ! [X: option_val,P: option_val > option5747939881698552298on_val > $o,Y3: option5747939881698552298on_val] :
      ( ( ( X = none_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_P1334921381875262201on_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: val,B: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( some_val @ A ) )
             => ( ( Y3
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_57_combine__options__cases,axiom,
    ! [X: option_state,P: option_state > option5747939881698552298on_val > $o,Y3: option5747939881698552298on_val] :
      ( ( ( X = none_state )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_P1334921381875262201on_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: state,B: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( some_state @ A ) )
             => ( ( Y3
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_58_combine__options__cases,axiom,
    ! [X: option5747939881698552298on_val,P: option5747939881698552298on_val > option_val > $o,Y3: option_val] :
      ( ( ( X = none_P1334921381875262201on_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: produc1457211279475724562t_char > option_val,B: val] :
              ( ( X
                = ( some_P7669353234731512949on_val @ A ) )
             => ( ( Y3
                  = ( some_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_59_combine__options__cases,axiom,
    ! [X: option5747939881698552298on_val,P: option5747939881698552298on_val > option_state > $o,Y3: option_state] :
      ( ( ( X = none_P1334921381875262201on_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_state )
         => ( P @ X @ Y3 ) )
       => ( ! [A: produc1457211279475724562t_char > option_val,B: state] :
              ( ( X
                = ( some_P7669353234731512949on_val @ A ) )
             => ( ( Y3
                  = ( some_state @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_60_combine__options__cases,axiom,
    ! [X: option5747939881698552298on_val,P: option5747939881698552298on_val > option5747939881698552298on_val > $o,Y3: option5747939881698552298on_val] :
      ( ( ( X = none_P1334921381875262201on_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_P1334921381875262201on_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( some_P7669353234731512949on_val @ A ) )
             => ( ( Y3
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_61_combine__options__cases,axiom,
    ! [X: option_val,P: option_val > option8887860577033306220on_val > $o,Y3: option8887860577033306220on_val] :
      ( ( ( X = none_val )
       => ( P @ X @ Y3 ) )
     => ( ( ( Y3 = none_P8728355543607141243on_val )
         => ( P @ X @ Y3 ) )
       => ( ! [A: val,B: produc9003781588162623004on_val] :
              ( ( X
                = ( some_val @ A ) )
             => ( ( Y3
                  = ( some_P2581650809551911671on_val @ B ) )
               => ( P @ X @ Y3 ) ) )
         => ( P @ X @ Y3 ) ) ) ) ).

% combine_options_cases
thf(fact_62_split__option__all,axiom,
    ( ( ^ [P2: option8887860577033306220on_val > $o] :
        ! [X5: option8887860577033306220on_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option8887860577033306220on_val > $o] :
          ( ( P3 @ none_P8728355543607141243on_val )
          & ! [X4: produc9003781588162623004on_val] : ( P3 @ ( some_P2581650809551911671on_val @ X4 ) ) ) ) ) ).

% split_option_all
thf(fact_63_split__option__all,axiom,
    ( ( ^ [P2: option5747939881698552298on_val > $o] :
        ! [X5: option5747939881698552298on_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option5747939881698552298on_val > $o] :
          ( ( P3 @ none_P1334921381875262201on_val )
          & ! [X4: produc1457211279475724562t_char > option_val] : ( P3 @ ( some_P7669353234731512949on_val @ X4 ) ) ) ) ) ).

% split_option_all
thf(fact_64_split__option__all,axiom,
    ( ( ^ [P2: option_val > $o] :
        ! [X5: option_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option_val > $o] :
          ( ( P3 @ none_val )
          & ! [X4: val] : ( P3 @ ( some_val @ X4 ) ) ) ) ) ).

% split_option_all
thf(fact_65_split__option__all,axiom,
    ( ( ^ [P2: option_state > $o] :
        ! [X5: option_state] : ( P2 @ X5 ) )
    = ( ^ [P3: option_state > $o] :
          ( ( P3 @ none_state )
          & ! [X4: state] : ( P3 @ ( some_state @ X4 ) ) ) ) ) ).

% split_option_all
thf(fact_66_split__option__ex,axiom,
    ( ( ^ [P2: option8887860577033306220on_val > $o] :
        ? [X5: option8887860577033306220on_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option8887860577033306220on_val > $o] :
          ( ( P3 @ none_P8728355543607141243on_val )
          | ? [X4: produc9003781588162623004on_val] : ( P3 @ ( some_P2581650809551911671on_val @ X4 ) ) ) ) ) ).

% split_option_ex
thf(fact_67_split__option__ex,axiom,
    ( ( ^ [P2: option5747939881698552298on_val > $o] :
        ? [X5: option5747939881698552298on_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option5747939881698552298on_val > $o] :
          ( ( P3 @ none_P1334921381875262201on_val )
          | ? [X4: produc1457211279475724562t_char > option_val] : ( P3 @ ( some_P7669353234731512949on_val @ X4 ) ) ) ) ) ).

% split_option_ex
thf(fact_68_split__option__ex,axiom,
    ( ( ^ [P2: option_val > $o] :
        ? [X5: option_val] : ( P2 @ X5 ) )
    = ( ^ [P3: option_val > $o] :
          ( ( P3 @ none_val )
          | ? [X4: val] : ( P3 @ ( some_val @ X4 ) ) ) ) ) ).

% split_option_ex
thf(fact_69_split__option__ex,axiom,
    ( ( ^ [P2: option_state > $o] :
        ? [X5: option_state] : ( P2 @ X5 ) )
    = ( ^ [P3: option_state > $o] :
          ( ( P3 @ none_state )
          | ? [X4: state] : ( P3 @ ( some_state @ X4 ) ) ) ) ) ).

% split_option_ex
thf(fact_70_option_Oexhaust,axiom,
    ! [Y3: option8887860577033306220on_val] :
      ( ( Y3 != none_P8728355543607141243on_val )
     => ~ ! [X22: produc9003781588162623004on_val] :
            ( Y3
           != ( some_P2581650809551911671on_val @ X22 ) ) ) ).

% option.exhaust
thf(fact_71_option_Oexhaust,axiom,
    ! [Y3: option5747939881698552298on_val] :
      ( ( Y3 != none_P1334921381875262201on_val )
     => ~ ! [X22: produc1457211279475724562t_char > option_val] :
            ( Y3
           != ( some_P7669353234731512949on_val @ X22 ) ) ) ).

% option.exhaust
thf(fact_72_option_Oexhaust,axiom,
    ! [Y3: option_val] :
      ( ( Y3 != none_val )
     => ~ ! [X22: val] :
            ( Y3
           != ( some_val @ X22 ) ) ) ).

% option.exhaust
thf(fact_73_option_Oexhaust,axiom,
    ! [Y3: option_state] :
      ( ( Y3 != none_state )
     => ~ ! [X22: state] :
            ( Y3
           != ( some_state @ X22 ) ) ) ).

% option.exhaust
thf(fact_74_option_OdiscI,axiom,
    ! [Option: option8887860577033306220on_val,X2: produc9003781588162623004on_val] :
      ( ( Option
        = ( some_P2581650809551911671on_val @ X2 ) )
     => ( Option != none_P8728355543607141243on_val ) ) ).

% option.discI
thf(fact_75_option_OdiscI,axiom,
    ! [Option: option5747939881698552298on_val,X2: produc1457211279475724562t_char > option_val] :
      ( ( Option
        = ( some_P7669353234731512949on_val @ X2 ) )
     => ( Option != none_P1334921381875262201on_val ) ) ).

% option.discI
thf(fact_76_option_OdiscI,axiom,
    ! [Option: option_val,X2: val] :
      ( ( Option
        = ( some_val @ X2 ) )
     => ( Option != none_val ) ) ).

% option.discI
thf(fact_77_option_OdiscI,axiom,
    ! [Option: option_state,X2: state] :
      ( ( Option
        = ( some_state @ X2 ) )
     => ( Option != none_state ) ) ).

% option.discI
thf(fact_78_option_Odistinct_I1_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( none_P8728355543607141243on_val
     != ( some_P2581650809551911671on_val @ X2 ) ) ).

% option.distinct(1)
thf(fact_79_option_Odistinct_I1_J,axiom,
    ! [X2: produc1457211279475724562t_char > option_val] :
      ( none_P1334921381875262201on_val
     != ( some_P7669353234731512949on_val @ X2 ) ) ).

% option.distinct(1)
thf(fact_80_option_Odistinct_I1_J,axiom,
    ! [X2: val] :
      ( none_val
     != ( some_val @ X2 ) ) ).

% option.distinct(1)
thf(fact_81_option_Odistinct_I1_J,axiom,
    ! [X2: state] :
      ( none_state
     != ( some_state @ X2 ) ) ).

% option.distinct(1)
thf(fact_82_compatible__options_Oelims_I1_J,axiom,
    ! [X: option8887860577033306220on_val,Xa: option8887860577033306220on_val,Y3: $o] :
      ( ( ( compat6602494657299208312on_val @ X @ Xa )
        = Y3 )
     => ( ! [A: produc9003781588162623004on_val] :
            ( ( X
              = ( some_P2581650809551911671on_val @ A ) )
           => ! [B: produc9003781588162623004on_val] :
                ( ( Xa
                  = ( some_P2581650809551911671on_val @ B ) )
               => ( Y3
                  = ( A != B ) ) ) )
       => ( ( ( X = none_P8728355543607141243on_val )
           => ~ Y3 )
         => ~ ( ( Xa = none_P8728355543607141243on_val )
             => ~ Y3 ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_83_compatible__options_Oelims_I1_J,axiom,
    ! [X: option5747939881698552298on_val,Xa: option5747939881698552298on_val,Y3: $o] :
      ( ( ( compat2032066794789061494on_val @ X @ Xa )
        = Y3 )
     => ( ! [A: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( some_P7669353234731512949on_val @ A ) )
           => ! [B: produc1457211279475724562t_char > option_val] :
                ( ( Xa
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( Y3
                  = ( A != B ) ) ) )
       => ( ( ( X = none_P1334921381875262201on_val )
           => ~ Y3 )
         => ~ ( ( Xa = none_P1334921381875262201on_val )
             => ~ Y3 ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_84_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_val,Xa: option_val,Y3: $o] :
      ( ( ( compat7209469420100717861ns_val @ X @ Xa )
        = Y3 )
     => ( ! [A: val] :
            ( ( X
              = ( some_val @ A ) )
           => ! [B: val] :
                ( ( Xa
                  = ( some_val @ B ) )
               => ( Y3
                  = ( A != B ) ) ) )
       => ( ( ( X = none_val )
           => ~ Y3 )
         => ~ ( ( Xa = none_val )
             => ~ Y3 ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_85_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_state,Xa: option_state,Y3: $o] :
      ( ( ( compat2278460363914054422_state @ X @ Xa )
        = Y3 )
     => ( ! [A: state] :
            ( ( X
              = ( some_state @ A ) )
           => ! [B: state] :
                ( ( Xa
                  = ( some_state @ B ) )
               => ( Y3
                  = ( A != B ) ) ) )
       => ( ( ( X = none_state )
           => ~ Y3 )
         => ~ ( ( Xa = none_state )
             => ~ Y3 ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_86_compatible__options_Oelims_I2_J,axiom,
    ! [X: option8887860577033306220on_val,Xa: option8887860577033306220on_val] :
      ( ( compat6602494657299208312on_val @ X @ Xa )
     => ( ! [A: produc9003781588162623004on_val] :
            ( ( X
              = ( some_P2581650809551911671on_val @ A ) )
           => ! [B: produc9003781588162623004on_val] :
                ( ( Xa
                  = ( some_P2581650809551911671on_val @ B ) )
               => ( A != B ) ) )
       => ( ( X != none_P8728355543607141243on_val )
         => ( Xa = none_P8728355543607141243on_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_87_compatible__options_Oelims_I2_J,axiom,
    ! [X: option5747939881698552298on_val,Xa: option5747939881698552298on_val] :
      ( ( compat2032066794789061494on_val @ X @ Xa )
     => ( ! [A: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( some_P7669353234731512949on_val @ A ) )
           => ! [B: produc1457211279475724562t_char > option_val] :
                ( ( Xa
                  = ( some_P7669353234731512949on_val @ B ) )
               => ( A != B ) ) )
       => ( ( X != none_P1334921381875262201on_val )
         => ( Xa = none_P1334921381875262201on_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_88_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_val,Xa: option_val] :
      ( ( compat7209469420100717861ns_val @ X @ Xa )
     => ( ! [A: val] :
            ( ( X
              = ( some_val @ A ) )
           => ! [B: val] :
                ( ( Xa
                  = ( some_val @ B ) )
               => ( A != B ) ) )
       => ( ( X != none_val )
         => ( Xa = none_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_89_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_state,Xa: option_state] :
      ( ( compat2278460363914054422_state @ X @ Xa )
     => ( ! [A: state] :
            ( ( X
              = ( some_state @ A ) )
           => ! [B: state] :
                ( ( Xa
                  = ( some_state @ B ) )
               => ( A != B ) ) )
       => ( ( X != none_state )
         => ( Xa = none_state ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_90_upper__valid,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A2 )
     => ( ( A2
          = ( add_ma6586698345353345811t_char @ B2 @ C ) )
       => ( ( valid_mask @ B2 )
          & ( valid_mask @ C ) ) ) ) ).

% upper_valid
thf(fact_91_upper__valid__aux,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A2 )
     => ( ( A2
          = ( add_ma6586698345353345811t_char @ B2 @ C ) )
       => ( valid_mask @ B2 ) ) ) ).

% upper_valid_aux
thf(fact_92_empty__heap__def,axiom,
    ( empty_7512026568161686585ar_val
    = ( ^ [Hl2: produc1457211279475724562t_char] : none_val ) ) ).

% empty_heap_def
thf(fact_93_plus__charact_I2_J,axiom,
    ! [A2: state,B2: state,X: state] :
      ( ( ( plus @ A2 @ B2 )
        = ( some_state @ X ) )
     => ( ( get_h @ X )
        = ( map_ad2908576761495157028ar_val @ ( get_h @ A2 ) @ ( get_h @ B2 ) ) ) ) ).

% plus_charact(2)
thf(fact_94_add__masks__asso,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( add_ma6586698345353345811t_char @ ( add_ma6586698345353345811t_char @ A2 @ B2 ) @ C )
      = ( add_ma6586698345353345811t_char @ A2 @ ( add_ma6586698345353345811t_char @ B2 @ C ) ) ) ).

% add_masks_asso
thf(fact_95_mem__Collect__eq,axiom,
    ! [A2: produc9003781588162623004on_val,P: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ A2 @ ( collec7475294502966882545on_val @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_96_mem__Collect__eq,axiom,
    ! [A2: option_state,P: option_state > $o] :
      ( ( member_option_state @ A2 @ ( collect_option_state @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_97_mem__Collect__eq,axiom,
    ! [A2: option_val,P: option_val > $o] :
      ( ( member_option_val @ A2 @ ( collect_option_val @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_98_mem__Collect__eq,axiom,
    ! [A2: val,P: val > $o] :
      ( ( member_val @ A2 @ ( collect_val @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_99_mem__Collect__eq,axiom,
    ! [A2: produc1457211279475724562t_char > prat,P: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( member2336342582916103932r_prat @ A2 @ ( collec7093475260167521854r_prat @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_100_Collect__mem__eq,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [X4: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X4 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_101_Collect__mem__eq,axiom,
    ! [A4: set_option_state] :
      ( ( collect_option_state
        @ ^ [X4: option_state] : ( member_option_state @ X4 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_102_Collect__mem__eq,axiom,
    ! [A4: set_option_val] :
      ( ( collect_option_val
        @ ^ [X4: option_val] : ( member_option_val @ X4 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_103_Collect__mem__eq,axiom,
    ! [A4: set_val] :
      ( ( collect_val
        @ ^ [X4: val] : ( member_val @ X4 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_104_Collect__mem__eq,axiom,
    ! [A4: set_Pr3433046674199179443r_prat] :
      ( ( collec7093475260167521854r_prat
        @ ^ [X4: produc1457211279475724562t_char > prat] : ( member2336342582916103932r_prat @ X4 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_105_add__masks__comm,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [A3: produc1457211279475724562t_char > prat,B3: produc1457211279475724562t_char > prat] : ( add_ma6586698345353345811t_char @ B3 @ A3 ) ) ) ).

% add_masks_comm
thf(fact_106_add__masks__cancellative,axiom,
    ! [B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ B2 @ C )
        = ( add_ma6586698345353345811t_char @ B2 @ D ) )
     => ( C = D ) ) ).

% add_masks_cancellative
thf(fact_107_option_Ocollapse,axiom,
    ! [Option: option8887860577033306220on_val] :
      ( ( Option != none_P8728355543607141243on_val )
     => ( ( some_P2581650809551911671on_val @ ( the_Pr3639693038709580936on_val @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_108_option_Ocollapse,axiom,
    ! [Option: option5747939881698552298on_val] :
      ( ( Option != none_P1334921381875262201on_val )
     => ( ( some_P7669353234731512949on_val @ ( the_Pr646328391962797958on_val @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_109_option_Ocollapse,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( ( some_val @ ( the_val @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_110_option_Ocollapse,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( ( some_state @ ( the_state @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_111_PartialHeapSA_Ostable__def,axiom,
    ( stable
    = ( ^ [Phi3: state] :
        ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi3 @ Hl2 ) )
          = ( ( get_h @ Phi3 @ Hl2 )
           != none_val ) ) ) ) ).

% PartialHeapSA.stable_def
thf(fact_112_bind__split,axiom,
    ! [P: option_state > $o,M: option_val,F: val > option_state] :
      ( ( P @ ( bind_val_state @ M @ F ) )
      = ( ( ( M = none_val )
         => ( P @ none_state ) )
        & ! [V: val] :
            ( ( M
              = ( some_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_113_bind__split,axiom,
    ! [P: option_val > $o,M: option_val,F: val > option_val] :
      ( ( P @ ( bind_val_val @ M @ F ) )
      = ( ( ( M = none_val )
         => ( P @ none_val ) )
        & ! [V: val] :
            ( ( M
              = ( some_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_114_bind__split,axiom,
    ! [P: option_state > $o,M: option_state,F: state > option_state] :
      ( ( P @ ( bind_state_state @ M @ F ) )
      = ( ( ( M = none_state )
         => ( P @ none_state ) )
        & ! [V: state] :
            ( ( M
              = ( some_state @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_115_bind__split,axiom,
    ! [P: option_val > $o,M: option_state,F: state > option_val] :
      ( ( P @ ( bind_state_val @ M @ F ) )
      = ( ( ( M = none_state )
         => ( P @ none_val ) )
        & ! [V: state] :
            ( ( M
              = ( some_state @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_116_bind__split,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option_val,F: val > option5747939881698552298on_val] :
      ( ( P @ ( bind_v3756559123625202269on_val @ M @ F ) )
      = ( ( ( M = none_val )
         => ( P @ none_P1334921381875262201on_val ) )
        & ! [V: val] :
            ( ( M
              = ( some_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_117_bind__split,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option_state,F: state > option5747939881698552298on_val] :
      ( ( P @ ( bind_s7388421589535509396on_val @ M @ F ) )
      = ( ( ( M = none_state )
         => ( P @ none_P1334921381875262201on_val ) )
        & ! [V: state] :
            ( ( M
              = ( some_state @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_118_bind__split,axiom,
    ! [P: option_state > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_state] :
      ( ( P @ ( bind_P6102080752330912020_state @ M @ F ) )
      = ( ( ( M = none_P1334921381875262201on_val )
         => ( P @ none_state ) )
        & ! [V: produc1457211279475724562t_char > option_val] :
            ( ( M
              = ( some_P7669353234731512949on_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_119_bind__split,axiom,
    ! [P: option_val > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_val] :
      ( ( P @ ( bind_P5848121846087789735al_val @ M @ F ) )
      = ( ( ( M = none_P1334921381875262201on_val )
         => ( P @ none_val ) )
        & ! [V: produc1457211279475724562t_char > option_val] :
            ( ( M
              = ( some_P7669353234731512949on_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_120_bind__split,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val] :
      ( ( P @ ( bind_P4424090778364213876on_val @ M @ F ) )
      = ( ( ( M = none_P1334921381875262201on_val )
         => ( P @ none_P1334921381875262201on_val ) )
        & ! [V: produc1457211279475724562t_char > option_val] :
            ( ( M
              = ( some_P7669353234731512949on_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_121_bind__split,axiom,
    ! [P: option8887860577033306220on_val > $o,M: option_val,F: val > option8887860577033306220on_val] :
      ( ( P @ ( bind_v217880529008409823on_val @ M @ F ) )
      = ( ( ( M = none_val )
         => ( P @ none_P8728355543607141243on_val ) )
        & ! [V: val] :
            ( ( M
              = ( some_val @ V ) )
           => ( P @ ( F @ V ) ) ) ) ) ).

% bind_split
thf(fact_122_bind__split__asm,axiom,
    ! [P: option_state > $o,M: option_val,F: val > option_state] :
      ( ( P @ ( bind_val_state @ M @ F ) )
      = ( ~ ( ( ( M = none_val )
              & ~ ( P @ none_state ) )
            | ? [X4: val] :
                ( ( M
                  = ( some_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_123_bind__split__asm,axiom,
    ! [P: option_val > $o,M: option_val,F: val > option_val] :
      ( ( P @ ( bind_val_val @ M @ F ) )
      = ( ~ ( ( ( M = none_val )
              & ~ ( P @ none_val ) )
            | ? [X4: val] :
                ( ( M
                  = ( some_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_124_bind__split__asm,axiom,
    ! [P: option_state > $o,M: option_state,F: state > option_state] :
      ( ( P @ ( bind_state_state @ M @ F ) )
      = ( ~ ( ( ( M = none_state )
              & ~ ( P @ none_state ) )
            | ? [X4: state] :
                ( ( M
                  = ( some_state @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_125_bind__split__asm,axiom,
    ! [P: option_val > $o,M: option_state,F: state > option_val] :
      ( ( P @ ( bind_state_val @ M @ F ) )
      = ( ~ ( ( ( M = none_state )
              & ~ ( P @ none_val ) )
            | ? [X4: state] :
                ( ( M
                  = ( some_state @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_126_bind__split__asm,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option_val,F: val > option5747939881698552298on_val] :
      ( ( P @ ( bind_v3756559123625202269on_val @ M @ F ) )
      = ( ~ ( ( ( M = none_val )
              & ~ ( P @ none_P1334921381875262201on_val ) )
            | ? [X4: val] :
                ( ( M
                  = ( some_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_127_bind__split__asm,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option_state,F: state > option5747939881698552298on_val] :
      ( ( P @ ( bind_s7388421589535509396on_val @ M @ F ) )
      = ( ~ ( ( ( M = none_state )
              & ~ ( P @ none_P1334921381875262201on_val ) )
            | ? [X4: state] :
                ( ( M
                  = ( some_state @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_128_bind__split__asm,axiom,
    ! [P: option_state > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_state] :
      ( ( P @ ( bind_P6102080752330912020_state @ M @ F ) )
      = ( ~ ( ( ( M = none_P1334921381875262201on_val )
              & ~ ( P @ none_state ) )
            | ? [X4: produc1457211279475724562t_char > option_val] :
                ( ( M
                  = ( some_P7669353234731512949on_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_129_bind__split__asm,axiom,
    ! [P: option_val > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_val] :
      ( ( P @ ( bind_P5848121846087789735al_val @ M @ F ) )
      = ( ~ ( ( ( M = none_P1334921381875262201on_val )
              & ~ ( P @ none_val ) )
            | ? [X4: produc1457211279475724562t_char > option_val] :
                ( ( M
                  = ( some_P7669353234731512949on_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_130_bind__split__asm,axiom,
    ! [P: option5747939881698552298on_val > $o,M: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val] :
      ( ( P @ ( bind_P4424090778364213876on_val @ M @ F ) )
      = ( ~ ( ( ( M = none_P1334921381875262201on_val )
              & ~ ( P @ none_P1334921381875262201on_val ) )
            | ? [X4: produc1457211279475724562t_char > option_val] :
                ( ( M
                  = ( some_P7669353234731512949on_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_131_bind__split__asm,axiom,
    ! [P: option8887860577033306220on_val > $o,M: option_val,F: val > option8887860577033306220on_val] :
      ( ( P @ ( bind_v217880529008409823on_val @ M @ F ) )
      = ( ~ ( ( ( M = none_val )
              & ~ ( P @ none_P8728355543607141243on_val ) )
            | ? [X4: val] :
                ( ( M
                  = ( some_val @ X4 ) )
                & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).

% bind_split_asm
thf(fact_132_map__add__assoc,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val,M3: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ M1 @ ( map_ad2908576761495157028ar_val @ M2 @ M3 ) )
      = ( map_ad2908576761495157028ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) @ M3 ) ) ).

% map_add_assoc
thf(fact_133_map__add__find__right,axiom,
    ! [N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,Xx: val,M: produc1457211279475724562t_char > option_val] :
      ( ( ( N @ K )
        = ( some_val @ Xx ) )
     => ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ Xx ) ) ) ).

% map_add_find_right
thf(fact_134_map__add__eq__empty__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( ( map_ad2908576761495157028ar_val @ F @ G )
        = ( ^ [X4: produc1457211279475724562t_char] : none_val ) )
      = ( ( F
          = ( ^ [X4: produc1457211279475724562t_char] : none_val ) )
        & ( G
          = ( ^ [X4: produc1457211279475724562t_char] : none_val ) ) ) ) ).

% map_add_eq_empty_iff
thf(fact_135_map__add__None,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = none_val )
      = ( ( ( N @ K )
          = none_val )
        & ( ( M @ K )
          = none_val ) ) ) ).

% map_add_None
thf(fact_136_bind__runit,axiom,
    ! [X: option8887860577033306220on_val] :
      ( ( bind_P2485767298420691192on_val @ X @ some_P2581650809551911671on_val )
      = X ) ).

% bind_runit
thf(fact_137_bind__runit,axiom,
    ! [X: option5747939881698552298on_val] :
      ( ( bind_P4424090778364213876on_val @ X @ some_P7669353234731512949on_val )
      = X ) ).

% bind_runit
thf(fact_138_bind__runit,axiom,
    ! [X: option_val] :
      ( ( bind_val_val @ X @ some_val )
      = X ) ).

% bind_runit
thf(fact_139_bind__runit,axiom,
    ! [X: option_state] :
      ( ( bind_state_state @ X @ some_state )
      = X ) ).

% bind_runit
thf(fact_140_bind__option__cong__code,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_val] :
      ( ( X = Y3 )
     => ( ( bind_state_val @ X @ F )
        = ( bind_state_val @ Y3 @ F ) ) ) ).

% bind_option_cong_code
thf(fact_141_bind__option__cong__code,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_state] :
      ( ( X = Y3 )
     => ( ( bind_state_state @ X @ F )
        = ( bind_state_state @ Y3 @ F ) ) ) ).

% bind_option_cong_code
thf(fact_142_bind__option__cong__code,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_val] :
      ( ( X = Y3 )
     => ( ( bind_val_val @ X @ F )
        = ( bind_val_val @ Y3 @ F ) ) ) ).

% bind_option_cong_code
thf(fact_143_bind__option__cong__code,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_state] :
      ( ( X = Y3 )
     => ( ( bind_val_state @ X @ F )
        = ( bind_val_state @ Y3 @ F ) ) ) ).

% bind_option_cong_code
thf(fact_144_bind__eq__None__conv,axiom,
    ! [A2: option_state,F: state > option_state] :
      ( ( ( bind_state_state @ A2 @ F )
        = none_state )
      = ( ( A2 = none_state )
        | ( ( F @ ( the_state @ A2 ) )
          = none_state ) ) ) ).

% bind_eq_None_conv
thf(fact_145_bind__eq__None__conv,axiom,
    ! [A2: option_val,F: val > option_state] :
      ( ( ( bind_val_state @ A2 @ F )
        = none_state )
      = ( ( A2 = none_val )
        | ( ( F @ ( the_val @ A2 ) )
          = none_state ) ) ) ).

% bind_eq_None_conv
thf(fact_146_bind__eq__None__conv,axiom,
    ! [A2: option_state,F: state > option_val] :
      ( ( ( bind_state_val @ A2 @ F )
        = none_val )
      = ( ( A2 = none_state )
        | ( ( F @ ( the_state @ A2 ) )
          = none_val ) ) ) ).

% bind_eq_None_conv
thf(fact_147_bind__eq__None__conv,axiom,
    ! [A2: option_val,F: val > option_val] :
      ( ( ( bind_val_val @ A2 @ F )
        = none_val )
      = ( ( A2 = none_val )
        | ( ( F @ ( the_val @ A2 ) )
          = none_val ) ) ) ).

% bind_eq_None_conv
thf(fact_148_bind__eq__None__conv,axiom,
    ! [A2: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_state] :
      ( ( ( bind_P6102080752330912020_state @ A2 @ F )
        = none_state )
      = ( ( A2 = none_P1334921381875262201on_val )
        | ( ( F @ ( the_Pr646328391962797958on_val @ A2 ) )
          = none_state ) ) ) ).

% bind_eq_None_conv
thf(fact_149_bind__eq__None__conv,axiom,
    ! [A2: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option_val] :
      ( ( ( bind_P5848121846087789735al_val @ A2 @ F )
        = none_val )
      = ( ( A2 = none_P1334921381875262201on_val )
        | ( ( F @ ( the_Pr646328391962797958on_val @ A2 ) )
          = none_val ) ) ) ).

% bind_eq_None_conv
thf(fact_150_bind__eq__None__conv,axiom,
    ! [A2: option_state,F: state > option5747939881698552298on_val] :
      ( ( ( bind_s7388421589535509396on_val @ A2 @ F )
        = none_P1334921381875262201on_val )
      = ( ( A2 = none_state )
        | ( ( F @ ( the_state @ A2 ) )
          = none_P1334921381875262201on_val ) ) ) ).

% bind_eq_None_conv
thf(fact_151_bind__eq__None__conv,axiom,
    ! [A2: option_val,F: val > option5747939881698552298on_val] :
      ( ( ( bind_v3756559123625202269on_val @ A2 @ F )
        = none_P1334921381875262201on_val )
      = ( ( A2 = none_val )
        | ( ( F @ ( the_val @ A2 ) )
          = none_P1334921381875262201on_val ) ) ) ).

% bind_eq_None_conv
thf(fact_152_bind__eq__None__conv,axiom,
    ! [A2: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val] :
      ( ( ( bind_P4424090778364213876on_val @ A2 @ F )
        = none_P1334921381875262201on_val )
      = ( ( A2 = none_P1334921381875262201on_val )
        | ( ( F @ ( the_Pr646328391962797958on_val @ A2 ) )
          = none_P1334921381875262201on_val ) ) ) ).

% bind_eq_None_conv
thf(fact_153_bind__eq__None__conv,axiom,
    ! [A2: option8887860577033306220on_val,F: produc9003781588162623004on_val > option_state] :
      ( ( ( bind_P2178757275261240214_state @ A2 @ F )
        = none_state )
      = ( ( A2 = none_P8728355543607141243on_val )
        | ( ( F @ ( the_Pr3639693038709580936on_val @ A2 ) )
          = none_state ) ) ) ).

% bind_eq_None_conv
thf(fact_154_option_Osel,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ( the_Pr3639693038709580936on_val @ ( some_P2581650809551911671on_val @ X2 ) )
      = X2 ) ).

% option.sel
thf(fact_155_option_Osel,axiom,
    ! [X2: produc1457211279475724562t_char > option_val] :
      ( ( the_Pr646328391962797958on_val @ ( some_P7669353234731512949on_val @ X2 ) )
      = X2 ) ).

% option.sel
thf(fact_156_option_Osel,axiom,
    ! [X2: val] :
      ( ( the_val @ ( some_val @ X2 ) )
      = X2 ) ).

% option.sel
thf(fact_157_option_Osel,axiom,
    ! [X2: state] :
      ( ( the_state @ ( some_state @ X2 ) )
      = X2 ) ).

% option.sel
thf(fact_158_option_Oexpand,axiom,
    ! [Option: option8887860577033306220on_val,Option2: option8887860577033306220on_val] :
      ( ( ( Option = none_P8728355543607141243on_val )
        = ( Option2 = none_P8728355543607141243on_val ) )
     => ( ( ( Option != none_P8728355543607141243on_val )
         => ( ( Option2 != none_P8728355543607141243on_val )
           => ( ( the_Pr3639693038709580936on_val @ Option )
              = ( the_Pr3639693038709580936on_val @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
thf(fact_159_option_Oexpand,axiom,
    ! [Option: option5747939881698552298on_val,Option2: option5747939881698552298on_val] :
      ( ( ( Option = none_P1334921381875262201on_val )
        = ( Option2 = none_P1334921381875262201on_val ) )
     => ( ( ( Option != none_P1334921381875262201on_val )
         => ( ( Option2 != none_P1334921381875262201on_val )
           => ( ( the_Pr646328391962797958on_val @ Option )
              = ( the_Pr646328391962797958on_val @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
thf(fact_160_option_Oexpand,axiom,
    ! [Option: option_state,Option2: option_state] :
      ( ( ( Option = none_state )
        = ( Option2 = none_state ) )
     => ( ( ( Option != none_state )
         => ( ( Option2 != none_state )
           => ( ( the_state @ Option )
              = ( the_state @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
thf(fact_161_option_Oexpand,axiom,
    ! [Option: option_val,Option2: option_val] :
      ( ( ( Option = none_val )
        = ( Option2 = none_val ) )
     => ( ( ( Option != none_val )
         => ( ( Option2 != none_val )
           => ( ( the_val @ Option )
              = ( the_val @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
thf(fact_162_bind_Obind__lunit,axiom,
    ! [X: val,F: val > option_val] :
      ( ( bind_val_val @ ( some_val @ X ) @ F )
      = ( F @ X ) ) ).

% bind.bind_lunit
thf(fact_163_bind_Obind__lunit,axiom,
    ! [X: val,F: val > option_state] :
      ( ( bind_val_state @ ( some_val @ X ) @ F )
      = ( F @ X ) ) ).

% bind.bind_lunit
thf(fact_164_bind_Obind__lunit,axiom,
    ! [X: state,F: state > option_val] :
      ( ( bind_state_val @ ( some_state @ X ) @ F )
      = ( F @ X ) ) ).

% bind.bind_lunit
thf(fact_165_bind_Obind__lunit,axiom,
    ! [X: state,F: state > option_state] :
      ( ( bind_state_state @ ( some_state @ X ) @ F )
      = ( F @ X ) ) ).

% bind.bind_lunit
thf(fact_166_Option_Obind__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_val,G: val > option_val] :
      ( ( X = Y3 )
     => ( ! [A: val] :
            ( ( Y3
              = ( some_val @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( bind_val_val @ X @ F )
          = ( bind_val_val @ Y3 @ G ) ) ) ) ).

% Option.bind_cong
thf(fact_167_Option_Obind__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_state,G: val > option_state] :
      ( ( X = Y3 )
     => ( ! [A: val] :
            ( ( Y3
              = ( some_val @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( bind_val_state @ X @ F )
          = ( bind_val_state @ Y3 @ G ) ) ) ) ).

% Option.bind_cong
thf(fact_168_Option_Obind__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_val,G: state > option_val] :
      ( ( X = Y3 )
     => ( ! [A: state] :
            ( ( Y3
              = ( some_state @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( bind_state_val @ X @ F )
          = ( bind_state_val @ Y3 @ G ) ) ) ) ).

% Option.bind_cong
thf(fact_169_Option_Obind__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_state,G: state > option_state] :
      ( ( X = Y3 )
     => ( ! [A: state] :
            ( ( Y3
              = ( some_state @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( bind_state_state @ X @ F )
          = ( bind_state_state @ Y3 @ G ) ) ) ) ).

% Option.bind_cong
thf(fact_170_bind__eq__Some__conv,axiom,
    ! [F: option_val,G: val > option_val,X: val] :
      ( ( ( bind_val_val @ F @ G )
        = ( some_val @ X ) )
      = ( ? [Y: val] :
            ( ( F
              = ( some_val @ Y ) )
            & ( ( G @ Y )
              = ( some_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_171_bind__eq__Some__conv,axiom,
    ! [F: option_state,G: state > option_val,X: val] :
      ( ( ( bind_state_val @ F @ G )
        = ( some_val @ X ) )
      = ( ? [Y: state] :
            ( ( F
              = ( some_state @ Y ) )
            & ( ( G @ Y )
              = ( some_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_172_bind__eq__Some__conv,axiom,
    ! [F: option_val,G: val > option_state,X: state] :
      ( ( ( bind_val_state @ F @ G )
        = ( some_state @ X ) )
      = ( ? [Y: val] :
            ( ( F
              = ( some_val @ Y ) )
            & ( ( G @ Y )
              = ( some_state @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_173_bind__eq__Some__conv,axiom,
    ! [F: option_state,G: state > option_state,X: state] :
      ( ( ( bind_state_state @ F @ G )
        = ( some_state @ X ) )
      = ( ? [Y: state] :
            ( ( F
              = ( some_state @ Y ) )
            & ( ( G @ Y )
              = ( some_state @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_174_bind__eq__Some__conv,axiom,
    ! [F: option5747939881698552298on_val,G: ( produc1457211279475724562t_char > option_val ) > option_val,X: val] :
      ( ( ( bind_P5848121846087789735al_val @ F @ G )
        = ( some_val @ X ) )
      = ( ? [Y: produc1457211279475724562t_char > option_val] :
            ( ( F
              = ( some_P7669353234731512949on_val @ Y ) )
            & ( ( G @ Y )
              = ( some_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_175_bind__eq__Some__conv,axiom,
    ! [F: option5747939881698552298on_val,G: ( produc1457211279475724562t_char > option_val ) > option_state,X: state] :
      ( ( ( bind_P6102080752330912020_state @ F @ G )
        = ( some_state @ X ) )
      = ( ? [Y: produc1457211279475724562t_char > option_val] :
            ( ( F
              = ( some_P7669353234731512949on_val @ Y ) )
            & ( ( G @ Y )
              = ( some_state @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_176_bind__eq__Some__conv,axiom,
    ! [F: option_val,G: val > option5747939881698552298on_val,X: produc1457211279475724562t_char > option_val] :
      ( ( ( bind_v3756559123625202269on_val @ F @ G )
        = ( some_P7669353234731512949on_val @ X ) )
      = ( ? [Y: val] :
            ( ( F
              = ( some_val @ Y ) )
            & ( ( G @ Y )
              = ( some_P7669353234731512949on_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_177_bind__eq__Some__conv,axiom,
    ! [F: option_state,G: state > option5747939881698552298on_val,X: produc1457211279475724562t_char > option_val] :
      ( ( ( bind_s7388421589535509396on_val @ F @ G )
        = ( some_P7669353234731512949on_val @ X ) )
      = ( ? [Y: state] :
            ( ( F
              = ( some_state @ Y ) )
            & ( ( G @ Y )
              = ( some_P7669353234731512949on_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_178_bind__eq__Some__conv,axiom,
    ! [F: option5747939881698552298on_val,G: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > option_val] :
      ( ( ( bind_P4424090778364213876on_val @ F @ G )
        = ( some_P7669353234731512949on_val @ X ) )
      = ( ? [Y: produc1457211279475724562t_char > option_val] :
            ( ( F
              = ( some_P7669353234731512949on_val @ Y ) )
            & ( ( G @ Y )
              = ( some_P7669353234731512949on_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_179_bind__eq__Some__conv,axiom,
    ! [F: option8887860577033306220on_val,G: produc9003781588162623004on_val > option_val,X: val] :
      ( ( ( bind_P8603646205577311397al_val @ F @ G )
        = ( some_val @ X ) )
      = ( ? [Y: produc9003781588162623004on_val] :
            ( ( F
              = ( some_P2581650809551911671on_val @ Y ) )
            & ( ( G @ Y )
              = ( some_val @ X ) ) ) ) ) ).

% bind_eq_Some_conv
thf(fact_180_bind_Obind__lzero,axiom,
    ! [F: state > option_state] :
      ( ( bind_state_state @ none_state @ F )
      = none_state ) ).

% bind.bind_lzero
thf(fact_181_bind_Obind__lzero,axiom,
    ! [F: state > option_val] :
      ( ( bind_state_val @ none_state @ F )
      = none_val ) ).

% bind.bind_lzero
thf(fact_182_bind_Obind__lzero,axiom,
    ! [F: val > option_state] :
      ( ( bind_val_state @ none_val @ F )
      = none_state ) ).

% bind.bind_lzero
thf(fact_183_bind_Obind__lzero,axiom,
    ! [F: val > option_val] :
      ( ( bind_val_val @ none_val @ F )
      = none_val ) ).

% bind.bind_lzero
thf(fact_184_bind_Obind__lzero,axiom,
    ! [F: state > option5747939881698552298on_val] :
      ( ( bind_s7388421589535509396on_val @ none_state @ F )
      = none_P1334921381875262201on_val ) ).

% bind.bind_lzero
thf(fact_185_bind_Obind__lzero,axiom,
    ! [F: val > option5747939881698552298on_val] :
      ( ( bind_v3756559123625202269on_val @ none_val @ F )
      = none_P1334921381875262201on_val ) ).

% bind.bind_lzero
thf(fact_186_bind_Obind__lzero,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > option_state] :
      ( ( bind_P6102080752330912020_state @ none_P1334921381875262201on_val @ F )
      = none_state ) ).

% bind.bind_lzero
thf(fact_187_bind_Obind__lzero,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > option_val] :
      ( ( bind_P5848121846087789735al_val @ none_P1334921381875262201on_val @ F )
      = none_val ) ).

% bind.bind_lzero
thf(fact_188_bind_Obind__lzero,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > option5747939881698552298on_val] :
      ( ( bind_P4424090778364213876on_val @ none_P1334921381875262201on_val @ F )
      = none_P1334921381875262201on_val ) ).

% bind.bind_lzero
thf(fact_189_bind_Obind__lzero,axiom,
    ! [F: state > option8887860577033306220on_val] :
      ( ( bind_s5745438296695018390on_val @ none_state @ F )
      = none_P8728355543607141243on_val ) ).

% bind.bind_lzero
thf(fact_190_larger__heaps__sum__ineq,axiom,
    ! [A5: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char > option_val,B4: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A5 @ A2 )
     => ( ( larger1532547405891354081ar_val @ B4 @ B2 )
       => ( ( compatible_heaps @ A5 @ B4 )
         => ( larger1532547405891354081ar_val @ ( map_ad2908576761495157028ar_val @ A5 @ B4 ) @ ( map_ad2908576761495157028ar_val @ A2 @ B2 ) ) ) ) ) ).

% larger_heaps_sum_ineq
thf(fact_191_compatible__heaps__comm,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A2 @ B2 )
     => ( ( map_ad2908576761495157028ar_val @ A2 @ B2 )
        = ( map_ad2908576761495157028ar_val @ B2 @ A2 ) ) ) ).

% compatible_heaps_comm
thf(fact_192_compatible__heaps__sum,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A2 @ B2 )
     => ( ( compatible_heaps @ A2 @ C )
       => ( compatible_heaps @ A2 @ ( map_ad2908576761495157028ar_val @ B2 @ C ) ) ) ) ).

% compatible_heaps_sum
thf(fact_193_larger__heap__plus,axiom,
    ! [A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A2 @ B2 )
     => ( ( larger1532547405891354081ar_val @ A2 @ C )
       => ( larger1532547405891354081ar_val @ A2 @ ( map_ad2908576761495157028ar_val @ B2 @ C ) ) ) ) ).

% larger_heap_plus
thf(fact_194_map__add__Some__iff,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ X ) )
      = ( ( ( N @ K )
          = ( some_val @ X ) )
        | ( ( ( N @ K )
            = none_val )
          & ( ( M @ K )
            = ( some_val @ X ) ) ) ) ) ).

% map_add_Some_iff
thf(fact_195_map__add__SomeD,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ X ) )
     => ( ( ( N @ K )
          = ( some_val @ X ) )
        | ( ( ( N @ K )
            = none_val )
          & ( ( M @ K )
            = ( some_val @ X ) ) ) ) ) ).

% map_add_SomeD
thf(fact_196_option_Oexhaust__sel,axiom,
    ! [Option: option8887860577033306220on_val] :
      ( ( Option != none_P8728355543607141243on_val )
     => ( Option
        = ( some_P2581650809551911671on_val @ ( the_Pr3639693038709580936on_val @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_197_option_Oexhaust__sel,axiom,
    ! [Option: option5747939881698552298on_val] :
      ( ( Option != none_P1334921381875262201on_val )
     => ( Option
        = ( some_P7669353234731512949on_val @ ( the_Pr646328391962797958on_val @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_198_option_Oexhaust__sel,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( Option
        = ( some_val @ ( the_val @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_199_option_Oexhaust__sel,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( Option
        = ( some_state @ ( the_state @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_200_valid__heapI,axiom,
    ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ! [Hl: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi @ Hl ) )
         => ( ( H @ Hl )
           != none_val ) )
     => ( valid_heap @ Pi @ H ) ) ).

% valid_heapI
thf(fact_201_valid__heap__def,axiom,
    ( valid_heap
    = ( ^ [Pi2: produc1457211279475724562t_char > prat,H4: produc1457211279475724562t_char > option_val] :
        ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi2 @ Hl2 ) )
         => ( ( H4 @ Hl2 )
           != none_val ) ) ) ) ).

% valid_heap_def
thf(fact_202_valid__mask__full__mask,axiom,
    valid_mask @ full_mask ).

% valid_mask_full_mask
thf(fact_203_add__masks__equiv__valid__null,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat] :
      ( ( valid_null @ ( add_ma6586698345353345811t_char @ A2 @ B2 ) )
      = ( ( valid_null @ A2 )
        & ( valid_null @ B2 ) ) ) ).

% add_masks_equiv_valid_null
thf(fact_204_is__none__bind,axiom,
    ! [F: option_state,G: state > option_state] :
      ( ( is_none_state @ ( bind_state_state @ F @ G ) )
      = ( ( is_none_state @ F )
        | ( is_none_state @ ( G @ ( the_state @ F ) ) ) ) ) ).

% is_none_bind
thf(fact_205_is__none__bind,axiom,
    ! [F: option_state,G: state > option_val] :
      ( ( is_none_val @ ( bind_state_val @ F @ G ) )
      = ( ( is_none_state @ F )
        | ( is_none_val @ ( G @ ( the_state @ F ) ) ) ) ) ).

% is_none_bind
thf(fact_206_is__none__bind,axiom,
    ! [F: option_val,G: val > option_state] :
      ( ( is_none_state @ ( bind_val_state @ F @ G ) )
      = ( ( is_none_val @ F )
        | ( is_none_state @ ( G @ ( the_val @ F ) ) ) ) ) ).

% is_none_bind
thf(fact_207_is__none__bind,axiom,
    ! [F: option_val,G: val > option_val] :
      ( ( is_none_val @ ( bind_val_val @ F @ G ) )
      = ( ( is_none_val @ F )
        | ( is_none_val @ ( G @ ( the_val @ F ) ) ) ) ) ).

% is_none_bind
thf(fact_208_option_Oset__sel,axiom,
    ! [A2: option_option_state] :
      ( ( A2 != none_option_state )
     => ( member_option_state @ ( the_option_state @ A2 ) @ ( set_op5162993263733338108_state @ A2 ) ) ) ).

% option.set_sel
thf(fact_209_option_Oset__sel,axiom,
    ! [A2: option_option_val] :
      ( ( A2 != none_option_val )
     => ( member_option_val @ ( the_option_val @ A2 ) @ ( set_op911010586042427349on_val @ A2 ) ) ) ).

% option.set_sel
thf(fact_210_option_Oset__sel,axiom,
    ! [A2: option3572569098863364761r_prat] :
      ( ( A2 != none_P6742040017396684084r_prat )
     => ( member2336342582916103932r_prat @ ( the_Pr3206600365949932263r_prat @ A2 ) @ ( set_op923924987228895969r_prat @ A2 ) ) ) ).

% option.set_sel
thf(fact_211_option_Oset__sel,axiom,
    ! [A2: option8887860577033306220on_val] :
      ( ( A2 != none_P8728355543607141243on_val )
     => ( member2879030624002546611on_val @ ( the_Pr3639693038709580936on_val @ A2 ) @ ( set_op9004752959087400718on_val @ A2 ) ) ) ).

% option.set_sel
thf(fact_212_option_Oset__sel,axiom,
    ! [A2: option5747939881698552298on_val] :
      ( ( A2 != none_P1334921381875262201on_val )
     => ( member1577473829074448177on_val @ ( the_Pr646328391962797958on_val @ A2 ) @ ( set_op1770538635792728844on_val @ A2 ) ) ) ).

% option.set_sel
thf(fact_213_option_Oset__sel,axiom,
    ! [A2: option_state] :
      ( ( A2 != none_state )
     => ( member_state @ ( the_state @ A2 ) @ ( set_option_state2 @ A2 ) ) ) ).

% option.set_sel
thf(fact_214_option_Oset__sel,axiom,
    ! [A2: option_val] :
      ( ( A2 != none_val )
     => ( member_val @ ( the_val @ A2 ) @ ( set_option_val2 @ A2 ) ) ) ).

% option.set_sel
thf(fact_215_minus__empty,axiom,
    ! [Pi: produc1457211279475724562t_char > prat] :
      ( Pi
      = ( add_ma6586698345353345811t_char @ Pi @ empty_3446695950879338768t_char ) ) ).

% minus_empty
thf(fact_216_elem__set,axiom,
    ! [X: option_state,Xo: option_option_state] :
      ( ( member_option_state @ X @ ( set_op5162993263733338108_state @ Xo ) )
      = ( Xo
        = ( some_option_state @ X ) ) ) ).

% elem_set
thf(fact_217_elem__set,axiom,
    ! [X: option_val,Xo: option_option_val] :
      ( ( member_option_val @ X @ ( set_op911010586042427349on_val @ Xo ) )
      = ( Xo
        = ( some_option_val @ X ) ) ) ).

% elem_set
thf(fact_218_elem__set,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xo: option3572569098863364761r_prat] :
      ( ( member2336342582916103932r_prat @ X @ ( set_op923924987228895969r_prat @ Xo ) )
      = ( Xo
        = ( some_P8530153984677361336r_prat @ X ) ) ) ).

% elem_set
thf(fact_219_elem__set,axiom,
    ! [X: produc9003781588162623004on_val,Xo: option8887860577033306220on_val] :
      ( ( member2879030624002546611on_val @ X @ ( set_op9004752959087400718on_val @ Xo ) )
      = ( Xo
        = ( some_P2581650809551911671on_val @ X ) ) ) ).

% elem_set
thf(fact_220_elem__set,axiom,
    ! [X: produc1457211279475724562t_char > option_val,Xo: option5747939881698552298on_val] :
      ( ( member1577473829074448177on_val @ X @ ( set_op1770538635792728844on_val @ Xo ) )
      = ( Xo
        = ( some_P7669353234731512949on_val @ X ) ) ) ).

% elem_set
thf(fact_221_elem__set,axiom,
    ! [X: val,Xo: option_val] :
      ( ( member_val @ X @ ( set_option_val2 @ Xo ) )
      = ( Xo
        = ( some_val @ X ) ) ) ).

% elem_set
thf(fact_222_elem__set,axiom,
    ! [X: state,Xo: option_state] :
      ( ( member_state @ X @ ( set_option_state2 @ Xo ) )
      = ( Xo
        = ( some_state @ X ) ) ) ).

% elem_set
thf(fact_223_is__none__code_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ~ ( is_non3468859156093823296on_val @ ( some_P2581650809551911671on_val @ X ) ) ).

% is_none_code(2)
thf(fact_224_is__none__code_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > option_val] :
      ~ ( is_non6205214127102033982on_val @ ( some_P7669353234731512949on_val @ X ) ) ).

% is_none_code(2)
thf(fact_225_is__none__code_I2_J,axiom,
    ! [X: val] :
      ~ ( is_none_val @ ( some_val @ X ) ) ).

% is_none_code(2)
thf(fact_226_is__none__code_I2_J,axiom,
    ! [X: state] :
      ~ ( is_none_state @ ( some_state @ X ) ) ).

% is_none_code(2)
thf(fact_227_is__none__code_I1_J,axiom,
    is_non3468859156093823296on_val @ none_P8728355543607141243on_val ).

% is_none_code(1)
thf(fact_228_is__none__code_I1_J,axiom,
    is_non6205214127102033982on_val @ none_P1334921381875262201on_val ).

% is_none_code(1)
thf(fact_229_is__none__code_I1_J,axiom,
    is_none_state @ none_state ).

% is_none_code(1)
thf(fact_230_is__none__code_I1_J,axiom,
    is_none_val @ none_val ).

% is_none_code(1)
thf(fact_231_ospec,axiom,
    ! [A4: option8887860577033306220on_val,P: produc9003781588162623004on_val > $o,X: produc9003781588162623004on_val] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X3 @ ( set_op9004752959087400718on_val @ A4 ) )
         => ( P @ X3 ) )
     => ( ( A4
          = ( some_P2581650809551911671on_val @ X ) )
       => ( P @ X ) ) ) ).

% ospec
thf(fact_232_ospec,axiom,
    ! [A4: option5747939881698552298on_val,P: ( produc1457211279475724562t_char > option_val ) > $o,X: produc1457211279475724562t_char > option_val] :
      ( ! [X3: produc1457211279475724562t_char > option_val] :
          ( ( member1577473829074448177on_val @ X3 @ ( set_op1770538635792728844on_val @ A4 ) )
         => ( P @ X3 ) )
     => ( ( A4
          = ( some_P7669353234731512949on_val @ X ) )
       => ( P @ X ) ) ) ).

% ospec
thf(fact_233_ospec,axiom,
    ! [A4: option_val,P: val > $o,X: val] :
      ( ! [X3: val] :
          ( ( member_val @ X3 @ ( set_option_val2 @ A4 ) )
         => ( P @ X3 ) )
     => ( ( A4
          = ( some_val @ X ) )
       => ( P @ X ) ) ) ).

% ospec
thf(fact_234_ospec,axiom,
    ! [A4: option_state,P: state > $o,X: state] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ ( set_option_state2 @ A4 ) )
         => ( P @ X3 ) )
     => ( ( A4
          = ( some_state @ X ) )
       => ( P @ X ) ) ) ).

% ospec
thf(fact_235_option_Oset__intros,axiom,
    ! [X2: option_state] : ( member_option_state @ X2 @ ( set_op5162993263733338108_state @ ( some_option_state @ X2 ) ) ) ).

% option.set_intros
thf(fact_236_option_Oset__intros,axiom,
    ! [X2: option_val] : ( member_option_val @ X2 @ ( set_op911010586042427349on_val @ ( some_option_val @ X2 ) ) ) ).

% option.set_intros
thf(fact_237_option_Oset__intros,axiom,
    ! [X2: produc1457211279475724562t_char > prat] : ( member2336342582916103932r_prat @ X2 @ ( set_op923924987228895969r_prat @ ( some_P8530153984677361336r_prat @ X2 ) ) ) ).

% option.set_intros
thf(fact_238_option_Oset__intros,axiom,
    ! [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ ( set_op9004752959087400718on_val @ ( some_P2581650809551911671on_val @ X2 ) ) ) ).

% option.set_intros
thf(fact_239_option_Oset__intros,axiom,
    ! [X2: produc1457211279475724562t_char > option_val] : ( member1577473829074448177on_val @ X2 @ ( set_op1770538635792728844on_val @ ( some_P7669353234731512949on_val @ X2 ) ) ) ).

% option.set_intros
thf(fact_240_option_Oset__intros,axiom,
    ! [X2: val] : ( member_val @ X2 @ ( set_option_val2 @ ( some_val @ X2 ) ) ) ).

% option.set_intros
thf(fact_241_option_Oset__intros,axiom,
    ! [X2: state] : ( member_state @ X2 @ ( set_option_state2 @ ( some_state @ X2 ) ) ) ).

% option.set_intros
thf(fact_242_option_Oset__cases,axiom,
    ! [E: option_state,A2: option_option_state] :
      ( ( member_option_state @ E @ ( set_op5162993263733338108_state @ A2 ) )
     => ( A2
        = ( some_option_state @ E ) ) ) ).

% option.set_cases
thf(fact_243_option_Oset__cases,axiom,
    ! [E: option_val,A2: option_option_val] :
      ( ( member_option_val @ E @ ( set_op911010586042427349on_val @ A2 ) )
     => ( A2
        = ( some_option_val @ E ) ) ) ).

% option.set_cases
thf(fact_244_option_Oset__cases,axiom,
    ! [E: produc1457211279475724562t_char > prat,A2: option3572569098863364761r_prat] :
      ( ( member2336342582916103932r_prat @ E @ ( set_op923924987228895969r_prat @ A2 ) )
     => ( A2
        = ( some_P8530153984677361336r_prat @ E ) ) ) ).

% option.set_cases
thf(fact_245_option_Oset__cases,axiom,
    ! [E: produc9003781588162623004on_val,A2: option8887860577033306220on_val] :
      ( ( member2879030624002546611on_val @ E @ ( set_op9004752959087400718on_val @ A2 ) )
     => ( A2
        = ( some_P2581650809551911671on_val @ E ) ) ) ).

% option.set_cases
thf(fact_246_option_Oset__cases,axiom,
    ! [E: produc1457211279475724562t_char > option_val,A2: option5747939881698552298on_val] :
      ( ( member1577473829074448177on_val @ E @ ( set_op1770538635792728844on_val @ A2 ) )
     => ( A2
        = ( some_P7669353234731512949on_val @ E ) ) ) ).

% option.set_cases
thf(fact_247_option_Oset__cases,axiom,
    ! [E: val,A2: option_val] :
      ( ( member_val @ E @ ( set_option_val2 @ A2 ) )
     => ( A2
        = ( some_val @ E ) ) ) ).

% option.set_cases
thf(fact_248_option_Oset__cases,axiom,
    ! [E: state,A2: option_state] :
      ( ( member_state @ E @ ( set_option_state2 @ A2 ) )
     => ( A2
        = ( some_state @ E ) ) ) ).

% option.set_cases
thf(fact_249_bind__option__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_val,G: val > option_val] :
      ( ( X = Y3 )
     => ( ! [Z: val] :
            ( ( member_val @ Z @ ( set_option_val2 @ Y3 ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( bind_val_val @ X @ F )
          = ( bind_val_val @ Y3 @ G ) ) ) ) ).

% bind_option_cong
thf(fact_250_bind__option__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > option_state,G: val > option_state] :
      ( ( X = Y3 )
     => ( ! [Z: val] :
            ( ( member_val @ Z @ ( set_option_val2 @ Y3 ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( bind_val_state @ X @ F )
          = ( bind_val_state @ Y3 @ G ) ) ) ) ).

% bind_option_cong
thf(fact_251_bind__option__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_val,G: state > option_val] :
      ( ( X = Y3 )
     => ( ! [Z: state] :
            ( ( member_state @ Z @ ( set_option_state2 @ Y3 ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( bind_state_val @ X @ F )
          = ( bind_state_val @ Y3 @ G ) ) ) ) ).

% bind_option_cong
thf(fact_252_bind__option__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > option_state,G: state > option_state] :
      ( ( X = Y3 )
     => ( ! [Z: state] :
            ( ( member_state @ Z @ ( set_option_state2 @ Y3 ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( bind_state_state @ X @ F )
          = ( bind_state_state @ Y3 @ G ) ) ) ) ).

% bind_option_cong
thf(fact_253_is__none__simps_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ~ ( is_non3468859156093823296on_val @ ( some_P2581650809551911671on_val @ X ) ) ).

% is_none_simps(2)
thf(fact_254_is__none__simps_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > option_val] :
      ~ ( is_non6205214127102033982on_val @ ( some_P7669353234731512949on_val @ X ) ) ).

% is_none_simps(2)
thf(fact_255_is__none__simps_I2_J,axiom,
    ! [X: val] :
      ~ ( is_none_val @ ( some_val @ X ) ) ).

% is_none_simps(2)
thf(fact_256_is__none__simps_I2_J,axiom,
    ! [X: state] :
      ~ ( is_none_state @ ( some_state @ X ) ) ).

% is_none_simps(2)
thf(fact_257_is__none__simps_I1_J,axiom,
    is_non3468859156093823296on_val @ none_P8728355543607141243on_val ).

% is_none_simps(1)
thf(fact_258_is__none__simps_I1_J,axiom,
    is_non6205214127102033982on_val @ none_P1334921381875262201on_val ).

% is_none_simps(1)
thf(fact_259_is__none__simps_I1_J,axiom,
    is_none_state @ none_state ).

% is_none_simps(1)
thf(fact_260_is__none__simps_I1_J,axiom,
    is_none_val @ none_val ).

% is_none_simps(1)
thf(fact_261_Option_Ois__none__def,axiom,
    ( is_non3468859156093823296on_val
    = ( ^ [X4: option8887860577033306220on_val] : ( X4 = none_P8728355543607141243on_val ) ) ) ).

% Option.is_none_def
thf(fact_262_Option_Ois__none__def,axiom,
    ( is_non6205214127102033982on_val
    = ( ^ [X4: option5747939881698552298on_val] : ( X4 = none_P1334921381875262201on_val ) ) ) ).

% Option.is_none_def
thf(fact_263_Option_Ois__none__def,axiom,
    ( is_none_state
    = ( ^ [X4: option_state] : ( X4 = none_state ) ) ) ).

% Option.is_none_def
thf(fact_264_Option_Ois__none__def,axiom,
    ( is_none_val
    = ( ^ [X4: option_val] : ( X4 = none_val ) ) ) ).

% Option.is_none_def
thf(fact_265_valid__empty,axiom,
    valid_mask @ empty_3446695950879338768t_char ).

% valid_empty
thf(fact_266_valid__larger__mask,axiom,
    ( valid_mask
    = ( greate7680731506090375811t_char @ full_mask ) ) ).

% valid_larger_mask
thf(fact_267_set__empty__eq,axiom,
    ! [Xo: option5747939881698552298on_val] :
      ( ( ( set_op1770538635792728844on_val @ Xo )
        = bot_bo5671083314777306084on_val )
      = ( Xo = none_P1334921381875262201on_val ) ) ).

% set_empty_eq
thf(fact_268_set__empty__eq,axiom,
    ! [Xo: option2736423997234022232t_char] :
      ( ( ( set_op7440730737645789856t_char @ Xo )
        = bot_bo1414094081888755934t_char )
      = ( Xo = none_P5486107665612286067t_char ) ) ).

% set_empty_eq
thf(fact_269_set__empty__eq,axiom,
    ! [Xo: option8887860577033306220on_val] :
      ( ( ( set_op9004752959087400718on_val @ Xo )
        = bot_bo6722054719108133734on_val )
      = ( Xo = none_P8728355543607141243on_val ) ) ).

% set_empty_eq
thf(fact_270_set__empty__eq,axiom,
    ! [Xo: option_option_state] :
      ( ( ( set_op5162993263733338108_state @ Xo )
        = bot_bo710180891245420500_state )
      = ( Xo = none_option_state ) ) ).

% set_empty_eq
thf(fact_271_set__empty__eq,axiom,
    ! [Xo: option_option_val] :
      ( ( ( set_op911010586042427349on_val @ Xo )
        = bot_bo5906790151302476563on_val )
      = ( Xo = none_option_val ) ) ).

% set_empty_eq
thf(fact_272_set__empty__eq,axiom,
    ! [Xo: option_state] :
      ( ( ( set_option_state2 @ Xo )
        = bot_bot_set_state )
      = ( Xo = none_state ) ) ).

% set_empty_eq
thf(fact_273_set__empty__eq,axiom,
    ! [Xo: option_val] :
      ( ( ( set_option_val2 @ Xo )
        = bot_bot_set_val )
      = ( Xo = none_val ) ) ).

% set_empty_eq
thf(fact_274_map__add__upd,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( map_ad6375351378680859759on_val @ F @ ( fun_up273046073882939271on_val @ G @ X @ ( some_P2581650809551911671on_val @ Y3 ) ) )
      = ( fun_up273046073882939271on_val @ ( map_ad6375351378680859759on_val @ F @ G ) @ X @ ( some_P2581650809551911671on_val @ Y3 ) ) ) ).

% map_add_upd
thf(fact_275_map__add__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2898753242718228216on_val @ F @ ( fun_up1601731230164360576on_val @ G @ X @ ( some_P7669353234731512949on_val @ Y3 ) ) )
      = ( fun_up1601731230164360576on_val @ ( map_ad2898753242718228216on_val @ F @ G ) @ X @ ( some_P7669353234731512949on_val @ Y3 ) ) ) ).

% map_add_upd
thf(fact_276_map__add__upd,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: val] :
      ( ( map_ad2908576761495157028ar_val @ F @ ( fun_up5735975307950539954on_val @ G @ X @ ( some_val @ Y3 ) ) )
      = ( fun_up5735975307950539954on_val @ ( map_ad2908576761495157028ar_val @ F @ G ) @ X @ ( some_val @ Y3 ) ) ) ).

% map_add_upd
thf(fact_277_option_Osimps_I14_J,axiom,
    ( ( set_op1770538635792728844on_val @ none_P1334921381875262201on_val )
    = bot_bo5671083314777306084on_val ) ).

% option.simps(14)
thf(fact_278_option_Osimps_I14_J,axiom,
    ( ( set_op7440730737645789856t_char @ none_P5486107665612286067t_char )
    = bot_bo1414094081888755934t_char ) ).

% option.simps(14)
thf(fact_279_option_Osimps_I14_J,axiom,
    ( ( set_op9004752959087400718on_val @ none_P8728355543607141243on_val )
    = bot_bo6722054719108133734on_val ) ).

% option.simps(14)
thf(fact_280_option_Osimps_I14_J,axiom,
    ( ( set_op5162993263733338108_state @ none_option_state )
    = bot_bo710180891245420500_state ) ).

% option.simps(14)
thf(fact_281_option_Osimps_I14_J,axiom,
    ( ( set_op911010586042427349on_val @ none_option_val )
    = bot_bo5906790151302476563on_val ) ).

% option.simps(14)
thf(fact_282_option_Osimps_I14_J,axiom,
    ( ( set_option_state2 @ none_state )
    = bot_bot_set_state ) ).

% option.simps(14)
thf(fact_283_option_Osimps_I14_J,axiom,
    ( ( set_option_val2 @ none_val )
    = bot_bot_set_val ) ).

% option.simps(14)
thf(fact_284_combine__options__simps_I2_J,axiom,
    ! [F: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val,X: option8887860577033306220on_val] :
      ( ( combin6222804963853957469on_val @ F @ X @ none_P8728355543607141243on_val )
      = X ) ).

% combine_options_simps(2)
thf(fact_285_combine__options__simps_I2_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,X: option5747939881698552298on_val] :
      ( ( combin3271118981050854363on_val @ F @ X @ none_P1334921381875262201on_val )
      = X ) ).

% combine_options_simps(2)
thf(fact_286_combine__options__simps_I2_J,axiom,
    ! [F: state > state > state,X: option_state] :
      ( ( combin3633514924185701883_state @ F @ X @ none_state )
      = X ) ).

% combine_options_simps(2)
thf(fact_287_combine__options__simps_I2_J,axiom,
    ! [F: val > val > val,X: option_val] :
      ( ( combine_options_val @ F @ X @ none_val )
      = X ) ).

% combine_options_simps(2)
thf(fact_288_combine__options__simps_I1_J,axiom,
    ! [F: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( combin6222804963853957469on_val @ F @ none_P8728355543607141243on_val @ Y3 )
      = Y3 ) ).

% combine_options_simps(1)
thf(fact_289_combine__options__simps_I1_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,Y3: option5747939881698552298on_val] :
      ( ( combin3271118981050854363on_val @ F @ none_P1334921381875262201on_val @ Y3 )
      = Y3 ) ).

% combine_options_simps(1)
thf(fact_290_combine__options__simps_I1_J,axiom,
    ! [F: state > state > state,Y3: option_state] :
      ( ( combin3633514924185701883_state @ F @ none_state @ Y3 )
      = Y3 ) ).

% combine_options_simps(1)
thf(fact_291_combine__options__simps_I1_J,axiom,
    ! [F: val > val > val,Y3: option_val] :
      ( ( combine_options_val @ F @ none_val @ Y3 )
      = Y3 ) ).

% combine_options_simps(1)
thf(fact_292_combine__options__simps_I3_J,axiom,
    ! [F: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val,A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
      ( ( combin6222804963853957469on_val @ F @ ( some_P2581650809551911671on_val @ A2 ) @ ( some_P2581650809551911671on_val @ B2 ) )
      = ( some_P2581650809551911671on_val @ ( F @ A2 @ B2 ) ) ) ).

% combine_options_simps(3)
thf(fact_293_combine__options__simps_I3_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( combin3271118981050854363on_val @ F @ ( some_P7669353234731512949on_val @ A2 ) @ ( some_P7669353234731512949on_val @ B2 ) )
      = ( some_P7669353234731512949on_val @ ( F @ A2 @ B2 ) ) ) ).

% combine_options_simps(3)
thf(fact_294_combine__options__simps_I3_J,axiom,
    ! [F: val > val > val,A2: val,B2: val] :
      ( ( combine_options_val @ F @ ( some_val @ A2 ) @ ( some_val @ B2 ) )
      = ( some_val @ ( F @ A2 @ B2 ) ) ) ).

% combine_options_simps(3)
thf(fact_295_combine__options__simps_I3_J,axiom,
    ! [F: state > state > state,A2: state,B2: state] :
      ( ( combin3633514924185701883_state @ F @ ( some_state @ A2 ) @ ( some_state @ B2 ) )
      = ( some_state @ ( F @ A2 @ B2 ) ) ) ).

% combine_options_simps(3)
thf(fact_296_the__map__option,axiom,
    ! [X: option_state,F: state > state] :
      ( ~ ( is_none_state @ X )
     => ( ( the_state @ ( map_op2726735944305651201_state @ F @ X ) )
        = ( F @ ( the_state @ X ) ) ) ) ).

% the_map_option
thf(fact_297_the__map__option,axiom,
    ! [X: option_val,F: val > state] :
      ( ~ ( is_none_val @ X )
     => ( ( the_state @ ( map_option_val_state @ F @ X ) )
        = ( F @ ( the_val @ X ) ) ) ) ).

% the_map_option
thf(fact_298_the__map__option,axiom,
    ! [X: option_state,F: state > val] :
      ( ~ ( is_none_state @ X )
     => ( ( the_val @ ( map_option_state_val @ F @ X ) )
        = ( F @ ( the_state @ X ) ) ) ) ).

% the_map_option
thf(fact_299_the__map__option,axiom,
    ! [X: option_val,F: val > val] :
      ( ~ ( is_none_val @ X )
     => ( ( the_val @ ( map_option_val_val @ F @ X ) )
        = ( F @ ( the_val @ X ) ) ) ) ).

% the_map_option
thf(fact_300_map__option__eq__Some,axiom,
    ! [F: val > val,Xo: option_val,Y3: val] :
      ( ( ( map_option_val_val @ F @ Xo )
        = ( some_val @ Y3 ) )
      = ( ? [Z2: val] :
            ( ( Xo
              = ( some_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_301_map__option__eq__Some,axiom,
    ! [F: state > val,Xo: option_state,Y3: val] :
      ( ( ( map_option_state_val @ F @ Xo )
        = ( some_val @ Y3 ) )
      = ( ? [Z2: state] :
            ( ( Xo
              = ( some_state @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_302_map__option__eq__Some,axiom,
    ! [F: val > state,Xo: option_val,Y3: state] :
      ( ( ( map_option_val_state @ F @ Xo )
        = ( some_state @ Y3 ) )
      = ( ? [Z2: val] :
            ( ( Xo
              = ( some_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_303_map__option__eq__Some,axiom,
    ! [F: state > state,Xo: option_state,Y3: state] :
      ( ( ( map_op2726735944305651201_state @ F @ Xo )
        = ( some_state @ Y3 ) )
      = ( ? [Z2: state] :
            ( ( Xo
              = ( some_state @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_304_map__option__eq__Some,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,Xo: option5747939881698552298on_val,Y3: val] :
      ( ( ( map_op880068700720311194al_val @ F @ Xo )
        = ( some_val @ Y3 ) )
      = ( ? [Z2: produc1457211279475724562t_char > option_val] :
            ( ( Xo
              = ( some_P7669353234731512949on_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_305_map__option__eq__Some,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,Xo: option5747939881698552298on_val,Y3: state] :
      ( ( ( map_op1814185762381987425_state @ F @ Xo )
        = ( some_state @ Y3 ) )
      = ( ? [Z2: produc1457211279475724562t_char > option_val] :
            ( ( Xo
              = ( some_P7669353234731512949on_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_306_map__option__eq__Some,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,Xo: option_val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( map_op8011878015112499536on_val @ F @ Xo )
        = ( some_P7669353234731512949on_val @ Y3 ) )
      = ( ? [Z2: val] :
            ( ( Xo
              = ( some_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_307_map__option__eq__Some,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,Xo: option_state,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( map_op3100526599586584801on_val @ F @ Xo )
        = ( some_P7669353234731512949on_val @ Y3 ) )
      = ( ? [Z2: state] :
            ( ( Xo
              = ( some_state @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_308_map__option__eq__Some,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,Xo: option5747939881698552298on_val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( map_op5506263056045291841on_val @ F @ Xo )
        = ( some_P7669353234731512949on_val @ Y3 ) )
      = ( ? [Z2: produc1457211279475724562t_char > option_val] :
            ( ( Xo
              = ( some_P7669353234731512949on_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_309_map__option__eq__Some,axiom,
    ! [F: produc9003781588162623004on_val > val,Xo: option8887860577033306220on_val,Y3: val] :
      ( ( ( map_op3059972737968092952al_val @ F @ Xo )
        = ( some_val @ Y3 ) )
      = ( ? [Z2: produc9003781588162623004on_val] :
            ( ( Xo
              = ( some_P2581650809551911671on_val @ Z2 ) )
            & ( ( F @ Z2 )
              = Y3 ) ) ) ) ).

% map_option_eq_Some
thf(fact_310_None__eq__map__option__iff,axiom,
    ! [F: state > state,X: option_state] :
      ( ( none_state
        = ( map_op2726735944305651201_state @ F @ X ) )
      = ( X = none_state ) ) ).

% None_eq_map_option_iff
thf(fact_311_None__eq__map__option__iff,axiom,
    ! [F: val > state,X: option_val] :
      ( ( none_state
        = ( map_option_val_state @ F @ X ) )
      = ( X = none_val ) ) ).

% None_eq_map_option_iff
thf(fact_312_None__eq__map__option__iff,axiom,
    ! [F: state > val,X: option_state] :
      ( ( none_val
        = ( map_option_state_val @ F @ X ) )
      = ( X = none_state ) ) ).

% None_eq_map_option_iff
thf(fact_313_None__eq__map__option__iff,axiom,
    ! [F: val > val,X: option_val] :
      ( ( none_val
        = ( map_option_val_val @ F @ X ) )
      = ( X = none_val ) ) ).

% None_eq_map_option_iff
thf(fact_314_None__eq__map__option__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,X: option5747939881698552298on_val] :
      ( ( none_state
        = ( map_op1814185762381987425_state @ F @ X ) )
      = ( X = none_P1334921381875262201on_val ) ) ).

% None_eq_map_option_iff
thf(fact_315_None__eq__map__option__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,X: option5747939881698552298on_val] :
      ( ( none_val
        = ( map_op880068700720311194al_val @ F @ X ) )
      = ( X = none_P1334921381875262201on_val ) ) ).

% None_eq_map_option_iff
thf(fact_316_None__eq__map__option__iff,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,X: option_state] :
      ( ( none_P1334921381875262201on_val
        = ( map_op3100526599586584801on_val @ F @ X ) )
      = ( X = none_state ) ) ).

% None_eq_map_option_iff
thf(fact_317_None__eq__map__option__iff,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,X: option_val] :
      ( ( none_P1334921381875262201on_val
        = ( map_op8011878015112499536on_val @ F @ X ) )
      = ( X = none_val ) ) ).

% None_eq_map_option_iff
thf(fact_318_None__eq__map__option__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,X: option5747939881698552298on_val] :
      ( ( none_P1334921381875262201on_val
        = ( map_op5506263056045291841on_val @ F @ X ) )
      = ( X = none_P1334921381875262201on_val ) ) ).

% None_eq_map_option_iff
thf(fact_319_None__eq__map__option__iff,axiom,
    ! [F: produc9003781588162623004on_val > state,X: option8887860577033306220on_val] :
      ( ( none_state
        = ( map_op7858788696028474723_state @ F @ X ) )
      = ( X = none_P8728355543607141243on_val ) ) ).

% None_eq_map_option_iff
thf(fact_320_map__option__is__None,axiom,
    ! [F: state > state,Opt: option_state] :
      ( ( ( map_op2726735944305651201_state @ F @ Opt )
        = none_state )
      = ( Opt = none_state ) ) ).

% map_option_is_None
thf(fact_321_map__option__is__None,axiom,
    ! [F: val > state,Opt: option_val] :
      ( ( ( map_option_val_state @ F @ Opt )
        = none_state )
      = ( Opt = none_val ) ) ).

% map_option_is_None
thf(fact_322_map__option__is__None,axiom,
    ! [F: state > val,Opt: option_state] :
      ( ( ( map_option_state_val @ F @ Opt )
        = none_val )
      = ( Opt = none_state ) ) ).

% map_option_is_None
thf(fact_323_map__option__is__None,axiom,
    ! [F: val > val,Opt: option_val] :
      ( ( ( map_option_val_val @ F @ Opt )
        = none_val )
      = ( Opt = none_val ) ) ).

% map_option_is_None
thf(fact_324_map__option__is__None,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,Opt: option5747939881698552298on_val] :
      ( ( ( map_op1814185762381987425_state @ F @ Opt )
        = none_state )
      = ( Opt = none_P1334921381875262201on_val ) ) ).

% map_option_is_None
thf(fact_325_map__option__is__None,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,Opt: option5747939881698552298on_val] :
      ( ( ( map_op880068700720311194al_val @ F @ Opt )
        = none_val )
      = ( Opt = none_P1334921381875262201on_val ) ) ).

% map_option_is_None
thf(fact_326_map__option__is__None,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,Opt: option_state] :
      ( ( ( map_op3100526599586584801on_val @ F @ Opt )
        = none_P1334921381875262201on_val )
      = ( Opt = none_state ) ) ).

% map_option_is_None
thf(fact_327_map__option__is__None,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,Opt: option_val] :
      ( ( ( map_op8011878015112499536on_val @ F @ Opt )
        = none_P1334921381875262201on_val )
      = ( Opt = none_val ) ) ).

% map_option_is_None
thf(fact_328_map__option__is__None,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,Opt: option5747939881698552298on_val] :
      ( ( ( map_op5506263056045291841on_val @ F @ Opt )
        = none_P1334921381875262201on_val )
      = ( Opt = none_P1334921381875262201on_val ) ) ).

% map_option_is_None
thf(fact_329_map__option__is__None,axiom,
    ! [F: produc9003781588162623004on_val > state,Opt: option8887860577033306220on_val] :
      ( ( ( map_op7858788696028474723_state @ F @ Opt )
        = none_state )
      = ( Opt = none_P8728355543607141243on_val ) ) ).

% map_option_is_None
thf(fact_330_option_Omap__disc__iff,axiom,
    ! [F: state > state,A2: option_state] :
      ( ( ( map_op2726735944305651201_state @ F @ A2 )
        = none_state )
      = ( A2 = none_state ) ) ).

% option.map_disc_iff
thf(fact_331_option_Omap__disc__iff,axiom,
    ! [F: val > state,A2: option_val] :
      ( ( ( map_option_val_state @ F @ A2 )
        = none_state )
      = ( A2 = none_val ) ) ).

% option.map_disc_iff
thf(fact_332_option_Omap__disc__iff,axiom,
    ! [F: state > val,A2: option_state] :
      ( ( ( map_option_state_val @ F @ A2 )
        = none_val )
      = ( A2 = none_state ) ) ).

% option.map_disc_iff
thf(fact_333_option_Omap__disc__iff,axiom,
    ! [F: val > val,A2: option_val] :
      ( ( ( map_option_val_val @ F @ A2 )
        = none_val )
      = ( A2 = none_val ) ) ).

% option.map_disc_iff
thf(fact_334_option_Omap__disc__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,A2: option5747939881698552298on_val] :
      ( ( ( map_op1814185762381987425_state @ F @ A2 )
        = none_state )
      = ( A2 = none_P1334921381875262201on_val ) ) ).

% option.map_disc_iff
thf(fact_335_option_Omap__disc__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,A2: option5747939881698552298on_val] :
      ( ( ( map_op880068700720311194al_val @ F @ A2 )
        = none_val )
      = ( A2 = none_P1334921381875262201on_val ) ) ).

% option.map_disc_iff
thf(fact_336_option_Omap__disc__iff,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,A2: option_state] :
      ( ( ( map_op3100526599586584801on_val @ F @ A2 )
        = none_P1334921381875262201on_val )
      = ( A2 = none_state ) ) ).

% option.map_disc_iff
thf(fact_337_option_Omap__disc__iff,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,A2: option_val] :
      ( ( ( map_op8011878015112499536on_val @ F @ A2 )
        = none_P1334921381875262201on_val )
      = ( A2 = none_val ) ) ).

% option.map_disc_iff
thf(fact_338_option_Omap__disc__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,A2: option5747939881698552298on_val] :
      ( ( ( map_op5506263056045291841on_val @ F @ A2 )
        = none_P1334921381875262201on_val )
      = ( A2 = none_P1334921381875262201on_val ) ) ).

% option.map_disc_iff
thf(fact_339_option_Omap__disc__iff,axiom,
    ! [F: produc9003781588162623004on_val > state,A2: option8887860577033306220on_val] :
      ( ( ( map_op7858788696028474723_state @ F @ A2 )
        = none_state )
      = ( A2 = none_P8728355543607141243on_val ) ) ).

% option.map_disc_iff
thf(fact_340_is__none__map__option,axiom,
    ! [F: state > state,X: option_state] :
      ( ( is_none_state @ ( map_op2726735944305651201_state @ F @ X ) )
      = ( is_none_state @ X ) ) ).

% is_none_map_option
thf(fact_341_is__none__map__option,axiom,
    ! [F: val > state,X: option_val] :
      ( ( is_none_state @ ( map_option_val_state @ F @ X ) )
      = ( is_none_val @ X ) ) ).

% is_none_map_option
thf(fact_342_is__none__map__option,axiom,
    ! [F: state > val,X: option_state] :
      ( ( is_none_val @ ( map_option_state_val @ F @ X ) )
      = ( is_none_state @ X ) ) ).

% is_none_map_option
thf(fact_343_is__none__map__option,axiom,
    ! [F: val > val,X: option_val] :
      ( ( is_none_val @ ( map_option_val_val @ F @ X ) )
      = ( is_none_val @ X ) ) ).

% is_none_map_option
thf(fact_344_combine__options__assoc,axiom,
    ! [F: val > val > val,X: option_val,Y3: option_val,Z3: option_val] :
      ( ! [X3: val,Y4: val,Z: val] :
          ( ( F @ ( F @ X3 @ Y4 ) @ Z )
          = ( F @ X3 @ ( F @ Y4 @ Z ) ) )
     => ( ( combine_options_val @ F @ ( combine_options_val @ F @ X @ Y3 ) @ Z3 )
        = ( combine_options_val @ F @ X @ ( combine_options_val @ F @ Y3 @ Z3 ) ) ) ) ).

% combine_options_assoc
thf(fact_345_combine__options__assoc,axiom,
    ! [F: state > state > state,X: option_state,Y3: option_state,Z3: option_state] :
      ( ! [X3: state,Y4: state,Z: state] :
          ( ( F @ ( F @ X3 @ Y4 ) @ Z )
          = ( F @ X3 @ ( F @ Y4 @ Z ) ) )
     => ( ( combin3633514924185701883_state @ F @ ( combin3633514924185701883_state @ F @ X @ Y3 ) @ Z3 )
        = ( combin3633514924185701883_state @ F @ X @ ( combin3633514924185701883_state @ F @ Y3 @ Z3 ) ) ) ) ).

% combine_options_assoc
thf(fact_346_combine__options__commute,axiom,
    ! [F: val > val > val,X: option_val,Y3: option_val] :
      ( ! [X3: val,Y4: val] :
          ( ( F @ X3 @ Y4 )
          = ( F @ Y4 @ X3 ) )
     => ( ( combine_options_val @ F @ X @ Y3 )
        = ( combine_options_val @ F @ Y3 @ X ) ) ) ).

% combine_options_commute
thf(fact_347_combine__options__commute,axiom,
    ! [F: state > state > state,X: option_state,Y3: option_state] :
      ( ! [X3: state,Y4: state] :
          ( ( F @ X3 @ Y4 )
          = ( F @ Y4 @ X3 ) )
     => ( ( combin3633514924185701883_state @ F @ X @ Y3 )
        = ( combin3633514924185701883_state @ F @ Y3 @ X ) ) ) ).

% combine_options_commute
thf(fact_348_combine__options__left__commute,axiom,
    ! [F: val > val > val,Y3: option_val,X: option_val,Z3: option_val] :
      ( ! [X3: val,Y4: val] :
          ( ( F @ X3 @ Y4 )
          = ( F @ Y4 @ X3 ) )
     => ( ! [X3: val,Y4: val,Z: val] :
            ( ( F @ ( F @ X3 @ Y4 ) @ Z )
            = ( F @ X3 @ ( F @ Y4 @ Z ) ) )
       => ( ( combine_options_val @ F @ Y3 @ ( combine_options_val @ F @ X @ Z3 ) )
          = ( combine_options_val @ F @ X @ ( combine_options_val @ F @ Y3 @ Z3 ) ) ) ) ) ).

% combine_options_left_commute
thf(fact_349_combine__options__left__commute,axiom,
    ! [F: state > state > state,Y3: option_state,X: option_state,Z3: option_state] :
      ( ! [X3: state,Y4: state] :
          ( ( F @ X3 @ Y4 )
          = ( F @ Y4 @ X3 ) )
     => ( ! [X3: state,Y4: state,Z: state] :
            ( ( F @ ( F @ X3 @ Y4 ) @ Z )
            = ( F @ X3 @ ( F @ Y4 @ Z ) ) )
       => ( ( combin3633514924185701883_state @ F @ Y3 @ ( combin3633514924185701883_state @ F @ X @ Z3 ) )
          = ( combin3633514924185701883_state @ F @ X @ ( combin3633514924185701883_state @ F @ Y3 @ Z3 ) ) ) ) ) ).

% combine_options_left_commute
thf(fact_350_greater__mask__properties_I3_J,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ Pi3 @ Pi )
        & ( greate7680731506090375811t_char @ Pi @ Pi3 ) )
     => ( Pi = Pi3 ) ) ).

% greater_mask_properties(3)
thf(fact_351_greater__mask__properties_I2_J,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ A2 @ B2 )
        & ( greate7680731506090375811t_char @ B2 @ C ) )
     => ( greate7680731506090375811t_char @ A2 @ C ) ) ).

% greater_mask_properties(2)
thf(fact_352_greater__mask__properties_I1_J,axiom,
    ! [Pi: produc1457211279475724562t_char > prat] : ( greate7680731506090375811t_char @ Pi @ Pi ) ).

% greater_mask_properties(1)
thf(fact_353_map__upd__eqD1,axiom,
    ! [M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,X: val,N: produc1457211279475724562t_char > option_val,Y3: val] :
      ( ( ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ X ) )
        = ( fun_up5735975307950539954on_val @ N @ A2 @ ( some_val @ Y3 ) ) )
     => ( X = Y3 ) ) ).

% map_upd_eqD1
thf(fact_354_map__upd__eqD1,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,A2: produc9003781588162623004on_val,X: produc9003781588162623004on_val,N: produc9003781588162623004on_val > option8887860577033306220on_val,Y3: produc9003781588162623004on_val] :
      ( ( ( fun_up273046073882939271on_val @ M @ A2 @ ( some_P2581650809551911671on_val @ X ) )
        = ( fun_up273046073882939271on_val @ N @ A2 @ ( some_P2581650809551911671on_val @ Y3 ) ) )
     => ( X = Y3 ) ) ).

% map_upd_eqD1
thf(fact_355_map__upd__eqD1,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char > option_val,N: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( fun_up1601731230164360576on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ X ) )
        = ( fun_up1601731230164360576on_val @ N @ A2 @ ( some_P7669353234731512949on_val @ Y3 ) ) )
     => ( X = Y3 ) ) ).

% map_upd_eqD1
thf(fact_356_map__upd__triv,axiom,
    ! [T: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( ( T @ K )
        = ( some_val @ X ) )
     => ( ( fun_up5735975307950539954on_val @ T @ K @ ( some_val @ X ) )
        = T ) ) ).

% map_upd_triv
thf(fact_357_map__upd__triv,axiom,
    ! [T: produc9003781588162623004on_val > option8887860577033306220on_val,K: produc9003781588162623004on_val,X: produc9003781588162623004on_val] :
      ( ( ( T @ K )
        = ( some_P2581650809551911671on_val @ X ) )
     => ( ( fun_up273046073882939271on_val @ T @ K @ ( some_P2581650809551911671on_val @ X ) )
        = T ) ) ).

% map_upd_triv
thf(fact_358_map__upd__triv,axiom,
    ! [T: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char > option_val] :
      ( ( ( T @ K )
        = ( some_P7669353234731512949on_val @ X ) )
     => ( ( fun_up1601731230164360576on_val @ T @ K @ ( some_P7669353234731512949on_val @ X ) )
        = T ) ) ).

% map_upd_triv
thf(fact_359_map__upd__Some__unfold,axiom,
    ! [M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val,X: produc1457211279475724562t_char,Y3: val] :
      ( ( ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) @ X )
        = ( some_val @ Y3 ) )
      = ( ( ( X = A2 )
          & ( B2 = Y3 ) )
        | ( ( X != A2 )
          & ( ( M @ X )
            = ( some_val @ Y3 ) ) ) ) ) ).

% map_upd_Some_unfold
thf(fact_360_map__upd__Some__unfold,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( ( fun_up273046073882939271on_val @ M @ A2 @ ( some_P2581650809551911671on_val @ B2 ) @ X )
        = ( some_P2581650809551911671on_val @ Y3 ) )
      = ( ( ( X = A2 )
          & ( B2 = Y3 ) )
        | ( ( X != A2 )
          & ( ( M @ X )
            = ( some_P2581650809551911671on_val @ Y3 ) ) ) ) ) ).

% map_upd_Some_unfold
thf(fact_361_map__upd__Some__unfold,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( fun_up1601731230164360576on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ B2 ) @ X )
        = ( some_P7669353234731512949on_val @ Y3 ) )
      = ( ( ( X = A2 )
          & ( B2 = Y3 ) )
        | ( ( X != A2 )
          & ( ( M @ X )
            = ( some_P7669353234731512949on_val @ Y3 ) ) ) ) ) ).

% map_upd_Some_unfold
thf(fact_362_option_Osimps_I9_J,axiom,
    ! [F: val > val,X2: val] :
      ( ( map_option_val_val @ F @ ( some_val @ X2 ) )
      = ( some_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_363_option_Osimps_I9_J,axiom,
    ! [F: val > state,X2: val] :
      ( ( map_option_val_state @ F @ ( some_val @ X2 ) )
      = ( some_state @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_364_option_Osimps_I9_J,axiom,
    ! [F: state > val,X2: state] :
      ( ( map_option_state_val @ F @ ( some_state @ X2 ) )
      = ( some_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_365_option_Osimps_I9_J,axiom,
    ! [F: state > state,X2: state] :
      ( ( map_op2726735944305651201_state @ F @ ( some_state @ X2 ) )
      = ( some_state @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_366_option_Osimps_I9_J,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,X2: val] :
      ( ( map_op8011878015112499536on_val @ F @ ( some_val @ X2 ) )
      = ( some_P7669353234731512949on_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_367_option_Osimps_I9_J,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,X2: state] :
      ( ( map_op3100526599586584801on_val @ F @ ( some_state @ X2 ) )
      = ( some_P7669353234731512949on_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_368_option_Osimps_I9_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,X2: produc1457211279475724562t_char > option_val] :
      ( ( map_op880068700720311194al_val @ F @ ( some_P7669353234731512949on_val @ X2 ) )
      = ( some_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_369_option_Osimps_I9_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,X2: produc1457211279475724562t_char > option_val] :
      ( ( map_op1814185762381987425_state @ F @ ( some_P7669353234731512949on_val @ X2 ) )
      = ( some_state @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_370_option_Osimps_I9_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val,X2: produc1457211279475724562t_char > option_val] :
      ( ( map_op5506263056045291841on_val @ F @ ( some_P7669353234731512949on_val @ X2 ) )
      = ( some_P7669353234731512949on_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_371_option_Osimps_I9_J,axiom,
    ! [F: val > produc9003781588162623004on_val,X2: val] :
      ( ( map_op3897579098253967186on_val @ F @ ( some_val @ X2 ) )
      = ( some_P2581650809551911671on_val @ ( F @ X2 ) ) ) ).

% option.simps(9)
thf(fact_372_map__option__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > state,G: state > state] :
      ( ( X = Y3 )
     => ( ! [A: state] :
            ( ( Y3
              = ( some_state @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( map_op2726735944305651201_state @ F @ X )
          = ( map_op2726735944305651201_state @ G @ Y3 ) ) ) ) ).

% map_option_cong
thf(fact_373_map__option__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > state,G: val > state] :
      ( ( X = Y3 )
     => ( ! [A: val] :
            ( ( Y3
              = ( some_val @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( map_option_val_state @ F @ X )
          = ( map_option_val_state @ G @ Y3 ) ) ) ) ).

% map_option_cong
thf(fact_374_map__option__cong,axiom,
    ! [X: option_state,Y3: option_state,F: state > val,G: state > val] :
      ( ( X = Y3 )
     => ( ! [A: state] :
            ( ( Y3
              = ( some_state @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( map_option_state_val @ F @ X )
          = ( map_option_state_val @ G @ Y3 ) ) ) ) ).

% map_option_cong
thf(fact_375_map__option__cong,axiom,
    ! [X: option_val,Y3: option_val,F: val > val,G: val > val] :
      ( ( X = Y3 )
     => ( ! [A: val] :
            ( ( Y3
              = ( some_val @ A ) )
           => ( ( F @ A )
              = ( G @ A ) ) )
       => ( ( map_option_val_val @ F @ X )
          = ( map_option_val_val @ G @ Y3 ) ) ) ) ).

% map_option_cong
thf(fact_376_option_Osimps_I8_J,axiom,
    ! [F: state > state] :
      ( ( map_op2726735944305651201_state @ F @ none_state )
      = none_state ) ).

% option.simps(8)
thf(fact_377_option_Osimps_I8_J,axiom,
    ! [F: state > val] :
      ( ( map_option_state_val @ F @ none_state )
      = none_val ) ).

% option.simps(8)
thf(fact_378_option_Osimps_I8_J,axiom,
    ! [F: val > state] :
      ( ( map_option_val_state @ F @ none_val )
      = none_state ) ).

% option.simps(8)
thf(fact_379_option_Osimps_I8_J,axiom,
    ! [F: val > val] :
      ( ( map_option_val_val @ F @ none_val )
      = none_val ) ).

% option.simps(8)
thf(fact_380_option_Osimps_I8_J,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val] :
      ( ( map_op3100526599586584801on_val @ F @ none_state )
      = none_P1334921381875262201on_val ) ).

% option.simps(8)
thf(fact_381_option_Osimps_I8_J,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val] :
      ( ( map_op8011878015112499536on_val @ F @ none_val )
      = none_P1334921381875262201on_val ) ).

% option.simps(8)
thf(fact_382_option_Osimps_I8_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state] :
      ( ( map_op1814185762381987425_state @ F @ none_P1334921381875262201on_val )
      = none_state ) ).

% option.simps(8)
thf(fact_383_option_Osimps_I8_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val] :
      ( ( map_op880068700720311194al_val @ F @ none_P1334921381875262201on_val )
      = none_val ) ).

% option.simps(8)
thf(fact_384_option_Osimps_I8_J,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > produc1457211279475724562t_char > option_val] :
      ( ( map_op5506263056045291841on_val @ F @ none_P1334921381875262201on_val )
      = none_P1334921381875262201on_val ) ).

% option.simps(8)
thf(fact_385_option_Osimps_I8_J,axiom,
    ! [F: state > produc9003781588162623004on_val] :
      ( ( map_op2202097680607477091on_val @ F @ none_state )
      = none_P8728355543607141243on_val ) ).

% option.simps(8)
thf(fact_386_option_Omap__cong,axiom,
    ! [X: option_val,Ya: option_val,F: val > state,G: val > state] :
      ( ( X = Ya )
     => ( ! [Z: val] :
            ( ( member_val @ Z @ ( set_option_val2 @ Ya ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( map_option_val_state @ F @ X )
          = ( map_option_val_state @ G @ Ya ) ) ) ) ).

% option.map_cong
thf(fact_387_option_Omap__cong,axiom,
    ! [X: option_val,Ya: option_val,F: val > val,G: val > val] :
      ( ( X = Ya )
     => ( ! [Z: val] :
            ( ( member_val @ Z @ ( set_option_val2 @ Ya ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( map_option_val_val @ F @ X )
          = ( map_option_val_val @ G @ Ya ) ) ) ) ).

% option.map_cong
thf(fact_388_option_Omap__cong,axiom,
    ! [X: option_state,Ya: option_state,F: state > state,G: state > state] :
      ( ( X = Ya )
     => ( ! [Z: state] :
            ( ( member_state @ Z @ ( set_option_state2 @ Ya ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( map_op2726735944305651201_state @ F @ X )
          = ( map_op2726735944305651201_state @ G @ Ya ) ) ) ) ).

% option.map_cong
thf(fact_389_option_Omap__cong,axiom,
    ! [X: option_state,Ya: option_state,F: state > val,G: state > val] :
      ( ( X = Ya )
     => ( ! [Z: state] :
            ( ( member_state @ Z @ ( set_option_state2 @ Ya ) )
           => ( ( F @ Z )
              = ( G @ Z ) ) )
       => ( ( map_option_state_val @ F @ X )
          = ( map_option_state_val @ G @ Ya ) ) ) ) ).

% option.map_cong
thf(fact_390_option_Omap__cong0,axiom,
    ! [X: option_val,F: val > state,G: val > state] :
      ( ! [Z: val] :
          ( ( member_val @ Z @ ( set_option_val2 @ X ) )
         => ( ( F @ Z )
            = ( G @ Z ) ) )
     => ( ( map_option_val_state @ F @ X )
        = ( map_option_val_state @ G @ X ) ) ) ).

% option.map_cong0
thf(fact_391_option_Omap__cong0,axiom,
    ! [X: option_val,F: val > val,G: val > val] :
      ( ! [Z: val] :
          ( ( member_val @ Z @ ( set_option_val2 @ X ) )
         => ( ( F @ Z )
            = ( G @ Z ) ) )
     => ( ( map_option_val_val @ F @ X )
        = ( map_option_val_val @ G @ X ) ) ) ).

% option.map_cong0
thf(fact_392_option_Omap__cong0,axiom,
    ! [X: option_state,F: state > state,G: state > state] :
      ( ! [Z: state] :
          ( ( member_state @ Z @ ( set_option_state2 @ X ) )
         => ( ( F @ Z )
            = ( G @ Z ) ) )
     => ( ( map_op2726735944305651201_state @ F @ X )
        = ( map_op2726735944305651201_state @ G @ X ) ) ) ).

% option.map_cong0
thf(fact_393_option_Omap__cong0,axiom,
    ! [X: option_state,F: state > val,G: state > val] :
      ( ! [Z: state] :
          ( ( member_state @ Z @ ( set_option_state2 @ X ) )
         => ( ( F @ Z )
            = ( G @ Z ) ) )
     => ( ( map_option_state_val @ F @ X )
        = ( map_option_state_val @ G @ X ) ) ) ).

% option.map_cong0
thf(fact_394_option_Oinj__map__strong,axiom,
    ! [X: option_val,Xa: option_val,F: val > state,Fa: val > state] :
      ( ! [Z: val,Za: val] :
          ( ( member_val @ Z @ ( set_option_val2 @ X ) )
         => ( ( member_val @ Za @ ( set_option_val2 @ Xa ) )
           => ( ( ( F @ Z )
                = ( Fa @ Za ) )
             => ( Z = Za ) ) ) )
     => ( ( ( map_option_val_state @ F @ X )
          = ( map_option_val_state @ Fa @ Xa ) )
       => ( X = Xa ) ) ) ).

% option.inj_map_strong
thf(fact_395_option_Oinj__map__strong,axiom,
    ! [X: option_val,Xa: option_val,F: val > val,Fa: val > val] :
      ( ! [Z: val,Za: val] :
          ( ( member_val @ Z @ ( set_option_val2 @ X ) )
         => ( ( member_val @ Za @ ( set_option_val2 @ Xa ) )
           => ( ( ( F @ Z )
                = ( Fa @ Za ) )
             => ( Z = Za ) ) ) )
     => ( ( ( map_option_val_val @ F @ X )
          = ( map_option_val_val @ Fa @ Xa ) )
       => ( X = Xa ) ) ) ).

% option.inj_map_strong
thf(fact_396_option_Oinj__map__strong,axiom,
    ! [X: option_state,Xa: option_state,F: state > state,Fa: state > state] :
      ( ! [Z: state,Za: state] :
          ( ( member_state @ Z @ ( set_option_state2 @ X ) )
         => ( ( member_state @ Za @ ( set_option_state2 @ Xa ) )
           => ( ( ( F @ Z )
                = ( Fa @ Za ) )
             => ( Z = Za ) ) ) )
     => ( ( ( map_op2726735944305651201_state @ F @ X )
          = ( map_op2726735944305651201_state @ Fa @ Xa ) )
       => ( X = Xa ) ) ) ).

% option.inj_map_strong
thf(fact_397_option_Oinj__map__strong,axiom,
    ! [X: option_state,Xa: option_state,F: state > val,Fa: state > val] :
      ( ! [Z: state,Za: state] :
          ( ( member_state @ Z @ ( set_option_state2 @ X ) )
         => ( ( member_state @ Za @ ( set_option_state2 @ Xa ) )
           => ( ( ( F @ Z )
                = ( Fa @ Za ) )
             => ( Z = Za ) ) ) )
     => ( ( ( map_option_state_val @ F @ X )
          = ( map_option_state_val @ Fa @ Xa ) )
       => ( X = Xa ) ) ) ).

% option.inj_map_strong
thf(fact_398_option_Omap__ident__strong,axiom,
    ! [T: option8887860577033306220on_val,F: produc9003781588162623004on_val > produc9003781588162623004on_val] :
      ( ! [Z: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ Z @ ( set_op9004752959087400718on_val @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_op7709461780610975941on_val @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_399_option_Omap__ident__strong,axiom,
    ! [T: option_option_state,F: option_state > option_state] :
      ( ! [Z: option_state] :
          ( ( member_option_state @ Z @ ( set_op5162993263733338108_state @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_op5992293608522446881_state @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_400_option_Omap__ident__strong,axiom,
    ! [T: option_option_val,F: option_val > option_val] :
      ( ! [Z: option_val] :
          ( ( member_option_val @ Z @ ( set_op911010586042427349on_val @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_op2847309980797881419on_val @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_401_option_Omap__ident__strong,axiom,
    ! [T: option3572569098863364761r_prat,F: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat] :
      ( ! [Z: produc1457211279475724562t_char > prat] :
          ( ( member2336342582916103932r_prat @ Z @ ( set_op923924987228895969r_prat @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_op2194283413446040907r_prat @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_402_option_Omap__ident__strong,axiom,
    ! [T: option_val,F: val > val] :
      ( ! [Z: val] :
          ( ( member_val @ Z @ ( set_option_val2 @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_option_val_val @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_403_option_Omap__ident__strong,axiom,
    ! [T: option_state,F: state > state] :
      ( ! [Z: state] :
          ( ( member_state @ Z @ ( set_option_state2 @ T ) )
         => ( ( F @ Z )
            = Z ) )
     => ( ( map_op2726735944305651201_state @ F @ T )
        = T ) ) ).

% option.map_ident_strong
thf(fact_404_map__option__idI,axiom,
    ! [X: option8887860577033306220on_val,F: produc9003781588162623004on_val > produc9003781588162623004on_val] :
      ( ! [Y4: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ Y4 @ ( set_op9004752959087400718on_val @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_op7709461780610975941on_val @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_405_map__option__idI,axiom,
    ! [X: option_option_state,F: option_state > option_state] :
      ( ! [Y4: option_state] :
          ( ( member_option_state @ Y4 @ ( set_op5162993263733338108_state @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_op5992293608522446881_state @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_406_map__option__idI,axiom,
    ! [X: option_option_val,F: option_val > option_val] :
      ( ! [Y4: option_val] :
          ( ( member_option_val @ Y4 @ ( set_op911010586042427349on_val @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_op2847309980797881419on_val @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_407_map__option__idI,axiom,
    ! [X: option3572569098863364761r_prat,F: ( produc1457211279475724562t_char > prat ) > produc1457211279475724562t_char > prat] :
      ( ! [Y4: produc1457211279475724562t_char > prat] :
          ( ( member2336342582916103932r_prat @ Y4 @ ( set_op923924987228895969r_prat @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_op2194283413446040907r_prat @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_408_map__option__idI,axiom,
    ! [X: option_val,F: val > val] :
      ( ! [Y4: val] :
          ( ( member_val @ Y4 @ ( set_option_val2 @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_option_val_val @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_409_map__option__idI,axiom,
    ! [X: option_state,F: state > state] :
      ( ! [Y4: state] :
          ( ( member_state @ Y4 @ ( set_option_state2 @ X ) )
         => ( ( F @ Y4 )
            = Y4 ) )
     => ( ( map_op2726735944305651201_state @ F @ X )
        = X ) ) ).

% map_option_idI
thf(fact_410_const__sum__mask__greater,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ A2 @ B2 )
        = ( add_ma6586698345353345811t_char @ C @ D ) )
     => ( ( greate7680731506090375811t_char @ A2 @ C )
       => ( greate7680731506090375811t_char @ D @ B2 ) ) ) ).

% const_sum_mask_greater
thf(fact_411_greater__mask__decomp,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( greate7680731506090375811t_char @ A2 @ ( add_ma6586698345353345811t_char @ B2 @ C ) )
     => ? [A1: produc1457211279475724562t_char > prat,A22: produc1457211279475724562t_char > prat] :
          ( ( A2
            = ( add_ma6586698345353345811t_char @ A1 @ A22 ) )
          & ( greate7680731506090375811t_char @ A1 @ B2 )
          & ( greate7680731506090375811t_char @ A22 @ C ) ) ) ).

% greater_mask_decomp
thf(fact_412_greater__mask__def,axiom,
    ( greate7680731506090375811t_char
    = ( ^ [Pi4: produc1457211279475724562t_char > prat,Pi2: produc1457211279475724562t_char > prat] :
        ? [R: produc1457211279475724562t_char > prat] :
          ( Pi4
          = ( add_ma6586698345353345811t_char @ Pi2 @ R ) ) ) ) ).

% greater_mask_def
thf(fact_413_map__upd__nonempty,axiom,
    ! [T: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( fun_up5735975307950539954on_val @ T @ K @ ( some_val @ X ) )
     != ( ^ [X4: produc1457211279475724562t_char] : none_val ) ) ).

% map_upd_nonempty
thf(fact_414_map__upd__nonempty,axiom,
    ! [T: produc9003781588162623004on_val > option8887860577033306220on_val,K: produc9003781588162623004on_val,X: produc9003781588162623004on_val] :
      ( ( fun_up273046073882939271on_val @ T @ K @ ( some_P2581650809551911671on_val @ X ) )
     != ( ^ [X4: produc9003781588162623004on_val] : none_P8728355543607141243on_val ) ) ).

% map_upd_nonempty
thf(fact_415_map__upd__nonempty,axiom,
    ! [T: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char > option_val] :
      ( ( fun_up1601731230164360576on_val @ T @ K @ ( some_P7669353234731512949on_val @ X ) )
     != ( ^ [X4: produc1457211279475724562t_char > prat] : none_P1334921381875262201on_val ) ) ).

% map_upd_nonempty
thf(fact_416_option_Omap__sel,axiom,
    ! [A2: option8887860577033306220on_val,F: produc9003781588162623004on_val > state] :
      ( ( A2 != none_P8728355543607141243on_val )
     => ( ( the_state @ ( map_op7858788696028474723_state @ F @ A2 ) )
        = ( F @ ( the_Pr3639693038709580936on_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_417_option_Omap__sel,axiom,
    ! [A2: option8887860577033306220on_val,F: produc9003781588162623004on_val > val] :
      ( ( A2 != none_P8728355543607141243on_val )
     => ( ( the_val @ ( map_op3059972737968092952al_val @ F @ A2 ) )
        = ( F @ ( the_Pr3639693038709580936on_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_418_option_Omap__sel,axiom,
    ! [A2: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > state] :
      ( ( A2 != none_P1334921381875262201on_val )
     => ( ( the_state @ ( map_op1814185762381987425_state @ F @ A2 ) )
        = ( F @ ( the_Pr646328391962797958on_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_419_option_Omap__sel,axiom,
    ! [A2: option5747939881698552298on_val,F: ( produc1457211279475724562t_char > option_val ) > val] :
      ( ( A2 != none_P1334921381875262201on_val )
     => ( ( the_val @ ( map_op880068700720311194al_val @ F @ A2 ) )
        = ( F @ ( the_Pr646328391962797958on_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_420_option_Omap__sel,axiom,
    ! [A2: option_state,F: state > state] :
      ( ( A2 != none_state )
     => ( ( the_state @ ( map_op2726735944305651201_state @ F @ A2 ) )
        = ( F @ ( the_state @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_421_option_Omap__sel,axiom,
    ! [A2: option_val,F: val > state] :
      ( ( A2 != none_val )
     => ( ( the_state @ ( map_option_val_state @ F @ A2 ) )
        = ( F @ ( the_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_422_option_Omap__sel,axiom,
    ! [A2: option_state,F: state > val] :
      ( ( A2 != none_state )
     => ( ( the_val @ ( map_option_state_val @ F @ A2 ) )
        = ( F @ ( the_state @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_423_option_Omap__sel,axiom,
    ! [A2: option_val,F: val > val] :
      ( ( A2 != none_val )
     => ( ( the_val @ ( map_option_val_val @ F @ A2 ) )
        = ( F @ ( the_val @ A2 ) ) ) ) ).

% option.map_sel
thf(fact_424_fun__upd__apply,axiom,
    ( fun_up5735975307950539954on_val
    = ( ^ [F2: produc1457211279475724562t_char > option_val,X4: produc1457211279475724562t_char,Y: option_val,Z2: produc1457211279475724562t_char] : ( if_option_val @ ( Z2 = X4 ) @ Y @ ( F2 @ Z2 ) ) ) ) ).

% fun_upd_apply
thf(fact_425_fun__upd__apply,axiom,
    ( fun_up829850848796697765r_prat
    = ( ^ [F2: produc1457211279475724562t_char > prat,X4: produc1457211279475724562t_char,Y: prat,Z2: produc1457211279475724562t_char] : ( if_prat @ ( Z2 = X4 ) @ Y @ ( F2 @ Z2 ) ) ) ) ).

% fun_upd_apply
thf(fact_426_fun__upd__apply,axiom,
    ( fun_up273046073882939271on_val
    = ( ^ [F2: produc9003781588162623004on_val > option8887860577033306220on_val,X4: produc9003781588162623004on_val,Y: option8887860577033306220on_val,Z2: produc9003781588162623004on_val] : ( if_opt2965748431298708774on_val @ ( Z2 = X4 ) @ Y @ ( F2 @ Z2 ) ) ) ) ).

% fun_upd_apply
thf(fact_427_fun__upd__apply,axiom,
    ( fun_up1601731230164360576on_val
    = ( ^ [F2: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X4: produc1457211279475724562t_char > prat,Y: option5747939881698552298on_val,Z2: produc1457211279475724562t_char > prat] : ( if_opt6509584284076893604on_val @ ( Z2 = X4 ) @ Y @ ( F2 @ Z2 ) ) ) ) ).

% fun_upd_apply
thf(fact_428_fun__upd__triv,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char] :
      ( ( fun_up5735975307950539954on_val @ F @ X @ ( F @ X ) )
      = F ) ).

% fun_upd_triv
thf(fact_429_fun__upd__triv,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char] :
      ( ( fun_up829850848796697765r_prat @ F @ X @ ( F @ X ) )
      = F ) ).

% fun_upd_triv
thf(fact_430_fun__upd__triv,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val] :
      ( ( fun_up273046073882939271on_val @ F @ X @ ( F @ X ) )
      = F ) ).

% fun_upd_triv
thf(fact_431_fun__upd__triv,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat] :
      ( ( fun_up1601731230164360576on_val @ F @ X @ ( F @ X ) )
      = F ) ).

% fun_upd_triv
thf(fact_432_fun__upd__upd,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val,Z3: option_val] :
      ( ( fun_up5735975307950539954on_val @ ( fun_up5735975307950539954on_val @ F @ X @ Y3 ) @ X @ Z3 )
      = ( fun_up5735975307950539954on_val @ F @ X @ Z3 ) ) ).

% fun_upd_upd
thf(fact_433_fun__upd__upd,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat,Z3: prat] :
      ( ( fun_up829850848796697765r_prat @ ( fun_up829850848796697765r_prat @ F @ X @ Y3 ) @ X @ Z3 )
      = ( fun_up829850848796697765r_prat @ F @ X @ Z3 ) ) ).

% fun_upd_upd
thf(fact_434_fun__upd__upd,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val,Z3: option8887860577033306220on_val] :
      ( ( fun_up273046073882939271on_val @ ( fun_up273046073882939271on_val @ F @ X @ Y3 ) @ X @ Z3 )
      = ( fun_up273046073882939271on_val @ F @ X @ Z3 ) ) ).

% fun_upd_upd
thf(fact_435_fun__upd__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val,Z3: option5747939881698552298on_val] :
      ( ( fun_up1601731230164360576on_val @ ( fun_up1601731230164360576on_val @ F @ X @ Y3 ) @ X @ Z3 )
      = ( fun_up1601731230164360576on_val @ F @ X @ Z3 ) ) ).

% fun_upd_upd
thf(fact_436_empty__Collect__eq,axiom,
    ! [P: produc1457211279475724562t_char > $o] :
      ( ( bot_bo1414094081888755934t_char
        = ( collec2458894688891239037t_char @ P ) )
      = ( ! [X4: produc1457211279475724562t_char] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_437_empty__Collect__eq,axiom,
    ! [P: produc9003781588162623004on_val > $o] :
      ( ( bot_bo6722054719108133734on_val
        = ( collec7475294502966882545on_val @ P ) )
      = ( ! [X4: produc9003781588162623004on_val] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_438_empty__Collect__eq,axiom,
    ! [P: option_state > $o] :
      ( ( bot_bo710180891245420500_state
        = ( collect_option_state @ P ) )
      = ( ! [X4: option_state] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_439_empty__Collect__eq,axiom,
    ! [P: option_val > $o] :
      ( ( bot_bo5906790151302476563on_val
        = ( collect_option_val @ P ) )
      = ( ! [X4: option_val] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_440_empty__Collect__eq,axiom,
    ! [P: val > $o] :
      ( ( bot_bot_set_val
        = ( collect_val @ P ) )
      = ( ! [X4: val] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_441_Collect__empty__eq,axiom,
    ! [P: produc1457211279475724562t_char > $o] :
      ( ( ( collec2458894688891239037t_char @ P )
        = bot_bo1414094081888755934t_char )
      = ( ! [X4: produc1457211279475724562t_char] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_442_Collect__empty__eq,axiom,
    ! [P: produc9003781588162623004on_val > $o] :
      ( ( ( collec7475294502966882545on_val @ P )
        = bot_bo6722054719108133734on_val )
      = ( ! [X4: produc9003781588162623004on_val] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_443_Collect__empty__eq,axiom,
    ! [P: option_state > $o] :
      ( ( ( collect_option_state @ P )
        = bot_bo710180891245420500_state )
      = ( ! [X4: option_state] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_444_Collect__empty__eq,axiom,
    ! [P: option_val > $o] :
      ( ( ( collect_option_val @ P )
        = bot_bo5906790151302476563on_val )
      = ( ! [X4: option_val] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_445_Collect__empty__eq,axiom,
    ! [P: val > $o] :
      ( ( ( collect_val @ P )
        = bot_bot_set_val )
      = ( ! [X4: val] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_446_all__not__in__conv,axiom,
    ! [A4: set_Pr3433046674199179443r_prat] :
      ( ( ! [X4: produc1457211279475724562t_char > prat] :
            ~ ( member2336342582916103932r_prat @ X4 @ A4 ) )
      = ( A4 = bot_bo3164680191535668511r_prat ) ) ).

% all_not_in_conv
thf(fact_447_all__not__in__conv,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( ! [X4: produc1457211279475724562t_char] :
            ~ ( member484235747325421115t_char @ X4 @ A4 ) )
      = ( A4 = bot_bo1414094081888755934t_char ) ) ).

% all_not_in_conv
thf(fact_448_all__not__in__conv,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( ! [X4: produc9003781588162623004on_val] :
            ~ ( member2879030624002546611on_val @ X4 @ A4 ) )
      = ( A4 = bot_bo6722054719108133734on_val ) ) ).

% all_not_in_conv
thf(fact_449_all__not__in__conv,axiom,
    ! [A4: set_option_state] :
      ( ( ! [X4: option_state] :
            ~ ( member_option_state @ X4 @ A4 ) )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% all_not_in_conv
thf(fact_450_all__not__in__conv,axiom,
    ! [A4: set_option_val] :
      ( ( ! [X4: option_val] :
            ~ ( member_option_val @ X4 @ A4 ) )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% all_not_in_conv
thf(fact_451_all__not__in__conv,axiom,
    ! [A4: set_val] :
      ( ( ! [X4: val] :
            ~ ( member_val @ X4 @ A4 ) )
      = ( A4 = bot_bot_set_val ) ) ).

% all_not_in_conv
thf(fact_452_empty__iff,axiom,
    ! [C: produc1457211279475724562t_char > prat] :
      ~ ( member2336342582916103932r_prat @ C @ bot_bo3164680191535668511r_prat ) ).

% empty_iff
thf(fact_453_empty__iff,axiom,
    ! [C: produc1457211279475724562t_char] :
      ~ ( member484235747325421115t_char @ C @ bot_bo1414094081888755934t_char ) ).

% empty_iff
thf(fact_454_empty__iff,axiom,
    ! [C: produc9003781588162623004on_val] :
      ~ ( member2879030624002546611on_val @ C @ bot_bo6722054719108133734on_val ) ).

% empty_iff
thf(fact_455_empty__iff,axiom,
    ! [C: option_state] :
      ~ ( member_option_state @ C @ bot_bo710180891245420500_state ) ).

% empty_iff
thf(fact_456_empty__iff,axiom,
    ! [C: option_val] :
      ~ ( member_option_val @ C @ bot_bo5906790151302476563on_val ) ).

% empty_iff
thf(fact_457_empty__iff,axiom,
    ! [C: val] :
      ~ ( member_val @ C @ bot_bot_set_val ) ).

% empty_iff
thf(fact_458_map__le__imp__upd__le,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: val] :
      ( ( map_le3432596473071271956ar_val @ M1 @ M2 )
     => ( map_le3432596473071271956ar_val @ ( fun_up5735975307950539954on_val @ M1 @ X @ none_val ) @ ( fun_up5735975307950539954on_val @ M2 @ X @ ( some_val @ Y3 ) ) ) ) ).

% map_le_imp_upd_le
thf(fact_459_map__le__imp__upd__le,axiom,
    ! [M1: produc9003781588162623004on_val > option8887860577033306220on_val,M2: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( map_le1786601613863086943on_val @ M1 @ M2 )
     => ( map_le1786601613863086943on_val @ ( fun_up273046073882939271on_val @ M1 @ X @ none_P8728355543607141243on_val ) @ ( fun_up273046073882939271on_val @ M2 @ X @ ( some_P2581650809551911671on_val @ Y3 ) ) ) ) ).

% map_le_imp_upd_le
thf(fact_460_map__le__imp__upd__le,axiom,
    ! [M1: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,M2: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
      ( ( map_le7591542393800649736on_val @ M1 @ M2 )
     => ( map_le7591542393800649736on_val @ ( fun_up1601731230164360576on_val @ M1 @ X @ none_P1334921381875262201on_val ) @ ( fun_up1601731230164360576on_val @ M2 @ X @ ( some_P7669353234731512949on_val @ Y3 ) ) ) ) ).

% map_le_imp_upd_le
thf(fact_461_bot__set__def,axiom,
    ( bot_bo1414094081888755934t_char
    = ( collec2458894688891239037t_char @ bot_bo1808431002336377727char_o ) ) ).

% bot_set_def
thf(fact_462_bot__set__def,axiom,
    ( bot_bo6722054719108133734on_val
    = ( collec7475294502966882545on_val @ bot_bo6370234372831922335_val_o ) ) ).

% bot_set_def
thf(fact_463_bot__set__def,axiom,
    ( bot_bo710180891245420500_state
    = ( collect_option_state @ bot_bo4453335400789057457tate_o ) ) ).

% bot_set_def
thf(fact_464_bot__set__def,axiom,
    ( bot_bo5906790151302476563on_val
    = ( collect_option_val @ bot_bot_option_val_o ) ) ).

% bot_set_def
thf(fact_465_bot__set__def,axiom,
    ( bot_bot_set_val
    = ( collect_val @ bot_bot_val_o ) ) ).

% bot_set_def
thf(fact_466_map__le__antisym,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ G )
     => ( ( map_le3432596473071271956ar_val @ G @ F )
       => ( F = G ) ) ) ).

% map_le_antisym
thf(fact_467_map__le__trans,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val,M3: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ M1 @ M2 )
     => ( ( map_le3432596473071271956ar_val @ M2 @ M3 )
       => ( map_le3432596473071271956ar_val @ M1 @ M3 ) ) ) ).

% map_le_trans
thf(fact_468_map__le__refl,axiom,
    ! [F: produc1457211279475724562t_char > option_val] : ( map_le3432596473071271956ar_val @ F @ F ) ).

% map_le_refl
thf(fact_469_map__le__iff__map__add__commute,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ ( map_ad2908576761495157028ar_val @ F @ G ) )
      = ( ( map_ad2908576761495157028ar_val @ F @ G )
        = ( map_ad2908576761495157028ar_val @ G @ F ) ) ) ).

% map_le_iff_map_add_commute
thf(fact_470_map__add__subsumed2,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ G )
     => ( ( map_ad2908576761495157028ar_val @ G @ F )
        = G ) ) ).

% map_add_subsumed2
thf(fact_471_map__add__subsumed1,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ G )
     => ( ( map_ad2908576761495157028ar_val @ F @ G )
        = G ) ) ).

% map_add_subsumed1
thf(fact_472_map__add__le__mapI,axiom,
    ! [F: produc1457211279475724562t_char > option_val,H: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ H )
     => ( ( map_le3432596473071271956ar_val @ G @ H )
       => ( map_le3432596473071271956ar_val @ ( map_ad2908576761495157028ar_val @ F @ G ) @ H ) ) ) ).

% map_add_le_mapI
thf(fact_473_map__add__le__mapE,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,H: produc1457211279475724562t_char > option_val] :
      ( ( map_le3432596473071271956ar_val @ ( map_ad2908576761495157028ar_val @ F @ G ) @ H )
     => ( map_le3432596473071271956ar_val @ G @ H ) ) ).

% map_add_le_mapE
thf(fact_474_map__le__map__add,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] : ( map_le3432596473071271956ar_val @ F @ ( map_ad2908576761495157028ar_val @ G @ F ) ) ).

% map_le_map_add
thf(fact_475_map__le__upd,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: option_val] :
      ( ( map_le3432596473071271956ar_val @ F @ G )
     => ( map_le3432596473071271956ar_val @ ( fun_up5735975307950539954on_val @ F @ A2 @ B2 ) @ ( fun_up5735975307950539954on_val @ G @ A2 @ B2 ) ) ) ).

% map_le_upd
thf(fact_476_map__le__upd,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,A2: produc9003781588162623004on_val,B2: option8887860577033306220on_val] :
      ( ( map_le1786601613863086943on_val @ F @ G )
     => ( map_le1786601613863086943on_val @ ( fun_up273046073882939271on_val @ F @ A2 @ B2 ) @ ( fun_up273046073882939271on_val @ G @ A2 @ B2 ) ) ) ).

% map_le_upd
thf(fact_477_map__le__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,B2: option5747939881698552298on_val] :
      ( ( map_le7591542393800649736on_val @ F @ G )
     => ( map_le7591542393800649736on_val @ ( fun_up1601731230164360576on_val @ F @ A2 @ B2 ) @ ( fun_up1601731230164360576on_val @ G @ A2 @ B2 ) ) ) ).

% map_le_upd
thf(fact_478_upd__None__map__le,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char] : ( map_le3432596473071271956ar_val @ ( fun_up5735975307950539954on_val @ F @ X @ none_val ) @ F ) ).

% upd_None_map_le
thf(fact_479_upd__None__map__le,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val] : ( map_le1786601613863086943on_val @ ( fun_up273046073882939271on_val @ F @ X @ none_P8728355543607141243on_val ) @ F ) ).

% upd_None_map_le
thf(fact_480_upd__None__map__le,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat] : ( map_le7591542393800649736on_val @ ( fun_up1601731230164360576on_val @ F @ X @ none_P1334921381875262201on_val ) @ F ) ).

% upd_None_map_le
thf(fact_481_emptyE,axiom,
    ! [A2: produc1457211279475724562t_char > prat] :
      ~ ( member2336342582916103932r_prat @ A2 @ bot_bo3164680191535668511r_prat ) ).

% emptyE
thf(fact_482_emptyE,axiom,
    ! [A2: produc1457211279475724562t_char] :
      ~ ( member484235747325421115t_char @ A2 @ bot_bo1414094081888755934t_char ) ).

% emptyE
thf(fact_483_emptyE,axiom,
    ! [A2: produc9003781588162623004on_val] :
      ~ ( member2879030624002546611on_val @ A2 @ bot_bo6722054719108133734on_val ) ).

% emptyE
thf(fact_484_emptyE,axiom,
    ! [A2: option_state] :
      ~ ( member_option_state @ A2 @ bot_bo710180891245420500_state ) ).

% emptyE
thf(fact_485_emptyE,axiom,
    ! [A2: option_val] :
      ~ ( member_option_val @ A2 @ bot_bo5906790151302476563on_val ) ).

% emptyE
thf(fact_486_emptyE,axiom,
    ! [A2: val] :
      ~ ( member_val @ A2 @ bot_bot_set_val ) ).

% emptyE
thf(fact_487_equals0D,axiom,
    ! [A4: set_Pr3433046674199179443r_prat,A2: produc1457211279475724562t_char > prat] :
      ( ( A4 = bot_bo3164680191535668511r_prat )
     => ~ ( member2336342582916103932r_prat @ A2 @ A4 ) ) ).

% equals0D
thf(fact_488_equals0D,axiom,
    ! [A4: set_Pr2507339680178222706t_char,A2: produc1457211279475724562t_char] :
      ( ( A4 = bot_bo1414094081888755934t_char )
     => ~ ( member484235747325421115t_char @ A2 @ A4 ) ) ).

% equals0D
thf(fact_489_equals0D,axiom,
    ! [A4: set_Pr7649655576376376530on_val,A2: produc9003781588162623004on_val] :
      ( ( A4 = bot_bo6722054719108133734on_val )
     => ~ ( member2879030624002546611on_val @ A2 @ A4 ) ) ).

% equals0D
thf(fact_490_equals0D,axiom,
    ! [A4: set_option_state,A2: option_state] :
      ( ( A4 = bot_bo710180891245420500_state )
     => ~ ( member_option_state @ A2 @ A4 ) ) ).

% equals0D
thf(fact_491_equals0D,axiom,
    ! [A4: set_option_val,A2: option_val] :
      ( ( A4 = bot_bo5906790151302476563on_val )
     => ~ ( member_option_val @ A2 @ A4 ) ) ).

% equals0D
thf(fact_492_equals0D,axiom,
    ! [A4: set_val,A2: val] :
      ( ( A4 = bot_bot_set_val )
     => ~ ( member_val @ A2 @ A4 ) ) ).

% equals0D
thf(fact_493_equals0I,axiom,
    ! [A4: set_Pr3433046674199179443r_prat] :
      ( ! [Y4: produc1457211279475724562t_char > prat] :
          ~ ( member2336342582916103932r_prat @ Y4 @ A4 )
     => ( A4 = bot_bo3164680191535668511r_prat ) ) ).

% equals0I
thf(fact_494_equals0I,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ! [Y4: produc1457211279475724562t_char] :
          ~ ( member484235747325421115t_char @ Y4 @ A4 )
     => ( A4 = bot_bo1414094081888755934t_char ) ) ).

% equals0I
thf(fact_495_equals0I,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ! [Y4: produc9003781588162623004on_val] :
          ~ ( member2879030624002546611on_val @ Y4 @ A4 )
     => ( A4 = bot_bo6722054719108133734on_val ) ) ).

% equals0I
thf(fact_496_equals0I,axiom,
    ! [A4: set_option_state] :
      ( ! [Y4: option_state] :
          ~ ( member_option_state @ Y4 @ A4 )
     => ( A4 = bot_bo710180891245420500_state ) ) ).

% equals0I
thf(fact_497_equals0I,axiom,
    ! [A4: set_option_val] :
      ( ! [Y4: option_val] :
          ~ ( member_option_val @ Y4 @ A4 )
     => ( A4 = bot_bo5906790151302476563on_val ) ) ).

% equals0I
thf(fact_498_equals0I,axiom,
    ! [A4: set_val] :
      ( ! [Y4: val] :
          ~ ( member_val @ Y4 @ A4 )
     => ( A4 = bot_bot_set_val ) ) ).

% equals0I
thf(fact_499_ex__in__conv,axiom,
    ! [A4: set_Pr3433046674199179443r_prat] :
      ( ( ? [X4: produc1457211279475724562t_char > prat] : ( member2336342582916103932r_prat @ X4 @ A4 ) )
      = ( A4 != bot_bo3164680191535668511r_prat ) ) ).

% ex_in_conv
thf(fact_500_ex__in__conv,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( ? [X4: produc1457211279475724562t_char] : ( member484235747325421115t_char @ X4 @ A4 ) )
      = ( A4 != bot_bo1414094081888755934t_char ) ) ).

% ex_in_conv
thf(fact_501_ex__in__conv,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( ? [X4: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X4 @ A4 ) )
      = ( A4 != bot_bo6722054719108133734on_val ) ) ).

% ex_in_conv
thf(fact_502_ex__in__conv,axiom,
    ! [A4: set_option_state] :
      ( ( ? [X4: option_state] : ( member_option_state @ X4 @ A4 ) )
      = ( A4 != bot_bo710180891245420500_state ) ) ).

% ex_in_conv
thf(fact_503_ex__in__conv,axiom,
    ! [A4: set_option_val] :
      ( ( ? [X4: option_val] : ( member_option_val @ X4 @ A4 ) )
      = ( A4 != bot_bo5906790151302476563on_val ) ) ).

% ex_in_conv
thf(fact_504_ex__in__conv,axiom,
    ! [A4: set_val] :
      ( ( ? [X4: val] : ( member_val @ X4 @ A4 ) )
      = ( A4 != bot_bot_set_val ) ) ).

% ex_in_conv
thf(fact_505_fun__upd__def,axiom,
    ( fun_up5735975307950539954on_val
    = ( ^ [F2: produc1457211279475724562t_char > option_val,A3: produc1457211279475724562t_char,B3: option_val,X4: produc1457211279475724562t_char] : ( if_option_val @ ( X4 = A3 ) @ B3 @ ( F2 @ X4 ) ) ) ) ).

% fun_upd_def
thf(fact_506_fun__upd__def,axiom,
    ( fun_up829850848796697765r_prat
    = ( ^ [F2: produc1457211279475724562t_char > prat,A3: produc1457211279475724562t_char,B3: prat,X4: produc1457211279475724562t_char] : ( if_prat @ ( X4 = A3 ) @ B3 @ ( F2 @ X4 ) ) ) ) ).

% fun_upd_def
thf(fact_507_fun__upd__def,axiom,
    ( fun_up273046073882939271on_val
    = ( ^ [F2: produc9003781588162623004on_val > option8887860577033306220on_val,A3: produc9003781588162623004on_val,B3: option8887860577033306220on_val,X4: produc9003781588162623004on_val] : ( if_opt2965748431298708774on_val @ ( X4 = A3 ) @ B3 @ ( F2 @ X4 ) ) ) ) ).

% fun_upd_def
thf(fact_508_fun__upd__def,axiom,
    ( fun_up1601731230164360576on_val
    = ( ^ [F2: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A3: produc1457211279475724562t_char > prat,B3: option5747939881698552298on_val,X4: produc1457211279475724562t_char > prat] : ( if_opt6509584284076893604on_val @ ( X4 = A3 ) @ B3 @ ( F2 @ X4 ) ) ) ) ).

% fun_upd_def
thf(fact_509_fun__upd__eqD,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val,G: produc1457211279475724562t_char > option_val,Z3: option_val] :
      ( ( ( fun_up5735975307950539954on_val @ F @ X @ Y3 )
        = ( fun_up5735975307950539954on_val @ G @ X @ Z3 ) )
     => ( Y3 = Z3 ) ) ).

% fun_upd_eqD
thf(fact_510_fun__upd__eqD,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat,G: produc1457211279475724562t_char > prat,Z3: prat] :
      ( ( ( fun_up829850848796697765r_prat @ F @ X @ Y3 )
        = ( fun_up829850848796697765r_prat @ G @ X @ Z3 ) )
     => ( Y3 = Z3 ) ) ).

% fun_upd_eqD
thf(fact_511_fun__upd__eqD,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,Z3: option8887860577033306220on_val] :
      ( ( ( fun_up273046073882939271on_val @ F @ X @ Y3 )
        = ( fun_up273046073882939271on_val @ G @ X @ Z3 ) )
     => ( Y3 = Z3 ) ) ).

% fun_upd_eqD
thf(fact_512_fun__upd__eqD,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,Z3: option5747939881698552298on_val] :
      ( ( ( fun_up1601731230164360576on_val @ F @ X @ Y3 )
        = ( fun_up1601731230164360576on_val @ G @ X @ Z3 ) )
     => ( Y3 = Z3 ) ) ).

% fun_upd_eqD
thf(fact_513_fun__upd__idem,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( ( F @ X )
        = Y3 )
     => ( ( fun_up5735975307950539954on_val @ F @ X @ Y3 )
        = F ) ) ).

% fun_upd_idem
thf(fact_514_fun__upd__idem,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat] :
      ( ( ( F @ X )
        = Y3 )
     => ( ( fun_up829850848796697765r_prat @ F @ X @ Y3 )
        = F ) ) ).

% fun_upd_idem
thf(fact_515_fun__upd__idem,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( ( F @ X )
        = Y3 )
     => ( ( fun_up273046073882939271on_val @ F @ X @ Y3 )
        = F ) ) ).

% fun_upd_idem
thf(fact_516_fun__upd__idem,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val] :
      ( ( ( F @ X )
        = Y3 )
     => ( ( fun_up1601731230164360576on_val @ F @ X @ Y3 )
        = F ) ) ).

% fun_upd_idem
thf(fact_517_fun__upd__same,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( fun_up5735975307950539954on_val @ F @ X @ Y3 @ X )
      = Y3 ) ).

% fun_upd_same
thf(fact_518_fun__upd__same,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat] :
      ( ( fun_up829850848796697765r_prat @ F @ X @ Y3 @ X )
      = Y3 ) ).

% fun_upd_same
thf(fact_519_fun__upd__same,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( fun_up273046073882939271on_val @ F @ X @ Y3 @ X )
      = Y3 ) ).

% fun_upd_same
thf(fact_520_fun__upd__same,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val] :
      ( ( fun_up1601731230164360576on_val @ F @ X @ Y3 @ X )
      = Y3 ) ).

% fun_upd_same
thf(fact_521_fun__upd__other,axiom,
    ! [Z3: produc1457211279475724562t_char,X: produc1457211279475724562t_char,F: produc1457211279475724562t_char > option_val,Y3: option_val] :
      ( ( Z3 != X )
     => ( ( fun_up5735975307950539954on_val @ F @ X @ Y3 @ Z3 )
        = ( F @ Z3 ) ) ) ).

% fun_upd_other
thf(fact_522_fun__upd__other,axiom,
    ! [Z3: produc1457211279475724562t_char,X: produc1457211279475724562t_char,F: produc1457211279475724562t_char > prat,Y3: prat] :
      ( ( Z3 != X )
     => ( ( fun_up829850848796697765r_prat @ F @ X @ Y3 @ Z3 )
        = ( F @ Z3 ) ) ) ).

% fun_upd_other
thf(fact_523_fun__upd__other,axiom,
    ! [Z3: produc9003781588162623004on_val,X: produc9003781588162623004on_val,F: produc9003781588162623004on_val > option8887860577033306220on_val,Y3: option8887860577033306220on_val] :
      ( ( Z3 != X )
     => ( ( fun_up273046073882939271on_val @ F @ X @ Y3 @ Z3 )
        = ( F @ Z3 ) ) ) ).

% fun_upd_other
thf(fact_524_fun__upd__other,axiom,
    ! [Z3: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char > prat,F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,Y3: option5747939881698552298on_val] :
      ( ( Z3 != X )
     => ( ( fun_up1601731230164360576on_val @ F @ X @ Y3 @ Z3 )
        = ( F @ Z3 ) ) ) ).

% fun_upd_other
thf(fact_525_fun__upd__twist,axiom,
    ! [A2: produc1457211279475724562t_char,C: produc1457211279475724562t_char,M: produc1457211279475724562t_char > option_val,B2: option_val,D: option_val] :
      ( ( A2 != C )
     => ( ( fun_up5735975307950539954on_val @ ( fun_up5735975307950539954on_val @ M @ A2 @ B2 ) @ C @ D )
        = ( fun_up5735975307950539954on_val @ ( fun_up5735975307950539954on_val @ M @ C @ D ) @ A2 @ B2 ) ) ) ).

% fun_upd_twist
thf(fact_526_fun__upd__twist,axiom,
    ! [A2: produc1457211279475724562t_char,C: produc1457211279475724562t_char,M: produc1457211279475724562t_char > prat,B2: prat,D: prat] :
      ( ( A2 != C )
     => ( ( fun_up829850848796697765r_prat @ ( fun_up829850848796697765r_prat @ M @ A2 @ B2 ) @ C @ D )
        = ( fun_up829850848796697765r_prat @ ( fun_up829850848796697765r_prat @ M @ C @ D ) @ A2 @ B2 ) ) ) ).

% fun_upd_twist
thf(fact_527_fun__upd__twist,axiom,
    ! [A2: produc9003781588162623004on_val,C: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val,B2: option8887860577033306220on_val,D: option8887860577033306220on_val] :
      ( ( A2 != C )
     => ( ( fun_up273046073882939271on_val @ ( fun_up273046073882939271on_val @ M @ A2 @ B2 ) @ C @ D )
        = ( fun_up273046073882939271on_val @ ( fun_up273046073882939271on_val @ M @ C @ D ) @ A2 @ B2 ) ) ) ).

% fun_upd_twist
thf(fact_528_fun__upd__twist,axiom,
    ! [A2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,B2: option5747939881698552298on_val,D: option5747939881698552298on_val] :
      ( ( A2 != C )
     => ( ( fun_up1601731230164360576on_val @ ( fun_up1601731230164360576on_val @ M @ A2 @ B2 ) @ C @ D )
        = ( fun_up1601731230164360576on_val @ ( fun_up1601731230164360576on_val @ M @ C @ D ) @ A2 @ B2 ) ) ) ).

% fun_upd_twist
thf(fact_529_fun__upd__idem__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( ( fun_up5735975307950539954on_val @ F @ X @ Y3 )
        = F )
      = ( ( F @ X )
        = Y3 ) ) ).

% fun_upd_idem_iff
thf(fact_530_fun__upd__idem__iff,axiom,
    ! [F: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat] :
      ( ( ( fun_up829850848796697765r_prat @ F @ X @ Y3 )
        = F )
      = ( ( F @ X )
        = Y3 ) ) ).

% fun_upd_idem_iff
thf(fact_531_fun__upd__idem__iff,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( ( fun_up273046073882939271on_val @ F @ X @ Y3 )
        = F )
      = ( ( F @ X )
        = Y3 ) ) ).

% fun_upd_idem_iff
thf(fact_532_fun__upd__idem__iff,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val] :
      ( ( ( fun_up1601731230164360576on_val @ F @ X @ Y3 )
        = F )
      = ( ( F @ X )
        = Y3 ) ) ).

% fun_upd_idem_iff
thf(fact_533_Set_Ois__empty__def,axiom,
    ( is_emp609703007689476580t_char
    = ( ^ [A6: set_Pr2507339680178222706t_char] : ( A6 = bot_bo1414094081888755934t_char ) ) ) ).

% Set.is_empty_def
thf(fact_534_Set_Ois__empty__def,axiom,
    ( is_emp5364603196349043402on_val
    = ( ^ [A6: set_Pr7649655576376376530on_val] : ( A6 = bot_bo6722054719108133734on_val ) ) ) ).

% Set.is_empty_def
thf(fact_535_Set_Ois__empty__def,axiom,
    ( is_emp7138872393943660984_state
    = ( ^ [A6: set_option_state] : ( A6 = bot_bo710180891245420500_state ) ) ) ).

% Set.is_empty_def
thf(fact_536_Set_Ois__empty__def,axiom,
    ( is_empty_option_val
    = ( ^ [A6: set_option_val] : ( A6 = bot_bo5906790151302476563on_val ) ) ) ).

% Set.is_empty_def
thf(fact_537_Set_Ois__empty__def,axiom,
    ( is_empty_val
    = ( ^ [A6: set_val] : ( A6 = bot_bot_set_val ) ) ) ).

% Set.is_empty_def
thf(fact_538_map__option__o__map__upd,axiom,
    ! [F: val > state,M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( comp_o1559856024338158690t_char @ ( map_option_val_state @ F ) @ ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) ) )
      = ( fun_up6995552760743215839_state @ ( comp_o1559856024338158690t_char @ ( map_option_val_state @ F ) @ M ) @ A2 @ ( some_state @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_539_map__option__o__map__upd,axiom,
    ! [F: state > val,M: produc1457211279475724562t_char > option_state,A2: produc1457211279475724562t_char,B2: state] :
      ( ( comp_o5861356331151617272t_char @ ( map_option_state_val @ F ) @ ( fun_up6995552760743215839_state @ M @ A2 @ ( some_state @ B2 ) ) )
      = ( fun_up5735975307950539954on_val @ ( comp_o5861356331151617272t_char @ ( map_option_state_val @ F ) @ M ) @ A2 @ ( some_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_540_map__option__o__map__upd,axiom,
    ! [F: val > val,M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( comp_o7206986085106588079t_char @ ( map_option_val_val @ F ) @ ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) ) )
      = ( fun_up5735975307950539954on_val @ ( comp_o7206986085106588079t_char @ ( map_option_val_val @ F ) @ M ) @ A2 @ ( some_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_541_map__option__o__map__upd,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( comp_o7664117635472112386t_char @ ( map_op8011878015112499536on_val @ F ) @ ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) ) )
      = ( fun_up7235018766041795647on_val @ ( comp_o7664117635472112386t_char @ ( map_op8011878015112499536on_val @ F ) @ M ) @ A2 @ ( some_P7669353234731512949on_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_542_map__option__o__map__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,M: produc1457211279475724562t_char > option5747939881698552298on_val,A2: produc1457211279475724562t_char,B2: produc1457211279475724562t_char > option_val] :
      ( ( comp_o3878402015218311000t_char @ ( map_op880068700720311194al_val @ F ) @ ( fun_up7235018766041795647on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ B2 ) ) )
      = ( fun_up5735975307950539954on_val @ ( comp_o3878402015218311000t_char @ ( map_op880068700720311194al_val @ F ) @ M ) @ A2 @ ( some_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_543_map__option__o__map__upd,axiom,
    ! [F: val > produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option_val,A2: produc1457211279475724562t_char > prat,B2: val] :
      ( ( comp_o1018635247228614211r_prat @ ( map_op8011878015112499536on_val @ F ) @ ( fun_up5104302054361798705on_val @ M @ A2 @ ( some_val @ B2 ) ) )
      = ( fun_up1601731230164360576on_val @ ( comp_o1018635247228614211r_prat @ ( map_op8011878015112499536on_val @ F ) @ M ) @ A2 @ ( some_P7669353234731512949on_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_544_map__option__o__map__upd,axiom,
    ! [F: state > produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option_state,A2: produc1457211279475724562t_char > prat,B2: state] :
      ( ( comp_o9034235373990032058r_prat @ ( map_op3100526599586584801on_val @ F ) @ ( fun_up1585067318606691488_state @ M @ A2 @ ( some_state @ B2 ) ) )
      = ( fun_up1601731230164360576on_val @ ( comp_o9034235373990032058r_prat @ ( map_op3100526599586584801on_val @ F ) @ M ) @ A2 @ ( some_P7669353234731512949on_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_545_map__option__o__map__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val] :
      ( ( comp_o5748106371294530457r_prat @ ( map_op880068700720311194al_val @ F ) @ ( fun_up1601731230164360576on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ B2 ) ) )
      = ( fun_up5104302054361798705on_val @ ( comp_o5748106371294530457r_prat @ ( map_op880068700720311194al_val @ F ) @ M ) @ A2 @ ( some_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_546_map__option__o__map__upd,axiom,
    ! [F: ( produc1457211279475724562t_char > option_val ) > state,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val] :
      ( ( comp_o6942933442099041594r_prat @ ( map_op1814185762381987425_state @ F ) @ ( fun_up1601731230164360576on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ B2 ) ) )
      = ( fun_up1585067318606691488_state @ ( comp_o6942933442099041594r_prat @ ( map_op1814185762381987425_state @ F ) @ M ) @ A2 @ ( some_state @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_547_map__option__o__map__upd,axiom,
    ! [F: val > produc9003781588162623004on_val,M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( comp_o5741203133494854784t_char @ ( map_op3897579098253967186on_val @ F ) @ ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) ) )
      = ( fun_up4210561521004557121on_val @ ( comp_o5741203133494854784t_char @ ( map_op3897579098253967186on_val @ F ) @ M ) @ A2 @ ( some_P2581650809551911671on_val @ ( F @ B2 ) ) ) ) ).

% map_option_o_map_upd
thf(fact_548_uni__mask_Osimps,axiom,
    ( uni_ma6578582744724537101t_char
    = ( fun_up829850848796697765r_prat @ empty_3446695950879338768t_char ) ) ).

% uni_mask.simps
thf(fact_549_uni__mask_Oelims,axiom,
    ! [X: produc1457211279475724562t_char,Xa: prat,Y3: produc1457211279475724562t_char > prat] :
      ( ( ( uni_ma6578582744724537101t_char @ X @ Xa )
        = Y3 )
     => ( Y3
        = ( fun_up829850848796697765r_prat @ empty_3446695950879338768t_char @ X @ Xa ) ) ) ).

% uni_mask.elims
thf(fact_550_Collect__empty__eq__bot,axiom,
    ! [P: produc1457211279475724562t_char > $o] :
      ( ( ( collec2458894688891239037t_char @ P )
        = bot_bo1414094081888755934t_char )
      = ( P = bot_bo1808431002336377727char_o ) ) ).

% Collect_empty_eq_bot
thf(fact_551_Collect__empty__eq__bot,axiom,
    ! [P: produc9003781588162623004on_val > $o] :
      ( ( ( collec7475294502966882545on_val @ P )
        = bot_bo6722054719108133734on_val )
      = ( P = bot_bo6370234372831922335_val_o ) ) ).

% Collect_empty_eq_bot
thf(fact_552_Collect__empty__eq__bot,axiom,
    ! [P: option_state > $o] :
      ( ( ( collect_option_state @ P )
        = bot_bo710180891245420500_state )
      = ( P = bot_bo4453335400789057457tate_o ) ) ).

% Collect_empty_eq_bot
thf(fact_553_Collect__empty__eq__bot,axiom,
    ! [P: option_val > $o] :
      ( ( ( collect_option_val @ P )
        = bot_bo5906790151302476563on_val )
      = ( P = bot_bot_option_val_o ) ) ).

% Collect_empty_eq_bot
thf(fact_554_Collect__empty__eq__bot,axiom,
    ! [P: val > $o] :
      ( ( ( collect_val @ P )
        = bot_bot_set_val )
      = ( P = bot_bot_val_o ) ) ).

% Collect_empty_eq_bot
thf(fact_555_bot__empty__eq,axiom,
    ( bot_bo3932128351999234686prat_o
    = ( ^ [X4: produc1457211279475724562t_char > prat] : ( member2336342582916103932r_prat @ X4 @ bot_bo3164680191535668511r_prat ) ) ) ).

% bot_empty_eq
thf(fact_556_bot__empty__eq,axiom,
    ( bot_bo1808431002336377727char_o
    = ( ^ [X4: produc1457211279475724562t_char] : ( member484235747325421115t_char @ X4 @ bot_bo1414094081888755934t_char ) ) ) ).

% bot_empty_eq
thf(fact_557_bot__empty__eq,axiom,
    ( bot_bo6370234372831922335_val_o
    = ( ^ [X4: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X4 @ bot_bo6722054719108133734on_val ) ) ) ).

% bot_empty_eq
thf(fact_558_bot__empty__eq,axiom,
    ( bot_bo4453335400789057457tate_o
    = ( ^ [X4: option_state] : ( member_option_state @ X4 @ bot_bo710180891245420500_state ) ) ) ).

% bot_empty_eq
thf(fact_559_bot__empty__eq,axiom,
    ( bot_bot_option_val_o
    = ( ^ [X4: option_val] : ( member_option_val @ X4 @ bot_bo5906790151302476563on_val ) ) ) ).

% bot_empty_eq
thf(fact_560_bot__empty__eq,axiom,
    ( bot_bot_val_o
    = ( ^ [X4: val] : ( member_val @ X4 @ bot_bot_set_val ) ) ) ).

% bot_empty_eq
thf(fact_561_option_Osimps_I15_J,axiom,
    ! [X2: produc1317171644805857433on_val] :
      ( ( set_op5043251206941365031on_val @ ( some_P3086335783055994110on_val @ X2 ) )
      = ( insert7062705985672971881on_val @ X2 @ bot_bo402267660617762917on_val ) ) ).

% option.simps(15)
thf(fact_562_option_Osimps_I15_J,axiom,
    ! [X2: produc1457211279475724562t_char > option_val] :
      ( ( set_op1770538635792728844on_val @ ( some_P7669353234731512949on_val @ X2 ) )
      = ( insert216038912599248202on_val @ X2 @ bot_bo5671083314777306084on_val ) ) ).

% option.simps(15)
thf(fact_563_option_Osimps_I15_J,axiom,
    ! [X2: produc1457211279475724562t_char] :
      ( ( set_op7440730737645789856t_char @ ( some_P6851457240968045559t_char @ X2 ) )
      = ( insert3372640069787401954t_char @ X2 @ bot_bo1414094081888755934t_char ) ) ).

% option.simps(15)
thf(fact_564_option_Osimps_I15_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ( set_op9004752959087400718on_val @ ( some_P2581650809551911671on_val @ X2 ) )
      = ( insert3030518898131756108on_val @ X2 @ bot_bo6722054719108133734on_val ) ) ).

% option.simps(15)
thf(fact_565_option_Osimps_I15_J,axiom,
    ! [X2: option_state] :
      ( ( set_op5162993263733338108_state @ ( some_option_state @ X2 ) )
      = ( insert_option_state @ X2 @ bot_bo710180891245420500_state ) ) ).

% option.simps(15)
thf(fact_566_option_Osimps_I15_J,axiom,
    ! [X2: option_val] :
      ( ( set_op911010586042427349on_val @ ( some_option_val @ X2 ) )
      = ( insert_option_val @ X2 @ bot_bo5906790151302476563on_val ) ) ).

% option.simps(15)
thf(fact_567_option_Osimps_I15_J,axiom,
    ! [X2: val] :
      ( ( set_option_val2 @ ( some_val @ X2 ) )
      = ( insert_val @ X2 @ bot_bot_set_val ) ) ).

% option.simps(15)
thf(fact_568_option_Osimps_I15_J,axiom,
    ! [X2: state] :
      ( ( set_option_state2 @ ( some_state @ X2 ) )
      = ( insert_state @ X2 @ bot_bot_set_state ) ) ).

% option.simps(15)
thf(fact_569_map__add__upd__left,axiom,
    ! [M: produc1457211279475724562t_char,E2: produc1457211279475724562t_char > option_val,E1: produc1457211279475724562t_char > option_val,U1: val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ E2 ) )
     => ( ( map_ad2908576761495157028ar_val @ ( fun_up5735975307950539954on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up5735975307950539954on_val @ ( map_ad2908576761495157028ar_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_570_map__add__upd__left,axiom,
    ! [M: val,E2: val > option_val,E1: val > option_val,U1: val] :
      ( ~ ( member_val @ M @ ( dom_val_val @ E2 ) )
     => ( ( map_add_val_val @ ( fun_up735531404784515971on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up735531404784515971on_val @ ( map_add_val_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_571_map__add__upd__left,axiom,
    ! [M: val,E2: val > option_state,E1: val > option_state,U1: state] :
      ( ~ ( member_val @ M @ ( dom_val_state @ E2 ) )
     => ( ( map_add_val_state @ ( fun_up7100790768922270414_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up7100790768922270414_state @ ( map_add_val_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_572_map__add__upd__left,axiom,
    ! [M: option_state,E2: option_state > option_val,E1: option_state > option_val,U1: val] :
      ( ~ ( member_option_state @ M @ ( dom_option_state_val @ E2 ) )
     => ( ( map_ad304724714348188800te_val @ ( fun_up8652368643555229054on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up8652368643555229054on_val @ ( map_ad304724714348188800te_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_573_map__add__upd__left,axiom,
    ! [M: option_val,E2: option_val > option_val,E1: option_val > option_val,U1: val] :
      ( ~ ( member_option_val @ M @ ( dom_option_val_val @ E2 ) )
     => ( ( map_ad2791809220819668783al_val @ ( fun_up8761876891205509693on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up8761876891205509693on_val @ ( map_ad2791809220819668783al_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_574_map__add__upd__left,axiom,
    ! [M: option_state,E2: option_state > option_state,E1: option_state > option_state,U1: state] :
      ( ~ ( member_option_state @ M @ ( dom_op8569336450220619928_state @ E2 ) )
     => ( ( map_ad3143451158333058555_state @ ( fun_up6517640620910344979_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up6517640620910344979_state @ ( map_ad3143451158333058555_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_575_map__add__upd__left,axiom,
    ! [M: option_val,E2: option_val > option_state,E1: option_val > option_state,U1: state] :
      ( ~ ( member_option_val @ M @ ( dom_option_val_state @ E2 ) )
     => ( ( map_ad1596397661948740748_state @ ( fun_up2039547756584784788_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up2039547756584784788_state @ ( map_ad1596397661948740748_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_576_map__add__upd__left,axiom,
    ! [M: produc1457211279475724562t_char > prat,E2: ( produc1457211279475724562t_char > prat ) > option_val,E1: ( produc1457211279475724562t_char > prat ) > option_val,U1: val] :
      ( ~ ( member2336342582916103932r_prat @ M @ ( dom_Pr3224398758927333440at_val @ E2 ) )
     => ( ( map_ad5245944522959850275at_val @ ( fun_up5104302054361798705on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up5104302054361798705on_val @ ( map_ad5245944522959850275at_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_577_map__add__upd__left,axiom,
    ! [M: produc1457211279475724562t_char > prat,E2: ( produc1457211279475724562t_char > prat ) > option_state,E1: ( produc1457211279475724562t_char > prat ) > option_state,U1: state] :
      ( ~ ( member2336342582916103932r_prat @ M @ ( dom_Pr2103017623604714043_state @ E2 ) )
     => ( ( map_ad5796490619809589144_state @ ( fun_up1585067318606691488_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up1585067318606691488_state @ ( map_ad5796490619809589144_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_578_map__add__upd__left,axiom,
    ! [M: val,E2: val > option5747939881698552298on_val,E1: val > option5747939881698552298on_val,U1: produc1457211279475724562t_char > option_val] :
      ( ~ ( member_val @ M @ ( dom_va8931846639282357193on_val @ E2 ) )
     => ( ( map_ad4617731073159927590on_val @ ( fun_up8940424251277849774on_val @ E1 @ M @ ( some_P7669353234731512949on_val @ U1 ) ) @ E2 )
        = ( fun_up8940424251277849774on_val @ ( map_ad4617731073159927590on_val @ E1 @ E2 ) @ M @ ( some_P7669353234731512949on_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_579_insertCI,axiom,
    ! [A2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val,B2: produc1317171644805857433on_val] :
      ( ( ~ ( member6505152944228695362on_val @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_580_insertCI,axiom,
    ! [A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val] :
      ( ( ~ ( member2879030624002546611on_val @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_581_insertCI,axiom,
    ! [A2: option_state,B5: set_option_state,B2: option_state] :
      ( ( ~ ( member_option_state @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member_option_state @ A2 @ ( insert_option_state @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_582_insertCI,axiom,
    ! [A2: option_val,B5: set_option_val,B2: option_val] :
      ( ( ~ ( member_option_val @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member_option_val @ A2 @ ( insert_option_val @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_583_insertCI,axiom,
    ! [A2: val,B5: set_val,B2: val] :
      ( ( ~ ( member_val @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member_val @ A2 @ ( insert_val @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_584_insertCI,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat,B2: produc1457211279475724562t_char > prat] :
      ( ( ~ ( member2336342582916103932r_prat @ A2 @ B5 )
       => ( A2 = B2 ) )
     => ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ B2 @ B5 ) ) ) ).

% insertCI
thf(fact_585_insert__iff,axiom,
    ! [A2: produc1317171644805857433on_val,B2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member6505152944228695362on_val @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_586_insert__iff,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member2879030624002546611on_val @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_587_insert__iff,axiom,
    ! [A2: option_state,B2: option_state,A4: set_option_state] :
      ( ( member_option_state @ A2 @ ( insert_option_state @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member_option_state @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_588_insert__iff,axiom,
    ! [A2: option_val,B2: option_val,A4: set_option_val] :
      ( ( member_option_val @ A2 @ ( insert_option_val @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member_option_val @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_589_insert__iff,axiom,
    ! [A2: val,B2: val,A4: set_val] :
      ( ( member_val @ A2 @ ( insert_val @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member_val @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_590_insert__iff,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ B2 @ A4 ) )
      = ( ( A2 = B2 )
        | ( member2336342582916103932r_prat @ A2 @ A4 ) ) ) ).

% insert_iff
thf(fact_591_insert__absorb2,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( insert7062705985672971881on_val @ X @ ( insert7062705985672971881on_val @ X @ A4 ) )
      = ( insert7062705985672971881on_val @ X @ A4 ) ) ).

% insert_absorb2
thf(fact_592_insert__absorb2,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( insert3030518898131756108on_val @ X @ ( insert3030518898131756108on_val @ X @ A4 ) )
      = ( insert3030518898131756108on_val @ X @ A4 ) ) ).

% insert_absorb2
thf(fact_593_insert__absorb2,axiom,
    ! [X: option_state,A4: set_option_state] :
      ( ( insert_option_state @ X @ ( insert_option_state @ X @ A4 ) )
      = ( insert_option_state @ X @ A4 ) ) ).

% insert_absorb2
thf(fact_594_insert__absorb2,axiom,
    ! [X: option_val,A4: set_option_val] :
      ( ( insert_option_val @ X @ ( insert_option_val @ X @ A4 ) )
      = ( insert_option_val @ X @ A4 ) ) ).

% insert_absorb2
thf(fact_595_insert__absorb2,axiom,
    ! [X: val,A4: set_val] :
      ( ( insert_val @ X @ ( insert_val @ X @ A4 ) )
      = ( insert_val @ X @ A4 ) ) ).

% insert_absorb2
thf(fact_596_comp__apply,axiom,
    ( comp_o4916166309651032803_state
    = ( ^ [F2: option_state > state,G2: state > option_state,X4: state] : ( F2 @ ( G2 @ X4 ) ) ) ) ).

% comp_apply
thf(fact_597_comp__apply,axiom,
    ( comp_o5604524432708427236al_val
    = ( ^ [F2: option_val > val,G2: val > option_val,X4: val] : ( F2 @ ( G2 @ X4 ) ) ) ) ).

% comp_apply
thf(fact_598_singletonI,axiom,
    ! [A2: produc1317171644805857433on_val] : ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) ) ).

% singletonI
thf(fact_599_singletonI,axiom,
    ! [A2: produc1457211279475724562t_char > prat] : ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ A2 @ bot_bo3164680191535668511r_prat ) ) ).

% singletonI
thf(fact_600_singletonI,axiom,
    ! [A2: produc1457211279475724562t_char] : ( member484235747325421115t_char @ A2 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) ) ).

% singletonI
thf(fact_601_singletonI,axiom,
    ! [A2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) ).

% singletonI
thf(fact_602_singletonI,axiom,
    ! [A2: option_state] : ( member_option_state @ A2 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) ) ).

% singletonI
thf(fact_603_singletonI,axiom,
    ! [A2: option_val] : ( member_option_val @ A2 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) ) ).

% singletonI
thf(fact_604_singletonI,axiom,
    ! [A2: val] : ( member_val @ A2 @ ( insert_val @ A2 @ bot_bot_set_val ) ) ).

% singletonI
thf(fact_605_dom__eq__empty__conv,axiom,
    ! [F: val > option_state] :
      ( ( ( dom_val_state @ F )
        = bot_bot_set_val )
      = ( F
        = ( ^ [X4: val] : none_state ) ) ) ).

% dom_eq_empty_conv
thf(fact_606_dom__eq__empty__conv,axiom,
    ! [F: val > option_val] :
      ( ( ( dom_val_val @ F )
        = bot_bot_set_val )
      = ( F
        = ( ^ [X4: val] : none_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_607_dom__eq__empty__conv,axiom,
    ! [F: option_state > option_state] :
      ( ( ( dom_op8569336450220619928_state @ F )
        = bot_bo710180891245420500_state )
      = ( F
        = ( ^ [X4: option_state] : none_state ) ) ) ).

% dom_eq_empty_conv
thf(fact_608_dom__eq__empty__conv,axiom,
    ! [F: option_state > option_val] :
      ( ( ( dom_option_state_val @ F )
        = bot_bo710180891245420500_state )
      = ( F
        = ( ^ [X4: option_state] : none_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_609_dom__eq__empty__conv,axiom,
    ! [F: option_val > option_state] :
      ( ( ( dom_option_val_state @ F )
        = bot_bo5906790151302476563on_val )
      = ( F
        = ( ^ [X4: option_val] : none_state ) ) ) ).

% dom_eq_empty_conv
thf(fact_610_dom__eq__empty__conv,axiom,
    ! [F: option_val > option_val] :
      ( ( ( dom_option_val_val @ F )
        = bot_bo5906790151302476563on_val )
      = ( F
        = ( ^ [X4: option_val] : none_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_611_dom__eq__empty__conv,axiom,
    ! [F: produc1457211279475724562t_char > option_state] :
      ( ( ( dom_Pr24798649119601274_state @ F )
        = bot_bo1414094081888755934t_char )
      = ( F
        = ( ^ [X4: produc1457211279475724562t_char] : none_state ) ) ) ).

% dom_eq_empty_conv
thf(fact_612_dom__eq__empty__conv,axiom,
    ! [F: produc1457211279475724562t_char > option_val] :
      ( ( ( dom_Pr8989479155164304065ar_val @ F )
        = bot_bo1414094081888755934t_char )
      = ( F
        = ( ^ [X4: produc1457211279475724562t_char] : none_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_613_dom__eq__empty__conv,axiom,
    ! [F: val > option5747939881698552298on_val] :
      ( ( ( dom_va8931846639282357193on_val @ F )
        = bot_bot_set_val )
      = ( F
        = ( ^ [X4: val] : none_P1334921381875262201on_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_614_dom__eq__empty__conv,axiom,
    ! [F: option_state > option5747939881698552298on_val] :
      ( ( ( dom_op741179583939567608on_val @ F )
        = bot_bo710180891245420500_state )
      = ( F
        = ( ^ [X4: option_state] : none_P1334921381875262201on_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_615_case__map__option,axiom,
    ! [G: state,H: option_state > state,F: state > option_state,X: option_state] :
      ( ( case_o2237019792253254865_state @ G @ H @ ( map_op2929067089796592849_state @ F @ X ) )
      = ( case_o2102410670496921089_state @ G @ ( comp_o4916166309651032803_state @ H @ F ) @ X ) ) ).

% case_map_option
thf(fact_616_case__map__option,axiom,
    ! [G: val,H: option_val > val,F: val > option_val,X: option_val] :
      ( ( case_o5195096591205178001on_val @ G @ H @ ( map_op5819421865013908113on_val @ F @ X ) )
      = ( case_option_val_val @ G @ ( comp_o5604524432708427236al_val @ H @ F ) @ X ) ) ).

% case_map_option
thf(fact_617_fun__upd__None__if__notin__dom,axiom,
    ! [K: val,M: val > option_state] :
      ( ~ ( member_val @ K @ ( dom_val_state @ M ) )
     => ( ( fun_up7100790768922270414_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_618_fun__upd__None__if__notin__dom,axiom,
    ! [K: val,M: val > option_val] :
      ( ~ ( member_val @ K @ ( dom_val_val @ M ) )
     => ( ( fun_up735531404784515971on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_619_fun__upd__None__if__notin__dom,axiom,
    ! [K: option_state,M: option_state > option_state] :
      ( ~ ( member_option_state @ K @ ( dom_op8569336450220619928_state @ M ) )
     => ( ( fun_up6517640620910344979_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_620_fun__upd__None__if__notin__dom,axiom,
    ! [K: option_val,M: option_val > option_state] :
      ( ~ ( member_option_val @ K @ ( dom_option_val_state @ M ) )
     => ( ( fun_up2039547756584784788_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_621_fun__upd__None__if__notin__dom,axiom,
    ! [K: option_state,M: option_state > option_val] :
      ( ~ ( member_option_state @ K @ ( dom_option_state_val @ M ) )
     => ( ( fun_up8652368643555229054on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_622_fun__upd__None__if__notin__dom,axiom,
    ! [K: option_val,M: option_val > option_val] :
      ( ~ ( member_option_val @ K @ ( dom_option_val_val @ M ) )
     => ( ( fun_up8761876891205509693on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_623_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc1457211279475724562t_char,M: produc1457211279475724562t_char > option_val] :
      ( ~ ( member484235747325421115t_char @ K @ ( dom_Pr8989479155164304065ar_val @ M ) )
     => ( ( fun_up5735975307950539954on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_624_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_state] :
      ( ~ ( member2336342582916103932r_prat @ K @ ( dom_Pr2103017623604714043_state @ M ) )
     => ( ( fun_up1585067318606691488_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_625_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_val] :
      ( ~ ( member2336342582916103932r_prat @ K @ ( dom_Pr3224398758927333440at_val @ M ) )
     => ( ( fun_up5104302054361798705on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_626_fun__upd__None__if__notin__dom,axiom,
    ! [K: val,M: val > option5747939881698552298on_val] :
      ( ~ ( member_val @ K @ ( dom_va8931846639282357193on_val @ M ) )
     => ( ( fun_up8940424251277849774on_val @ M @ K @ none_P1334921381875262201on_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_627_dom__map__option__comp,axiom,
    ! [G: val > state,M: produc1457211279475724562t_char > option_val] :
      ( ( dom_Pr24798649119601274_state @ ( comp_o1559856024338158690t_char @ ( map_option_val_state @ G ) @ M ) )
      = ( dom_Pr8989479155164304065ar_val @ M ) ) ).

% dom_map_option_comp
thf(fact_628_dom__map__option__comp,axiom,
    ! [G: state > val,M: produc1457211279475724562t_char > option_state] :
      ( ( dom_Pr8989479155164304065ar_val @ ( comp_o5861356331151617272t_char @ ( map_option_state_val @ G ) @ M ) )
      = ( dom_Pr24798649119601274_state @ M ) ) ).

% dom_map_option_comp
thf(fact_629_dom__map__option__comp,axiom,
    ! [G: val > val,M: produc1457211279475724562t_char > option_val] :
      ( ( dom_Pr8989479155164304065ar_val @ ( comp_o7206986085106588079t_char @ ( map_option_val_val @ G ) @ M ) )
      = ( dom_Pr8989479155164304065ar_val @ M ) ) ).

% dom_map_option_comp
thf(fact_630_insertE,axiom,
    ! [A2: produc1317171644805857433on_val,B2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member6505152944228695362on_val @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_631_insertE,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member2879030624002546611on_val @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_632_insertE,axiom,
    ! [A2: option_state,B2: option_state,A4: set_option_state] :
      ( ( member_option_state @ A2 @ ( insert_option_state @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member_option_state @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_633_insertE,axiom,
    ! [A2: option_val,B2: option_val,A4: set_option_val] :
      ( ( member_option_val @ A2 @ ( insert_option_val @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member_option_val @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_634_insertE,axiom,
    ! [A2: val,B2: val,A4: set_val] :
      ( ( member_val @ A2 @ ( insert_val @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member_val @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_635_insertE,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ B2 @ A4 ) )
     => ( ( A2 != B2 )
       => ( member2336342582916103932r_prat @ A2 @ A4 ) ) ) ).

% insertE
thf(fact_636_comp__def,axiom,
    ( comp_o4916166309651032803_state
    = ( ^ [F2: option_state > state,G2: state > option_state,X4: state] : ( F2 @ ( G2 @ X4 ) ) ) ) ).

% comp_def
thf(fact_637_comp__def,axiom,
    ( comp_o5604524432708427236al_val
    = ( ^ [F2: option_val > val,G2: val > option_val,X4: val] : ( F2 @ ( G2 @ X4 ) ) ) ) ).

% comp_def
thf(fact_638_insertI1,axiom,
    ! [A2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val] : ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ A2 @ B5 ) ) ).

% insertI1
thf(fact_639_insertI1,axiom,
    ! [A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val] : ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ A2 @ B5 ) ) ).

% insertI1
thf(fact_640_insertI1,axiom,
    ! [A2: option_state,B5: set_option_state] : ( member_option_state @ A2 @ ( insert_option_state @ A2 @ B5 ) ) ).

% insertI1
thf(fact_641_insertI1,axiom,
    ! [A2: option_val,B5: set_option_val] : ( member_option_val @ A2 @ ( insert_option_val @ A2 @ B5 ) ) ).

% insertI1
thf(fact_642_insertI1,axiom,
    ! [A2: val,B5: set_val] : ( member_val @ A2 @ ( insert_val @ A2 @ B5 ) ) ).

% insertI1
thf(fact_643_insertI1,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat] : ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ A2 @ B5 ) ) ).

% insertI1
thf(fact_644_insertI2,axiom,
    ! [A2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val,B2: produc1317171644805857433on_val] :
      ( ( member6505152944228695362on_val @ A2 @ B5 )
     => ( member6505152944228695362on_val @ A2 @ ( insert7062705985672971881on_val @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_645_insertI2,axiom,
    ! [A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ A2 @ B5 )
     => ( member2879030624002546611on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_646_insertI2,axiom,
    ! [A2: option_state,B5: set_option_state,B2: option_state] :
      ( ( member_option_state @ A2 @ B5 )
     => ( member_option_state @ A2 @ ( insert_option_state @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_647_insertI2,axiom,
    ! [A2: option_val,B5: set_option_val,B2: option_val] :
      ( ( member_option_val @ A2 @ B5 )
     => ( member_option_val @ A2 @ ( insert_option_val @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_648_insertI2,axiom,
    ! [A2: val,B5: set_val,B2: val] :
      ( ( member_val @ A2 @ B5 )
     => ( member_val @ A2 @ ( insert_val @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_649_insertI2,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat,B2: produc1457211279475724562t_char > prat] :
      ( ( member2336342582916103932r_prat @ A2 @ B5 )
     => ( member2336342582916103932r_prat @ A2 @ ( insert8113562578550770211r_prat @ B2 @ B5 ) ) ) ).

% insertI2
thf(fact_650_comp__assoc,axiom,
    ! [F: option_state > state,G: state > option_state,H: state > state] :
      ( ( comp_s3787957668927766035_state @ ( comp_o4916166309651032803_state @ F @ G ) @ H )
      = ( comp_o4916166309651032803_state @ F @ ( comp_s2749706468613731939_state @ G @ H ) ) ) ).

% comp_assoc
thf(fact_651_comp__assoc,axiom,
    ! [F: option_val > val,G: val > option_val,H: val > val] :
      ( ( comp_val_val_val @ ( comp_o5604524432708427236al_val @ F @ G ) @ H )
      = ( comp_o5604524432708427236al_val @ F @ ( comp_v7980881360141566424al_val @ G @ H ) ) ) ).

% comp_assoc
thf(fact_652_comp__assoc,axiom,
    ! [F: state > state,G: option_state > state,H: state > option_state] :
      ( ( comp_o4916166309651032803_state @ ( comp_s5294034245180965347_state @ F @ G ) @ H )
      = ( comp_s3787957668927766035_state @ F @ ( comp_o4916166309651032803_state @ G @ H ) ) ) ).

% comp_assoc
thf(fact_653_comp__assoc,axiom,
    ! [F: option_state > state,G: option_state > option_state,H: state > option_state] :
      ( ( comp_o4916166309651032803_state @ ( comp_o2210334810017003187_state @ F @ G ) @ H )
      = ( comp_o4916166309651032803_state @ F @ ( comp_o8889379070304545587_state @ G @ H ) ) ) ).

% comp_assoc
thf(fact_654_comp__assoc,axiom,
    ! [F: val > val,G: option_val > val,H: val > option_val] :
      ( ( comp_o5604524432708427236al_val @ ( comp_v5381271067920388324on_val @ F @ G ) @ H )
      = ( comp_val_val_val @ F @ ( comp_o5604524432708427236al_val @ G @ H ) ) ) ).

% comp_assoc
thf(fact_655_comp__assoc,axiom,
    ! [F: option_val > val,G: option_val > option_val,H: val > option_val] :
      ( ( comp_o5604524432708427236al_val @ ( comp_o5868975259454090282on_val @ F @ G ) @ H )
      = ( comp_o5604524432708427236al_val @ F @ ( comp_o8468585551675268382al_val @ G @ H ) ) ) ).

% comp_assoc
thf(fact_656_Set_Oset__insert,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ X @ A4 )
     => ~ ! [B6: set_Pr4305388979797279737on_val] :
            ( ( A4
              = ( insert7062705985672971881on_val @ X @ B6 ) )
           => ( member6505152944228695362on_val @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_657_Set_Oset__insert,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X @ A4 )
     => ~ ! [B6: set_Pr7649655576376376530on_val] :
            ( ( A4
              = ( insert3030518898131756108on_val @ X @ B6 ) )
           => ( member2879030624002546611on_val @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_658_Set_Oset__insert,axiom,
    ! [X: option_state,A4: set_option_state] :
      ( ( member_option_state @ X @ A4 )
     => ~ ! [B6: set_option_state] :
            ( ( A4
              = ( insert_option_state @ X @ B6 ) )
           => ( member_option_state @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_659_Set_Oset__insert,axiom,
    ! [X: option_val,A4: set_option_val] :
      ( ( member_option_val @ X @ A4 )
     => ~ ! [B6: set_option_val] :
            ( ( A4
              = ( insert_option_val @ X @ B6 ) )
           => ( member_option_val @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_660_Set_Oset__insert,axiom,
    ! [X: val,A4: set_val] :
      ( ( member_val @ X @ A4 )
     => ~ ! [B6: set_val] :
            ( ( A4
              = ( insert_val @ X @ B6 ) )
           => ( member_val @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_661_Set_Oset__insert,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ X @ A4 )
     => ~ ! [B6: set_Pr3433046674199179443r_prat] :
            ( ( A4
              = ( insert8113562578550770211r_prat @ X @ B6 ) )
           => ( member2336342582916103932r_prat @ X @ B6 ) ) ) ).

% Set.set_insert
thf(fact_662_comp__eq__dest,axiom,
    ! [A2: option_state > state,B2: state > option_state,C: option_state > state,D: state > option_state,V2: state] :
      ( ( ( comp_o4916166309651032803_state @ A2 @ B2 )
        = ( comp_o4916166309651032803_state @ C @ D ) )
     => ( ( A2 @ ( B2 @ V2 ) )
        = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_dest
thf(fact_663_comp__eq__dest,axiom,
    ! [A2: option_val > val,B2: val > option_val,C: option_val > val,D: val > option_val,V2: val] :
      ( ( ( comp_o5604524432708427236al_val @ A2 @ B2 )
        = ( comp_o5604524432708427236al_val @ C @ D ) )
     => ( ( A2 @ ( B2 @ V2 ) )
        = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_dest
thf(fact_664_comp__eq__elim,axiom,
    ! [A2: option_state > state,B2: state > option_state,C: option_state > state,D: state > option_state] :
      ( ( ( comp_o4916166309651032803_state @ A2 @ B2 )
        = ( comp_o4916166309651032803_state @ C @ D ) )
     => ! [V3: state] :
          ( ( A2 @ ( B2 @ V3 ) )
          = ( C @ ( D @ V3 ) ) ) ) ).

% comp_eq_elim
thf(fact_665_comp__eq__elim,axiom,
    ! [A2: option_val > val,B2: val > option_val,C: option_val > val,D: val > option_val] :
      ( ( ( comp_o5604524432708427236al_val @ A2 @ B2 )
        = ( comp_o5604524432708427236al_val @ C @ D ) )
     => ! [V3: val] :
          ( ( A2 @ ( B2 @ V3 ) )
          = ( C @ ( D @ V3 ) ) ) ) ).

% comp_eq_elim
thf(fact_666_insert__ident,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val,B5: set_Pr4305388979797279737on_val] :
      ( ~ ( member6505152944228695362on_val @ X @ A4 )
     => ( ~ ( member6505152944228695362on_val @ X @ B5 )
       => ( ( ( insert7062705985672971881on_val @ X @ A4 )
            = ( insert7062705985672971881on_val @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_667_insert__ident,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ~ ( member2879030624002546611on_val @ X @ B5 )
       => ( ( ( insert3030518898131756108on_val @ X @ A4 )
            = ( insert3030518898131756108on_val @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_668_insert__ident,axiom,
    ! [X: option_state,A4: set_option_state,B5: set_option_state] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ~ ( member_option_state @ X @ B5 )
       => ( ( ( insert_option_state @ X @ A4 )
            = ( insert_option_state @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_669_insert__ident,axiom,
    ! [X: option_val,A4: set_option_val,B5: set_option_val] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ~ ( member_option_val @ X @ B5 )
       => ( ( ( insert_option_val @ X @ A4 )
            = ( insert_option_val @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_670_insert__ident,axiom,
    ! [X: val,A4: set_val,B5: set_val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ~ ( member_val @ X @ B5 )
       => ( ( ( insert_val @ X @ A4 )
            = ( insert_val @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_671_insert__ident,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ~ ( member2336342582916103932r_prat @ X @ B5 )
       => ( ( ( insert8113562578550770211r_prat @ X @ A4 )
            = ( insert8113562578550770211r_prat @ X @ B5 ) )
          = ( A4 = B5 ) ) ) ) ).

% insert_ident
thf(fact_672_insert__absorb,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ A2 @ A4 )
     => ( ( insert7062705985672971881on_val @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_673_insert__absorb,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A2 @ A4 )
     => ( ( insert3030518898131756108on_val @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_674_insert__absorb,axiom,
    ! [A2: option_state,A4: set_option_state] :
      ( ( member_option_state @ A2 @ A4 )
     => ( ( insert_option_state @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_675_insert__absorb,axiom,
    ! [A2: option_val,A4: set_option_val] :
      ( ( member_option_val @ A2 @ A4 )
     => ( ( insert_option_val @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_676_insert__absorb,axiom,
    ! [A2: val,A4: set_val] :
      ( ( member_val @ A2 @ A4 )
     => ( ( insert_val @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_677_insert__absorb,axiom,
    ! [A2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ A2 @ A4 )
     => ( ( insert8113562578550770211r_prat @ A2 @ A4 )
        = A4 ) ) ).

% insert_absorb
thf(fact_678_insert__eq__iff,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val,B2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val] :
      ( ~ ( member6505152944228695362on_val @ A2 @ A4 )
     => ( ~ ( member6505152944228695362on_val @ B2 @ B5 )
       => ( ( ( insert7062705985672971881on_val @ A2 @ A4 )
            = ( insert7062705985672971881on_val @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_Pr4305388979797279737on_val] :
                  ( ( A4
                    = ( insert7062705985672971881on_val @ B2 @ C2 ) )
                  & ~ ( member6505152944228695362on_val @ B2 @ C2 )
                  & ( B5
                    = ( insert7062705985672971881on_val @ A2 @ C2 ) )
                  & ~ ( member6505152944228695362on_val @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_679_insert__eq__iff,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ A2 @ A4 )
     => ( ~ ( member2879030624002546611on_val @ B2 @ B5 )
       => ( ( ( insert3030518898131756108on_val @ A2 @ A4 )
            = ( insert3030518898131756108on_val @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_Pr7649655576376376530on_val] :
                  ( ( A4
                    = ( insert3030518898131756108on_val @ B2 @ C2 ) )
                  & ~ ( member2879030624002546611on_val @ B2 @ C2 )
                  & ( B5
                    = ( insert3030518898131756108on_val @ A2 @ C2 ) )
                  & ~ ( member2879030624002546611on_val @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_680_insert__eq__iff,axiom,
    ! [A2: option_state,A4: set_option_state,B2: option_state,B5: set_option_state] :
      ( ~ ( member_option_state @ A2 @ A4 )
     => ( ~ ( member_option_state @ B2 @ B5 )
       => ( ( ( insert_option_state @ A2 @ A4 )
            = ( insert_option_state @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_option_state] :
                  ( ( A4
                    = ( insert_option_state @ B2 @ C2 ) )
                  & ~ ( member_option_state @ B2 @ C2 )
                  & ( B5
                    = ( insert_option_state @ A2 @ C2 ) )
                  & ~ ( member_option_state @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_681_insert__eq__iff,axiom,
    ! [A2: option_val,A4: set_option_val,B2: option_val,B5: set_option_val] :
      ( ~ ( member_option_val @ A2 @ A4 )
     => ( ~ ( member_option_val @ B2 @ B5 )
       => ( ( ( insert_option_val @ A2 @ A4 )
            = ( insert_option_val @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_option_val] :
                  ( ( A4
                    = ( insert_option_val @ B2 @ C2 ) )
                  & ~ ( member_option_val @ B2 @ C2 )
                  & ( B5
                    = ( insert_option_val @ A2 @ C2 ) )
                  & ~ ( member_option_val @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_682_insert__eq__iff,axiom,
    ! [A2: val,A4: set_val,B2: val,B5: set_val] :
      ( ~ ( member_val @ A2 @ A4 )
     => ( ~ ( member_val @ B2 @ B5 )
       => ( ( ( insert_val @ A2 @ A4 )
            = ( insert_val @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_val] :
                  ( ( A4
                    = ( insert_val @ B2 @ C2 ) )
                  & ~ ( member_val @ B2 @ C2 )
                  & ( B5
                    = ( insert_val @ A2 @ C2 ) )
                  & ~ ( member_val @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_683_insert__eq__iff,axiom,
    ! [A2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B2: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat] :
      ( ~ ( member2336342582916103932r_prat @ A2 @ A4 )
     => ( ~ ( member2336342582916103932r_prat @ B2 @ B5 )
       => ( ( ( insert8113562578550770211r_prat @ A2 @ A4 )
            = ( insert8113562578550770211r_prat @ B2 @ B5 ) )
          = ( ( ( A2 = B2 )
             => ( A4 = B5 ) )
            & ( ( A2 != B2 )
             => ? [C2: set_Pr3433046674199179443r_prat] :
                  ( ( A4
                    = ( insert8113562578550770211r_prat @ B2 @ C2 ) )
                  & ~ ( member2336342582916103932r_prat @ B2 @ C2 )
                  & ( B5
                    = ( insert8113562578550770211r_prat @ A2 @ C2 ) )
                  & ~ ( member2336342582916103932r_prat @ A2 @ C2 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_684_insert__commute,axiom,
    ! [X: produc1317171644805857433on_val,Y3: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( insert7062705985672971881on_val @ X @ ( insert7062705985672971881on_val @ Y3 @ A4 ) )
      = ( insert7062705985672971881on_val @ Y3 @ ( insert7062705985672971881on_val @ X @ A4 ) ) ) ).

% insert_commute
thf(fact_685_insert__commute,axiom,
    ! [X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( insert3030518898131756108on_val @ X @ ( insert3030518898131756108on_val @ Y3 @ A4 ) )
      = ( insert3030518898131756108on_val @ Y3 @ ( insert3030518898131756108on_val @ X @ A4 ) ) ) ).

% insert_commute
thf(fact_686_insert__commute,axiom,
    ! [X: option_state,Y3: option_state,A4: set_option_state] :
      ( ( insert_option_state @ X @ ( insert_option_state @ Y3 @ A4 ) )
      = ( insert_option_state @ Y3 @ ( insert_option_state @ X @ A4 ) ) ) ).

% insert_commute
thf(fact_687_insert__commute,axiom,
    ! [X: option_val,Y3: option_val,A4: set_option_val] :
      ( ( insert_option_val @ X @ ( insert_option_val @ Y3 @ A4 ) )
      = ( insert_option_val @ Y3 @ ( insert_option_val @ X @ A4 ) ) ) ).

% insert_commute
thf(fact_688_insert__commute,axiom,
    ! [X: val,Y3: val,A4: set_val] :
      ( ( insert_val @ X @ ( insert_val @ Y3 @ A4 ) )
      = ( insert_val @ Y3 @ ( insert_val @ X @ A4 ) ) ) ).

% insert_commute
thf(fact_689_comp__eq__dest__lhs,axiom,
    ! [A2: option_state > state,B2: state > option_state,C: state > state,V2: state] :
      ( ( ( comp_o4916166309651032803_state @ A2 @ B2 )
        = C )
     => ( ( A2 @ ( B2 @ V2 ) )
        = ( C @ V2 ) ) ) ).

% comp_eq_dest_lhs
thf(fact_690_comp__eq__dest__lhs,axiom,
    ! [A2: option_val > val,B2: val > option_val,C: val > val,V2: val] :
      ( ( ( comp_o5604524432708427236al_val @ A2 @ B2 )
        = C )
     => ( ( A2 @ ( B2 @ V2 ) )
        = ( C @ V2 ) ) ) ).

% comp_eq_dest_lhs
thf(fact_691_mk__disjoint__insert,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ A2 @ A4 )
     => ? [B6: set_Pr4305388979797279737on_val] :
          ( ( A4
            = ( insert7062705985672971881on_val @ A2 @ B6 ) )
          & ~ ( member6505152944228695362on_val @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_692_mk__disjoint__insert,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A2 @ A4 )
     => ? [B6: set_Pr7649655576376376530on_val] :
          ( ( A4
            = ( insert3030518898131756108on_val @ A2 @ B6 ) )
          & ~ ( member2879030624002546611on_val @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_693_mk__disjoint__insert,axiom,
    ! [A2: option_state,A4: set_option_state] :
      ( ( member_option_state @ A2 @ A4 )
     => ? [B6: set_option_state] :
          ( ( A4
            = ( insert_option_state @ A2 @ B6 ) )
          & ~ ( member_option_state @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_694_mk__disjoint__insert,axiom,
    ! [A2: option_val,A4: set_option_val] :
      ( ( member_option_val @ A2 @ A4 )
     => ? [B6: set_option_val] :
          ( ( A4
            = ( insert_option_val @ A2 @ B6 ) )
          & ~ ( member_option_val @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_695_mk__disjoint__insert,axiom,
    ! [A2: val,A4: set_val] :
      ( ( member_val @ A2 @ A4 )
     => ? [B6: set_val] :
          ( ( A4
            = ( insert_val @ A2 @ B6 ) )
          & ~ ( member_val @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_696_mk__disjoint__insert,axiom,
    ! [A2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ A2 @ A4 )
     => ? [B6: set_Pr3433046674199179443r_prat] :
          ( ( A4
            = ( insert8113562578550770211r_prat @ A2 @ B6 ) )
          & ~ ( member2336342582916103932r_prat @ A2 @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_697_insert__dom,axiom,
    ! [F: val > option_val,X: val,Y3: val] :
      ( ( ( F @ X )
        = ( some_val @ Y3 ) )
     => ( ( insert_val @ X @ ( dom_val_val @ F ) )
        = ( dom_val_val @ F ) ) ) ).

% insert_dom
thf(fact_698_insert__dom,axiom,
    ! [F: val > option_state,X: val,Y3: state] :
      ( ( ( F @ X )
        = ( some_state @ Y3 ) )
     => ( ( insert_val @ X @ ( dom_val_state @ F ) )
        = ( dom_val_state @ F ) ) ) ).

% insert_dom
thf(fact_699_insert__dom,axiom,
    ! [F: option_state > option_val,X: option_state,Y3: val] :
      ( ( ( F @ X )
        = ( some_val @ Y3 ) )
     => ( ( insert_option_state @ X @ ( dom_option_state_val @ F ) )
        = ( dom_option_state_val @ F ) ) ) ).

% insert_dom
thf(fact_700_insert__dom,axiom,
    ! [F: option_val > option_val,X: option_val,Y3: val] :
      ( ( ( F @ X )
        = ( some_val @ Y3 ) )
     => ( ( insert_option_val @ X @ ( dom_option_val_val @ F ) )
        = ( dom_option_val_val @ F ) ) ) ).

% insert_dom
thf(fact_701_insert__dom,axiom,
    ! [F: option_state > option_state,X: option_state,Y3: state] :
      ( ( ( F @ X )
        = ( some_state @ Y3 ) )
     => ( ( insert_option_state @ X @ ( dom_op8569336450220619928_state @ F ) )
        = ( dom_op8569336450220619928_state @ F ) ) ) ).

% insert_dom
thf(fact_702_insert__dom,axiom,
    ! [F: option_val > option_state,X: option_val,Y3: state] :
      ( ( ( F @ X )
        = ( some_state @ Y3 ) )
     => ( ( insert_option_val @ X @ ( dom_option_val_state @ F ) )
        = ( dom_option_val_state @ F ) ) ) ).

% insert_dom
thf(fact_703_insert__dom,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: val] :
      ( ( ( F @ X )
        = ( some_val @ Y3 ) )
     => ( ( insert3372640069787401954t_char @ X @ ( dom_Pr8989479155164304065ar_val @ F ) )
        = ( dom_Pr8989479155164304065ar_val @ F ) ) ) ).

% insert_dom
thf(fact_704_insert__dom,axiom,
    ! [F: val > option5747939881698552298on_val,X: val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( F @ X )
        = ( some_P7669353234731512949on_val @ Y3 ) )
     => ( ( insert_val @ X @ ( dom_va8931846639282357193on_val @ F ) )
        = ( dom_va8931846639282357193on_val @ F ) ) ) ).

% insert_dom
thf(fact_705_insert__dom,axiom,
    ! [F: option_state > option5747939881698552298on_val,X: option_state,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( F @ X )
        = ( some_P7669353234731512949on_val @ Y3 ) )
     => ( ( insert_option_state @ X @ ( dom_op741179583939567608on_val @ F ) )
        = ( dom_op741179583939567608on_val @ F ) ) ) ).

% insert_dom
thf(fact_706_insert__dom,axiom,
    ! [F: option_val > option5747939881698552298on_val,X: option_val,Y3: produc1457211279475724562t_char > option_val] :
      ( ( ( F @ X )
        = ( some_P7669353234731512949on_val @ Y3 ) )
     => ( ( insert_option_val @ X @ ( dom_op3430095273566047759on_val @ F ) )
        = ( dom_op3430095273566047759on_val @ F ) ) ) ).

% insert_dom
thf(fact_707_map__option_Ocomp,axiom,
    ! [F: option_state > state,G: state > option_state] :
      ( ( comp_o4730161381108774995_state @ ( map_op384739313229359441_state @ F ) @ ( map_op2929067089796592849_state @ G ) )
      = ( map_op2726735944305651201_state @ ( comp_o4916166309651032803_state @ F @ G ) ) ) ).

% map_option.comp
thf(fact_708_map__option_Ocomp,axiom,
    ! [F: option_val > val,G: val > option_val] :
      ( ( comp_o5089890310235258666on_val @ ( map_op8419032157235086213al_val @ F ) @ ( map_op5819421865013908113on_val @ G ) )
      = ( map_option_val_val @ ( comp_o5604524432708427236al_val @ F @ G ) ) ) ).

% map_option.comp
thf(fact_709_map__option_Ocomp,axiom,
    ! [F: state > state,G: state > state] :
      ( ( comp_o1977787000485117699_state @ ( map_op2726735944305651201_state @ F ) @ ( map_op2726735944305651201_state @ G ) )
      = ( map_op2726735944305651201_state @ ( comp_s3787957668927766035_state @ F @ G ) ) ) ).

% map_option.comp
thf(fact_710_map__option_Ocomp,axiom,
    ! [F: state > state,G: val > state] :
      ( ( comp_o8735098318613718414on_val @ ( map_op2726735944305651201_state @ F ) @ ( map_option_val_state @ G ) )
      = ( map_option_val_state @ ( comp_state_state_val @ F @ G ) ) ) ).

% map_option.comp
thf(fact_711_map__option_Ocomp,axiom,
    ! [F: val > state,G: state > val] :
      ( ( comp_o9000648883196993210_state @ ( map_option_val_state @ F ) @ ( map_option_state_val @ G ) )
      = ( map_op2726735944305651201_state @ ( comp_val_state_state @ F @ G ) ) ) ).

% map_option.comp
thf(fact_712_map__option_Ocomp,axiom,
    ! [F: val > state,G: val > val] :
      ( ( comp_o1688524877211496087on_val @ ( map_option_val_state @ F ) @ ( map_option_val_val @ G ) )
      = ( map_option_val_state @ ( comp_val_state_val @ F @ G ) ) ) ).

% map_option.comp
thf(fact_713_map__option_Ocomp,axiom,
    ! [F: state > val,G: state > state] :
      ( ( comp_o2122277431643274148_state @ ( map_option_state_val @ F ) @ ( map_op2726735944305651201_state @ G ) )
      = ( map_option_state_val @ ( comp_state_val_state @ F @ G ) ) ) ).

% map_option.comp
thf(fact_714_map__option_Ocomp,axiom,
    ! [F: state > val,G: val > state] :
      ( ( comp_o2128577701018291757on_val @ ( map_option_state_val @ F ) @ ( map_option_val_state @ G ) )
      = ( map_option_val_val @ ( comp_state_val_val @ F @ G ) ) ) ).

% map_option.comp
thf(fact_715_map__option_Ocomp,axiom,
    ! [F: val > val,G: state > val] :
      ( ( comp_o4299076027095827629_state @ ( map_option_val_val @ F ) @ ( map_option_state_val @ G ) )
      = ( map_option_state_val @ ( comp_val_val_state @ F @ G ) ) ) ).

% map_option.comp
thf(fact_716_map__option_Ocomp,axiom,
    ! [F: val > val,G: val > val] :
      ( ( comp_o1349245612712103012on_val @ ( map_option_val_val @ F ) @ ( map_option_val_val @ G ) )
      = ( map_option_val_val @ ( comp_val_val_val @ F @ G ) ) ) ).

% map_option.comp
thf(fact_717_override__on__insert,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,X6: set_Pr2507339680178222706t_char] :
      ( ( overri6326584771168529523on_val @ F @ G @ ( insert3372640069787401954t_char @ X @ X6 ) )
      = ( fun_up5735975307950539954on_val @ ( overri6326584771168529523on_val @ F @ G @ X6 ) @ X @ ( G @ X ) ) ) ).

% override_on_insert
thf(fact_718_override__on__insert,axiom,
    ! [F: produc1457211279475724562t_char > prat,G: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,X6: set_Pr2507339680178222706t_char] :
      ( ( overri4208557840210724900r_prat @ F @ G @ ( insert3372640069787401954t_char @ X @ X6 ) )
      = ( fun_up829850848796697765r_prat @ ( overri4208557840210724900r_prat @ F @ G @ X6 ) @ X @ ( G @ X ) ) ) ).

% override_on_insert
thf(fact_719_override__on__insert,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,X6: set_Pr7649655576376376530on_val] :
      ( ( overri6608491219596025288on_val @ F @ G @ ( insert3030518898131756108on_val @ X @ X6 ) )
      = ( fun_up273046073882939271on_val @ ( overri6608491219596025288on_val @ F @ G @ X6 ) @ X @ ( G @ X ) ) ) ).

% override_on_insert
thf(fact_720_override__on__insert,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,X6: set_Pr3433046674199179443r_prat] :
      ( ( overri3784772535335278463on_val @ F @ G @ ( insert8113562578550770211r_prat @ X @ X6 ) )
      = ( fun_up1601731230164360576on_val @ ( overri3784772535335278463on_val @ F @ G @ X6 ) @ X @ ( G @ X ) ) ) ).

% override_on_insert
thf(fact_721_override__on__insert_H,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,X6: set_Pr2507339680178222706t_char] :
      ( ( overri6326584771168529523on_val @ F @ G @ ( insert3372640069787401954t_char @ X @ X6 ) )
      = ( overri6326584771168529523on_val @ ( fun_up5735975307950539954on_val @ F @ X @ ( G @ X ) ) @ G @ X6 ) ) ).

% override_on_insert'
thf(fact_722_override__on__insert_H,axiom,
    ! [F: produc1457211279475724562t_char > prat,G: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,X6: set_Pr2507339680178222706t_char] :
      ( ( overri4208557840210724900r_prat @ F @ G @ ( insert3372640069787401954t_char @ X @ X6 ) )
      = ( overri4208557840210724900r_prat @ ( fun_up829850848796697765r_prat @ F @ X @ ( G @ X ) ) @ G @ X6 ) ) ).

% override_on_insert'
thf(fact_723_override__on__insert_H,axiom,
    ! [F: produc9003781588162623004on_val > option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,X6: set_Pr7649655576376376530on_val] :
      ( ( overri6608491219596025288on_val @ F @ G @ ( insert3030518898131756108on_val @ X @ X6 ) )
      = ( overri6608491219596025288on_val @ ( fun_up273046073882939271on_val @ F @ X @ ( G @ X ) ) @ G @ X6 ) ) ).

% override_on_insert'
thf(fact_724_override__on__insert_H,axiom,
    ! [F: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,X6: set_Pr3433046674199179443r_prat] :
      ( ( overri3784772535335278463on_val @ F @ G @ ( insert8113562578550770211r_prat @ X @ X6 ) )
      = ( overri3784772535335278463on_val @ ( fun_up1601731230164360576on_val @ F @ X @ ( G @ X ) ) @ G @ X6 ) ) ).

% override_on_insert'
thf(fact_725_domD,axiom,
    ! [A2: val,M: val > option_val] :
      ( ( member_val @ A2 @ ( dom_val_val @ M ) )
     => ? [B: val] :
          ( ( M @ A2 )
          = ( some_val @ B ) ) ) ).

% domD
thf(fact_726_domD,axiom,
    ! [A2: val,M: val > option_state] :
      ( ( member_val @ A2 @ ( dom_val_state @ M ) )
     => ? [B: state] :
          ( ( M @ A2 )
          = ( some_state @ B ) ) ) ).

% domD
thf(fact_727_domD,axiom,
    ! [A2: option_state,M: option_state > option_val] :
      ( ( member_option_state @ A2 @ ( dom_option_state_val @ M ) )
     => ? [B: val] :
          ( ( M @ A2 )
          = ( some_val @ B ) ) ) ).

% domD
thf(fact_728_domD,axiom,
    ! [A2: option_val,M: option_val > option_val] :
      ( ( member_option_val @ A2 @ ( dom_option_val_val @ M ) )
     => ? [B: val] :
          ( ( M @ A2 )
          = ( some_val @ B ) ) ) ).

% domD
thf(fact_729_domD,axiom,
    ! [A2: option_state,M: option_state > option_state] :
      ( ( member_option_state @ A2 @ ( dom_op8569336450220619928_state @ M ) )
     => ? [B: state] :
          ( ( M @ A2 )
          = ( some_state @ B ) ) ) ).

% domD
thf(fact_730_domD,axiom,
    ! [A2: option_val,M: option_val > option_state] :
      ( ( member_option_val @ A2 @ ( dom_option_val_state @ M ) )
     => ? [B: state] :
          ( ( M @ A2 )
          = ( some_state @ B ) ) ) ).

% domD
thf(fact_731_domD,axiom,
    ! [A2: produc1457211279475724562t_char,M: produc1457211279475724562t_char > option_val] :
      ( ( member484235747325421115t_char @ A2 @ ( dom_Pr8989479155164304065ar_val @ M ) )
     => ? [B: val] :
          ( ( M @ A2 )
          = ( some_val @ B ) ) ) ).

% domD
thf(fact_732_domD,axiom,
    ! [A2: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_val] :
      ( ( member2336342582916103932r_prat @ A2 @ ( dom_Pr3224398758927333440at_val @ M ) )
     => ? [B: val] :
          ( ( M @ A2 )
          = ( some_val @ B ) ) ) ).

% domD
thf(fact_733_domD,axiom,
    ! [A2: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_state] :
      ( ( member2336342582916103932r_prat @ A2 @ ( dom_Pr2103017623604714043_state @ M ) )
     => ? [B: state] :
          ( ( M @ A2 )
          = ( some_state @ B ) ) ) ).

% domD
thf(fact_734_domD,axiom,
    ! [A2: val,M: val > option5747939881698552298on_val] :
      ( ( member_val @ A2 @ ( dom_va8931846639282357193on_val @ M ) )
     => ? [B: produc1457211279475724562t_char > option_val] :
          ( ( M @ A2 )
          = ( some_P7669353234731512949on_val @ B ) ) ) ).

% domD
thf(fact_735_domI,axiom,
    ! [M: val > option_val,A2: val,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member_val @ A2 @ ( dom_val_val @ M ) ) ) ).

% domI
thf(fact_736_domI,axiom,
    ! [M: val > option_state,A2: val,B2: state] :
      ( ( ( M @ A2 )
        = ( some_state @ B2 ) )
     => ( member_val @ A2 @ ( dom_val_state @ M ) ) ) ).

% domI
thf(fact_737_domI,axiom,
    ! [M: option_state > option_val,A2: option_state,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member_option_state @ A2 @ ( dom_option_state_val @ M ) ) ) ).

% domI
thf(fact_738_domI,axiom,
    ! [M: option_val > option_val,A2: option_val,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member_option_val @ A2 @ ( dom_option_val_val @ M ) ) ) ).

% domI
thf(fact_739_domI,axiom,
    ! [M: option_state > option_state,A2: option_state,B2: state] :
      ( ( ( M @ A2 )
        = ( some_state @ B2 ) )
     => ( member_option_state @ A2 @ ( dom_op8569336450220619928_state @ M ) ) ) ).

% domI
thf(fact_740_domI,axiom,
    ! [M: option_val > option_state,A2: option_val,B2: state] :
      ( ( ( M @ A2 )
        = ( some_state @ B2 ) )
     => ( member_option_val @ A2 @ ( dom_option_val_state @ M ) ) ) ).

% domI
thf(fact_741_domI,axiom,
    ! [M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member484235747325421115t_char @ A2 @ ( dom_Pr8989479155164304065ar_val @ M ) ) ) ).

% domI
thf(fact_742_domI,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option_val,A2: produc1457211279475724562t_char > prat,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member2336342582916103932r_prat @ A2 @ ( dom_Pr3224398758927333440at_val @ M ) ) ) ).

% domI
thf(fact_743_domI,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option_state,A2: produc1457211279475724562t_char > prat,B2: state] :
      ( ( ( M @ A2 )
        = ( some_state @ B2 ) )
     => ( member2336342582916103932r_prat @ A2 @ ( dom_Pr2103017623604714043_state @ M ) ) ) ).

% domI
thf(fact_744_domI,axiom,
    ! [M: val > option5747939881698552298on_val,A2: val,B2: produc1457211279475724562t_char > option_val] :
      ( ( ( M @ A2 )
        = ( some_P7669353234731512949on_val @ B2 ) )
     => ( member_val @ A2 @ ( dom_va8931846639282357193on_val @ M ) ) ) ).

% domI
thf(fact_745_singleton__inject,axiom,
    ! [A2: produc1317171644805857433on_val,B2: produc1317171644805857433on_val] :
      ( ( ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val )
        = ( insert7062705985672971881on_val @ B2 @ bot_bo402267660617762917on_val ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_746_singleton__inject,axiom,
    ! [A2: produc1457211279475724562t_char,B2: produc1457211279475724562t_char] :
      ( ( ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char )
        = ( insert3372640069787401954t_char @ B2 @ bot_bo1414094081888755934t_char ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_747_singleton__inject,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
      ( ( ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val )
        = ( insert3030518898131756108on_val @ B2 @ bot_bo6722054719108133734on_val ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_748_singleton__inject,axiom,
    ! [A2: option_state,B2: option_state] :
      ( ( ( insert_option_state @ A2 @ bot_bo710180891245420500_state )
        = ( insert_option_state @ B2 @ bot_bo710180891245420500_state ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_749_singleton__inject,axiom,
    ! [A2: option_val,B2: option_val] :
      ( ( ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val )
        = ( insert_option_val @ B2 @ bot_bo5906790151302476563on_val ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_750_singleton__inject,axiom,
    ! [A2: val,B2: val] :
      ( ( ( insert_val @ A2 @ bot_bot_set_val )
        = ( insert_val @ B2 @ bot_bot_set_val ) )
     => ( A2 = B2 ) ) ).

% singleton_inject
thf(fact_751_insert__not__empty,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( insert7062705985672971881on_val @ A2 @ A4 )
     != bot_bo402267660617762917on_val ) ).

% insert_not_empty
thf(fact_752_insert__not__empty,axiom,
    ! [A2: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char] :
      ( ( insert3372640069787401954t_char @ A2 @ A4 )
     != bot_bo1414094081888755934t_char ) ).

% insert_not_empty
thf(fact_753_insert__not__empty,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( insert3030518898131756108on_val @ A2 @ A4 )
     != bot_bo6722054719108133734on_val ) ).

% insert_not_empty
thf(fact_754_insert__not__empty,axiom,
    ! [A2: option_state,A4: set_option_state] :
      ( ( insert_option_state @ A2 @ A4 )
     != bot_bo710180891245420500_state ) ).

% insert_not_empty
thf(fact_755_insert__not__empty,axiom,
    ! [A2: option_val,A4: set_option_val] :
      ( ( insert_option_val @ A2 @ A4 )
     != bot_bo5906790151302476563on_val ) ).

% insert_not_empty
thf(fact_756_insert__not__empty,axiom,
    ! [A2: val,A4: set_val] :
      ( ( insert_val @ A2 @ A4 )
     != bot_bot_set_val ) ).

% insert_not_empty
thf(fact_757_doubleton__eq__iff,axiom,
    ! [A2: produc1317171644805857433on_val,B2: produc1317171644805857433on_val,C: produc1317171644805857433on_val,D: produc1317171644805857433on_val] :
      ( ( ( insert7062705985672971881on_val @ A2 @ ( insert7062705985672971881on_val @ B2 @ bot_bo402267660617762917on_val ) )
        = ( insert7062705985672971881on_val @ C @ ( insert7062705985672971881on_val @ D @ bot_bo402267660617762917on_val ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_758_doubleton__eq__iff,axiom,
    ! [A2: produc1457211279475724562t_char,B2: produc1457211279475724562t_char,C: produc1457211279475724562t_char,D: produc1457211279475724562t_char] :
      ( ( ( insert3372640069787401954t_char @ A2 @ ( insert3372640069787401954t_char @ B2 @ bot_bo1414094081888755934t_char ) )
        = ( insert3372640069787401954t_char @ C @ ( insert3372640069787401954t_char @ D @ bot_bo1414094081888755934t_char ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_759_doubleton__eq__iff,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,C: produc9003781588162623004on_val,D: produc9003781588162623004on_val] :
      ( ( ( insert3030518898131756108on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ bot_bo6722054719108133734on_val ) )
        = ( insert3030518898131756108on_val @ C @ ( insert3030518898131756108on_val @ D @ bot_bo6722054719108133734on_val ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_760_doubleton__eq__iff,axiom,
    ! [A2: option_state,B2: option_state,C: option_state,D: option_state] :
      ( ( ( insert_option_state @ A2 @ ( insert_option_state @ B2 @ bot_bo710180891245420500_state ) )
        = ( insert_option_state @ C @ ( insert_option_state @ D @ bot_bo710180891245420500_state ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_761_doubleton__eq__iff,axiom,
    ! [A2: option_val,B2: option_val,C: option_val,D: option_val] :
      ( ( ( insert_option_val @ A2 @ ( insert_option_val @ B2 @ bot_bo5906790151302476563on_val ) )
        = ( insert_option_val @ C @ ( insert_option_val @ D @ bot_bo5906790151302476563on_val ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_762_doubleton__eq__iff,axiom,
    ! [A2: val,B2: val,C: val,D: val] :
      ( ( ( insert_val @ A2 @ ( insert_val @ B2 @ bot_bot_set_val ) )
        = ( insert_val @ C @ ( insert_val @ D @ bot_bot_set_val ) ) )
      = ( ( ( A2 = C )
          & ( B2 = D ) )
        | ( ( A2 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_763_singleton__iff,axiom,
    ! [B2: produc1317171644805857433on_val,A2: produc1317171644805857433on_val] :
      ( ( member6505152944228695362on_val @ B2 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_764_singleton__iff,axiom,
    ! [B2: produc1457211279475724562t_char > prat,A2: produc1457211279475724562t_char > prat] :
      ( ( member2336342582916103932r_prat @ B2 @ ( insert8113562578550770211r_prat @ A2 @ bot_bo3164680191535668511r_prat ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_765_singleton__iff,axiom,
    ! [B2: produc1457211279475724562t_char,A2: produc1457211279475724562t_char] :
      ( ( member484235747325421115t_char @ B2 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_766_singleton__iff,axiom,
    ! [B2: produc9003781588162623004on_val,A2: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ B2 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_767_singleton__iff,axiom,
    ! [B2: option_state,A2: option_state] :
      ( ( member_option_state @ B2 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_768_singleton__iff,axiom,
    ! [B2: option_val,A2: option_val] :
      ( ( member_option_val @ B2 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_769_singleton__iff,axiom,
    ! [B2: val,A2: val] :
      ( ( member_val @ B2 @ ( insert_val @ A2 @ bot_bot_set_val ) )
      = ( B2 = A2 ) ) ).

% singleton_iff
thf(fact_770_singletonD,axiom,
    ! [B2: produc1317171644805857433on_val,A2: produc1317171644805857433on_val] :
      ( ( member6505152944228695362on_val @ B2 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_771_singletonD,axiom,
    ! [B2: produc1457211279475724562t_char > prat,A2: produc1457211279475724562t_char > prat] :
      ( ( member2336342582916103932r_prat @ B2 @ ( insert8113562578550770211r_prat @ A2 @ bot_bo3164680191535668511r_prat ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_772_singletonD,axiom,
    ! [B2: produc1457211279475724562t_char,A2: produc1457211279475724562t_char] :
      ( ( member484235747325421115t_char @ B2 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_773_singletonD,axiom,
    ! [B2: produc9003781588162623004on_val,A2: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ B2 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_774_singletonD,axiom,
    ! [B2: option_state,A2: option_state] :
      ( ( member_option_state @ B2 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_775_singletonD,axiom,
    ! [B2: option_val,A2: option_val] :
      ( ( member_option_val @ B2 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_776_singletonD,axiom,
    ! [B2: val,A2: val] :
      ( ( member_val @ B2 @ ( insert_val @ A2 @ bot_bot_set_val ) )
     => ( B2 = A2 ) ) ).

% singletonD
thf(fact_777_domIff,axiom,
    ! [A2: val,M: val > option_state] :
      ( ( member_val @ A2 @ ( dom_val_state @ M ) )
      = ( ( M @ A2 )
       != none_state ) ) ).

% domIff
thf(fact_778_domIff,axiom,
    ! [A2: val,M: val > option_val] :
      ( ( member_val @ A2 @ ( dom_val_val @ M ) )
      = ( ( M @ A2 )
       != none_val ) ) ).

% domIff
thf(fact_779_domIff,axiom,
    ! [A2: option_state,M: option_state > option_state] :
      ( ( member_option_state @ A2 @ ( dom_op8569336450220619928_state @ M ) )
      = ( ( M @ A2 )
       != none_state ) ) ).

% domIff
thf(fact_780_domIff,axiom,
    ! [A2: option_val,M: option_val > option_state] :
      ( ( member_option_val @ A2 @ ( dom_option_val_state @ M ) )
      = ( ( M @ A2 )
       != none_state ) ) ).

% domIff
thf(fact_781_domIff,axiom,
    ! [A2: option_state,M: option_state > option_val] :
      ( ( member_option_state @ A2 @ ( dom_option_state_val @ M ) )
      = ( ( M @ A2 )
       != none_val ) ) ).

% domIff
thf(fact_782_domIff,axiom,
    ! [A2: option_val,M: option_val > option_val] :
      ( ( member_option_val @ A2 @ ( dom_option_val_val @ M ) )
      = ( ( M @ A2 )
       != none_val ) ) ).

% domIff
thf(fact_783_domIff,axiom,
    ! [A2: produc1457211279475724562t_char,M: produc1457211279475724562t_char > option_val] :
      ( ( member484235747325421115t_char @ A2 @ ( dom_Pr8989479155164304065ar_val @ M ) )
      = ( ( M @ A2 )
       != none_val ) ) ).

% domIff
thf(fact_784_domIff,axiom,
    ! [A2: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_state] :
      ( ( member2336342582916103932r_prat @ A2 @ ( dom_Pr2103017623604714043_state @ M ) )
      = ( ( M @ A2 )
       != none_state ) ) ).

% domIff
thf(fact_785_domIff,axiom,
    ! [A2: produc1457211279475724562t_char > prat,M: ( produc1457211279475724562t_char > prat ) > option_val] :
      ( ( member2336342582916103932r_prat @ A2 @ ( dom_Pr3224398758927333440at_val @ M ) )
      = ( ( M @ A2 )
       != none_val ) ) ).

% domIff
thf(fact_786_domIff,axiom,
    ! [A2: val,M: val > option5747939881698552298on_val] :
      ( ( member_val @ A2 @ ( dom_va8931846639282357193on_val @ M ) )
      = ( ( M @ A2 )
       != none_P1334921381875262201on_val ) ) ).

% domIff
thf(fact_787_fun__upd__comp,axiom,
    ! [F: option_state > state,G: state > option_state,X: state,Y3: option_state] :
      ( ( comp_o4916166309651032803_state @ F @ ( fun_up8843634000204221123_state @ G @ X @ Y3 ) )
      = ( fun_upd_state_state @ ( comp_o4916166309651032803_state @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_788_fun__upd__comp,axiom,
    ! [F: option_val > val,G: val > option_val,X: val,Y3: option_val] :
      ( ( comp_o5604524432708427236al_val @ F @ ( fun_up735531404784515971on_val @ G @ X @ Y3 ) )
      = ( fun_upd_val_val @ ( comp_o5604524432708427236al_val @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_789_fun__upd__comp,axiom,
    ! [F: option_val > option_val,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( comp_o7206986085106588079t_char @ F @ ( fun_up5735975307950539954on_val @ G @ X @ Y3 ) )
      = ( fun_up5735975307950539954on_val @ ( comp_o7206986085106588079t_char @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_790_fun__upd__comp,axiom,
    ! [F: option_val > prat,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( comp_o4096340722787922972t_char @ F @ ( fun_up5735975307950539954on_val @ G @ X @ Y3 ) )
      = ( fun_up829850848796697765r_prat @ ( comp_o4096340722787922972t_char @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_791_fun__upd__comp,axiom,
    ! [F: prat > option_val,G: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat] :
      ( ( comp_p7839051931923448766t_char @ F @ ( fun_up829850848796697765r_prat @ G @ X @ Y3 ) )
      = ( fun_up5735975307950539954on_val @ ( comp_p7839051931923448766t_char @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_792_fun__upd__comp,axiom,
    ! [F: prat > prat,G: produc1457211279475724562t_char > prat,X: produc1457211279475724562t_char,Y3: prat] :
      ( ( comp_p2042986060831646413t_char @ F @ ( fun_up829850848796697765r_prat @ G @ X @ Y3 ) )
      = ( fun_up829850848796697765r_prat @ ( comp_p2042986060831646413t_char @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_793_fun__upd__comp,axiom,
    ! [F: option8887860577033306220on_val > option8887860577033306220on_val,G: produc9003781588162623004on_val > option8887860577033306220on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( comp_o7026769649805512793on_val @ F @ ( fun_up273046073882939271on_val @ G @ X @ Y3 ) )
      = ( fun_up273046073882939271on_val @ ( comp_o7026769649805512793on_val @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_794_fun__upd__comp,axiom,
    ! [F: option5747939881698552298on_val > option5747939881698552298on_val,G: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val] :
      ( ( comp_o1785488210378369114r_prat @ F @ ( fun_up1601731230164360576on_val @ G @ X @ Y3 ) )
      = ( fun_up1601731230164360576on_val @ ( comp_o1785488210378369114r_prat @ F @ G ) @ X @ ( F @ Y3 ) ) ) ).

% fun_upd_comp
thf(fact_795_option_Omap__comp,axiom,
    ! [G: option_state > state,F: state > option_state,V2: option_state] :
      ( ( map_op384739313229359441_state @ G @ ( map_op2929067089796592849_state @ F @ V2 ) )
      = ( map_op2726735944305651201_state @ ( comp_o4916166309651032803_state @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_796_option_Omap__comp,axiom,
    ! [G: option_val > val,F: val > option_val,V2: option_val] :
      ( ( map_op8419032157235086213al_val @ G @ ( map_op5819421865013908113on_val @ F @ V2 ) )
      = ( map_option_val_val @ ( comp_o5604524432708427236al_val @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_797_option_Omap__comp,axiom,
    ! [G: state > state,F: state > state,V2: option_state] :
      ( ( map_op2726735944305651201_state @ G @ ( map_op2726735944305651201_state @ F @ V2 ) )
      = ( map_op2726735944305651201_state @ ( comp_s3787957668927766035_state @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_798_option_Omap__comp,axiom,
    ! [G: state > state,F: val > state,V2: option_val] :
      ( ( map_op2726735944305651201_state @ G @ ( map_option_val_state @ F @ V2 ) )
      = ( map_option_val_state @ ( comp_state_state_val @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_799_option_Omap__comp,axiom,
    ! [G: val > state,F: state > val,V2: option_state] :
      ( ( map_option_val_state @ G @ ( map_option_state_val @ F @ V2 ) )
      = ( map_op2726735944305651201_state @ ( comp_val_state_state @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_800_option_Omap__comp,axiom,
    ! [G: val > state,F: val > val,V2: option_val] :
      ( ( map_option_val_state @ G @ ( map_option_val_val @ F @ V2 ) )
      = ( map_option_val_state @ ( comp_val_state_val @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_801_option_Omap__comp,axiom,
    ! [G: state > val,F: state > state,V2: option_state] :
      ( ( map_option_state_val @ G @ ( map_op2726735944305651201_state @ F @ V2 ) )
      = ( map_option_state_val @ ( comp_state_val_state @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_802_option_Omap__comp,axiom,
    ! [G: state > val,F: val > state,V2: option_val] :
      ( ( map_option_state_val @ G @ ( map_option_val_state @ F @ V2 ) )
      = ( map_option_val_val @ ( comp_state_val_val @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_803_option_Omap__comp,axiom,
    ! [G: val > val,F: state > val,V2: option_state] :
      ( ( map_option_val_val @ G @ ( map_option_state_val @ F @ V2 ) )
      = ( map_option_state_val @ ( comp_val_val_state @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_804_option_Omap__comp,axiom,
    ! [G: val > val,F: val > val,V2: option_val] :
      ( ( map_option_val_val @ G @ ( map_option_val_val @ F @ V2 ) )
      = ( map_option_val_val @ ( comp_val_val_val @ G @ F ) @ V2 ) ) ).

% option.map_comp
thf(fact_805_map__option_Ocompositionality,axiom,
    ! [F: option_state > state,G: state > option_state,Option: option_state] :
      ( ( map_op384739313229359441_state @ F @ ( map_op2929067089796592849_state @ G @ Option ) )
      = ( map_op2726735944305651201_state @ ( comp_o4916166309651032803_state @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_806_map__option_Ocompositionality,axiom,
    ! [F: option_val > val,G: val > option_val,Option: option_val] :
      ( ( map_op8419032157235086213al_val @ F @ ( map_op5819421865013908113on_val @ G @ Option ) )
      = ( map_option_val_val @ ( comp_o5604524432708427236al_val @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_807_map__option_Ocompositionality,axiom,
    ! [F: state > state,G: state > state,Option: option_state] :
      ( ( map_op2726735944305651201_state @ F @ ( map_op2726735944305651201_state @ G @ Option ) )
      = ( map_op2726735944305651201_state @ ( comp_s3787957668927766035_state @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_808_map__option_Ocompositionality,axiom,
    ! [F: state > state,G: val > state,Option: option_val] :
      ( ( map_op2726735944305651201_state @ F @ ( map_option_val_state @ G @ Option ) )
      = ( map_option_val_state @ ( comp_state_state_val @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_809_map__option_Ocompositionality,axiom,
    ! [F: val > state,G: state > val,Option: option_state] :
      ( ( map_option_val_state @ F @ ( map_option_state_val @ G @ Option ) )
      = ( map_op2726735944305651201_state @ ( comp_val_state_state @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_810_map__option_Ocompositionality,axiom,
    ! [F: val > state,G: val > val,Option: option_val] :
      ( ( map_option_val_state @ F @ ( map_option_val_val @ G @ Option ) )
      = ( map_option_val_state @ ( comp_val_state_val @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_811_map__option_Ocompositionality,axiom,
    ! [F: state > val,G: state > state,Option: option_state] :
      ( ( map_option_state_val @ F @ ( map_op2726735944305651201_state @ G @ Option ) )
      = ( map_option_state_val @ ( comp_state_val_state @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_812_map__option_Ocompositionality,axiom,
    ! [F: state > val,G: val > state,Option: option_val] :
      ( ( map_option_state_val @ F @ ( map_option_val_state @ G @ Option ) )
      = ( map_option_val_val @ ( comp_state_val_val @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_813_map__option_Ocompositionality,axiom,
    ! [F: val > val,G: state > val,Option: option_state] :
      ( ( map_option_val_val @ F @ ( map_option_state_val @ G @ Option ) )
      = ( map_option_state_val @ ( comp_val_val_state @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_814_map__option_Ocompositionality,axiom,
    ! [F: val > val,G: val > val,Option: option_val] :
      ( ( map_option_val_val @ F @ ( map_option_val_val @ G @ Option ) )
      = ( map_option_val_val @ ( comp_val_val_val @ F @ G ) @ Option ) ) ).

% map_option.compositionality
thf(fact_815_map__add__dom__app__simps_I3_J,axiom,
    ! [M: produc1457211279475724562t_char,L2: produc1457211279475724562t_char > option_val,L1: produc1457211279475724562t_char > option_val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L2 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L1 @ M ) ) ) ).

% map_add_dom_app_simps(3)
thf(fact_816_map__add__dom__app__simps_I2_J,axiom,
    ! [M: produc1457211279475724562t_char,L1: produc1457211279475724562t_char > option_val,L2: produc1457211279475724562t_char > option_val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L1 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L2 @ M ) ) ) ).

% map_add_dom_app_simps(2)
thf(fact_817_map__add__dom__app__simps_I1_J,axiom,
    ! [M: produc1457211279475724562t_char,L2: produc1457211279475724562t_char > option_val,L1: produc1457211279475724562t_char > option_val] :
      ( ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L2 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L2 @ M ) ) ) ).

% map_add_dom_app_simps(1)
thf(fact_818_map__le__def,axiom,
    ( map_le3432596473071271956ar_val
    = ( ^ [M_1: produc1457211279475724562t_char > option_val,M_2: produc1457211279475724562t_char > option_val] :
        ! [X4: produc1457211279475724562t_char] :
          ( ( member484235747325421115t_char @ X4 @ ( dom_Pr8989479155164304065ar_val @ M_1 ) )
         => ( ( M_1 @ X4 )
            = ( M_2 @ X4 ) ) ) ) ) ).

% map_le_def
thf(fact_819_bind__map__option,axiom,
    ! [F: state > state,X: option_state,G: state > option_val] :
      ( ( bind_state_val @ ( map_op2726735944305651201_state @ F @ X ) @ G )
      = ( bind_state_val @ X @ ( comp_s6403480550475472420_state @ G @ F ) ) ) ).

% bind_map_option
thf(fact_820_bind__map__option,axiom,
    ! [F: state > state,X: option_state,G: state > option_state] :
      ( ( bind_state_state @ ( map_op2726735944305651201_state @ F @ X ) @ G )
      = ( bind_state_state @ X @ ( comp_s2749706468613731939_state @ G @ F ) ) ) ).

% bind_map_option
thf(fact_821_bind__map__option,axiom,
    ! [F: val > state,X: option_val,G: state > option_val] :
      ( ( bind_state_val @ ( map_option_val_state @ F @ X ) @ G )
      = ( bind_val_val @ X @ ( comp_s256881845002425239al_val @ G @ F ) ) ) ).

% bind_map_option
thf(fact_822_bind__map__option,axiom,
    ! [F: val > state,X: option_val,G: state > option_state] :
      ( ( bind_state_state @ ( map_option_val_state @ F @ X ) @ G )
      = ( bind_val_state @ X @ ( comp_s5111807602874920472te_val @ G @ F ) ) ) ).

% bind_map_option
thf(fact_823_bind__map__option,axiom,
    ! [F: state > val,X: option_state,G: val > option_val] :
      ( ( bind_val_val @ ( map_option_state_val @ F @ X ) @ G )
      = ( bind_state_val @ X @ ( comp_v2440280314650358435_state @ G @ F ) ) ) ).

% bind_map_option
thf(fact_824_bind__map__option,axiom,
    ! [F: state > val,X: option_state,G: val > option_state] :
      ( ( bind_val_state @ ( map_option_state_val @ F @ X ) @ G )
      = ( bind_state_state @ X @ ( comp_v956742881576431396_state @ G @ F ) ) ) ).

% bind_map_option
thf(fact_825_bind__map__option,axiom,
    ! [F: val > val,X: option_val,G: val > option_val] :
      ( ( bind_val_val @ ( map_option_val_val @ F @ X ) @ G )
      = ( bind_val_val @ X @ ( comp_v7980881360141566424al_val @ G @ F ) ) ) ).

% bind_map_option
thf(fact_826_bind__map__option,axiom,
    ! [F: val > val,X: option_val,G: val > option_state] :
      ( ( bind_val_state @ ( map_option_val_val @ F @ X ) @ G )
      = ( bind_val_state @ X @ ( comp_v1148607367049806487te_val @ G @ F ) ) ) ).

% bind_map_option
thf(fact_827_map__option__bind,axiom,
    ! [F: state > state,X: option_state,G: state > option_state] :
      ( ( map_op2726735944305651201_state @ F @ ( bind_state_state @ X @ G ) )
      = ( bind_state_state @ X @ ( comp_o8889379070304545587_state @ ( map_op2726735944305651201_state @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_828_map__option__bind,axiom,
    ! [F: state > state,X: option_val,G: val > option_state] :
      ( ( map_op2726735944305651201_state @ F @ ( bind_val_state @ X @ G ) )
      = ( bind_val_state @ X @ ( comp_o5664597564486991176te_val @ ( map_op2726735944305651201_state @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_829_map__option__bind,axiom,
    ! [F: val > state,X: option_state,G: state > option_val] :
      ( ( map_option_val_state @ F @ ( bind_state_val @ X @ G ) )
      = ( bind_state_state @ X @ ( comp_o8110046981998356842_state @ ( map_option_val_state @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_830_map__option__bind,axiom,
    ! [F: val > state,X: option_val,G: val > option_val] :
      ( ( map_option_val_state @ F @ ( bind_val_val @ X @ G ) )
      = ( bind_val_state @ X @ ( comp_o1838292368024209361te_val @ ( map_option_val_state @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_831_map__option__bind,axiom,
    ! [F: state > val,X: option_state,G: state > option_state] :
      ( ( map_option_state_val @ F @ ( bind_state_state @ X @ G ) )
      = ( bind_state_val @ X @ ( comp_o6956270512087543124_state @ ( map_option_state_val @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_832_map__option__bind,axiom,
    ! [F: state > val,X: option_val,G: val > option_state] :
      ( ( map_option_state_val @ F @ ( bind_val_state @ X @ G ) )
      = ( bind_val_val @ X @ ( comp_o1385090485725692007al_val @ ( map_option_state_val @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_833_map__option__bind,axiom,
    ! [F: val > val,X: option_state,G: state > option_val] :
      ( ( map_option_val_val @ F @ ( bind_state_val @ X @ G ) )
      = ( bind_state_val @ X @ ( comp_o3129965315624761309_state @ ( map_option_val_val @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_834_map__option__bind,axiom,
    ! [F: val > val,X: option_val,G: val > option_val] :
      ( ( map_option_val_val @ F @ ( bind_val_val @ X @ G ) )
      = ( bind_val_val @ X @ ( comp_o8468585551675268382al_val @ ( map_option_val_val @ F ) @ G ) ) ) ).

% map_option_bind
thf(fact_835_map__conv__bind__option,axiom,
    ( map_op2726735944305651201_state
    = ( ^ [F2: state > state,X4: option_state] : ( bind_state_state @ X4 @ ( comp_s2749706468613731939_state @ some_state @ F2 ) ) ) ) ).

% map_conv_bind_option
thf(fact_836_map__conv__bind__option,axiom,
    ( map_option_val_state
    = ( ^ [F2: val > state,X4: option_val] : ( bind_val_state @ X4 @ ( comp_s5111807602874920472te_val @ some_state @ F2 ) ) ) ) ).

% map_conv_bind_option
thf(fact_837_map__conv__bind__option,axiom,
    ( map_option_state_val
    = ( ^ [F2: state > val,X4: option_state] : ( bind_state_val @ X4 @ ( comp_v2440280314650358435_state @ some_val @ F2 ) ) ) ) ).

% map_conv_bind_option
thf(fact_838_map__conv__bind__option,axiom,
    ( map_option_val_val
    = ( ^ [F2: val > val,X4: option_val] : ( bind_val_val @ X4 @ ( comp_v7980881360141566424al_val @ some_val @ F2 ) ) ) ) ).

% map_conv_bind_option
thf(fact_839_the__elem__eq,axiom,
    ! [X: produc1317171644805857433on_val] :
      ( ( the_el5720079856748460558on_val @ ( insert7062705985672971881on_val @ X @ bot_bo402267660617762917on_val ) )
      = X ) ).

% the_elem_eq
thf(fact_840_the__elem__eq,axiom,
    ! [X: produc1457211279475724562t_char] :
      ( ( the_el4510683560064399623t_char @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) )
      = X ) ).

% the_elem_eq
thf(fact_841_the__elem__eq,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( the_el8055350808190710247on_val @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) )
      = X ) ).

% the_elem_eq
thf(fact_842_the__elem__eq,axiom,
    ! [X: option_state] :
      ( ( the_el1618976816499768149_state @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) )
      = X ) ).

% the_elem_eq
thf(fact_843_the__elem__eq,axiom,
    ! [X: option_val] :
      ( ( the_elem_option_val @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) )
      = X ) ).

% the_elem_eq
thf(fact_844_the__elem__eq,axiom,
    ! [X: val] :
      ( ( the_elem_val @ ( insert_val @ X @ bot_bot_set_val ) )
      = X ) ).

% the_elem_eq
thf(fact_845_is__singletonI,axiom,
    ! [X: produc1317171644805857433on_val] : ( is_sin7597786275116224909on_val @ ( insert7062705985672971881on_val @ X @ bot_bo402267660617762917on_val ) ) ).

% is_singletonI
thf(fact_846_is__singletonI,axiom,
    ! [X: produc1457211279475724562t_char] : ( is_sin3863772449867033606t_char @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ).

% is_singletonI
thf(fact_847_is__singletonI,axiom,
    ! [X: produc9003781588162623004on_val] : ( is_sin1022367449962840616on_val @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ).

% is_singletonI
thf(fact_848_is__singletonI,axiom,
    ! [X: option_state] : ( is_sin8559911096322084886_state @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ).

% is_singletonI
thf(fact_849_is__singletonI,axiom,
    ! [X: option_val] : ( is_sin5830670008703254587on_val @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ).

% is_singletonI
thf(fact_850_is__singletonI,axiom,
    ! [X: val] : ( is_singleton_val @ ( insert_val @ X @ bot_bot_set_val ) ) ).

% is_singletonI
thf(fact_851_add__acc__uni__mask,axiom,
    ( add_ac6043276672051819257t_char
    = ( ^ [Pi2: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char,P4: prat] : ( add_ma6586698345353345811t_char @ Pi2 @ ( uni_ma6578582744724537101t_char @ Hl2 @ P4 ) ) ) ) ).

% add_acc_uni_mask
thf(fact_852_ran__map__upd,axiom,
    ! [M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( ( M @ A2 )
        = none_val )
     => ( ( ran_Pr786515303459910110ar_val @ ( fun_up5735975307950539954on_val @ M @ A2 @ ( some_val @ B2 ) ) )
        = ( insert_val @ B2 @ ( ran_Pr786515303459910110ar_val @ M ) ) ) ) ).

% ran_map_upd
thf(fact_853_ran__map__upd,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
      ( ( ( M @ A2 )
        = none_P8728355543607141243on_val )
     => ( ( ran_Pr1583955956598603305on_val @ ( fun_up273046073882939271on_val @ M @ A2 @ ( some_P2581650809551911671on_val @ B2 ) ) )
        = ( insert3030518898131756108on_val @ B2 @ ( ran_Pr1583955956598603305on_val @ M ) ) ) ) ).

% ran_map_upd
thf(fact_854_ran__map__upd,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val] :
      ( ( ( M @ A2 )
        = none_P1334921381875262201on_val )
     => ( ( ran_Pr878516737976613822on_val @ ( fun_up1601731230164360576on_val @ M @ A2 @ ( some_P7669353234731512949on_val @ B2 ) ) )
        = ( insert216038912599248202on_val @ B2 @ ( ran_Pr878516737976613822on_val @ M ) ) ) ) ).

% ran_map_upd
thf(fact_855_dom__fun__upd,axiom,
    ! [Y3: option_state,F: val > option_state,X: val] :
      ( ( ( Y3 = none_state )
       => ( ( dom_val_state @ ( fun_up7100790768922270414_state @ F @ X @ Y3 ) )
          = ( minus_minus_set_val @ ( dom_val_state @ F ) @ ( insert_val @ X @ bot_bot_set_val ) ) ) )
      & ( ( Y3 != none_state )
       => ( ( dom_val_state @ ( fun_up7100790768922270414_state @ F @ X @ Y3 ) )
          = ( insert_val @ X @ ( dom_val_state @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_856_dom__fun__upd,axiom,
    ! [Y3: option_val,F: val > option_val,X: val] :
      ( ( ( Y3 = none_val )
       => ( ( dom_val_val @ ( fun_up735531404784515971on_val @ F @ X @ Y3 ) )
          = ( minus_minus_set_val @ ( dom_val_val @ F ) @ ( insert_val @ X @ bot_bot_set_val ) ) ) )
      & ( ( Y3 != none_val )
       => ( ( dom_val_val @ ( fun_up735531404784515971on_val @ F @ X @ Y3 ) )
          = ( insert_val @ X @ ( dom_val_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_857_dom__fun__upd,axiom,
    ! [Y3: option_state,F: option_state > option_state,X: option_state] :
      ( ( ( Y3 = none_state )
       => ( ( dom_op8569336450220619928_state @ ( fun_up6517640620910344979_state @ F @ X @ Y3 ) )
          = ( minus_7537472381646091673_state @ ( dom_op8569336450220619928_state @ F ) @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) )
      & ( ( Y3 != none_state )
       => ( ( dom_op8569336450220619928_state @ ( fun_up6517640620910344979_state @ F @ X @ Y3 ) )
          = ( insert_option_state @ X @ ( dom_op8569336450220619928_state @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_858_dom__fun__upd,axiom,
    ! [Y3: option_val,F: option_state > option_val,X: option_state] :
      ( ( ( Y3 = none_val )
       => ( ( dom_option_state_val @ ( fun_up8652368643555229054on_val @ F @ X @ Y3 ) )
          = ( minus_7537472381646091673_state @ ( dom_option_state_val @ F ) @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) )
      & ( ( Y3 != none_val )
       => ( ( dom_option_state_val @ ( fun_up8652368643555229054on_val @ F @ X @ Y3 ) )
          = ( insert_option_state @ X @ ( dom_option_state_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_859_dom__fun__upd,axiom,
    ! [Y3: option_state,F: option_val > option_state,X: option_val] :
      ( ( ( Y3 = none_state )
       => ( ( dom_option_val_state @ ( fun_up2039547756584784788_state @ F @ X @ Y3 ) )
          = ( minus_3256168188512067470on_val @ ( dom_option_val_state @ F ) @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) )
      & ( ( Y3 != none_state )
       => ( ( dom_option_val_state @ ( fun_up2039547756584784788_state @ F @ X @ Y3 ) )
          = ( insert_option_val @ X @ ( dom_option_val_state @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_860_dom__fun__upd,axiom,
    ! [Y3: option_val,F: option_val > option_val,X: option_val] :
      ( ( ( Y3 = none_val )
       => ( ( dom_option_val_val @ ( fun_up8761876891205509693on_val @ F @ X @ Y3 ) )
          = ( minus_3256168188512067470on_val @ ( dom_option_val_val @ F ) @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) )
      & ( ( Y3 != none_val )
       => ( ( dom_option_val_val @ ( fun_up8761876891205509693on_val @ F @ X @ Y3 ) )
          = ( insert_option_val @ X @ ( dom_option_val_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_861_dom__fun__upd,axiom,
    ! [Y3: option_state,F: produc1457211279475724562t_char > option_state,X: produc1457211279475724562t_char] :
      ( ( ( Y3 = none_state )
       => ( ( dom_Pr24798649119601274_state @ ( fun_up6995552760743215839_state @ F @ X @ Y3 ) )
          = ( minus_6181227053800976857t_char @ ( dom_Pr24798649119601274_state @ F ) @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) )
      & ( ( Y3 != none_state )
       => ( ( dom_Pr24798649119601274_state @ ( fun_up6995552760743215839_state @ F @ X @ Y3 ) )
          = ( insert3372640069787401954t_char @ X @ ( dom_Pr24798649119601274_state @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_862_dom__fun__upd,axiom,
    ! [Y3: option_val,F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char] :
      ( ( ( Y3 = none_val )
       => ( ( dom_Pr8989479155164304065ar_val @ ( fun_up5735975307950539954on_val @ F @ X @ Y3 ) )
          = ( minus_6181227053800976857t_char @ ( dom_Pr8989479155164304065ar_val @ F ) @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) )
      & ( ( Y3 != none_val )
       => ( ( dom_Pr8989479155164304065ar_val @ ( fun_up5735975307950539954on_val @ F @ X @ Y3 ) )
          = ( insert3372640069787401954t_char @ X @ ( dom_Pr8989479155164304065ar_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_863_dom__fun__upd,axiom,
    ! [Y3: option5747939881698552298on_val,F: val > option5747939881698552298on_val,X: val] :
      ( ( ( Y3 = none_P1334921381875262201on_val )
       => ( ( dom_va8931846639282357193on_val @ ( fun_up8940424251277849774on_val @ F @ X @ Y3 ) )
          = ( minus_minus_set_val @ ( dom_va8931846639282357193on_val @ F ) @ ( insert_val @ X @ bot_bot_set_val ) ) ) )
      & ( ( Y3 != none_P1334921381875262201on_val )
       => ( ( dom_va8931846639282357193on_val @ ( fun_up8940424251277849774on_val @ F @ X @ Y3 ) )
          = ( insert_val @ X @ ( dom_va8931846639282357193on_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_864_dom__fun__upd,axiom,
    ! [Y3: option5747939881698552298on_val,F: option_state > option5747939881698552298on_val,X: option_state] :
      ( ( ( Y3 = none_P1334921381875262201on_val )
       => ( ( dom_op741179583939567608on_val @ ( fun_up3115773442321631859on_val @ F @ X @ Y3 ) )
          = ( minus_7537472381646091673_state @ ( dom_op741179583939567608on_val @ F ) @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) )
      & ( ( Y3 != none_P1334921381875262201on_val )
       => ( ( dom_op741179583939567608on_val @ ( fun_up3115773442321631859on_val @ F @ X @ Y3 ) )
          = ( insert_option_state @ X @ ( dom_op741179583939567608on_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_865_these__insert__Some,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_op7951517479864145599on_val] :
      ( ( these_4429819578991166294on_val @ ( insert4270431555848968111on_val @ ( some_P3086335783055994110on_val @ X ) @ A4 ) )
      = ( insert7062705985672971881on_val @ X @ ( these_4429819578991166294on_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_866_these__insert__Some,axiom,
    ! [X: option_state,A4: set_op9003753404445127824_state] :
      ( ( these_option_state @ ( insert7535573567550883338_state @ ( some_option_state @ X ) @ A4 ) )
      = ( insert_option_state @ X @ ( these_option_state @ A4 ) ) ) ).

% these_insert_Some
thf(fact_867_these__insert__Some,axiom,
    ! [X: option_val,A4: set_op1974636978870893421on_val] :
      ( ( these_option_val @ ( insert7563226391266834525on_val @ ( some_option_val @ X ) @ A4 ) )
      = ( insert_option_val @ X @ ( these_option_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_868_these__insert__Some,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_op6240181410663953058on_val] :
      ( ( these_3919539662624406175on_val @ ( insert751572358616671900on_val @ ( some_P2581650809551911671on_val @ X ) @ A4 ) )
      = ( insert3030518898131756108on_val @ X @ ( these_3919539662624406175on_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_869_these__insert__Some,axiom,
    ! [X: produc1457211279475724562t_char > option_val,A4: set_op8153969091884965280on_val] :
      ( ( these_602426935119867933on_val @ ( insert4694516387090290714on_val @ ( some_P7669353234731512949on_val @ X ) @ A4 ) )
      = ( insert216038912599248202on_val @ X @ ( these_602426935119867933on_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_870_these__insert__Some,axiom,
    ! [X: val,A4: set_option_val] :
      ( ( these_val @ ( insert_option_val @ ( some_val @ X ) @ A4 ) )
      = ( insert_val @ X @ ( these_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_871_these__insert__Some,axiom,
    ! [X: state,A4: set_option_state] :
      ( ( these_state @ ( insert_option_state @ ( some_state @ X ) @ A4 ) )
      = ( insert_state @ X @ ( these_state @ A4 ) ) ) ).

% these_insert_Some
thf(fact_872_is__singletonE,axiom,
    ! [A4: set_Pr4305388979797279737on_val] :
      ( ( is_sin7597786275116224909on_val @ A4 )
     => ~ ! [X3: produc1317171644805857433on_val] :
            ( A4
           != ( insert7062705985672971881on_val @ X3 @ bot_bo402267660617762917on_val ) ) ) ).

% is_singletonE
thf(fact_873_is__singletonE,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( is_sin3863772449867033606t_char @ A4 )
     => ~ ! [X3: produc1457211279475724562t_char] :
            ( A4
           != ( insert3372640069787401954t_char @ X3 @ bot_bo1414094081888755934t_char ) ) ) ).

% is_singletonE
thf(fact_874_is__singletonE,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( is_sin1022367449962840616on_val @ A4 )
     => ~ ! [X3: produc9003781588162623004on_val] :
            ( A4
           != ( insert3030518898131756108on_val @ X3 @ bot_bo6722054719108133734on_val ) ) ) ).

% is_singletonE
thf(fact_875_is__singletonE,axiom,
    ! [A4: set_option_state] :
      ( ( is_sin8559911096322084886_state @ A4 )
     => ~ ! [X3: option_state] :
            ( A4
           != ( insert_option_state @ X3 @ bot_bo710180891245420500_state ) ) ) ).

% is_singletonE
thf(fact_876_is__singletonE,axiom,
    ! [A4: set_option_val] :
      ( ( is_sin5830670008703254587on_val @ A4 )
     => ~ ! [X3: option_val] :
            ( A4
           != ( insert_option_val @ X3 @ bot_bo5906790151302476563on_val ) ) ) ).

% is_singletonE
thf(fact_877_is__singletonE,axiom,
    ! [A4: set_val] :
      ( ( is_singleton_val @ A4 )
     => ~ ! [X3: val] :
            ( A4
           != ( insert_val @ X3 @ bot_bot_set_val ) ) ) ).

% is_singletonE
thf(fact_878_is__singleton__def,axiom,
    ( is_sin7597786275116224909on_val
    = ( ^ [A6: set_Pr4305388979797279737on_val] :
        ? [X4: produc1317171644805857433on_val] :
          ( A6
          = ( insert7062705985672971881on_val @ X4 @ bot_bo402267660617762917on_val ) ) ) ) ).

% is_singleton_def
thf(fact_879_is__singleton__def,axiom,
    ( is_sin3863772449867033606t_char
    = ( ^ [A6: set_Pr2507339680178222706t_char] :
        ? [X4: produc1457211279475724562t_char] :
          ( A6
          = ( insert3372640069787401954t_char @ X4 @ bot_bo1414094081888755934t_char ) ) ) ) ).

% is_singleton_def
thf(fact_880_is__singleton__def,axiom,
    ( is_sin1022367449962840616on_val
    = ( ^ [A6: set_Pr7649655576376376530on_val] :
        ? [X4: produc9003781588162623004on_val] :
          ( A6
          = ( insert3030518898131756108on_val @ X4 @ bot_bo6722054719108133734on_val ) ) ) ) ).

% is_singleton_def
thf(fact_881_is__singleton__def,axiom,
    ( is_sin8559911096322084886_state
    = ( ^ [A6: set_option_state] :
        ? [X4: option_state] :
          ( A6
          = ( insert_option_state @ X4 @ bot_bo710180891245420500_state ) ) ) ) ).

% is_singleton_def
thf(fact_882_is__singleton__def,axiom,
    ( is_sin5830670008703254587on_val
    = ( ^ [A6: set_option_val] :
        ? [X4: option_val] :
          ( A6
          = ( insert_option_val @ X4 @ bot_bo5906790151302476563on_val ) ) ) ) ).

% is_singleton_def
thf(fact_883_is__singleton__def,axiom,
    ( is_singleton_val
    = ( ^ [A6: set_val] :
        ? [X4: val] :
          ( A6
          = ( insert_val @ X4 @ bot_bot_set_val ) ) ) ) ).

% is_singleton_def
thf(fact_884_Diff__iff,axiom,
    ! [C: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( minus_9160195963678339755on_val @ A4 @ B5 ) )
      = ( ( member2879030624002546611on_val @ C @ A4 )
        & ~ ( member2879030624002546611on_val @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_885_Diff__iff,axiom,
    ! [C: option_state,A4: set_option_state,B5: set_option_state] :
      ( ( member_option_state @ C @ ( minus_7537472381646091673_state @ A4 @ B5 ) )
      = ( ( member_option_state @ C @ A4 )
        & ~ ( member_option_state @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_886_Diff__iff,axiom,
    ! [C: option_val,A4: set_option_val,B5: set_option_val] :
      ( ( member_option_val @ C @ ( minus_3256168188512067470on_val @ A4 @ B5 ) )
      = ( ( member_option_val @ C @ A4 )
        & ~ ( member_option_val @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_887_Diff__iff,axiom,
    ! [C: val,A4: set_val,B5: set_val] :
      ( ( member_val @ C @ ( minus_minus_set_val @ A4 @ B5 ) )
      = ( ( member_val @ C @ A4 )
        & ~ ( member_val @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_888_Diff__iff,axiom,
    ! [C: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ C @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) )
      = ( ( member2336342582916103932r_prat @ C @ A4 )
        & ~ ( member2336342582916103932r_prat @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_889_DiffI,axiom,
    ! [C: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ A4 )
     => ( ~ ( member2879030624002546611on_val @ C @ B5 )
       => ( member2879030624002546611on_val @ C @ ( minus_9160195963678339755on_val @ A4 @ B5 ) ) ) ) ).

% DiffI
thf(fact_890_DiffI,axiom,
    ! [C: option_state,A4: set_option_state,B5: set_option_state] :
      ( ( member_option_state @ C @ A4 )
     => ( ~ ( member_option_state @ C @ B5 )
       => ( member_option_state @ C @ ( minus_7537472381646091673_state @ A4 @ B5 ) ) ) ) ).

% DiffI
thf(fact_891_DiffI,axiom,
    ! [C: option_val,A4: set_option_val,B5: set_option_val] :
      ( ( member_option_val @ C @ A4 )
     => ( ~ ( member_option_val @ C @ B5 )
       => ( member_option_val @ C @ ( minus_3256168188512067470on_val @ A4 @ B5 ) ) ) ) ).

% DiffI
thf(fact_892_DiffI,axiom,
    ! [C: val,A4: set_val,B5: set_val] :
      ( ( member_val @ C @ A4 )
     => ( ~ ( member_val @ C @ B5 )
       => ( member_val @ C @ ( minus_minus_set_val @ A4 @ B5 ) ) ) ) ).

% DiffI
thf(fact_893_DiffI,axiom,
    ! [C: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ C @ A4 )
     => ( ~ ( member2336342582916103932r_prat @ C @ B5 )
       => ( member2336342582916103932r_prat @ C @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) ) ) ) ).

% DiffI
thf(fact_894_Diff__empty,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( minus_6181227053800976857t_char @ A4 @ bot_bo1414094081888755934t_char )
      = A4 ) ).

% Diff_empty
thf(fact_895_Diff__empty,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( minus_9160195963678339755on_val @ A4 @ bot_bo6722054719108133734on_val )
      = A4 ) ).

% Diff_empty
thf(fact_896_Diff__empty,axiom,
    ! [A4: set_option_state] :
      ( ( minus_7537472381646091673_state @ A4 @ bot_bo710180891245420500_state )
      = A4 ) ).

% Diff_empty
thf(fact_897_Diff__empty,axiom,
    ! [A4: set_option_val] :
      ( ( minus_3256168188512067470on_val @ A4 @ bot_bo5906790151302476563on_val )
      = A4 ) ).

% Diff_empty
thf(fact_898_Diff__empty,axiom,
    ! [A4: set_val] :
      ( ( minus_minus_set_val @ A4 @ bot_bot_set_val )
      = A4 ) ).

% Diff_empty
thf(fact_899_empty__Diff,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( minus_6181227053800976857t_char @ bot_bo1414094081888755934t_char @ A4 )
      = bot_bo1414094081888755934t_char ) ).

% empty_Diff
thf(fact_900_empty__Diff,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( minus_9160195963678339755on_val @ bot_bo6722054719108133734on_val @ A4 )
      = bot_bo6722054719108133734on_val ) ).

% empty_Diff
thf(fact_901_empty__Diff,axiom,
    ! [A4: set_option_state] :
      ( ( minus_7537472381646091673_state @ bot_bo710180891245420500_state @ A4 )
      = bot_bo710180891245420500_state ) ).

% empty_Diff
thf(fact_902_empty__Diff,axiom,
    ! [A4: set_option_val] :
      ( ( minus_3256168188512067470on_val @ bot_bo5906790151302476563on_val @ A4 )
      = bot_bo5906790151302476563on_val ) ).

% empty_Diff
thf(fact_903_empty__Diff,axiom,
    ! [A4: set_val] :
      ( ( minus_minus_set_val @ bot_bot_set_val @ A4 )
      = bot_bot_set_val ) ).

% empty_Diff
thf(fact_904_Diff__cancel,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( minus_6181227053800976857t_char @ A4 @ A4 )
      = bot_bo1414094081888755934t_char ) ).

% Diff_cancel
thf(fact_905_Diff__cancel,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( minus_9160195963678339755on_val @ A4 @ A4 )
      = bot_bo6722054719108133734on_val ) ).

% Diff_cancel
thf(fact_906_Diff__cancel,axiom,
    ! [A4: set_option_state] :
      ( ( minus_7537472381646091673_state @ A4 @ A4 )
      = bot_bo710180891245420500_state ) ).

% Diff_cancel
thf(fact_907_Diff__cancel,axiom,
    ! [A4: set_option_val] :
      ( ( minus_3256168188512067470on_val @ A4 @ A4 )
      = bot_bo5906790151302476563on_val ) ).

% Diff_cancel
thf(fact_908_Diff__cancel,axiom,
    ! [A4: set_val] :
      ( ( minus_minus_set_val @ A4 @ A4 )
      = bot_bot_set_val ) ).

% Diff_cancel
thf(fact_909_insert__Diff1,axiom,
    ! [X: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ X @ B5 )
     => ( ( minus_7211471524202483680on_val @ ( insert7062705985672971881on_val @ X @ A4 ) @ B5 )
        = ( minus_7211471524202483680on_val @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_910_insert__Diff1,axiom,
    ! [X: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X @ B5 )
     => ( ( minus_9160195963678339755on_val @ ( insert3030518898131756108on_val @ X @ A4 ) @ B5 )
        = ( minus_9160195963678339755on_val @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_911_insert__Diff1,axiom,
    ! [X: option_state,B5: set_option_state,A4: set_option_state] :
      ( ( member_option_state @ X @ B5 )
     => ( ( minus_7537472381646091673_state @ ( insert_option_state @ X @ A4 ) @ B5 )
        = ( minus_7537472381646091673_state @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_912_insert__Diff1,axiom,
    ! [X: option_val,B5: set_option_val,A4: set_option_val] :
      ( ( member_option_val @ X @ B5 )
     => ( ( minus_3256168188512067470on_val @ ( insert_option_val @ X @ A4 ) @ B5 )
        = ( minus_3256168188512067470on_val @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_913_insert__Diff1,axiom,
    ! [X: val,B5: set_val,A4: set_val] :
      ( ( member_val @ X @ B5 )
     => ( ( minus_minus_set_val @ ( insert_val @ X @ A4 ) @ B5 )
        = ( minus_minus_set_val @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_914_insert__Diff1,axiom,
    ! [X: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ X @ B5 )
     => ( ( minus_7863043754688659098r_prat @ ( insert8113562578550770211r_prat @ X @ A4 ) @ B5 )
        = ( minus_7863043754688659098r_prat @ A4 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_915_Diff__insert0,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val,B5: set_Pr4305388979797279737on_val] :
      ( ~ ( member6505152944228695362on_val @ X @ A4 )
     => ( ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ X @ B5 ) )
        = ( minus_7211471524202483680on_val @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_916_Diff__insert0,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ X @ B5 ) )
        = ( minus_9160195963678339755on_val @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_917_Diff__insert0,axiom,
    ! [X: option_state,A4: set_option_state,B5: set_option_state] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ X @ B5 ) )
        = ( minus_7537472381646091673_state @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_918_Diff__insert0,axiom,
    ! [X: option_val,A4: set_option_val,B5: set_option_val] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ X @ B5 ) )
        = ( minus_3256168188512067470on_val @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_919_Diff__insert0,axiom,
    ! [X: val,A4: set_val,B5: set_val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( minus_minus_set_val @ A4 @ ( insert_val @ X @ B5 ) )
        = ( minus_minus_set_val @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_920_Diff__insert0,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( minus_7863043754688659098r_prat @ A4 @ ( insert8113562578550770211r_prat @ X @ B5 ) )
        = ( minus_7863043754688659098r_prat @ A4 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_921_these__empty,axiom,
    ( ( these_2739680984639915599t_char @ bot_bo2782010437066608292t_char )
    = bot_bo1414094081888755934t_char ) ).

% these_empty
thf(fact_922_these__empty,axiom,
    ( ( these_3919539662624406175on_val @ bot_bo6421125907362167606on_val )
    = bot_bo6722054719108133734on_val ) ).

% these_empty
thf(fact_923_these__empty,axiom,
    ( ( these_option_state @ bot_bo489212050006660900_state )
    = bot_bo710180891245420500_state ) ).

% these_empty
thf(fact_924_these__empty,axiom,
    ( ( these_option_val @ bot_bo6240080102570541529on_val )
    = bot_bo5906790151302476563on_val ) ).

% these_empty
thf(fact_925_these__empty,axiom,
    ( ( these_state @ bot_bo710180891245420500_state )
    = bot_bot_set_state ) ).

% these_empty
thf(fact_926_these__empty,axiom,
    ( ( these_val @ bot_bo5906790151302476563on_val )
    = bot_bot_set_val ) ).

% these_empty
thf(fact_927_insert__Diff__single,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( insert7062705985672971881on_val @ A2 @ ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) ) )
      = ( insert7062705985672971881on_val @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_928_insert__Diff__single,axiom,
    ! [A2: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char] :
      ( ( insert3372640069787401954t_char @ A2 @ ( minus_6181227053800976857t_char @ A4 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) ) )
      = ( insert3372640069787401954t_char @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_929_insert__Diff__single,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( insert3030518898131756108on_val @ A2 @ ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) )
      = ( insert3030518898131756108on_val @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_930_insert__Diff__single,axiom,
    ! [A2: option_state,A4: set_option_state] :
      ( ( insert_option_state @ A2 @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) ) )
      = ( insert_option_state @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_931_insert__Diff__single,axiom,
    ! [A2: option_val,A4: set_option_val] :
      ( ( insert_option_val @ A2 @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) ) )
      = ( insert_option_val @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_932_insert__Diff__single,axiom,
    ! [A2: val,A4: set_val] :
      ( ( insert_val @ A2 @ ( minus_minus_set_val @ A4 @ ( insert_val @ A2 @ bot_bot_set_val ) ) )
      = ( insert_val @ A2 @ A4 ) ) ).

% insert_Diff_single
thf(fact_933_these__insert__None,axiom,
    ! [A4: set_op6240181410663953058on_val] :
      ( ( these_3919539662624406175on_val @ ( insert751572358616671900on_val @ none_P8728355543607141243on_val @ A4 ) )
      = ( these_3919539662624406175on_val @ A4 ) ) ).

% these_insert_None
thf(fact_934_these__insert__None,axiom,
    ! [A4: set_op8153969091884965280on_val] :
      ( ( these_602426935119867933on_val @ ( insert4694516387090290714on_val @ none_P1334921381875262201on_val @ A4 ) )
      = ( these_602426935119867933on_val @ A4 ) ) ).

% these_insert_None
thf(fact_935_these__insert__None,axiom,
    ! [A4: set_option_state] :
      ( ( these_state @ ( insert_option_state @ none_state @ A4 ) )
      = ( these_state @ A4 ) ) ).

% these_insert_None
thf(fact_936_these__insert__None,axiom,
    ! [A4: set_option_val] :
      ( ( these_val @ ( insert_option_val @ none_val @ A4 ) )
      = ( these_val @ A4 ) ) ).

% these_insert_None
thf(fact_937_DiffD2,axiom,
    ! [C: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( minus_9160195963678339755on_val @ A4 @ B5 ) )
     => ~ ( member2879030624002546611on_val @ C @ B5 ) ) ).

% DiffD2
thf(fact_938_DiffD2,axiom,
    ! [C: option_state,A4: set_option_state,B5: set_option_state] :
      ( ( member_option_state @ C @ ( minus_7537472381646091673_state @ A4 @ B5 ) )
     => ~ ( member_option_state @ C @ B5 ) ) ).

% DiffD2
thf(fact_939_DiffD2,axiom,
    ! [C: option_val,A4: set_option_val,B5: set_option_val] :
      ( ( member_option_val @ C @ ( minus_3256168188512067470on_val @ A4 @ B5 ) )
     => ~ ( member_option_val @ C @ B5 ) ) ).

% DiffD2
thf(fact_940_DiffD2,axiom,
    ! [C: val,A4: set_val,B5: set_val] :
      ( ( member_val @ C @ ( minus_minus_set_val @ A4 @ B5 ) )
     => ~ ( member_val @ C @ B5 ) ) ).

% DiffD2
thf(fact_941_DiffD2,axiom,
    ! [C: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ C @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) )
     => ~ ( member2336342582916103932r_prat @ C @ B5 ) ) ).

% DiffD2
thf(fact_942_DiffD1,axiom,
    ! [C: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( minus_9160195963678339755on_val @ A4 @ B5 ) )
     => ( member2879030624002546611on_val @ C @ A4 ) ) ).

% DiffD1
thf(fact_943_DiffD1,axiom,
    ! [C: option_state,A4: set_option_state,B5: set_option_state] :
      ( ( member_option_state @ C @ ( minus_7537472381646091673_state @ A4 @ B5 ) )
     => ( member_option_state @ C @ A4 ) ) ).

% DiffD1
thf(fact_944_DiffD1,axiom,
    ! [C: option_val,A4: set_option_val,B5: set_option_val] :
      ( ( member_option_val @ C @ ( minus_3256168188512067470on_val @ A4 @ B5 ) )
     => ( member_option_val @ C @ A4 ) ) ).

% DiffD1
thf(fact_945_DiffD1,axiom,
    ! [C: val,A4: set_val,B5: set_val] :
      ( ( member_val @ C @ ( minus_minus_set_val @ A4 @ B5 ) )
     => ( member_val @ C @ A4 ) ) ).

% DiffD1
thf(fact_946_DiffD1,axiom,
    ! [C: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ C @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) )
     => ( member2336342582916103932r_prat @ C @ A4 ) ) ).

% DiffD1
thf(fact_947_DiffE,axiom,
    ! [C: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( minus_9160195963678339755on_val @ A4 @ B5 ) )
     => ~ ( ( member2879030624002546611on_val @ C @ A4 )
         => ( member2879030624002546611on_val @ C @ B5 ) ) ) ).

% DiffE
thf(fact_948_DiffE,axiom,
    ! [C: option_state,A4: set_option_state,B5: set_option_state] :
      ( ( member_option_state @ C @ ( minus_7537472381646091673_state @ A4 @ B5 ) )
     => ~ ( ( member_option_state @ C @ A4 )
         => ( member_option_state @ C @ B5 ) ) ) ).

% DiffE
thf(fact_949_DiffE,axiom,
    ! [C: option_val,A4: set_option_val,B5: set_option_val] :
      ( ( member_option_val @ C @ ( minus_3256168188512067470on_val @ A4 @ B5 ) )
     => ~ ( ( member_option_val @ C @ A4 )
         => ( member_option_val @ C @ B5 ) ) ) ).

% DiffE
thf(fact_950_DiffE,axiom,
    ! [C: val,A4: set_val,B5: set_val] :
      ( ( member_val @ C @ ( minus_minus_set_val @ A4 @ B5 ) )
     => ~ ( ( member_val @ C @ A4 )
         => ( member_val @ C @ B5 ) ) ) ).

% DiffE
thf(fact_951_DiffE,axiom,
    ! [C: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,B5: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ C @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) )
     => ~ ( ( member2336342582916103932r_prat @ C @ A4 )
         => ( member2336342582916103932r_prat @ C @ B5 ) ) ) ).

% DiffE
thf(fact_952_insert__Diff__if,axiom,
    ! [X: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( ( member6505152944228695362on_val @ X @ B5 )
       => ( ( minus_7211471524202483680on_val @ ( insert7062705985672971881on_val @ X @ A4 ) @ B5 )
          = ( minus_7211471524202483680on_val @ A4 @ B5 ) ) )
      & ( ~ ( member6505152944228695362on_val @ X @ B5 )
       => ( ( minus_7211471524202483680on_val @ ( insert7062705985672971881on_val @ X @ A4 ) @ B5 )
          = ( insert7062705985672971881on_val @ X @ ( minus_7211471524202483680on_val @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_953_insert__Diff__if,axiom,
    ! [X: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( ( member2879030624002546611on_val @ X @ B5 )
       => ( ( minus_9160195963678339755on_val @ ( insert3030518898131756108on_val @ X @ A4 ) @ B5 )
          = ( minus_9160195963678339755on_val @ A4 @ B5 ) ) )
      & ( ~ ( member2879030624002546611on_val @ X @ B5 )
       => ( ( minus_9160195963678339755on_val @ ( insert3030518898131756108on_val @ X @ A4 ) @ B5 )
          = ( insert3030518898131756108on_val @ X @ ( minus_9160195963678339755on_val @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_954_insert__Diff__if,axiom,
    ! [X: option_state,B5: set_option_state,A4: set_option_state] :
      ( ( ( member_option_state @ X @ B5 )
       => ( ( minus_7537472381646091673_state @ ( insert_option_state @ X @ A4 ) @ B5 )
          = ( minus_7537472381646091673_state @ A4 @ B5 ) ) )
      & ( ~ ( member_option_state @ X @ B5 )
       => ( ( minus_7537472381646091673_state @ ( insert_option_state @ X @ A4 ) @ B5 )
          = ( insert_option_state @ X @ ( minus_7537472381646091673_state @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_955_insert__Diff__if,axiom,
    ! [X: option_val,B5: set_option_val,A4: set_option_val] :
      ( ( ( member_option_val @ X @ B5 )
       => ( ( minus_3256168188512067470on_val @ ( insert_option_val @ X @ A4 ) @ B5 )
          = ( minus_3256168188512067470on_val @ A4 @ B5 ) ) )
      & ( ~ ( member_option_val @ X @ B5 )
       => ( ( minus_3256168188512067470on_val @ ( insert_option_val @ X @ A4 ) @ B5 )
          = ( insert_option_val @ X @ ( minus_3256168188512067470on_val @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_956_insert__Diff__if,axiom,
    ! [X: val,B5: set_val,A4: set_val] :
      ( ( ( member_val @ X @ B5 )
       => ( ( minus_minus_set_val @ ( insert_val @ X @ A4 ) @ B5 )
          = ( minus_minus_set_val @ A4 @ B5 ) ) )
      & ( ~ ( member_val @ X @ B5 )
       => ( ( minus_minus_set_val @ ( insert_val @ X @ A4 ) @ B5 )
          = ( insert_val @ X @ ( minus_minus_set_val @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_957_insert__Diff__if,axiom,
    ! [X: produc1457211279475724562t_char > prat,B5: set_Pr3433046674199179443r_prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( ( member2336342582916103932r_prat @ X @ B5 )
       => ( ( minus_7863043754688659098r_prat @ ( insert8113562578550770211r_prat @ X @ A4 ) @ B5 )
          = ( minus_7863043754688659098r_prat @ A4 @ B5 ) ) )
      & ( ~ ( member2336342582916103932r_prat @ X @ B5 )
       => ( ( minus_7863043754688659098r_prat @ ( insert8113562578550770211r_prat @ X @ A4 ) @ B5 )
          = ( insert8113562578550770211r_prat @ X @ ( minus_7863043754688659098r_prat @ A4 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_958_ranI,axiom,
    ! [M: produc1457211279475724562t_char > option_val,A2: produc1457211279475724562t_char,B2: val] :
      ( ( ( M @ A2 )
        = ( some_val @ B2 ) )
     => ( member_val @ B2 @ ( ran_Pr786515303459910110ar_val @ M ) ) ) ).

% ranI
thf(fact_959_Diff__insert,axiom,
    ! [A4: set_Pr4305388979797279737on_val,A2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val] :
      ( ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ A2 @ B5 ) )
      = ( minus_7211471524202483680on_val @ ( minus_7211471524202483680on_val @ A4 @ B5 ) @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) ) ) ).

% Diff_insert
thf(fact_960_Diff__insert,axiom,
    ! [A4: set_Pr2507339680178222706t_char,A2: produc1457211279475724562t_char,B5: set_Pr2507339680178222706t_char] :
      ( ( minus_6181227053800976857t_char @ A4 @ ( insert3372640069787401954t_char @ A2 @ B5 ) )
      = ( minus_6181227053800976857t_char @ ( minus_6181227053800976857t_char @ A4 @ B5 ) @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) ) ) ).

% Diff_insert
thf(fact_961_Diff__insert,axiom,
    ! [A4: set_Pr7649655576376376530on_val,A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ B5 ) )
      = ( minus_9160195963678339755on_val @ ( minus_9160195963678339755on_val @ A4 @ B5 ) @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) ) ).

% Diff_insert
thf(fact_962_Diff__insert,axiom,
    ! [A4: set_option_state,A2: option_state,B5: set_option_state] :
      ( ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ A2 @ B5 ) )
      = ( minus_7537472381646091673_state @ ( minus_7537472381646091673_state @ A4 @ B5 ) @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) ) ) ).

% Diff_insert
thf(fact_963_Diff__insert,axiom,
    ! [A4: set_option_val,A2: option_val,B5: set_option_val] :
      ( ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ A2 @ B5 ) )
      = ( minus_3256168188512067470on_val @ ( minus_3256168188512067470on_val @ A4 @ B5 ) @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) ) ) ).

% Diff_insert
thf(fact_964_Diff__insert,axiom,
    ! [A4: set_val,A2: val,B5: set_val] :
      ( ( minus_minus_set_val @ A4 @ ( insert_val @ A2 @ B5 ) )
      = ( minus_minus_set_val @ ( minus_minus_set_val @ A4 @ B5 ) @ ( insert_val @ A2 @ bot_bot_set_val ) ) ) ).

% Diff_insert
thf(fact_965_insert__Diff,axiom,
    ! [A2: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ( member6505152944228695362on_val @ A2 @ A4 )
     => ( ( insert7062705985672971881on_val @ A2 @ ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_966_insert__Diff,axiom,
    ! [A2: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ A2 @ A4 )
     => ( ( insert8113562578550770211r_prat @ A2 @ ( minus_7863043754688659098r_prat @ A4 @ ( insert8113562578550770211r_prat @ A2 @ bot_bo3164680191535668511r_prat ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_967_insert__Diff,axiom,
    ! [A2: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char] :
      ( ( member484235747325421115t_char @ A2 @ A4 )
     => ( ( insert3372640069787401954t_char @ A2 @ ( minus_6181227053800976857t_char @ A4 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_968_insert__Diff,axiom,
    ! [A2: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A2 @ A4 )
     => ( ( insert3030518898131756108on_val @ A2 @ ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_969_insert__Diff,axiom,
    ! [A2: option_state,A4: set_option_state] :
      ( ( member_option_state @ A2 @ A4 )
     => ( ( insert_option_state @ A2 @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_970_insert__Diff,axiom,
    ! [A2: option_val,A4: set_option_val] :
      ( ( member_option_val @ A2 @ A4 )
     => ( ( insert_option_val @ A2 @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_971_insert__Diff,axiom,
    ! [A2: val,A4: set_val] :
      ( ( member_val @ A2 @ A4 )
     => ( ( insert_val @ A2 @ ( minus_minus_set_val @ A4 @ ( insert_val @ A2 @ bot_bot_set_val ) ) )
        = A4 ) ) ).

% insert_Diff
thf(fact_972_Diff__insert2,axiom,
    ! [A4: set_Pr4305388979797279737on_val,A2: produc1317171644805857433on_val,B5: set_Pr4305388979797279737on_val] :
      ( ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ A2 @ B5 ) )
      = ( minus_7211471524202483680on_val @ ( minus_7211471524202483680on_val @ A4 @ ( insert7062705985672971881on_val @ A2 @ bot_bo402267660617762917on_val ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_973_Diff__insert2,axiom,
    ! [A4: set_Pr2507339680178222706t_char,A2: produc1457211279475724562t_char,B5: set_Pr2507339680178222706t_char] :
      ( ( minus_6181227053800976857t_char @ A4 @ ( insert3372640069787401954t_char @ A2 @ B5 ) )
      = ( minus_6181227053800976857t_char @ ( minus_6181227053800976857t_char @ A4 @ ( insert3372640069787401954t_char @ A2 @ bot_bo1414094081888755934t_char ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_974_Diff__insert2,axiom,
    ! [A4: set_Pr7649655576376376530on_val,A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val] :
      ( ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ B5 ) )
      = ( minus_9160195963678339755on_val @ ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_975_Diff__insert2,axiom,
    ! [A4: set_option_state,A2: option_state,B5: set_option_state] :
      ( ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ A2 @ B5 ) )
      = ( minus_7537472381646091673_state @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ A2 @ bot_bo710180891245420500_state ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_976_Diff__insert2,axiom,
    ! [A4: set_option_val,A2: option_val,B5: set_option_val] :
      ( ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ A2 @ B5 ) )
      = ( minus_3256168188512067470on_val @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ A2 @ bot_bo5906790151302476563on_val ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_977_Diff__insert2,axiom,
    ! [A4: set_val,A2: val,B5: set_val] :
      ( ( minus_minus_set_val @ A4 @ ( insert_val @ A2 @ B5 ) )
      = ( minus_minus_set_val @ ( minus_minus_set_val @ A4 @ ( insert_val @ A2 @ bot_bot_set_val ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_978_Diff__insert__absorb,axiom,
    ! [X: produc1317171644805857433on_val,A4: set_Pr4305388979797279737on_val] :
      ( ~ ( member6505152944228695362on_val @ X @ A4 )
     => ( ( minus_7211471524202483680on_val @ ( insert7062705985672971881on_val @ X @ A4 ) @ ( insert7062705985672971881on_val @ X @ bot_bo402267660617762917on_val ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_979_Diff__insert__absorb,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( minus_7863043754688659098r_prat @ ( insert8113562578550770211r_prat @ X @ A4 ) @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_980_Diff__insert__absorb,axiom,
    ! [X: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char] :
      ( ~ ( member484235747325421115t_char @ X @ A4 )
     => ( ( minus_6181227053800976857t_char @ ( insert3372640069787401954t_char @ X @ A4 ) @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_981_Diff__insert__absorb,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( minus_9160195963678339755on_val @ ( insert3030518898131756108on_val @ X @ A4 ) @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_982_Diff__insert__absorb,axiom,
    ! [X: option_state,A4: set_option_state] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( minus_7537472381646091673_state @ ( insert_option_state @ X @ A4 ) @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_983_Diff__insert__absorb,axiom,
    ! [X: option_val,A4: set_option_val] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( minus_3256168188512067470on_val @ ( insert_option_val @ X @ A4 ) @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_984_Diff__insert__absorb,axiom,
    ! [X: val,A4: set_val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( minus_minus_set_val @ ( insert_val @ X @ A4 ) @ ( insert_val @ X @ bot_bot_set_val ) )
        = A4 ) ) ).

% Diff_insert_absorb
thf(fact_985_in__these__eq,axiom,
    ! [X: option_state,A4: set_op9003753404445127824_state] :
      ( ( member_option_state @ X @ ( these_option_state @ A4 ) )
      = ( member1079230918592710257_state @ ( some_option_state @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_986_in__these__eq,axiom,
    ! [X: option_val,A4: set_op1974636978870893421on_val] :
      ( ( member_option_val @ X @ ( these_option_val @ A4 ) )
      = ( member8465289789052943542on_val @ ( some_option_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_987_in__these__eq,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_op1110311134966800505r_prat] :
      ( ( member2336342582916103932r_prat @ X @ ( these_2482516890548509968r_prat @ A4 ) )
      = ( member8024166271143588802r_prat @ ( some_P8530153984677361336r_prat @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_988_in__these__eq,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_op6240181410663953058on_val] :
      ( ( member2879030624002546611on_val @ X @ ( these_3919539662624406175on_val @ A4 ) )
      = ( member4602090469187516291on_val @ ( some_P2581650809551911671on_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_989_in__these__eq,axiom,
    ! [X: produc1457211279475724562t_char > option_val,A4: set_op8153969091884965280on_val] :
      ( ( member1577473829074448177on_val @ X @ ( these_602426935119867933on_val @ A4 ) )
      = ( member7216203038034776961on_val @ ( some_P7669353234731512949on_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_990_in__these__eq,axiom,
    ! [X: val,A4: set_option_val] :
      ( ( member_val @ X @ ( these_val @ A4 ) )
      = ( member_option_val @ ( some_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_991_in__these__eq,axiom,
    ! [X: state,A4: set_option_state] :
      ( ( member_state @ X @ ( these_state @ A4 ) )
      = ( member_option_state @ ( some_state @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_992_is__singleton__the__elem,axiom,
    ( is_sin7597786275116224909on_val
    = ( ^ [A6: set_Pr4305388979797279737on_val] :
          ( A6
          = ( insert7062705985672971881on_val @ ( the_el5720079856748460558on_val @ A6 ) @ bot_bo402267660617762917on_val ) ) ) ) ).

% is_singleton_the_elem
thf(fact_993_is__singleton__the__elem,axiom,
    ( is_sin3863772449867033606t_char
    = ( ^ [A6: set_Pr2507339680178222706t_char] :
          ( A6
          = ( insert3372640069787401954t_char @ ( the_el4510683560064399623t_char @ A6 ) @ bot_bo1414094081888755934t_char ) ) ) ) ).

% is_singleton_the_elem
thf(fact_994_is__singleton__the__elem,axiom,
    ( is_sin1022367449962840616on_val
    = ( ^ [A6: set_Pr7649655576376376530on_val] :
          ( A6
          = ( insert3030518898131756108on_val @ ( the_el8055350808190710247on_val @ A6 ) @ bot_bo6722054719108133734on_val ) ) ) ) ).

% is_singleton_the_elem
thf(fact_995_is__singleton__the__elem,axiom,
    ( is_sin8559911096322084886_state
    = ( ^ [A6: set_option_state] :
          ( A6
          = ( insert_option_state @ ( the_el1618976816499768149_state @ A6 ) @ bot_bo710180891245420500_state ) ) ) ) ).

% is_singleton_the_elem
thf(fact_996_is__singleton__the__elem,axiom,
    ( is_sin5830670008703254587on_val
    = ( ^ [A6: set_option_val] :
          ( A6
          = ( insert_option_val @ ( the_elem_option_val @ A6 ) @ bot_bo5906790151302476563on_val ) ) ) ) ).

% is_singleton_the_elem
thf(fact_997_is__singleton__the__elem,axiom,
    ( is_singleton_val
    = ( ^ [A6: set_val] :
          ( A6
          = ( insert_val @ ( the_elem_val @ A6 ) @ bot_bot_set_val ) ) ) ) ).

% is_singleton_the_elem
thf(fact_998_is__singletonI_H,axiom,
    ! [A4: set_Pr3433046674199179443r_prat] :
      ( ( A4 != bot_bo3164680191535668511r_prat )
     => ( ! [X3: produc1457211279475724562t_char > prat,Y4: produc1457211279475724562t_char > prat] :
            ( ( member2336342582916103932r_prat @ X3 @ A4 )
           => ( ( member2336342582916103932r_prat @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_sin6650292796724890951r_prat @ A4 ) ) ) ).

% is_singletonI'
thf(fact_999_is__singletonI_H,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ( A4 != bot_bo1414094081888755934t_char )
     => ( ! [X3: produc1457211279475724562t_char,Y4: produc1457211279475724562t_char] :
            ( ( member484235747325421115t_char @ X3 @ A4 )
           => ( ( member484235747325421115t_char @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_sin3863772449867033606t_char @ A4 ) ) ) ).

% is_singletonI'
thf(fact_1000_is__singletonI_H,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( A4 != bot_bo6722054719108133734on_val )
     => ( ! [X3: produc9003781588162623004on_val,Y4: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ A4 )
           => ( ( member2879030624002546611on_val @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_sin1022367449962840616on_val @ A4 ) ) ) ).

% is_singletonI'
thf(fact_1001_is__singletonI_H,axiom,
    ! [A4: set_option_state] :
      ( ( A4 != bot_bo710180891245420500_state )
     => ( ! [X3: option_state,Y4: option_state] :
            ( ( member_option_state @ X3 @ A4 )
           => ( ( member_option_state @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_sin8559911096322084886_state @ A4 ) ) ) ).

% is_singletonI'
thf(fact_1002_is__singletonI_H,axiom,
    ! [A4: set_option_val] :
      ( ( A4 != bot_bo5906790151302476563on_val )
     => ( ! [X3: option_val,Y4: option_val] :
            ( ( member_option_val @ X3 @ A4 )
           => ( ( member_option_val @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_sin5830670008703254587on_val @ A4 ) ) ) ).

% is_singletonI'
thf(fact_1003_is__singletonI_H,axiom,
    ! [A4: set_val] :
      ( ( A4 != bot_bot_set_val )
     => ( ! [X3: val,Y4: val] :
            ( ( member_val @ X3 @ A4 )
           => ( ( member_val @ Y4 @ A4 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_val @ A4 ) ) ) ).

% is_singletonI'
thf(fact_1004_dom__minus,axiom,
    ! [F: val > option_state,X: val,A4: set_val] :
      ( ( ( F @ X )
        = none_state )
     => ( ( minus_minus_set_val @ ( dom_val_state @ F ) @ ( insert_val @ X @ A4 ) )
        = ( minus_minus_set_val @ ( dom_val_state @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1005_dom__minus,axiom,
    ! [F: val > option_val,X: val,A4: set_val] :
      ( ( ( F @ X )
        = none_val )
     => ( ( minus_minus_set_val @ ( dom_val_val @ F ) @ ( insert_val @ X @ A4 ) )
        = ( minus_minus_set_val @ ( dom_val_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1006_dom__minus,axiom,
    ! [F: option_state > option_state,X: option_state,A4: set_option_state] :
      ( ( ( F @ X )
        = none_state )
     => ( ( minus_7537472381646091673_state @ ( dom_op8569336450220619928_state @ F ) @ ( insert_option_state @ X @ A4 ) )
        = ( minus_7537472381646091673_state @ ( dom_op8569336450220619928_state @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1007_dom__minus,axiom,
    ! [F: option_val > option_state,X: option_val,A4: set_option_val] :
      ( ( ( F @ X )
        = none_state )
     => ( ( minus_3256168188512067470on_val @ ( dom_option_val_state @ F ) @ ( insert_option_val @ X @ A4 ) )
        = ( minus_3256168188512067470on_val @ ( dom_option_val_state @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1008_dom__minus,axiom,
    ! [F: option_state > option_val,X: option_state,A4: set_option_state] :
      ( ( ( F @ X )
        = none_val )
     => ( ( minus_7537472381646091673_state @ ( dom_option_state_val @ F ) @ ( insert_option_state @ X @ A4 ) )
        = ( minus_7537472381646091673_state @ ( dom_option_state_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1009_dom__minus,axiom,
    ! [F: option_val > option_val,X: option_val,A4: set_option_val] :
      ( ( ( F @ X )
        = none_val )
     => ( ( minus_3256168188512067470on_val @ ( dom_option_val_val @ F ) @ ( insert_option_val @ X @ A4 ) )
        = ( minus_3256168188512067470on_val @ ( dom_option_val_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1010_dom__minus,axiom,
    ! [F: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char] :
      ( ( ( F @ X )
        = none_val )
     => ( ( minus_6181227053800976857t_char @ ( dom_Pr8989479155164304065ar_val @ F ) @ ( insert3372640069787401954t_char @ X @ A4 ) )
        = ( minus_6181227053800976857t_char @ ( dom_Pr8989479155164304065ar_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1011_dom__minus,axiom,
    ! [F: val > option5747939881698552298on_val,X: val,A4: set_val] :
      ( ( ( F @ X )
        = none_P1334921381875262201on_val )
     => ( ( minus_minus_set_val @ ( dom_va8931846639282357193on_val @ F ) @ ( insert_val @ X @ A4 ) )
        = ( minus_minus_set_val @ ( dom_va8931846639282357193on_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1012_dom__minus,axiom,
    ! [F: option_state > option5747939881698552298on_val,X: option_state,A4: set_option_state] :
      ( ( ( F @ X )
        = none_P1334921381875262201on_val )
     => ( ( minus_7537472381646091673_state @ ( dom_op741179583939567608on_val @ F ) @ ( insert_option_state @ X @ A4 ) )
        = ( minus_7537472381646091673_state @ ( dom_op741179583939567608on_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1013_dom__minus,axiom,
    ! [F: option_val > option5747939881698552298on_val,X: option_val,A4: set_option_val] :
      ( ( ( F @ X )
        = none_P1334921381875262201on_val )
     => ( ( minus_3256168188512067470on_val @ ( dom_op3430095273566047759on_val @ F ) @ ( insert_option_val @ X @ A4 ) )
        = ( minus_3256168188512067470on_val @ ( dom_op3430095273566047759on_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1014_these__empty__eq,axiom,
    ! [B5: set_op8153969091884965280on_val] :
      ( ( ( these_602426935119867933on_val @ B5 )
        = bot_bo5671083314777306084on_val )
      = ( ( B5 = bot_bo832982859489559604on_val )
        | ( B5
          = ( insert4694516387090290714on_val @ none_P1334921381875262201on_val @ bot_bo832982859489559604on_val ) ) ) ) ).

% these_empty_eq
thf(fact_1015_these__empty__eq,axiom,
    ! [B5: set_op9137726805559506488t_char] :
      ( ( ( these_2739680984639915599t_char @ B5 )
        = bot_bo1414094081888755934t_char )
      = ( ( B5 = bot_bo2782010437066608292t_char )
        | ( B5
          = ( insert213255421748673832t_char @ none_P5486107665612286067t_char @ bot_bo2782010437066608292t_char ) ) ) ) ).

% these_empty_eq
thf(fact_1016_these__empty__eq,axiom,
    ! [B5: set_op6240181410663953058on_val] :
      ( ( ( these_3919539662624406175on_val @ B5 )
        = bot_bo6722054719108133734on_val )
      = ( ( B5 = bot_bo6421125907362167606on_val )
        | ( B5
          = ( insert751572358616671900on_val @ none_P8728355543607141243on_val @ bot_bo6421125907362167606on_val ) ) ) ) ).

% these_empty_eq
thf(fact_1017_these__empty__eq,axiom,
    ! [B5: set_op9003753404445127824_state] :
      ( ( ( these_option_state @ B5 )
        = bot_bo710180891245420500_state )
      = ( ( B5 = bot_bo489212050006660900_state )
        | ( B5
          = ( insert7535573567550883338_state @ none_option_state @ bot_bo489212050006660900_state ) ) ) ) ).

% these_empty_eq
thf(fact_1018_these__empty__eq,axiom,
    ! [B5: set_op1974636978870893421on_val] :
      ( ( ( these_option_val @ B5 )
        = bot_bo5906790151302476563on_val )
      = ( ( B5 = bot_bo6240080102570541529on_val )
        | ( B5
          = ( insert7563226391266834525on_val @ none_option_val @ bot_bo6240080102570541529on_val ) ) ) ) ).

% these_empty_eq
thf(fact_1019_these__empty__eq,axiom,
    ! [B5: set_option_state] :
      ( ( ( these_state @ B5 )
        = bot_bot_set_state )
      = ( ( B5 = bot_bo710180891245420500_state )
        | ( B5
          = ( insert_option_state @ none_state @ bot_bo710180891245420500_state ) ) ) ) ).

% these_empty_eq
thf(fact_1020_these__empty__eq,axiom,
    ! [B5: set_option_val] :
      ( ( ( these_val @ B5 )
        = bot_bot_set_val )
      = ( ( B5 = bot_bo5906790151302476563on_val )
        | ( B5
          = ( insert_option_val @ none_val @ bot_bo5906790151302476563on_val ) ) ) ) ).

% these_empty_eq
thf(fact_1021_these__not__empty__eq,axiom,
    ! [B5: set_op8153969091884965280on_val] :
      ( ( ( these_602426935119867933on_val @ B5 )
       != bot_bo5671083314777306084on_val )
      = ( ( B5 != bot_bo832982859489559604on_val )
        & ( B5
         != ( insert4694516387090290714on_val @ none_P1334921381875262201on_val @ bot_bo832982859489559604on_val ) ) ) ) ).

% these_not_empty_eq
thf(fact_1022_these__not__empty__eq,axiom,
    ! [B5: set_op9137726805559506488t_char] :
      ( ( ( these_2739680984639915599t_char @ B5 )
       != bot_bo1414094081888755934t_char )
      = ( ( B5 != bot_bo2782010437066608292t_char )
        & ( B5
         != ( insert213255421748673832t_char @ none_P5486107665612286067t_char @ bot_bo2782010437066608292t_char ) ) ) ) ).

% these_not_empty_eq
thf(fact_1023_these__not__empty__eq,axiom,
    ! [B5: set_op6240181410663953058on_val] :
      ( ( ( these_3919539662624406175on_val @ B5 )
       != bot_bo6722054719108133734on_val )
      = ( ( B5 != bot_bo6421125907362167606on_val )
        & ( B5
         != ( insert751572358616671900on_val @ none_P8728355543607141243on_val @ bot_bo6421125907362167606on_val ) ) ) ) ).

% these_not_empty_eq
thf(fact_1024_these__not__empty__eq,axiom,
    ! [B5: set_op9003753404445127824_state] :
      ( ( ( these_option_state @ B5 )
       != bot_bo710180891245420500_state )
      = ( ( B5 != bot_bo489212050006660900_state )
        & ( B5
         != ( insert7535573567550883338_state @ none_option_state @ bot_bo489212050006660900_state ) ) ) ) ).

% these_not_empty_eq
thf(fact_1025_these__not__empty__eq,axiom,
    ! [B5: set_op1974636978870893421on_val] :
      ( ( ( these_option_val @ B5 )
       != bot_bo5906790151302476563on_val )
      = ( ( B5 != bot_bo6240080102570541529on_val )
        & ( B5
         != ( insert7563226391266834525on_val @ none_option_val @ bot_bo6240080102570541529on_val ) ) ) ) ).

% these_not_empty_eq
thf(fact_1026_these__not__empty__eq,axiom,
    ! [B5: set_option_state] :
      ( ( ( these_state @ B5 )
       != bot_bot_set_state )
      = ( ( B5 != bot_bo710180891245420500_state )
        & ( B5
         != ( insert_option_state @ none_state @ bot_bo710180891245420500_state ) ) ) ) ).

% these_not_empty_eq
thf(fact_1027_these__not__empty__eq,axiom,
    ! [B5: set_option_val] :
      ( ( ( these_val @ B5 )
       != bot_bot_set_val )
      = ( ( B5 != bot_bo5906790151302476563on_val )
        & ( B5
         != ( insert_option_val @ none_val @ bot_bo5906790151302476563on_val ) ) ) ) ).

% these_not_empty_eq
thf(fact_1028_fun__upd__None__restrict,axiom,
    ! [X: val,D2: set_val,M: val > option_state] :
      ( ( ( member_val @ X @ D2 )
       => ( ( fun_up7100790768922270414_state @ ( restri6351330254082781323_state @ M @ D2 ) @ X @ none_state )
          = ( restri6351330254082781323_state @ M @ ( minus_minus_set_val @ D2 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) )
      & ( ~ ( member_val @ X @ D2 )
       => ( ( fun_up7100790768922270414_state @ ( restri6351330254082781323_state @ M @ D2 ) @ X @ none_state )
          = ( restri6351330254082781323_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1029_fun__upd__None__restrict,axiom,
    ! [X: val,D2: set_val,M: val > option_val] :
      ( ( ( member_val @ X @ D2 )
       => ( ( fun_up735531404784515971on_val @ ( restrict_map_val_val @ M @ D2 ) @ X @ none_val )
          = ( restrict_map_val_val @ M @ ( minus_minus_set_val @ D2 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) )
      & ( ~ ( member_val @ X @ D2 )
       => ( ( fun_up735531404784515971on_val @ ( restrict_map_val_val @ M @ D2 ) @ X @ none_val )
          = ( restrict_map_val_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1030_fun__upd__None__restrict,axiom,
    ! [X: option_state,D2: set_option_state,M: option_state > option_state] :
      ( ( ( member_option_state @ X @ D2 )
       => ( ( fun_up6517640620910344979_state @ ( restri4758375023823916406_state @ M @ D2 ) @ X @ none_state )
          = ( restri4758375023823916406_state @ M @ ( minus_7537472381646091673_state @ D2 @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) ) )
      & ( ~ ( member_option_state @ X @ D2 )
       => ( ( fun_up6517640620910344979_state @ ( restri4758375023823916406_state @ M @ D2 ) @ X @ none_state )
          = ( restri4758375023823916406_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1031_fun__upd__None__restrict,axiom,
    ! [X: option_state,D2: set_option_state,M: option_state > option_val] :
      ( ( ( member_option_state @ X @ D2 )
       => ( ( fun_up8652368643555229054on_val @ ( restri7550271351055745733te_val @ M @ D2 ) @ X @ none_val )
          = ( restri7550271351055745733te_val @ M @ ( minus_7537472381646091673_state @ D2 @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) ) )
      & ( ~ ( member_option_state @ X @ D2 )
       => ( ( fun_up8652368643555229054on_val @ ( restri7550271351055745733te_val @ M @ D2 ) @ X @ none_val )
          = ( restri7550271351055745733te_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1032_fun__upd__None__restrict,axiom,
    ! [X: option_val,D2: set_option_val,M: option_val > option_state] :
      ( ( ( member_option_val @ X @ D2 )
       => ( ( fun_up2039547756584784788_state @ ( restri8841944298656297681_state @ M @ D2 ) @ X @ none_state )
          = ( restri8841944298656297681_state @ M @ ( minus_3256168188512067470on_val @ D2 @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) ) )
      & ( ~ ( member_option_val @ X @ D2 )
       => ( ( fun_up2039547756584784788_state @ ( restri8841944298656297681_state @ M @ D2 ) @ X @ none_state )
          = ( restri8841944298656297681_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1033_fun__upd__None__restrict,axiom,
    ! [X: option_val,D2: set_option_val,M: option_val > option_val] :
      ( ( ( member_option_val @ X @ D2 )
       => ( ( fun_up8761876891205509693on_val @ ( restri7980214582795305770al_val @ M @ D2 ) @ X @ none_val )
          = ( restri7980214582795305770al_val @ M @ ( minus_3256168188512067470on_val @ D2 @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) ) )
      & ( ~ ( member_option_val @ X @ D2 )
       => ( ( fun_up8761876891205509693on_val @ ( restri7980214582795305770al_val @ M @ D2 ) @ X @ none_val )
          = ( restri7980214582795305770al_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1034_fun__upd__None__restrict,axiom,
    ! [X: produc1457211279475724562t_char,D2: set_Pr2507339680178222706t_char,M: produc1457211279475724562t_char > option_state] :
      ( ( ( member484235747325421115t_char @ X @ D2 )
       => ( ( fun_up6995552760743215839_state @ ( restri8083244519320860188_state @ M @ D2 ) @ X @ none_state )
          = ( restri8083244519320860188_state @ M @ ( minus_6181227053800976857t_char @ D2 @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) ) )
      & ( ~ ( member484235747325421115t_char @ X @ D2 )
       => ( ( fun_up6995552760743215839_state @ ( restri8083244519320860188_state @ M @ D2 ) @ X @ none_state )
          = ( restri8083244519320860188_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1035_fun__upd__None__restrict,axiom,
    ! [X: produc1457211279475724562t_char,D2: set_Pr2507339680178222706t_char,M: produc1457211279475724562t_char > option_val] :
      ( ( ( member484235747325421115t_char @ X @ D2 )
       => ( ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ D2 ) @ X @ none_val )
          = ( restri4256959289591943583ar_val @ M @ ( minus_6181227053800976857t_char @ D2 @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) ) )
      & ( ~ ( member484235747325421115t_char @ X @ D2 )
       => ( ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ D2 ) @ X @ none_val )
          = ( restri4256959289591943583ar_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1036_fun__upd__None__restrict,axiom,
    ! [X: produc1457211279475724562t_char > prat,D2: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_state] :
      ( ( ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( fun_up1585067318606691488_state @ ( restri738375759408046301_state @ M @ D2 ) @ X @ none_state )
          = ( restri738375759408046301_state @ M @ ( minus_7863043754688659098r_prat @ D2 @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) ) ) ) )
      & ( ~ ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( fun_up1585067318606691488_state @ ( restri738375759408046301_state @ M @ D2 ) @ X @ none_state )
          = ( restri738375759408046301_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1037_fun__upd__None__restrict,axiom,
    ! [X: produc1457211279475724562t_char > prat,D2: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_val] :
      ( ( ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( fun_up5104302054361798705on_val @ ( restri9007081556893774878at_val @ M @ D2 ) @ X @ none_val )
          = ( restri9007081556893774878at_val @ M @ ( minus_7863043754688659098r_prat @ D2 @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) ) ) ) )
      & ( ~ ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( fun_up5104302054361798705on_val @ ( restri9007081556893774878at_val @ M @ D2 ) @ X @ none_val )
          = ( restri9007081556893774878at_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1038_fun__upd__restrict__conv,axiom,
    ! [X: produc1457211279475724562t_char > prat,D2: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,Y3: option5747939881698552298on_val] :
      ( ( member2336342582916103932r_prat @ X @ D2 )
     => ( ( fun_up1601731230164360576on_val @ ( restri7594233908965391805on_val @ M @ D2 ) @ X @ Y3 )
        = ( fun_up1601731230164360576on_val @ ( restri7594233908965391805on_val @ M @ ( minus_7863043754688659098r_prat @ D2 @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) ) ) @ X @ Y3 ) ) ) ).

% fun_upd_restrict_conv
thf(fact_1039_fun__upd__restrict__conv,axiom,
    ! [X: produc1457211279475724562t_char,D2: set_Pr2507339680178222706t_char,M: produc1457211279475724562t_char > option_val,Y3: option_val] :
      ( ( member484235747325421115t_char @ X @ D2 )
     => ( ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ D2 ) @ X @ Y3 )
        = ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ ( minus_6181227053800976857t_char @ D2 @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) @ X @ Y3 ) ) ) ).

% fun_upd_restrict_conv
thf(fact_1040_fun__upd__restrict__conv,axiom,
    ! [X: produc9003781588162623004on_val,D2: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val,Y3: option8887860577033306220on_val] :
      ( ( member2879030624002546611on_val @ X @ D2 )
     => ( ( fun_up273046073882939271on_val @ ( restri2354629191430751338on_val @ M @ D2 ) @ X @ Y3 )
        = ( fun_up273046073882939271on_val @ ( restri2354629191430751338on_val @ M @ ( minus_9160195963678339755on_val @ D2 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ) @ X @ Y3 ) ) ) ).

% fun_upd_restrict_conv
thf(fact_1041_restrict__fun__upd,axiom,
    ! [X: produc1457211279475724562t_char > prat,D2: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,Y3: option5747939881698552298on_val] :
      ( ( ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( restri7594233908965391805on_val @ ( fun_up1601731230164360576on_val @ M @ X @ Y3 ) @ D2 )
          = ( fun_up1601731230164360576on_val @ ( restri7594233908965391805on_val @ M @ ( minus_7863043754688659098r_prat @ D2 @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) ) ) @ X @ Y3 ) ) )
      & ( ~ ( member2336342582916103932r_prat @ X @ D2 )
       => ( ( restri7594233908965391805on_val @ ( fun_up1601731230164360576on_val @ M @ X @ Y3 ) @ D2 )
          = ( restri7594233908965391805on_val @ M @ D2 ) ) ) ) ).

% restrict_fun_upd
thf(fact_1042_restrict__fun__upd,axiom,
    ! [X: produc1457211279475724562t_char,D2: set_Pr2507339680178222706t_char,M: produc1457211279475724562t_char > option_val,Y3: option_val] :
      ( ( ( member484235747325421115t_char @ X @ D2 )
       => ( ( restri4256959289591943583ar_val @ ( fun_up5735975307950539954on_val @ M @ X @ Y3 ) @ D2 )
          = ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ ( minus_6181227053800976857t_char @ D2 @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) @ X @ Y3 ) ) )
      & ( ~ ( member484235747325421115t_char @ X @ D2 )
       => ( ( restri4256959289591943583ar_val @ ( fun_up5735975307950539954on_val @ M @ X @ Y3 ) @ D2 )
          = ( restri4256959289591943583ar_val @ M @ D2 ) ) ) ) ).

% restrict_fun_upd
thf(fact_1043_restrict__fun__upd,axiom,
    ! [X: produc9003781588162623004on_val,D2: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val,Y3: option8887860577033306220on_val] :
      ( ( ( member2879030624002546611on_val @ X @ D2 )
       => ( ( restri2354629191430751338on_val @ ( fun_up273046073882939271on_val @ M @ X @ Y3 ) @ D2 )
          = ( fun_up273046073882939271on_val @ ( restri2354629191430751338on_val @ M @ ( minus_9160195963678339755on_val @ D2 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ) @ X @ Y3 ) ) )
      & ( ~ ( member2879030624002546611on_val @ X @ D2 )
       => ( ( restri2354629191430751338on_val @ ( fun_up273046073882939271on_val @ M @ X @ Y3 ) @ D2 )
          = ( restri2354629191430751338on_val @ M @ D2 ) ) ) ) ).

% restrict_fun_upd
thf(fact_1044_remove__def,axiom,
    ( remove5903733279999771390on_val
    = ( ^ [X4: produc1317171644805857433on_val,A6: set_Pr4305388979797279737on_val] : ( minus_7211471524202483680on_val @ A6 @ ( insert7062705985672971881on_val @ X4 @ bot_bo402267660617762917on_val ) ) ) ) ).

% remove_def
thf(fact_1045_remove__def,axiom,
    ( remove1543384711646755319t_char
    = ( ^ [X4: produc1457211279475724562t_char,A6: set_Pr2507339680178222706t_char] : ( minus_6181227053800976857t_char @ A6 @ ( insert3372640069787401954t_char @ X4 @ bot_bo1414094081888755934t_char ) ) ) ) ).

% remove_def
thf(fact_1046_remove__def,axiom,
    ( remove6046006348179432695on_val
    = ( ^ [X4: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] : ( minus_9160195963678339755on_val @ A6 @ ( insert3030518898131756108on_val @ X4 @ bot_bo6722054719108133734on_val ) ) ) ) ).

% remove_def
thf(fact_1047_remove__def,axiom,
    ( remove_option_state
    = ( ^ [X4: option_state,A6: set_option_state] : ( minus_7537472381646091673_state @ A6 @ ( insert_option_state @ X4 @ bot_bo710180891245420500_state ) ) ) ) ).

% remove_def
thf(fact_1048_remove__def,axiom,
    ( remove_option_val
    = ( ^ [X4: option_val,A6: set_option_val] : ( minus_3256168188512067470on_val @ A6 @ ( insert_option_val @ X4 @ bot_bo5906790151302476563on_val ) ) ) ) ).

% remove_def
thf(fact_1049_remove__def,axiom,
    ( remove_val
    = ( ^ [X4: val,A6: set_val] : ( minus_minus_set_val @ A6 @ ( insert_val @ X4 @ bot_bot_set_val ) ) ) ) ).

% remove_def
thf(fact_1050_fun__upd__restrict,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,D2: set_Pr3433046674199179443r_prat,X: produc1457211279475724562t_char > prat,Y3: option5747939881698552298on_val] :
      ( ( fun_up1601731230164360576on_val @ ( restri7594233908965391805on_val @ M @ D2 ) @ X @ Y3 )
      = ( fun_up1601731230164360576on_val @ ( restri7594233908965391805on_val @ M @ ( minus_7863043754688659098r_prat @ D2 @ ( insert8113562578550770211r_prat @ X @ bot_bo3164680191535668511r_prat ) ) ) @ X @ Y3 ) ) ).

% fun_upd_restrict
thf(fact_1051_fun__upd__restrict,axiom,
    ! [M: produc1457211279475724562t_char > option_val,D2: set_Pr2507339680178222706t_char,X: produc1457211279475724562t_char,Y3: option_val] :
      ( ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ D2 ) @ X @ Y3 )
      = ( fun_up5735975307950539954on_val @ ( restri4256959289591943583ar_val @ M @ ( minus_6181227053800976857t_char @ D2 @ ( insert3372640069787401954t_char @ X @ bot_bo1414094081888755934t_char ) ) ) @ X @ Y3 ) ) ).

% fun_upd_restrict
thf(fact_1052_fun__upd__restrict,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,D2: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val,Y3: option8887860577033306220on_val] :
      ( ( fun_up273046073882939271on_val @ ( restri2354629191430751338on_val @ M @ D2 ) @ X @ Y3 )
      = ( fun_up273046073882939271on_val @ ( restri2354629191430751338on_val @ M @ ( minus_9160195963678339755on_val @ D2 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ) @ X @ Y3 ) ) ).

% fun_upd_restrict
thf(fact_1053_pairwise__alt,axiom,
    ( pairwi8980569249058178436on_val
    = ( ^ [R2: produc1317171644805857433on_val > produc1317171644805857433on_val > $o,S: set_Pr4305388979797279737on_val] :
        ! [X4: produc1317171644805857433on_val] :
          ( ( member6505152944228695362on_val @ X4 @ S )
         => ! [Y: produc1317171644805857433on_val] :
              ( ( member6505152944228695362on_val @ Y @ ( minus_7211471524202483680on_val @ S @ ( insert7062705985672971881on_val @ X4 @ bot_bo402267660617762917on_val ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1054_pairwise__alt,axiom,
    ( pairwi421018896454539133t_char
    = ( ^ [R2: produc1457211279475724562t_char > produc1457211279475724562t_char > $o,S: set_Pr2507339680178222706t_char] :
        ! [X4: produc1457211279475724562t_char] :
          ( ( member484235747325421115t_char @ X4 @ S )
         => ! [Y: produc1457211279475724562t_char] :
              ( ( member484235747325421115t_char @ Y @ ( minus_6181227053800976857t_char @ S @ ( insert3372640069787401954t_char @ X4 @ bot_bo1414094081888755934t_char ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1055_pairwise__alt,axiom,
    ( pairwi3211334688826577905on_val
    = ( ^ [R2: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,S: set_Pr7649655576376376530on_val] :
        ! [X4: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X4 @ S )
         => ! [Y: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ Y @ ( minus_9160195963678339755on_val @ S @ ( insert3030518898131756108on_val @ X4 @ bot_bo6722054719108133734on_val ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1056_pairwise__alt,axiom,
    ( pairwi7845604448133876319_state
    = ( ^ [R2: option_state > option_state > $o,S: set_option_state] :
        ! [X4: option_state] :
          ( ( member_option_state @ X4 @ S )
         => ! [Y: option_state] :
              ( ( member_option_state @ Y @ ( minus_7537472381646091673_state @ S @ ( insert_option_state @ X4 @ bot_bo710180891245420500_state ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1057_pairwise__alt,axiom,
    ( pairwise_option_val
    = ( ^ [R2: option_val > option_val > $o,S: set_option_val] :
        ! [X4: option_val] :
          ( ( member_option_val @ X4 @ S )
         => ! [Y: option_val] :
              ( ( member_option_val @ Y @ ( minus_3256168188512067470on_val @ S @ ( insert_option_val @ X4 @ bot_bo5906790151302476563on_val ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1058_pairwise__alt,axiom,
    ( pairwise_val
    = ( ^ [R2: val > val > $o,S: set_val] :
        ! [X4: val] :
          ( ( member_val @ X4 @ S )
         => ! [Y: val] :
              ( ( member_val @ Y @ ( minus_minus_set_val @ S @ ( insert_val @ X4 @ bot_bot_set_val ) ) )
             => ( R2 @ X4 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1059_fun__upd__image,axiom,
    ! [X: val,A4: set_val,F: val > val,Y3: val] :
      ( ( ( member_val @ X @ A4 )
       => ( ( image_val_val @ ( fun_upd_val_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_val @ Y3 @ ( image_val_val @ F @ ( minus_minus_set_val @ A4 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) )
      & ( ~ ( member_val @ X @ A4 )
       => ( ( image_val_val @ ( fun_upd_val_val @ F @ X @ Y3 ) @ A4 )
          = ( image_val_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1060_fun__upd__image,axiom,
    ! [X: state,A4: set_state,F: state > option_state,Y3: option_state] :
      ( ( ( member_state @ X @ A4 )
       => ( ( image_6076465424260689483_state @ ( fun_up8843634000204221123_state @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_state @ Y3 @ ( image_6076465424260689483_state @ F @ ( minus_3933957440811877961_state @ A4 @ ( insert_state @ X @ bot_bot_set_state ) ) ) ) ) )
      & ( ~ ( member_state @ X @ A4 )
       => ( ( image_6076465424260689483_state @ ( fun_up8843634000204221123_state @ F @ X @ Y3 ) @ A4 )
          = ( image_6076465424260689483_state @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1061_fun__upd__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > val,Y3: val] :
      ( ( ( member_option_state @ X @ A4 )
       => ( ( image_7609484285346866096te_val @ ( fun_up6339919150111145272te_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_val @ Y3 @ ( image_7609484285346866096te_val @ F @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) ) ) )
      & ( ~ ( member_option_state @ X @ A4 )
       => ( ( image_7609484285346866096te_val @ ( fun_up6339919150111145272te_val @ F @ X @ Y3 ) @ A4 )
          = ( image_7609484285346866096te_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1062_fun__upd__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > val,Y3: val] :
      ( ( ( member_option_val @ X @ A4 )
       => ( ( image_option_val_val @ ( fun_up3335141697005694071al_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_val @ Y3 @ ( image_option_val_val @ F @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) ) ) )
      & ( ~ ( member_option_val @ X @ A4 )
       => ( ( image_option_val_val @ ( fun_up3335141697005694071al_val @ F @ X @ Y3 ) @ A4 )
          = ( image_option_val_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1063_fun__upd__image,axiom,
    ! [X: val,A4: set_val,F: val > option_state,Y3: option_state] :
      ( ( ( member_val @ X @ A4 )
       => ( ( image_8370355904157991238_state @ ( fun_up7100790768922270414_state @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_state @ Y3 @ ( image_8370355904157991238_state @ F @ ( minus_minus_set_val @ A4 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) )
      & ( ~ ( member_val @ X @ A4 )
       => ( ( image_8370355904157991238_state @ ( fun_up7100790768922270414_state @ F @ X @ Y3 ) @ A4 )
          = ( image_8370355904157991238_state @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1064_fun__upd__image,axiom,
    ! [X: val,A4: set_val,F: val > option_val,Y3: option_val] :
      ( ( ( member_val @ X @ A4 )
       => ( ( image_val_option_val @ ( fun_up735531404784515971on_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_val @ Y3 @ ( image_val_option_val @ F @ ( minus_minus_set_val @ A4 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) )
      & ( ~ ( member_val @ X @ A4 )
       => ( ( image_val_option_val @ ( fun_up735531404784515971on_val @ F @ X @ Y3 ) @ A4 )
          = ( image_val_option_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1065_fun__upd__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_state,Y3: option_state] :
      ( ( ( member_option_state @ X @ A4 )
       => ( ( image_8299601973402907291_state @ ( fun_up6517640620910344979_state @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_state @ Y3 @ ( image_8299601973402907291_state @ F @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) ) ) )
      & ( ~ ( member_option_state @ X @ A4 )
       => ( ( image_8299601973402907291_state @ ( fun_up6517640620910344979_state @ F @ X @ Y3 ) @ A4 )
          = ( image_8299601973402907291_state @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1066_fun__upd__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_val,Y3: option_val] :
      ( ( ( member_option_state @ X @ A4 )
       => ( ( image_52261995005186038on_val @ ( fun_up8652368643555229054on_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_val @ Y3 @ ( image_52261995005186038on_val @ F @ ( minus_7537472381646091673_state @ A4 @ ( insert_option_state @ X @ bot_bo710180891245420500_state ) ) ) ) ) )
      & ( ~ ( member_option_state @ X @ A4 )
       => ( ( image_52261995005186038on_val @ ( fun_up8652368643555229054on_val @ F @ X @ Y3 ) @ A4 )
          = ( image_52261995005186038on_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1067_fun__upd__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_state,Y3: option_state] :
      ( ( ( member_option_val @ X @ A4 )
       => ( ( image_2662813144889517580_state @ ( fun_up2039547756584784788_state @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_state @ Y3 @ ( image_2662813144889517580_state @ F @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) ) ) )
      & ( ~ ( member_option_val @ X @ A4 )
       => ( ( image_2662813144889517580_state @ ( fun_up2039547756584784788_state @ F @ X @ Y3 ) @ A4 )
          = ( image_2662813144889517580_state @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1068_fun__upd__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_val,Y3: option_val] :
      ( ( ( member_option_val @ X @ A4 )
       => ( ( image_5994708315261978053on_val @ ( fun_up8761876891205509693on_val @ F @ X @ Y3 ) @ A4 )
          = ( insert_option_val @ Y3 @ ( image_5994708315261978053on_val @ F @ ( minus_3256168188512067470on_val @ A4 @ ( insert_option_val @ X @ bot_bo5906790151302476563on_val ) ) ) ) ) )
      & ( ~ ( member_option_val @ X @ A4 )
       => ( ( image_5994708315261978053on_val @ ( fun_up8761876891205509693on_val @ F @ X @ Y3 ) @ A4 )
          = ( image_5994708315261978053on_val @ F @ A4 ) ) ) ) ).

% fun_upd_image
thf(fact_1069_image__eqI,axiom,
    ! [B2: val,F: val > val,X: val,A4: set_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_val @ X @ A4 )
       => ( member_val @ B2 @ ( image_val_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1070_image__eqI,axiom,
    ! [B2: option_state,F: state > option_state,X: state,A4: set_state] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_state @ X @ A4 )
       => ( member_option_state @ B2 @ ( image_6076465424260689483_state @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1071_image__eqI,axiom,
    ! [B2: val,F: option_state > val,X: option_state,A4: set_option_state] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_state @ X @ A4 )
       => ( member_val @ B2 @ ( image_7609484285346866096te_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1072_image__eqI,axiom,
    ! [B2: val,F: option_val > val,X: option_val,A4: set_option_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_val @ X @ A4 )
       => ( member_val @ B2 @ ( image_option_val_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1073_image__eqI,axiom,
    ! [B2: option_state,F: val > option_state,X: val,A4: set_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_val @ X @ A4 )
       => ( member_option_state @ B2 @ ( image_8370355904157991238_state @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1074_image__eqI,axiom,
    ! [B2: option_val,F: val > option_val,X: val,A4: set_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_val @ X @ A4 )
       => ( member_option_val @ B2 @ ( image_val_option_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1075_image__eqI,axiom,
    ! [B2: option_state,F: option_state > option_state,X: option_state,A4: set_option_state] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_state @ X @ A4 )
       => ( member_option_state @ B2 @ ( image_8299601973402907291_state @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1076_image__eqI,axiom,
    ! [B2: option_val,F: option_state > option_val,X: option_state,A4: set_option_state] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_state @ X @ A4 )
       => ( member_option_val @ B2 @ ( image_52261995005186038on_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1077_image__eqI,axiom,
    ! [B2: option_state,F: option_val > option_state,X: option_val,A4: set_option_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_val @ X @ A4 )
       => ( member_option_state @ B2 @ ( image_2662813144889517580_state @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1078_image__eqI,axiom,
    ! [B2: option_val,F: option_val > option_val,X: option_val,A4: set_option_val] :
      ( ( B2
        = ( F @ X ) )
     => ( ( member_option_val @ X @ A4 )
       => ( member_option_val @ B2 @ ( image_5994708315261978053on_val @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_1079_restrict__in,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val] :
      ( ( member2879030624002546611on_val @ X @ A4 )
     => ( ( restri2354629191430751338on_val @ M @ A4 @ X )
        = ( M @ X ) ) ) ).

% restrict_in
thf(fact_1080_restrict__in,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( restri7594233908965391805on_val @ M @ A4 @ X )
        = ( M @ X ) ) ) ).

% restrict_in
thf(fact_1081_member__remove,axiom,
    ! [X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X @ ( remove6046006348179432695on_val @ Y3 @ A4 ) )
      = ( ( member2879030624002546611on_val @ X @ A4 )
        & ( X != Y3 ) ) ) ).

% member_remove
thf(fact_1082_member__remove,axiom,
    ! [X: option_state,Y3: option_state,A4: set_option_state] :
      ( ( member_option_state @ X @ ( remove_option_state @ Y3 @ A4 ) )
      = ( ( member_option_state @ X @ A4 )
        & ( X != Y3 ) ) ) ).

% member_remove
thf(fact_1083_member__remove,axiom,
    ! [X: option_val,Y3: option_val,A4: set_option_val] :
      ( ( member_option_val @ X @ ( remove_option_val @ Y3 @ A4 ) )
      = ( ( member_option_val @ X @ A4 )
        & ( X != Y3 ) ) ) ).

% member_remove
thf(fact_1084_member__remove,axiom,
    ! [X: val,Y3: val,A4: set_val] :
      ( ( member_val @ X @ ( remove_val @ Y3 @ A4 ) )
      = ( ( member_val @ X @ A4 )
        & ( X != Y3 ) ) ) ).

% member_remove
thf(fact_1085_member__remove,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2336342582916103932r_prat @ X @ ( remove6968564113294249144r_prat @ Y3 @ A4 ) )
      = ( ( member2336342582916103932r_prat @ X @ A4 )
        & ( X != Y3 ) ) ) ).

% member_remove
thf(fact_1086_image__is__empty,axiom,
    ! [F: val > val,A4: set_val] :
      ( ( ( image_val_val @ F @ A4 )
        = bot_bot_set_val )
      = ( A4 = bot_bot_set_val ) ) ).

% image_is_empty
thf(fact_1087_image__is__empty,axiom,
    ! [F: state > option_state,A4: set_state] :
      ( ( ( image_6076465424260689483_state @ F @ A4 )
        = bot_bo710180891245420500_state )
      = ( A4 = bot_bot_set_state ) ) ).

% image_is_empty
thf(fact_1088_image__is__empty,axiom,
    ! [F: val > option_state,A4: set_val] :
      ( ( ( image_8370355904157991238_state @ F @ A4 )
        = bot_bo710180891245420500_state )
      = ( A4 = bot_bot_set_val ) ) ).

% image_is_empty
thf(fact_1089_image__is__empty,axiom,
    ! [F: val > option_val,A4: set_val] :
      ( ( ( image_val_option_val @ F @ A4 )
        = bot_bo5906790151302476563on_val )
      = ( A4 = bot_bot_set_val ) ) ).

% image_is_empty
thf(fact_1090_image__is__empty,axiom,
    ! [F: option_state > val,A4: set_option_state] :
      ( ( ( image_7609484285346866096te_val @ F @ A4 )
        = bot_bot_set_val )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% image_is_empty
thf(fact_1091_image__is__empty,axiom,
    ! [F: option_val > val,A4: set_option_val] :
      ( ( ( image_option_val_val @ F @ A4 )
        = bot_bot_set_val )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% image_is_empty
thf(fact_1092_image__is__empty,axiom,
    ! [F: option_state > option_state,A4: set_option_state] :
      ( ( ( image_8299601973402907291_state @ F @ A4 )
        = bot_bo710180891245420500_state )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% image_is_empty
thf(fact_1093_image__is__empty,axiom,
    ! [F: option_val > option_state,A4: set_option_val] :
      ( ( ( image_2662813144889517580_state @ F @ A4 )
        = bot_bo710180891245420500_state )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% image_is_empty
thf(fact_1094_image__is__empty,axiom,
    ! [F: option_state > option_val,A4: set_option_state] :
      ( ( ( image_52261995005186038on_val @ F @ A4 )
        = bot_bo5906790151302476563on_val )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% image_is_empty
thf(fact_1095_image__is__empty,axiom,
    ! [F: option_val > option_val,A4: set_option_val] :
      ( ( ( image_5994708315261978053on_val @ F @ A4 )
        = bot_bo5906790151302476563on_val )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% image_is_empty
thf(fact_1096_empty__is__image,axiom,
    ! [F: val > val,A4: set_val] :
      ( ( bot_bot_set_val
        = ( image_val_val @ F @ A4 ) )
      = ( A4 = bot_bot_set_val ) ) ).

% empty_is_image
thf(fact_1097_empty__is__image,axiom,
    ! [F: state > option_state,A4: set_state] :
      ( ( bot_bo710180891245420500_state
        = ( image_6076465424260689483_state @ F @ A4 ) )
      = ( A4 = bot_bot_set_state ) ) ).

% empty_is_image
thf(fact_1098_empty__is__image,axiom,
    ! [F: val > option_state,A4: set_val] :
      ( ( bot_bo710180891245420500_state
        = ( image_8370355904157991238_state @ F @ A4 ) )
      = ( A4 = bot_bot_set_val ) ) ).

% empty_is_image
thf(fact_1099_empty__is__image,axiom,
    ! [F: val > option_val,A4: set_val] :
      ( ( bot_bo5906790151302476563on_val
        = ( image_val_option_val @ F @ A4 ) )
      = ( A4 = bot_bot_set_val ) ) ).

% empty_is_image
thf(fact_1100_empty__is__image,axiom,
    ! [F: option_state > val,A4: set_option_state] :
      ( ( bot_bot_set_val
        = ( image_7609484285346866096te_val @ F @ A4 ) )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% empty_is_image
thf(fact_1101_empty__is__image,axiom,
    ! [F: option_val > val,A4: set_option_val] :
      ( ( bot_bot_set_val
        = ( image_option_val_val @ F @ A4 ) )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% empty_is_image
thf(fact_1102_empty__is__image,axiom,
    ! [F: option_state > option_state,A4: set_option_state] :
      ( ( bot_bo710180891245420500_state
        = ( image_8299601973402907291_state @ F @ A4 ) )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% empty_is_image
thf(fact_1103_empty__is__image,axiom,
    ! [F: option_val > option_state,A4: set_option_val] :
      ( ( bot_bo710180891245420500_state
        = ( image_2662813144889517580_state @ F @ A4 ) )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% empty_is_image
thf(fact_1104_empty__is__image,axiom,
    ! [F: option_state > option_val,A4: set_option_state] :
      ( ( bot_bo5906790151302476563on_val
        = ( image_52261995005186038on_val @ F @ A4 ) )
      = ( A4 = bot_bo710180891245420500_state ) ) ).

% empty_is_image
thf(fact_1105_empty__is__image,axiom,
    ! [F: option_val > option_val,A4: set_option_val] :
      ( ( bot_bo5906790151302476563on_val
        = ( image_5994708315261978053on_val @ F @ A4 ) )
      = ( A4 = bot_bo5906790151302476563on_val ) ) ).

% empty_is_image
thf(fact_1106_image__empty,axiom,
    ! [F: val > val] :
      ( ( image_val_val @ F @ bot_bot_set_val )
      = bot_bot_set_val ) ).

% image_empty
thf(fact_1107_image__empty,axiom,
    ! [F: state > option_state] :
      ( ( image_6076465424260689483_state @ F @ bot_bot_set_state )
      = bot_bo710180891245420500_state ) ).

% image_empty
thf(fact_1108_image__empty,axiom,
    ! [F: option_state > val] :
      ( ( image_7609484285346866096te_val @ F @ bot_bo710180891245420500_state )
      = bot_bot_set_val ) ).

% image_empty
thf(fact_1109_image__empty,axiom,
    ! [F: option_val > val] :
      ( ( image_option_val_val @ F @ bot_bo5906790151302476563on_val )
      = bot_bot_set_val ) ).

% image_empty
thf(fact_1110_image__empty,axiom,
    ! [F: val > option_state] :
      ( ( image_8370355904157991238_state @ F @ bot_bot_set_val )
      = bot_bo710180891245420500_state ) ).

% image_empty
thf(fact_1111_image__empty,axiom,
    ! [F: val > option_val] :
      ( ( image_val_option_val @ F @ bot_bot_set_val )
      = bot_bo5906790151302476563on_val ) ).

% image_empty
thf(fact_1112_image__empty,axiom,
    ! [F: option_state > option_state] :
      ( ( image_8299601973402907291_state @ F @ bot_bo710180891245420500_state )
      = bot_bo710180891245420500_state ) ).

% image_empty
thf(fact_1113_image__empty,axiom,
    ! [F: option_state > option_val] :
      ( ( image_52261995005186038on_val @ F @ bot_bo710180891245420500_state )
      = bot_bo5906790151302476563on_val ) ).

% image_empty
thf(fact_1114_image__empty,axiom,
    ! [F: option_val > option_state] :
      ( ( image_2662813144889517580_state @ F @ bot_bo5906790151302476563on_val )
      = bot_bo710180891245420500_state ) ).

% image_empty
thf(fact_1115_image__empty,axiom,
    ! [F: option_val > option_val] :
      ( ( image_5994708315261978053on_val @ F @ bot_bo5906790151302476563on_val )
      = bot_bo5906790151302476563on_val ) ).

% image_empty
thf(fact_1116_image__insert,axiom,
    ! [F: val > val,A2: val,B5: set_val] :
      ( ( image_val_val @ F @ ( insert_val @ A2 @ B5 ) )
      = ( insert_val @ ( F @ A2 ) @ ( image_val_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1117_image__insert,axiom,
    ! [F: state > option_state,A2: state,B5: set_state] :
      ( ( image_6076465424260689483_state @ F @ ( insert_state @ A2 @ B5 ) )
      = ( insert_option_state @ ( F @ A2 ) @ ( image_6076465424260689483_state @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1118_image__insert,axiom,
    ! [F: option_state > val,A2: option_state,B5: set_option_state] :
      ( ( image_7609484285346866096te_val @ F @ ( insert_option_state @ A2 @ B5 ) )
      = ( insert_val @ ( F @ A2 ) @ ( image_7609484285346866096te_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1119_image__insert,axiom,
    ! [F: option_val > val,A2: option_val,B5: set_option_val] :
      ( ( image_option_val_val @ F @ ( insert_option_val @ A2 @ B5 ) )
      = ( insert_val @ ( F @ A2 ) @ ( image_option_val_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1120_image__insert,axiom,
    ! [F: val > option_state,A2: val,B5: set_val] :
      ( ( image_8370355904157991238_state @ F @ ( insert_val @ A2 @ B5 ) )
      = ( insert_option_state @ ( F @ A2 ) @ ( image_8370355904157991238_state @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1121_image__insert,axiom,
    ! [F: val > option_val,A2: val,B5: set_val] :
      ( ( image_val_option_val @ F @ ( insert_val @ A2 @ B5 ) )
      = ( insert_option_val @ ( F @ A2 ) @ ( image_val_option_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1122_image__insert,axiom,
    ! [F: option_state > option_state,A2: option_state,B5: set_option_state] :
      ( ( image_8299601973402907291_state @ F @ ( insert_option_state @ A2 @ B5 ) )
      = ( insert_option_state @ ( F @ A2 ) @ ( image_8299601973402907291_state @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1123_image__insert,axiom,
    ! [F: option_state > option_val,A2: option_state,B5: set_option_state] :
      ( ( image_52261995005186038on_val @ F @ ( insert_option_state @ A2 @ B5 ) )
      = ( insert_option_val @ ( F @ A2 ) @ ( image_52261995005186038on_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1124_image__insert,axiom,
    ! [F: option_val > option_state,A2: option_val,B5: set_option_val] :
      ( ( image_2662813144889517580_state @ F @ ( insert_option_val @ A2 @ B5 ) )
      = ( insert_option_state @ ( F @ A2 ) @ ( image_2662813144889517580_state @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1125_image__insert,axiom,
    ! [F: option_val > option_val,A2: option_val,B5: set_option_val] :
      ( ( image_5994708315261978053on_val @ F @ ( insert_option_val @ A2 @ B5 ) )
      = ( insert_option_val @ ( F @ A2 ) @ ( image_5994708315261978053on_val @ F @ B5 ) ) ) ).

% image_insert
thf(fact_1126_insert__image,axiom,
    ! [X: val,A4: set_val,F: val > val] :
      ( ( member_val @ X @ A4 )
     => ( ( insert_val @ ( F @ X ) @ ( image_val_val @ F @ A4 ) )
        = ( image_val_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1127_insert__image,axiom,
    ! [X: state,A4: set_state,F: state > option_state] :
      ( ( member_state @ X @ A4 )
     => ( ( insert_option_state @ ( F @ X ) @ ( image_6076465424260689483_state @ F @ A4 ) )
        = ( image_6076465424260689483_state @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1128_insert__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > val] :
      ( ( member_option_state @ X @ A4 )
     => ( ( insert_val @ ( F @ X ) @ ( image_7609484285346866096te_val @ F @ A4 ) )
        = ( image_7609484285346866096te_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1129_insert__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > val] :
      ( ( member_option_val @ X @ A4 )
     => ( ( insert_val @ ( F @ X ) @ ( image_option_val_val @ F @ A4 ) )
        = ( image_option_val_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1130_insert__image,axiom,
    ! [X: val,A4: set_val,F: val > option_state] :
      ( ( member_val @ X @ A4 )
     => ( ( insert_option_state @ ( F @ X ) @ ( image_8370355904157991238_state @ F @ A4 ) )
        = ( image_8370355904157991238_state @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1131_insert__image,axiom,
    ! [X: val,A4: set_val,F: val > option_val] :
      ( ( member_val @ X @ A4 )
     => ( ( insert_option_val @ ( F @ X ) @ ( image_val_option_val @ F @ A4 ) )
        = ( image_val_option_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1132_insert__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_state] :
      ( ( member_option_state @ X @ A4 )
     => ( ( insert_option_state @ ( F @ X ) @ ( image_8299601973402907291_state @ F @ A4 ) )
        = ( image_8299601973402907291_state @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1133_insert__image,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_val] :
      ( ( member_option_state @ X @ A4 )
     => ( ( insert_option_val @ ( F @ X ) @ ( image_52261995005186038on_val @ F @ A4 ) )
        = ( image_52261995005186038on_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1134_insert__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_state] :
      ( ( member_option_val @ X @ A4 )
     => ( ( insert_option_state @ ( F @ X ) @ ( image_2662813144889517580_state @ F @ A4 ) )
        = ( image_2662813144889517580_state @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1135_insert__image,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_val] :
      ( ( member_option_val @ X @ A4 )
     => ( ( insert_option_val @ ( F @ X ) @ ( image_5994708315261978053on_val @ F @ A4 ) )
        = ( image_5994708315261978053on_val @ F @ A4 ) ) ) ).

% insert_image
thf(fact_1136_image__map__upd,axiom,
    ! [X: val,A4: set_val,M: val > option_val,Y3: val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( image_val_option_val @ ( fun_up735531404784515971on_val @ M @ X @ ( some_val @ Y3 ) ) @ A4 )
        = ( image_val_option_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1137_image__map__upd,axiom,
    ! [X: state,A4: set_state,M: state > option_state,Y3: state] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( image_6076465424260689483_state @ ( fun_up8843634000204221123_state @ M @ X @ ( some_state @ Y3 ) ) @ A4 )
        = ( image_6076465424260689483_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1138_image__map__upd,axiom,
    ! [X: val,A4: set_val,M: val > option_state,Y3: state] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( image_8370355904157991238_state @ ( fun_up7100790768922270414_state @ M @ X @ ( some_state @ Y3 ) ) @ A4 )
        = ( image_8370355904157991238_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1139_image__map__upd,axiom,
    ! [X: option_state,A4: set_option_state,M: option_state > option_val,Y3: val] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( image_52261995005186038on_val @ ( fun_up8652368643555229054on_val @ M @ X @ ( some_val @ Y3 ) ) @ A4 )
        = ( image_52261995005186038on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1140_image__map__upd,axiom,
    ! [X: option_val,A4: set_option_val,M: option_val > option_val,Y3: val] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( image_5994708315261978053on_val @ ( fun_up8761876891205509693on_val @ M @ X @ ( some_val @ Y3 ) ) @ A4 )
        = ( image_5994708315261978053on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1141_image__map__upd,axiom,
    ! [X: option_state,A4: set_option_state,M: option_state > option_state,Y3: state] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( image_8299601973402907291_state @ ( fun_up6517640620910344979_state @ M @ X @ ( some_state @ Y3 ) ) @ A4 )
        = ( image_8299601973402907291_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1142_image__map__upd,axiom,
    ! [X: option_val,A4: set_option_val,M: option_val > option_state,Y3: state] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( image_2662813144889517580_state @ ( fun_up2039547756584784788_state @ M @ X @ ( some_state @ Y3 ) ) @ A4 )
        = ( image_2662813144889517580_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1143_image__map__upd,axiom,
    ! [X: produc1457211279475724562t_char,A4: set_Pr2507339680178222706t_char,M: produc1457211279475724562t_char > option_val,Y3: val] :
      ( ~ ( member484235747325421115t_char @ X @ A4 )
     => ( ( image_4269386950610408506on_val @ ( fun_up5735975307950539954on_val @ M @ X @ ( some_val @ Y3 ) ) @ A4 )
        = ( image_4269386950610408506on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1144_image__map__upd,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_val,Y3: val] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( image_1941897556587066297on_val @ ( fun_up5104302054361798705on_val @ M @ X @ ( some_val @ Y3 ) ) @ A4 )
        = ( image_1941897556587066297on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1145_image__map__upd,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_state,Y3: state] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( image_4340244011621553944_state @ ( fun_up1585067318606691488_state @ M @ X @ ( some_state @ Y3 ) ) @ A4 )
        = ( image_4340244011621553944_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1146_restrict__out,axiom,
    ! [X: val,A4: set_val,M: val > option_state] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( restri6351330254082781323_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_1147_restrict__out,axiom,
    ! [X: val,A4: set_val,M: val > option_val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( restrict_map_val_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_1148_restrict__out,axiom,
    ! [X: option_state,A4: set_option_state,M: option_state > option_state] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( restri4758375023823916406_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_1149_restrict__out,axiom,
    ! [X: option_val,A4: set_option_val,M: option_val > option_state] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( restri8841944298656297681_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_1150_restrict__out,axiom,
    ! [X: option_state,A4: set_option_state,M: option_state > option_val] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( restri7550271351055745733te_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_1151_restrict__out,axiom,
    ! [X: option_val,A4: set_option_val,M: option_val > option_val] :
      ( ~ ( member_option_val @ X @ A4 )
     => ( ( restri7980214582795305770al_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_1152_restrict__out,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_state] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( restri738375759408046301_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_1153_restrict__out,axiom,
    ! [X: produc1457211279475724562t_char > prat,A4: set_Pr3433046674199179443r_prat,M: ( produc1457211279475724562t_char > prat ) > option_val] :
      ( ~ ( member2336342582916103932r_prat @ X @ A4 )
     => ( ( restri9007081556893774878at_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_1154_restrict__out,axiom,
    ! [X: val,A4: set_val,M: val > option5747939881698552298on_val] :
      ( ~ ( member_val @ X @ A4 )
     => ( ( restri8187230408314553963on_val @ M @ A4 @ X )
        = none_P1334921381875262201on_val ) ) ).

% restrict_out
thf(fact_1155_restrict__out,axiom,
    ! [X: option_state,A4: set_option_state,M: option_state > option5747939881698552298on_val] :
      ( ~ ( member_option_state @ X @ A4 )
     => ( ( restri3062571084349347286on_val @ M @ A4 @ X )
        = none_P1334921381875262201on_val ) ) ).

% restrict_out
thf(fact_1156_these__image__Some__eq,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( these_3919539662624406175on_val @ ( image_4416128703135814415on_val @ some_P2581650809551911671on_val @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_1157_these__image__Some__eq,axiom,
    ! [A4: set_Pr1004501353197068112on_val] :
      ( ( these_602426935119867933on_val @ ( image_5626594990718149899on_val @ some_P7669353234731512949on_val @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_1158_these__image__Some__eq,axiom,
    ! [A4: set_val] :
      ( ( these_val @ ( image_val_option_val @ some_val @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_1159_these__image__Some__eq,axiom,
    ! [A4: set_state] :
      ( ( these_state @ ( image_6076465424260689483_state @ some_state @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_1160_restrict__map__to__empty,axiom,
    ! [M: val > option_state] :
      ( ( restri6351330254082781323_state @ M @ bot_bot_set_val )
      = ( ^ [X4: val] : none_state ) ) ).

% restrict_map_to_empty
thf(fact_1161_restrict__map__to__empty,axiom,
    ! [M: val > option_val] :
      ( ( restrict_map_val_val @ M @ bot_bot_set_val )
      = ( ^ [X4: val] : none_val ) ) ).

% restrict_map_to_empty
thf(fact_1162_restrict__map__to__empty,axiom,
    ! [M: option_state > option_state] :
      ( ( restri4758375023823916406_state @ M @ bot_bo710180891245420500_state )
      = ( ^ [X4: option_state] : none_state ) ) ).

% restrict_map_to_empty
thf(fact_1163_restrict__map__to__empty,axiom,
    ! [M: option_state > option_val] :
      ( ( restri7550271351055745733te_val @ M @ bot_bo710180891245420500_state )
      = ( ^ [X4: option_state] : none_val ) ) ).

% restrict_map_to_empty
thf(fact_1164_restrict__map__to__empty,axiom,
    ! [M: option_val > option_state] :
      ( ( restri8841944298656297681_state @ M @ bot_bo5906790151302476563on_val )
      = ( ^ [X4: option_val] : none_state ) ) ).

% restrict_map_to_empty
thf(fact_1165_restrict__map__to__empty,axiom,
    ! [M: option_val > option_val] :
      ( ( restri7980214582795305770al_val @ M @ bot_bo5906790151302476563on_val )
      = ( ^ [X4: option_val] : none_val ) ) ).

% restrict_map_to_empty
thf(fact_1166_restrict__map__to__empty,axiom,
    ! [M: produc1457211279475724562t_char > option_state] :
      ( ( restri8083244519320860188_state @ M @ bot_bo1414094081888755934t_char )
      = ( ^ [X4: produc1457211279475724562t_char] : none_state ) ) ).

% restrict_map_to_empty
thf(fact_1167_restrict__map__to__empty,axiom,
    ! [M: produc1457211279475724562t_char > option_val] :
      ( ( restri4256959289591943583ar_val @ M @ bot_bo1414094081888755934t_char )
      = ( ^ [X4: produc1457211279475724562t_char] : none_val ) ) ).

% restrict_map_to_empty
thf(fact_1168_restrict__map__to__empty,axiom,
    ! [M: val > option5747939881698552298on_val] :
      ( ( restri8187230408314553963on_val @ M @ bot_bot_set_val )
      = ( ^ [X4: val] : none_P1334921381875262201on_val ) ) ).

% restrict_map_to_empty
thf(fact_1169_restrict__map__to__empty,axiom,
    ! [M: option_state > option5747939881698552298on_val] :
      ( ( restri3062571084349347286on_val @ M @ bot_bo710180891245420500_state )
      = ( ^ [X4: option_state] : none_P1334921381875262201on_val ) ) ).

% restrict_map_to_empty
thf(fact_1170_imageI,axiom,
    ! [X: val,A4: set_val,F: val > val] :
      ( ( member_val @ X @ A4 )
     => ( member_val @ ( F @ X ) @ ( image_val_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1171_imageI,axiom,
    ! [X: state,A4: set_state,F: state > option_state] :
      ( ( member_state @ X @ A4 )
     => ( member_option_state @ ( F @ X ) @ ( image_6076465424260689483_state @ F @ A4 ) ) ) ).

% imageI
thf(fact_1172_imageI,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > val] :
      ( ( member_option_state @ X @ A4 )
     => ( member_val @ ( F @ X ) @ ( image_7609484285346866096te_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1173_imageI,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > val] :
      ( ( member_option_val @ X @ A4 )
     => ( member_val @ ( F @ X ) @ ( image_option_val_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1174_imageI,axiom,
    ! [X: val,A4: set_val,F: val > option_state] :
      ( ( member_val @ X @ A4 )
     => ( member_option_state @ ( F @ X ) @ ( image_8370355904157991238_state @ F @ A4 ) ) ) ).

% imageI
thf(fact_1175_imageI,axiom,
    ! [X: val,A4: set_val,F: val > option_val] :
      ( ( member_val @ X @ A4 )
     => ( member_option_val @ ( F @ X ) @ ( image_val_option_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1176_imageI,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_state] :
      ( ( member_option_state @ X @ A4 )
     => ( member_option_state @ ( F @ X ) @ ( image_8299601973402907291_state @ F @ A4 ) ) ) ).

% imageI
thf(fact_1177_imageI,axiom,
    ! [X: option_state,A4: set_option_state,F: option_state > option_val] :
      ( ( member_option_state @ X @ A4 )
     => ( member_option_val @ ( F @ X ) @ ( image_52261995005186038on_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1178_imageI,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_state] :
      ( ( member_option_val @ X @ A4 )
     => ( member_option_state @ ( F @ X ) @ ( image_2662813144889517580_state @ F @ A4 ) ) ) ).

% imageI
thf(fact_1179_imageI,axiom,
    ! [X: option_val,A4: set_option_val,F: option_val > option_val] :
      ( ( member_option_val @ X @ A4 )
     => ( member_option_val @ ( F @ X ) @ ( image_5994708315261978053on_val @ F @ A4 ) ) ) ).

% imageI
thf(fact_1180_image__iff,axiom,
    ! [Z3: option_state,F: state > option_state,A4: set_state] :
      ( ( member_option_state @ Z3 @ ( image_6076465424260689483_state @ F @ A4 ) )
      = ( ? [X4: state] :
            ( ( member_state @ X4 @ A4 )
            & ( Z3
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_1181_image__iff,axiom,
    ! [Z3: option_val,F: val > option_val,A4: set_val] :
      ( ( member_option_val @ Z3 @ ( image_val_option_val @ F @ A4 ) )
      = ( ? [X4: val] :
            ( ( member_val @ X4 @ A4 )
            & ( Z3
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_1182_image__iff,axiom,
    ! [Z3: option_val,F: produc1457211279475724562t_char > option_val,A4: set_Pr2507339680178222706t_char] :
      ( ( member_option_val @ Z3 @ ( image_4269386950610408506on_val @ F @ A4 ) )
      = ( ? [X4: produc1457211279475724562t_char] :
            ( ( member484235747325421115t_char @ X4 @ A4 )
            & ( Z3
              = ( F @ X4 ) ) ) ) ) ).

% image_iff
thf(fact_1183_pairwiseD,axiom,
    ! [R3: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,S2: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( pairwi3211334688826577905on_val @ R3 @ S2 )
     => ( ( member2879030624002546611on_val @ X @ S2 )
       => ( ( member2879030624002546611on_val @ Y3 @ S2 )
         => ( ( X != Y3 )
           => ( R3 @ X @ Y3 ) ) ) ) ) ).

% pairwiseD
thf(fact_1184_pairwiseD,axiom,
    ! [R3: option_state > option_state > $o,S2: set_option_state,X: option_state,Y3: option_state] :
      ( ( pairwi7845604448133876319_state @ R3 @ S2 )
     => ( ( member_option_state @ X @ S2 )
       => ( ( member_option_state @ Y3 @ S2 )
         => ( ( X != Y3 )
           => ( R3 @ X @ Y3 ) ) ) ) ) ).

% pairwiseD
thf(fact_1185_pairwiseD,axiom,
    ! [R3: option_val > option_val > $o,S2: set_option_val,X: option_val,Y3: option_val] :
      ( ( pairwise_option_val @ R3 @ S2 )
     => ( ( member_option_val @ X @ S2 )
       => ( ( member_option_val @ Y3 @ S2 )
         => ( ( X != Y3 )
           => ( R3 @ X @ Y3 ) ) ) ) ) ).

% pairwiseD
thf(fact_1186_pairwiseD,axiom,
    ! [R3: val > val > $o,S2: set_val,X: val,Y3: val] :
      ( ( pairwise_val @ R3 @ S2 )
     => ( ( member_val @ X @ S2 )
       => ( ( member_val @ Y3 @ S2 )
         => ( ( X != Y3 )
           => ( R3 @ X @ Y3 ) ) ) ) ) ).

% pairwiseD
thf(fact_1187_pairwiseD,axiom,
    ! [R3: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,S2: set_Pr3433046674199179443r_prat,X: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > prat] :
      ( ( pairwi5837023185793671998r_prat @ R3 @ S2 )
     => ( ( member2336342582916103932r_prat @ X @ S2 )
       => ( ( member2336342582916103932r_prat @ Y3 @ S2 )
         => ( ( X != Y3 )
           => ( R3 @ X @ Y3 ) ) ) ) ) ).

% pairwiseD
thf(fact_1188_pairwiseI,axiom,
    ! [S2: set_Pr7649655576376376530on_val,R3: produc9003781588162623004on_val > produc9003781588162623004on_val > $o] :
      ( ! [X3: produc9003781588162623004on_val,Y4: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X3 @ S2 )
         => ( ( member2879030624002546611on_val @ Y4 @ S2 )
           => ( ( X3 != Y4 )
             => ( R3 @ X3 @ Y4 ) ) ) )
     => ( pairwi3211334688826577905on_val @ R3 @ S2 ) ) ).

% pairwiseI
thf(fact_1189_pairwiseI,axiom,
    ! [S2: set_option_state,R3: option_state > option_state > $o] :
      ( ! [X3: option_state,Y4: option_state] :
          ( ( member_option_state @ X3 @ S2 )
         => ( ( member_option_state @ Y4 @ S2 )
           => ( ( X3 != Y4 )
             => ( R3 @ X3 @ Y4 ) ) ) )
     => ( pairwi7845604448133876319_state @ R3 @ S2 ) ) ).

% pairwiseI
thf(fact_1190_pairwiseI,axiom,
    ! [S2: set_option_val,R3: option_val > option_val > $o] :
      ( ! [X3: option_val,Y4: option_val] :
          ( ( member_option_val @ X3 @ S2 )
         => ( ( member_option_val @ Y4 @ S2 )
           => ( ( X3 != Y4 )
             => ( R3 @ X3 @ Y4 ) ) ) )
     => ( pairwise_option_val @ R3 @ S2 ) ) ).

% pairwiseI
thf(fact_1191_pairwiseI,axiom,
    ! [S2: set_val,R3: val > val > $o] :
      ( ! [X3: val,Y4: val] :
          ( ( member_val @ X3 @ S2 )
         => ( ( member_val @ Y4 @ S2 )
           => ( ( X3 != Y4 )
             => ( R3 @ X3 @ Y4 ) ) ) )
     => ( pairwise_val @ R3 @ S2 ) ) ).

% pairwiseI
thf(fact_1192_pairwiseI,axiom,
    ! [S2: set_Pr3433046674199179443r_prat,R3: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o] :
      ( ! [X3: produc1457211279475724562t_char > prat,Y4: produc1457211279475724562t_char > prat] :
          ( ( member2336342582916103932r_prat @ X3 @ S2 )
         => ( ( member2336342582916103932r_prat @ Y4 @ S2 )
           => ( ( X3 != Y4 )
             => ( R3 @ X3 @ Y4 ) ) ) )
     => ( pairwi5837023185793671998r_prat @ R3 @ S2 ) ) ).

% pairwiseI
thf(fact_1193_bex__imageD,axiom,
    ! [F: state > option_state,A4: set_state,P: option_state > $o] :
      ( ? [X7: option_state] :
          ( ( member_option_state @ X7 @ ( image_6076465424260689483_state @ F @ A4 ) )
          & ( P @ X7 ) )
     => ? [X3: state] :
          ( ( member_state @ X3 @ A4 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_1194_bex__imageD,axiom,
    ! [F: val > option_val,A4: set_val,P: option_val > $o] :
      ( ? [X7: option_val] :
          ( ( member_option_val @ X7 @ ( image_val_option_val @ F @ A4 ) )
          & ( P @ X7 ) )
     => ? [X3: val] :
          ( ( member_val @ X3 @ A4 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_1195_bex__imageD,axiom,
    ! [F: produc1457211279475724562t_char > option_val,A4: set_Pr2507339680178222706t_char,P: option_val > $o] :
      ( ? [X7: option_val] :
          ( ( member_option_val @ X7 @ ( image_4269386950610408506on_val @ F @ A4 ) )
          & ( P @ X7 ) )
     => ? [X3: produc1457211279475724562t_char] :
          ( ( member484235747325421115t_char @ X3 @ A4 )
          & ( P @ ( F @ X3 ) ) ) ) ).

% bex_imageD
thf(fact_1196_image__cong,axiom,
    ! [M4: set_state,N2: set_state,F: state > option_state,G: state > option_state] :
      ( ( M4 = N2 )
     => ( ! [X3: state] :
            ( ( member_state @ X3 @ N2 )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_6076465424260689483_state @ F @ M4 )
          = ( image_6076465424260689483_state @ G @ N2 ) ) ) ) ).

% image_cong
thf(fact_1197_image__cong,axiom,
    ! [M4: set_Pr2507339680178222706t_char,N2: set_Pr2507339680178222706t_char,F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( M4 = N2 )
     => ( ! [X3: produc1457211279475724562t_char] :
            ( ( member484235747325421115t_char @ X3 @ N2 )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_4269386950610408506on_val @ F @ M4 )
          = ( image_4269386950610408506on_val @ G @ N2 ) ) ) ) ).

% image_cong
thf(fact_1198_image__cong,axiom,
    ! [M4: set_val,N2: set_val,F: val > option_val,G: val > option_val] :
      ( ( M4 = N2 )
     => ( ! [X3: val] :
            ( ( member_val @ X3 @ N2 )
           => ( ( F @ X3 )
              = ( G @ X3 ) ) )
       => ( ( image_val_option_val @ F @ M4 )
          = ( image_val_option_val @ G @ N2 ) ) ) ) ).

% image_cong
thf(fact_1199_ball__imageD,axiom,
    ! [F: state > option_state,A4: set_state,P: option_state > $o] :
      ( ! [X3: option_state] :
          ( ( member_option_state @ X3 @ ( image_6076465424260689483_state @ F @ A4 ) )
         => ( P @ X3 ) )
     => ! [X7: state] :
          ( ( member_state @ X7 @ A4 )
         => ( P @ ( F @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_1200_ball__imageD,axiom,
    ! [F: val > option_val,A4: set_val,P: option_val > $o] :
      ( ! [X3: option_val] :
          ( ( member_option_val @ X3 @ ( image_val_option_val @ F @ A4 ) )
         => ( P @ X3 ) )
     => ! [X7: val] :
          ( ( member_val @ X7 @ A4 )
         => ( P @ ( F @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_1201_ball__imageD,axiom,
    ! [F: produc1457211279475724562t_char > option_val,A4: set_Pr2507339680178222706t_char,P: option_val > $o] :
      ( ! [X3: option_val] :
          ( ( member_option_val @ X3 @ ( image_4269386950610408506on_val @ F @ A4 ) )
         => ( P @ X3 ) )
     => ! [X7: produc1457211279475724562t_char] :
          ( ( member484235747325421115t_char @ X7 @ A4 )
         => ( P @ ( F @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_1202_rev__image__eqI,axiom,
    ! [X: val,A4: set_val,B2: val,F: val > val] :
      ( ( member_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_val @ B2 @ ( image_val_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1203_rev__image__eqI,axiom,
    ! [X: state,A4: set_state,B2: option_state,F: state > option_state] :
      ( ( member_state @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_state @ B2 @ ( image_6076465424260689483_state @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1204_rev__image__eqI,axiom,
    ! [X: option_state,A4: set_option_state,B2: val,F: option_state > val] :
      ( ( member_option_state @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_val @ B2 @ ( image_7609484285346866096te_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1205_rev__image__eqI,axiom,
    ! [X: option_val,A4: set_option_val,B2: val,F: option_val > val] :
      ( ( member_option_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_val @ B2 @ ( image_option_val_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1206_rev__image__eqI,axiom,
    ! [X: val,A4: set_val,B2: option_state,F: val > option_state] :
      ( ( member_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_state @ B2 @ ( image_8370355904157991238_state @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1207_rev__image__eqI,axiom,
    ! [X: val,A4: set_val,B2: option_val,F: val > option_val] :
      ( ( member_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_val @ B2 @ ( image_val_option_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1208_rev__image__eqI,axiom,
    ! [X: option_state,A4: set_option_state,B2: option_state,F: option_state > option_state] :
      ( ( member_option_state @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_state @ B2 @ ( image_8299601973402907291_state @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1209_rev__image__eqI,axiom,
    ! [X: option_state,A4: set_option_state,B2: option_val,F: option_state > option_val] :
      ( ( member_option_state @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_val @ B2 @ ( image_52261995005186038on_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1210_rev__image__eqI,axiom,
    ! [X: option_val,A4: set_option_val,B2: option_state,F: option_val > option_state] :
      ( ( member_option_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_state @ B2 @ ( image_2662813144889517580_state @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1211_rev__image__eqI,axiom,
    ! [X: option_val,A4: set_option_val,B2: option_val,F: option_val > option_val] :
      ( ( member_option_val @ X @ A4 )
     => ( ( B2
          = ( F @ X ) )
       => ( member_option_val @ B2 @ ( image_5994708315261978053on_val @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_1212_pairwise__imageI,axiom,
    ! [A4: set_state,F: state > option_state,P: option_state > option_state > $o] :
      ( ! [X3: state,Y4: state] :
          ( ( member_state @ X3 @ A4 )
         => ( ( member_state @ Y4 @ A4 )
           => ( ( X3 != Y4 )
             => ( ( ( F @ X3 )
                 != ( F @ Y4 ) )
               => ( P @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) )
     => ( pairwi7845604448133876319_state @ P @ ( image_6076465424260689483_state @ F @ A4 ) ) ) ).

% pairwise_imageI
thf(fact_1213_pairwise__imageI,axiom,
    ! [A4: set_Pr2507339680178222706t_char,F: produc1457211279475724562t_char > option_val,P: option_val > option_val > $o] :
      ( ! [X3: produc1457211279475724562t_char,Y4: produc1457211279475724562t_char] :
          ( ( member484235747325421115t_char @ X3 @ A4 )
         => ( ( member484235747325421115t_char @ Y4 @ A4 )
           => ( ( X3 != Y4 )
             => ( ( ( F @ X3 )
                 != ( F @ Y4 ) )
               => ( P @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) )
     => ( pairwise_option_val @ P @ ( image_4269386950610408506on_val @ F @ A4 ) ) ) ).

% pairwise_imageI
thf(fact_1214_pairwise__imageI,axiom,
    ! [A4: set_val,F: val > option_val,P: option_val > option_val > $o] :
      ( ! [X3: val,Y4: val] :
          ( ( member_val @ X3 @ A4 )
         => ( ( member_val @ Y4 @ A4 )
           => ( ( X3 != Y4 )
             => ( ( ( F @ X3 )
                 != ( F @ Y4 ) )
               => ( P @ ( F @ X3 ) @ ( F @ Y4 ) ) ) ) ) )
     => ( pairwise_option_val @ P @ ( image_val_option_val @ F @ A4 ) ) ) ).

% pairwise_imageI
thf(fact_1215_image__comp,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > produc1457211279475724562t_char,R4: set_Pr2507339680178222706t_char] :
      ( ( image_4269386950610408506on_val @ F @ ( image_3726312381382425221t_char @ G @ R4 ) )
      = ( image_4269386950610408506on_val @ ( comp_P7186816004269530362t_char @ F @ G ) @ R4 ) ) ).

% image_comp
thf(fact_1216_None__notin__image__Some,axiom,
    ! [A4: set_val] :
      ~ ( member_option_val @ none_val @ ( image_val_option_val @ some_val @ A4 ) ) ).

% None_notin_image_Some
thf(fact_1217_None__notin__image__Some,axiom,
    ! [A4: set_state] :
      ~ ( member_option_state @ none_state @ ( image_6076465424260689483_state @ some_state @ A4 ) ) ).

% None_notin_image_Some
thf(fact_1218_comp__the__Some,axiom,
    ( ( comp_o5604524432708427236al_val @ the_val @ some_val )
    = id_val ) ).

% comp_the_Some
thf(fact_1219_comp__the__Some,axiom,
    ( ( comp_o4916166309651032803_state @ the_state @ some_state )
    = id_state ) ).

% comp_the_Some
thf(fact_1220_inj__on__map__add__dom,axiom,
    ! [M: produc1457211279475724562t_char > option_val,M5: produc1457211279475724562t_char > option_val] :
      ( ( inj_on4474484569326248358on_val @ ( map_ad2908576761495157028ar_val @ M @ M5 ) @ ( dom_Pr8989479155164304065ar_val @ M5 ) )
      = ( inj_on4474484569326248358on_val @ M5 @ ( dom_Pr8989479155164304065ar_val @ M5 ) ) ) ).

% inj_on_map_add_dom
thf(fact_1221_inj__Some,axiom,
    ! [A4: set_val] : ( inj_on4074814566786472055on_val @ some_val @ A4 ) ).

% inj_Some
thf(fact_1222_inj__Some,axiom,
    ! [A4: set_state] : ( inj_on3577428053172332983_state @ some_state @ A4 ) ).

% inj_Some
thf(fact_1223_add__masks_Oelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa: produc1457211279475724562t_char > prat,Xb: produc1457211279475724562t_char,Y3: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa @ Xb )
        = Y3 )
     => ( Y3
        = ( padd @ ( X @ Xb ) @ ( Xa @ Xb ) ) ) ) ).

% add_masks.elims
thf(fact_1224_add__masks_Osimps,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [Pi4: produc1457211279475724562t_char > prat,Pi2: produc1457211279475724562t_char > prat,Hl2: produc1457211279475724562t_char] : ( padd @ ( Pi4 @ Hl2 ) @ ( Pi2 @ Hl2 ) ) ) ) ).

% add_masks.simps
thf(fact_1225_ppos__add,axiom,
    ! [A2: prat,B2: prat] :
      ( ( ppos @ A2 )
     => ( ppos @ ( padd @ A2 @ B2 ) ) ) ).

% ppos_add
thf(fact_1226_dom__map__add,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val] :
      ( ( dom_Pr8989479155164304065ar_val @ ( map_ad2908576761495157028ar_val @ M @ N ) )
      = ( sup_su7899656352754981958t_char @ ( dom_Pr8989479155164304065ar_val @ N ) @ ( dom_Pr8989479155164304065ar_val @ M ) ) ) ).

% dom_map_add
thf(fact_1227_ran__map__add,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( ran_Pr786515303459910110ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) )
        = ( sup_sup_set_val @ ( ran_Pr786515303459910110ar_val @ M1 ) @ ( ran_Pr786515303459910110ar_val @ M2 ) ) ) ) ).

% ran_map_add
thf(fact_1228_map__add__comm,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( map_ad2908576761495157028ar_val @ M1 @ M2 )
        = ( map_ad2908576761495157028ar_val @ M2 @ M1 ) ) ) ).

% map_add_comm
thf(fact_1229_graph__map__add,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( graph_1733029056113894637ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) )
        = ( sup_su5754804325903363146ar_val @ ( graph_1733029056113894637ar_val @ M1 ) @ ( graph_1733029056113894637ar_val @ M2 ) ) ) ) ).

% graph_map_add
thf(fact_1230_graph__map__upd,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,V2: produc1457211279475724562t_char > option_val] :
      ( ( graph_1288227317702120175on_val @ ( fun_up1601731230164360576on_val @ M @ K @ ( some_P7669353234731512949on_val @ V2 ) ) )
      = ( insert3030518898131756108on_val @ ( produc74620467203698198on_val @ K @ V2 ) @ ( graph_1288227317702120175on_val @ ( fun_up1601731230164360576on_val @ M @ K @ none_P1334921381875262201on_val ) ) ) ) ).

% graph_map_upd
thf(fact_1231_graph__map__upd,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,K: produc9003781588162623004on_val,V2: produc9003781588162623004on_val] :
      ( ( graph_6108330199704490680on_val @ ( fun_up273046073882939271on_val @ M @ K @ ( some_P2581650809551911671on_val @ V2 ) ) )
      = ( insert7062705985672971881on_val @ ( produc4958730763592889809on_val @ K @ V2 ) @ ( graph_6108330199704490680on_val @ ( fun_up273046073882939271on_val @ M @ K @ none_P8728355543607141243on_val ) ) ) ) ).

% graph_map_upd
thf(fact_1232_compatible__options_Ocases,axiom,
    ! [X: produc5122021904355189735on_val] :
      ( ! [A: val,B: val] :
          ( X
         != ( produc904852209897547607on_val @ ( some_val @ A ) @ ( some_val @ B ) ) )
     => ( ! [Uv2: option_val] :
            ( X
           != ( produc904852209897547607on_val @ none_val @ Uv2 ) )
       => ~ ! [Uu2: option_val] :
              ( X
             != ( produc904852209897547607on_val @ Uu2 @ none_val ) ) ) ) ).

% compatible_options.cases
thf(fact_1233_compatible__options_Ocases,axiom,
    ! [X: produc3142500478612311029_state] :
      ( ! [A: state,B: state] :
          ( X
         != ( produc9160152616361873709_state @ ( some_state @ A ) @ ( some_state @ B ) ) )
     => ( ! [Uv2: option_state] :
            ( X
           != ( produc9160152616361873709_state @ none_state @ Uv2 ) )
       => ~ ! [Uu2: option_state] :
              ( X
             != ( produc9160152616361873709_state @ Uu2 @ none_state ) ) ) ) ).

% compatible_options.cases
thf(fact_1234_in__graphI,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,V2: produc1457211279475724562t_char > option_val] :
      ( ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V2 ) )
     => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V2 ) @ ( graph_1288227317702120175on_val @ M ) ) ) ).

% in_graphI
thf(fact_1235_in__graphI,axiom,
    ! [M: produc9003781588162623004on_val > option8887860577033306220on_val,K: produc9003781588162623004on_val,V2: produc9003781588162623004on_val] :
      ( ( ( M @ K )
        = ( some_P2581650809551911671on_val @ V2 ) )
     => ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ K @ V2 ) @ ( graph_6108330199704490680on_val @ M ) ) ) ).

% in_graphI
thf(fact_1236_in__graphD,axiom,
    ! [K: produc1457211279475724562t_char > prat,V2: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V2 ) @ ( graph_1288227317702120175on_val @ M ) )
     => ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V2 ) ) ) ).

% in_graphD
thf(fact_1237_in__graphD,axiom,
    ! [K: produc9003781588162623004on_val,V2: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val] :
      ( ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ K @ V2 ) @ ( graph_6108330199704490680on_val @ M ) )
     => ( ( M @ K )
        = ( some_P2581650809551911671on_val @ V2 ) ) ) ).

% in_graphD
thf(fact_1238_graph__restrictD_I1_J,axiom,
    ! [K: produc1457211279475724562t_char > prat,V2: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V2 ) @ ( graph_1288227317702120175on_val @ ( restri7594233908965391805on_val @ M @ A4 ) ) )
     => ( member2336342582916103932r_prat @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1239_graph__restrictD_I1_J,axiom,
    ! [K: produc9003781588162623004on_val,V2: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ K @ V2 ) @ ( graph_6108330199704490680on_val @ ( restri2354629191430751338on_val @ M @ A4 ) ) )
     => ( member2879030624002546611on_val @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1240_graph__restrictD_I2_J,axiom,
    ! [K: produc1457211279475724562t_char > prat,V2: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V2 ) @ ( graph_1288227317702120175on_val @ ( restri7594233908965391805on_val @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V2 ) ) ) ).

% graph_restrictD(2)
thf(fact_1241_graph__restrictD_I2_J,axiom,
    ! [K: produc9003781588162623004on_val,V2: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option8887860577033306220on_val,A4: set_Pr7649655576376376530on_val] :
      ( ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ K @ V2 ) @ ( graph_6108330199704490680on_val @ ( restri2354629191430751338on_val @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_P2581650809551911671on_val @ V2 ) ) ) ).

% graph_restrictD(2)
thf(fact_1242_add__states_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa )
        = Y3 )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ! [Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
                ( ( Xa
                  = ( produc74620467203698198on_val @ Pi6 @ H6 ) )
               => ( Y3
                 != ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi5 @ Pi6 ) @ ( map_ad2908576761495157028ar_val @ H5 @ H6 ) ) ) ) ) ) ).

% add_states.elims
thf(fact_1243_add__states_Osimps,axiom,
    ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val,Pi3: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
      ( ( add_states @ ( produc74620467203698198on_val @ Pi @ H ) @ ( produc74620467203698198on_val @ Pi3 @ H2 ) )
      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi @ Pi3 ) @ ( map_ad2908576761495157028ar_val @ H @ H2 ) ) ) ).

% add_states.simps
thf(fact_1244_Field__insert,axiom,
    ! [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,R4: set_Pr4305388979797279737on_val] :
      ( ( field_9010718613293825679on_val @ ( insert7062705985672971881on_val @ ( produc4958730763592889809on_val @ A2 @ B2 ) @ R4 ) )
      = ( sup_su7506060154676209150on_val @ ( insert3030518898131756108on_val @ A2 @ ( insert3030518898131756108on_val @ B2 @ bot_bo6722054719108133734on_val ) ) @ ( field_9010718613293825679on_val @ R4 ) ) ) ).

% Field_insert
thf(fact_1245_valid__stateI,axiom,
    ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_mask @ Pi )
     => ( ! [Hl: produc1457211279475724562t_char] :
            ( ( ppos @ ( Pi @ Hl ) )
           => ( ( H @ Hl )
             != none_val ) )
       => ( valid_state @ ( produc74620467203698198on_val @ Pi @ H ) ) ) ) ).

% valid_stateI
thf(fact_1246_add__states_Ocases,axiom,
    ! [X: produc1317171644805857433on_val] :
      ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val,Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ ( produc74620467203698198on_val @ Pi6 @ H6 ) ) ) ).

% add_states.cases
thf(fact_1247_valid__state_Ocases,axiom,
    ! [X: produc9003781588162623004on_val] :
      ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc74620467203698198on_val @ Pi5 @ H5 ) ) ).

% valid_state.cases
thf(fact_1248_valid__state__decompose,axiom,
    ! [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ A2 @ B2 ) @ H ) )
     => ( valid_state @ ( produc74620467203698198on_val @ A2 @ H ) ) ) ).

% valid_state_decompose
thf(fact_1249_valid__pre__unit,axiom,
    valid_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ).

% valid_pre_unit
thf(fact_1250_valid__state_Osimps,axiom,
    ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ Pi @ H ) )
      = ( ( valid_mask @ Pi )
        & ( valid_heap @ Pi @ H ) ) ) ).

% valid_state.simps
thf(fact_1251_valid__state_Oelims_I1_J,axiom,
    ! [X: produc9003781588162623004on_val,Y3: $o] :
      ( ( ( valid_state @ X )
        = Y3 )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ( Y3
              = ( ~ ( ( valid_mask @ Pi5 )
                    & ( valid_heap @ Pi5 @ H5 ) ) ) ) ) ) ).

% valid_state.elims(1)
thf(fact_1252_valid__state_Oelims_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( valid_state @ X )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ~ ( ( valid_mask @ Pi5 )
                & ( valid_heap @ Pi5 @ H5 ) ) ) ) ).

% valid_state.elims(2)
thf(fact_1253_valid__state_Oelims_I3_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ( ( valid_mask @ Pi5 )
              & ( valid_heap @ Pi5 @ H5 ) ) ) ) ).

% valid_state.elims(3)
thf(fact_1254_core__def,axiom,
    ( core
    = ( ^ [Phi3: state] : ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ ( get_h @ Phi3 ) ) ) ) ) ).

% core_def
thf(fact_1255_get__h__m,axiom,
    ( rep_state
    = ( ^ [X4: state] : ( produc74620467203698198on_val @ ( get_m @ X4 ) @ ( get_h @ X4 ) ) ) ) ).

% get_h_m
thf(fact_1256_refl__on__singleton,axiom,
    ! [X: produc9003781588162623004on_val] : ( refl_o6679066329051764061on_val @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) @ ( insert7062705985672971881on_val @ ( produc4958730763592889809on_val @ X @ X ) @ bot_bo402267660617762917on_val ) ) ).

% refl_on_singleton
thf(fact_1257_ssubsetI,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
      ( ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ A4 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ B5 ) )
     => ( ord_le6900622908513426738on_val @ A4 @ B5 ) ) ).

% ssubsetI
thf(fact_1258_ssubsetI,axiom,
    ! [A4: set_Pr4305388979797279737on_val,B5: set_Pr4305388979797279737on_val] :
      ( ! [Pi5: produc9003781588162623004on_val,H5: produc9003781588162623004on_val] :
          ( ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ Pi5 @ H5 ) @ A4 )
         => ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ Pi5 @ H5 ) @ B5 ) )
     => ( ord_le7224449410216889241on_val @ A4 @ B5 ) ) ).

% ssubsetI
thf(fact_1259_Rep__state__inject,axiom,
    ! [X: state,Y3: state] :
      ( ( ( rep_state @ X )
        = ( rep_state @ Y3 ) )
      = ( X = Y3 ) ) ).

% Rep_state_inject
thf(fact_1260_Rep__state__inverse,axiom,
    ! [X: state] :
      ( ( abs_state @ ( rep_state @ X ) )
      = X ) ).

% Rep_state_inverse
thf(fact_1261_unit__def,axiom,
    ( unit
    = ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ) ) ).

% unit_def
thf(fact_1262_plus__def,axiom,
    ( plus
    = ( ^ [A3: state,B3: state] : ( if_option_state @ ( compatible @ ( rep_state @ A3 ) @ ( rep_state @ B3 ) ) @ ( some_state @ ( abs_state @ ( add_states @ ( rep_state @ A3 ) @ ( rep_state @ B3 ) ) ) ) @ none_state ) ) ) ).

% plus_def
thf(fact_1263_add__states_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa )
        = Y3 )
     => ( ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ X @ Xa ) )
       => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
             => ! [Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
                  ( ( Xa
                    = ( produc74620467203698198on_val @ Pi6 @ H6 ) )
                 => ( ( Y3
                      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi5 @ Pi6 ) @ ( map_ad2908576761495157028ar_val @ H5 @ H6 ) ) )
                   => ~ ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ ( produc74620467203698198on_val @ Pi6 @ H6 ) ) ) ) ) ) ) ) ).

% add_states.pelims
thf(fact_1264_linear__order__on__singleton,axiom,
    ! [X: produc9003781588162623004on_val] : ( order_6061556925426544295on_val @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) @ ( insert7062705985672971881on_val @ ( produc4958730763592889809on_val @ X @ X ) @ bot_bo402267660617762917on_val ) ) ).

% linear_order_on_singleton
thf(fact_1265_Linear__order__Well__order__iff,axiom,
    ! [R4: set_Pr4305388979797279737on_val] :
      ( ( order_6061556925426544295on_val @ ( field_9010718613293825679on_val @ R4 ) @ R4 )
     => ( ( order_2579646547231075838on_val @ ( field_9010718613293825679on_val @ R4 ) @ R4 )
        = ( ! [A6: set_Pr7649655576376376530on_val] :
              ( ( ord_le6900622908513426738on_val @ A6 @ ( field_9010718613293825679on_val @ R4 ) )
             => ( ( A6 != bot_bo6722054719108133734on_val )
               => ? [X4: produc9003781588162623004on_val] :
                    ( ( member2879030624002546611on_val @ X4 @ A6 )
                    & ! [Y: produc9003781588162623004on_val] :
                        ( ( member2879030624002546611on_val @ Y @ A6 )
                       => ( member6505152944228695362on_val @ ( produc4958730763592889809on_val @ X4 @ Y ) @ R4 ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_1266_add__masks_Opelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa: produc1457211279475724562t_char > prat,Xb: produc1457211279475724562t_char,Y3: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa @ Xb )
        = Y3 )
     => ( ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa @ Xb ) ) )
       => ~ ( ( Y3
              = ( padd @ ( X @ Xb ) @ ( Xa @ Xb ) ) )
           => ~ ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa @ Xb ) ) ) ) ) ) ).

% add_masks.pelims
thf(fact_1267_UNIV__option__conv,axiom,
    ( top_to853123400021307383on_val
    = ( insert_option_val @ none_val @ ( image_val_option_val @ some_val @ top_top_set_val ) ) ) ).

% UNIV_option_conv
thf(fact_1268_UNIV__option__conv,axiom,
    ( top_to7666338855062656496_state
    = ( insert_option_state @ none_state @ ( image_6076465424260689483_state @ some_state @ top_top_set_state ) ) ) ).

% UNIV_option_conv
thf(fact_1269_notin__range__Some,axiom,
    ! [X: option_val] :
      ( ( ~ ( member_option_val @ X @ ( image_val_option_val @ some_val @ top_top_set_val ) ) )
      = ( X = none_val ) ) ).

% notin_range_Some
thf(fact_1270_notin__range__Some,axiom,
    ! [X: option_state] :
      ( ( ~ ( member_option_state @ X @ ( image_6076465424260689483_state @ some_state @ top_top_set_state ) ) )
      = ( X = none_state ) ) ).

% notin_range_Some
thf(fact_1271_trans__singleton,axiom,
    ! [A2: produc9003781588162623004on_val] : ( trans_3212976107463897212on_val @ top_to1561438921946393474on_val @ ( insert7062705985672971881on_val @ ( produc4958730763592889809on_val @ A2 @ A2 ) @ bot_bo402267660617762917on_val ) ) ).

% trans_singleton
thf(fact_1272_finite__range__Some,axiom,
    ( ( finite4212117559080419824on_val @ ( image_val_option_val @ some_val @ top_top_set_val ) )
    = ( finite_finite_val @ top_top_set_val ) ) ).

% finite_range_Some
thf(fact_1273_finite__range__Some,axiom,
    ( ( finite3180955649987104801_state @ ( image_6076465424260689483_state @ some_state @ top_top_set_state ) )
    = ( finite_finite_state @ top_top_set_state ) ) ).

% finite_range_Some
thf(fact_1274_finite__range__map__of__map__add,axiom,
    ! [F: produc1457211279475724562t_char > option_val,L: list_P375024181684815772ar_val] :
      ( ( finite4212117559080419824on_val @ ( image_4269386950610408506on_val @ F @ top_to1250346684925019074t_char ) )
     => ( finite4212117559080419824on_val @ ( image_4269386950610408506on_val @ ( map_ad2908576761495157028ar_val @ F @ ( map_of6844234013878170066ar_val @ L ) ) @ top_to1250346684925019074t_char ) ) ) ).

% finite_range_map_of_map_add

% Helper facts (11)
thf(help_If_2_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y3: prat] :
      ( ( if_prat @ $false @ X @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y3: prat] :
      ( ( if_prat @ $true @ X @ Y3 )
      = X ) ).

thf(help_If_2_1_If_001t__Option__Ooption_It__Mask__Oval_J_T,axiom,
    ! [X: option_val,Y3: option_val] :
      ( ( if_option_val @ $false @ X @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__Mask__Oval_J_T,axiom,
    ! [X: option_val,Y3: option_val] :
      ( ( if_option_val @ $true @ X @ Y3 )
      = X ) ).

thf(help_If_2_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X: option_state,Y3: option_state] :
      ( ( if_option_state @ $false @ X @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X: option_state,Y3: option_state] :
      ( ( if_option_state @ $true @ X @ Y3 )
      = X ) ).

thf(help_If_2_1_If_001t__Option__Ooption_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_T,axiom,
    ! [X: option5747939881698552298on_val,Y3: option5747939881698552298on_val] :
      ( ( if_opt6509584284076893604on_val @ $false @ X @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__Option__Ooption_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_T,axiom,
    ! [X: option5747939881698552298on_val,Y3: option5747939881698552298on_val] :
      ( ( if_opt6509584284076893604on_val @ $true @ X @ Y3 )
      = X ) ).

thf(help_If_3_1_If_001t__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_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__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_T,axiom,
    ! [X: option8887860577033306220on_val,Y3: option8887860577033306220on_val] :
      ( ( if_opt2965748431298708774on_val @ $false @ X @ Y3 )
      = Y3 ) ).

thf(help_If_1_1_If_001t__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_T,axiom,
    ! [X: option8887860577033306220on_val,Y3: option8887860577033306220on_val] :
      ( ( if_opt2965748431298708774on_val @ $true @ X @ Y3 )
      = X ) ).

% Conjectures (2)
thf(conj_0,hypothesis,
    ! [L3: produc1457211279475724562t_char,X7: val,Y5: val] :
      ( ( ( get_h @ b @ L3 )
        = ( some_val @ X7 ) )
     => ( ( ( get_h @ c @ L3 )
          = ( some_val @ Y5 ) )
       => ( ( X7 != Y5 )
         => thesis ) ) ) ).

thf(conj_1,conjecture,
    thesis ).

%------------------------------------------------------------------------------