TPTP Problem File: SLH0187^1.p

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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Combinable_Wands/0003_CombinableWands/prob_00633_030814__8381200_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1743 ( 509 unt; 460 typ;   0 def)
%            Number of atoms       : 4796 (1899 equ;   0 cnn)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives : 15576 ( 483   ~;  56   |; 668   &;12302   @)
%                                         (   0 <=>;2067  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (   8 avg)
%            Number of types       :   59 (  58 usr)
%            Number of type conns  : 2970 (2970   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  405 ( 402 usr;  37 con; 0-11 aty)
%            Number of variables   : 5171 ( 502   ^;4309   !; 360   ?;5171   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 09:09:23.980
%------------------------------------------------------------------------------
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% Explicit typings (402)
thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bNF_Ca2815325664443363616_state: set_Pr1688445902015331925_state > ( option_state > set_state ) > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_Finite__Set_OFpow_001t__PartialHeapSA__Ostate,type,
    finite_Fpow_state: set_state > set_set_state ).

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

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

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

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

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

thf(sy_c_Fun__Def_OTHE__default_001t__Mask__Oval,type,
    fun_THE_default_val: val > ( val > $o ) > val ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    sup_su4188871578264421970_state: set_set_state > set_set_state > set_set_state ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J_J,type,
    sup_su6129196281181032577_state: set_se1301818477132140373_state > set_se1301818477132140373_state > set_se1301818477132140373_state ).

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

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

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

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

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

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

thf(sy_c_Mask_Oempty__mask_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    empty_5858998862663000819_state: produc3142500478612311029_state > prat ).

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

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

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

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

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

thf(sy_c_Mask_Oempty__mask__rel_001t__Product____Type__Oprod_It__Option__Ooption_It__PartialHeapSA__Ostate_J_Mt__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    empty_3683758330361983676_state: produc3142500478612311029_state > produc3142500478612311029_state > $o ).

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

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

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

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

thf(sy_c_Mask_Onull_001t__Nat__Onat,type,
    null_nat: nat ).

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

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

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

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

thf(sy_c_Option_Ooption_ONone_001t__Mask__Oval,type,
    none_val: option_val ).

thf(sy_c_Option_Ooption_ONone_001t__PartialHeapSA__Ostate,type,
    none_state: option_state ).

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

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

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

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

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

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Mask__Oval,type,
    case_option_o_val: $o > ( val > $o ) > option_val > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__PartialHeapSA__Ostate,type,
    case_option_o_state: $o > ( state > $o ) > option_state > $o ).

thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Mask__Oval_J_001t__Mask__Oval,type,
    case_o7794706883426356101al_val: option_val > ( val > option_val ) > option_val > option_val ).

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

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

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

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__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    these_7452845017025203435_state: set_op3387789762728285652_state > set_Pr2391701600042252046_state ).

thf(sy_c_Option_Othese_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    these_4347185934205712492_state: set_op8023886964038656367_state > set_Pr4231240917283394591_state ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
    bot_bot_state_o: 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__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_M_Eo_J,type,
    bot_bo4916705512949510546tate_o: produc7272280185086996969_state > $o ).

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_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__PartialHeapSA__Ostate_J_J,type,
    bot_bo710180891245420500_state: set_option_state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bot_bot_set_state: set_state ).

thf(sy_c_Orderings_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__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    bot_bo3524941057552913786_state: set_Pr2391701600042252046_state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    bot_bo6430881413863817907_state: set_Pr4231240917283394591_state ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    bot_bo2271482359692755898_state: set_set_state ).

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

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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_062_It__Option__Ooption_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_062_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PosRat__Oprat_M_062_It__Set__Oset_It__PartialHeapSA__Ostate_J_M_Eo_J_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
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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,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__PosRat__Oprat_Mt__PartialHeapSA__Ostate_J_J,type,
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thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
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thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Mask__Oval_J,type,
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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,
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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 ).

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thf(sy_c_PackageLogic_Oaassertion_OAImp_001t__Mask__Oval,type,
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thf(sy_c_PackageLogic_Oaassertion_OAImp_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_PackageLogic_Oaassertion_OASem_001t__Mask__Oval,type,
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thf(sy_c_PackageLogic_Oaassertion_OASem_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_PackageLogic_Oaassertion_OAStar_001t__Mask__Oval,type,
    aStar_val: aassertion_val > aassertion_val > aassertion_val ).

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

thf(sy_c_PackageLogic_Opackage__logic_001t__Mask__Oval,type,
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thf(sy_c_PackageLogic_Opackage__logic_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_PackageLogic_Opackage__logic_Obool__conj_001t__Mask__Oval,type,
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thf(sy_c_PackageLogic_Opackage__logic_Obool__conj_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Mask__Oval,type,
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thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_PackageLogic_Opackage__logic_Ointuitionistic_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
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    packag1160585701684337059_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Ois__footprint__general_001t__Mask__Oval,type,
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thf(sy_c_PartialHeapSA_Ocompatible__heaps,type,
    compatible_heaps: ( produc1457211279475724562t_char > option_val ) > ( produc1457211279475724562t_char > option_val ) > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_PartialHeapSA_Ounit,type,
    unit: state ).

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

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

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

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

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

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

thf(sy_c_PosRat_Opnone,type,
    pnone: prat ).

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

thf(sy_c_PosRat_Opwrite,type,
    pwrite: prat ).

thf(sy_c_Product__Type_OPair_001_062_It__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__Mask__Oval_001_062_It__Mask__Oval_Mt__Mask__Oval_J,type,
    produc303288909735261391al_val: val > ( val > val ) > produc5503543764249810261al_val ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_M_062_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    produc5427679348311974809_state: produc3882902684156697774_state > produc2023215532613486146_state > produc6455357576889117855_state ).

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

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

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

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

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

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

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

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

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

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

thf(sy_c_SepAlgebra_Osep__algebra_001t__Mask__Oval,type,
    sep_algebra_val: ( val > val > option_val ) > ( val > val ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_001t__PartialHeapSA__Ostate,type,
    sep_algebra_state: ( state > state > option_state ) > ( state > state ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_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,
    sep_al5697130883215687421on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    sep_al8268612531242297357_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > produc3882902684156697774_state ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    sep_al4323785819428540618_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > produc7272280185086996969_state ) > $o ).

thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_001t__Mask__Oval,type,
    sep_add_set_val: ( val > val > option_val ) > set_val > set_val > set_val ).

thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_001t__PartialHeapSA__Ostate,type,
    sep_add_set_state: ( state > state > option_state ) > set_state > set_state > set_state ).

thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_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,
    sep_ad8320153009520438926on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    sep_ad8203089552910907580_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > set_Pr2391701600042252046_state > set_Pr2391701600042252046_state > set_Pr2391701600042252046_state ).

thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    sep_ad3908482799505143387_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state ).

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

thf(sy_c_SepAlgebra_Osep__algebra_Odefined_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Oequiv_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Ogreater_001t__Mask__Oval,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Ogreater_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Opure_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Osetify_001t__PartialHeapSA__Ostate,type,
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    member5752234768399382829_state: produc4357056439811976324_state > set_Pr523392378426063460_state > $o ).

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

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

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

thf(sy_v_A,type,
    a: set_state ).

thf(sy_v_B,type,
    b: set_state ).

thf(sy_v__092_060alpha_062____,type,
    alpha: prat ).

thf(sy_v__092_060beta_062____,type,
    beta: prat ).

thf(sy_v_a____,type,
    a2: state ).

thf(sy_v_ba____,type,
    ba: state ).

thf(sy_v_p____,type,
    p: prat ).

thf(sy_v_w____,type,
    w: state ).

thf(sy_v_wa____,type,
    wa: state ).

thf(sy_v_wb____,type,
    wb: state ).

thf(sy_v_x____,type,
    x: state ).

thf(sy_v_xa____,type,
    xa: state ).

thf(sy_v_xb____,type,
    xb: state ).

% Relevant facts (1275)
thf(fact_0__092_060open_062Some_Aw_A_061_Axa_A_092_060oplus_062_Axb_092_060close_062,axiom,
    ( ( some_state @ w )
    = ( plus @ xa @ xb ) ) ).

% \<open>Some w = xa \<oplus> xb\<close>
thf(fact_1_intuitionistic__def,axiom,
    ( intuitionistic
    = ( ^ [A: set_state] :
        ! [A2: state,B: state] :
          ( ( ( greater @ A2 @ B )
            & ( member_state @ B @ A ) )
         => ( member_state @ A2 @ A ) ) ) ) ).

% intuitionistic_def
thf(fact_2__092_060open_062xb_A_092_060succeq_062_Amultiply_A_092_060beta_062_Awb_092_060close_062,axiom,
    greater @ xb @ ( multiply @ beta @ wb ) ).

% \<open>xb \<succeq> multiply \<beta> wb\<close>
thf(fact_3_PartialSA_Osucc__refl,axiom,
    ! [A3: state] : ( greater @ A3 @ A3 ) ).

% PartialSA.succ_refl
thf(fact_4_PartialSA_Osucc__trans,axiom,
    ! [A3: state,B2: state,C: state] :
      ( ( greater @ A3 @ B2 )
     => ( ( greater @ B2 @ C )
       => ( greater @ A3 @ C ) ) ) ).

% PartialSA.succ_trans
thf(fact_5_PartialSA_Osucc__antisym,axiom,
    ! [A3: state,B2: state] :
      ( ( greater @ A3 @ B2 )
     => ( ( greater @ B2 @ A3 )
       => ( A3 = B2 ) ) ) ).

% PartialSA.succ_antisym
thf(fact_6__092_060open_062_092_060not_062_Ascalable_Aw_Aa_092_060close_062,axiom,
    ~ ( scalable @ w @ a2 ) ).

% \<open>\<not> scalable w a\<close>
thf(fact_7_assms_I2_J,axiom,
    intuitionistic @ b ).

% assms(2)
thf(fact_8_assms_I1_J,axiom,
    combinable @ b ).

% assms(1)
thf(fact_9_R__smaller,axiom,
    ! [W: state,A3: state] : ( greater @ W @ ( r @ A3 @ W ) ) ).

% R_smaller
thf(fact_10_PartialSA_Obigger__sum,axiom,
    ! [Phi: state,A3: state,B2: state,Phi2: state] :
      ( ( ( some_state @ Phi )
        = ( plus @ A3 @ B2 ) )
     => ( ( greater @ Phi2 @ Phi )
       => ? [B3: state] :
            ( ( greater @ B3 @ B2 )
            & ( ( some_state @ Phi2 )
              = ( plus @ A3 @ B3 ) ) ) ) ) ).

% PartialSA.bigger_sum
thf(fact_11_PartialSA_Ogreater__def,axiom,
    ( greater
    = ( ^ [A2: state,B: state] :
        ? [C2: state] :
          ( ( some_state @ A2 )
          = ( plus @ B @ C2 ) ) ) ) ).

% PartialSA.greater_def
thf(fact_12_PartialSA_Ogreater__equiv,axiom,
    ( greater
    = ( ^ [A2: state,B: state] :
        ? [C2: state] :
          ( ( some_state @ A2 )
          = ( plus @ C2 @ B ) ) ) ) ).

% PartialSA.greater_equiv
thf(fact_13_calculation_I5_J,axiom,
    ( ( some_state @ ba )
    = ( plus @ ( r @ a2 @ wa ) @ a2 ) ) ).

% calculation(5)
thf(fact_14_asso1,axiom,
    ! [A3: state,B2: state,Ab: state,C: state,Bc: state] :
      ( ( ( ( plus @ A3 @ B2 )
          = ( some_state @ Ab ) )
        & ( ( plus @ B2 @ C )
          = ( some_state @ Bc ) ) )
     => ( ( plus @ Ab @ C )
        = ( plus @ A3 @ Bc ) ) ) ).

% asso1
thf(fact_15_positivity,axiom,
    ! [A3: state,B2: state,C: state] :
      ( ( ( plus @ A3 @ B2 )
        = ( some_state @ C ) )
     => ( ( ( some_state @ C )
          = ( plus @ C @ C ) )
       => ( ( some_state @ A3 )
          = ( plus @ A3 @ A3 ) ) ) ) ).

% positivity
thf(fact_16_commutative,axiom,
    ( plus
    = ( ^ [A2: state,B: state] : ( plus @ B @ A2 ) ) ) ).

% commutative
thf(fact_17_PartialSA_Obigger__sum__smaller,axiom,
    ! [C: state,A3: state,B2: state,A4: state] :
      ( ( ( some_state @ C )
        = ( plus @ A3 @ B2 ) )
     => ( ( greater @ A3 @ A4 )
       => ? [B3: state] :
            ( ( greater @ B3 @ B2 )
            & ( ( some_state @ C )
              = ( plus @ A4 @ B3 ) ) ) ) ) ).

% PartialSA.bigger_sum_smaller
thf(fact_18_PartialSA_Oaddition__bigger,axiom,
    ! [A4: state,A3: state,X: state,B2: state,X2: state] :
      ( ( greater @ A4 @ A3 )
     => ( ( ( some_state @ X )
          = ( plus @ A4 @ B2 ) )
       => ( ( ( some_state @ X2 )
            = ( plus @ A3 @ B2 ) )
         => ( greater @ X @ X2 ) ) ) ) ).

% PartialSA.addition_bigger
thf(fact_19_asm1,axiom,
    ( ( member_state @ a2 @ a )
    & ( ( some_state @ x )
      = ( plus @ ( r @ a2 @ w ) @ a2 ) ) ) ).

% asm1
thf(fact_20_calculation_I2_J,axiom,
    defined @ a2 @ ( multiply @ p @ w ) ).

% calculation(2)
thf(fact_21_r_I2_J,axiom,
    ! [A3: state,X2: state] :
      ( ( ( member_state @ A3 @ a )
        & ( ( some_state @ X2 )
          = ( plus @ ( r @ A3 @ wb ) @ A3 ) ) )
     => ( member_state @ X2 @ b ) ) ).

% r(2)
thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ba_O_ASome_Aba_A_061_AR_Aa_Awa_A_092_060oplus_062_Aa_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Ba: state] :
        ( ( some_state @ Ba )
       != ( plus @ ( r @ a2 @ wa ) @ a2 ) ) ).

% \<open>\<And>thesis. (\<And>ba. Some ba = R a wa \<oplus> a \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_23__092_060open_062_092_060not_062_Ascalable_Awa_Aa_092_060close_062,axiom,
    ~ ( scalable @ wa @ a2 ) ).

% \<open>\<not> scalable wa a\<close>
thf(fact_24__092_060open_062xa_A_092_060succeq_062_Amultiply_A_092_060alpha_062_Awa_092_060close_062,axiom,
    greater @ xa @ ( multiply @ alpha @ wa ) ).

% \<open>xa \<succeq> multiply \<alpha> wa\<close>
thf(fact_25__092_060open_062wb_A_092_060in_062_Acwand_AA_AB_092_060close_062,axiom,
    member_state @ wb @ ( cwand @ a @ b ) ).

% \<open>wb \<in> cwand A B\<close>
thf(fact_26_option_Oinject,axiom,
    ! [X22: state,Y2: state] :
      ( ( ( some_state @ X22 )
        = ( some_state @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% option.inject
thf(fact_27_option_Oinject,axiom,
    ! [X22: val,Y2: val] :
      ( ( ( some_val @ X22 )
        = ( some_val @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% option.inject
thf(fact_28__092_060open_062_092_060And_062thesis_O_A_I_092_060lbrakk_062_092_060And_062a_Ax_O_Aa_A_092_060in_062_AA_A_092_060and_062_ASome_Ax_A_061_AR_Aa_Awa_A_092_060oplus_062_Aa_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AB_059_A_092_060And_062a_Ax_O_Aa_A_092_060in_062_AA_A_092_060and_062_ASome_Ax_A_061_AR_Aa_Awb_A_092_060oplus_062_Aa_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AB_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ( ! [A5: state,X3: state] :
          ( ( ( member_state @ A5 @ a )
            & ( ( some_state @ X3 )
              = ( plus @ ( r @ A5 @ wa ) @ A5 ) ) )
         => ( member_state @ X3 @ b ) )
     => ~ ! [A5: state,X3: state] :
            ( ( ( member_state @ A5 @ a )
              & ( ( some_state @ X3 )
                = ( plus @ ( r @ A5 @ wb ) @ A5 ) ) )
           => ( member_state @ X3 @ b ) ) ) ).

% \<open>\<And>thesis. (\<lbrakk>\<And>a x. a \<in> A \<and> Some x = R a wa \<oplus> a \<Longrightarrow> x \<in> B; \<And>a x. a \<in> A \<and> Some x = R a wb \<oplus> a \<Longrightarrow> x \<in> B\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_29__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062wa_Awb_O_A_092_060lbrakk_062wa_A_092_060in_062_Acwand_AA_AB_059_Awb_A_092_060in_062_Acwand_AA_AB_059_Axa_A_092_060succeq_062_Amultiply_A_092_060alpha_062_Awa_059_Axb_A_092_060succeq_062_Amultiply_A_092_060beta_062_Awb_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Wa: state] :
        ( ( member_state @ Wa @ ( cwand @ a @ b ) )
       => ! [Wb: state] :
            ( ( member_state @ Wb @ ( cwand @ a @ b ) )
           => ( ( greater @ xa @ ( multiply @ alpha @ Wa ) )
             => ~ ( greater @ xb @ ( multiply @ beta @ Wb ) ) ) ) ) ).

% \<open>\<And>thesis. (\<And>wa wb. \<lbrakk>wa \<in> cwand A B; wb \<in> cwand A B; xa \<succeq> multiply \<alpha> wa; xb \<succeq> multiply \<beta> wb\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_30__092_060open_062xb_A_092_060in_062_Amultiply__sem__assertion_A_092_060beta_062_A_Icwand_AA_AB_J_092_060close_062,axiom,
    member_state @ xb @ ( multip8064567061438756306ertion @ beta @ ( cwand @ a @ b ) ) ).

% \<open>xb \<in> multiply_sem_assertion \<beta> (cwand A B)\<close>
thf(fact_31_wandI,axiom,
    ! [A6: set_state,W: state,B4: set_state] :
      ( ! [A7: state,X4: state] :
          ( ( ( member_state @ A7 @ A6 )
            & ( ( some_state @ X4 )
              = ( plus @ A7 @ W ) ) )
         => ( member_state @ X4 @ B4 ) )
     => ( member_state @ W @ ( wand @ A6 @ B4 ) ) ) ).

% wandI
thf(fact_32__092_060open_062wa_A_092_060in_062_Acwand_AA_AB_092_060close_062,axiom,
    member_state @ wa @ ( cwand @ a @ b ) ).

% \<open>wa \<in> cwand A B\<close>
thf(fact_33__092_060open_062xa_A_092_060in_062_Amultiply__sem__assertion_A_092_060alpha_062_A_Icwand_AA_AB_J_092_060close_062,axiom,
    member_state @ xa @ ( multip8064567061438756306ertion @ alpha @ ( cwand @ a @ b ) ) ).

% \<open>xa \<in> multiply_sem_assertion \<alpha> (cwand A B)\<close>
thf(fact_34__092_060open_062R_Aa_Awa_A_124_D_124_Aa_092_060close_062,axiom,
    defined @ ( r @ a2 @ wa ) @ a2 ).

% \<open>R a wa |#| a\<close>
thf(fact_35_r_I1_J,axiom,
    ! [A3: state,X2: state] :
      ( ( ( member_state @ A3 @ a )
        & ( ( some_state @ X2 )
          = ( plus @ ( r @ A3 @ wa ) @ A3 ) ) )
     => ( member_state @ X2 @ b ) ) ).

% r(1)
thf(fact_36__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xa_Axb_O_A_092_060lbrakk_062Some_Aw_A_061_Axa_A_092_060oplus_062_Axb_059_Axa_A_092_060in_062_Amultiply__sem__assertion_A_092_060alpha_062_A_Icwand_AA_AB_J_059_Axb_A_092_060in_062_Amultiply__sem__assertion_A_092_060beta_062_A_Icwand_AA_AB_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Xa: state,Xb: state] :
        ( ( ( some_state @ w )
          = ( plus @ Xa @ Xb ) )
       => ( ( member_state @ Xa @ ( multip8064567061438756306ertion @ alpha @ ( cwand @ a @ b ) ) )
         => ~ ( member_state @ Xb @ ( multip8064567061438756306ertion @ beta @ ( cwand @ a @ b ) ) ) ) ) ).

% \<open>\<And>thesis. (\<And>xa xb. \<lbrakk>Some w = xa \<oplus> xb; xa \<in> multiply_sem_assertion \<alpha> (cwand A B); xb \<in> multiply_sem_assertion \<beta> (cwand A B)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_37_asm,axiom,
    member_state @ w @ ( add_set @ ( multip8064567061438756306ertion @ alpha @ ( cwand @ a @ b ) ) @ ( multip8064567061438756306ertion @ beta @ ( cwand @ a @ b ) ) ) ).

% asm
thf(fact_38_PartialSA_Osmaller__compatible,axiom,
    ! [A4: state,B2: state,A3: state] :
      ( ( defined @ A4 @ B2 )
     => ( ( greater @ A4 @ A3 )
       => ( defined @ A3 @ B2 ) ) ) ).

% PartialSA.smaller_compatible
thf(fact_39_R__compatible__same,axiom,
    ! [A3: state,W: state] :
      ( ( defined @ A3 @ W )
     => ( ( r @ A3 @ W )
        = W ) ) ).

% R_compatible_same
thf(fact_40_in__multiply__refl,axiom,
    ! [X2: state,A6: set_state,P: prat] :
      ( ( member_state @ X2 @ A6 )
     => ( member_state @ ( multiply @ P @ X2 ) @ ( multip8064567061438756306ertion @ P @ A6 ) ) ) ).

% in_multiply_refl
thf(fact_41_PartialSA_Odefined__sum__move,axiom,
    ! [A3: state,B2: state,X2: state,Y: state,A4: state] :
      ( ( defined @ A3 @ B2 )
     => ( ( ( some_state @ B2 )
          = ( plus @ X2 @ Y ) )
       => ( ( ( some_state @ A4 )
            = ( plus @ A3 @ X2 ) )
         => ( defined @ A4 @ Y ) ) ) ) ).

% PartialSA.defined_sum_move
thf(fact_42_in__multiply__sem,axiom,
    ! [X2: state,P: prat,A6: set_state] :
      ( ( member_state @ X2 @ ( multip8064567061438756306ertion @ P @ A6 ) )
     => ? [X4: state] :
          ( ( member_state @ X4 @ A6 )
          & ( greater @ X2 @ ( multiply @ P @ X4 ) ) ) ) ).

% in_multiply_sem
thf(fact_43_in__cwand,axiom,
    ! [A6: set_state,W: state,B4: set_state] :
      ( ! [A7: state,X4: state] :
          ( ( ( member_state @ A7 @ A6 )
            & ( ( some_state @ X4 )
              = ( plus @ ( r @ A7 @ W ) @ A7 ) ) )
         => ( member_state @ X4 @ B4 ) )
     => ( member_state @ W @ ( cwand @ A6 @ B4 ) ) ) ).

% in_cwand
thf(fact_44_scalable__def,axiom,
    ( scalable
    = ( ^ [W2: state,A2: state] :
        ! [X5: state] :
          ( ( member_state @ X5 @ ( scaled @ W2 ) )
         => ~ ( defined @ A2 @ X5 ) ) ) ) ).

% scalable_def
thf(fact_45_PartialSA_Osmaller__pure__sum__smaller,axiom,
    ! [Y: state,A3: state,B2: state,X2: state] :
      ( ( greater @ Y @ A3 )
     => ( ( greater @ Y @ B2 )
       => ( ( ( some_state @ X2 )
            = ( plus @ A3 @ B2 ) )
         => ( ( sep_pure_state @ plus @ B2 )
           => ( greater @ Y @ X2 ) ) ) ) ) ).

% PartialSA.smaller_pure_sum_smaller
thf(fact_46_mem__Collect__eq,axiom,
    ! [A3: produc3882902684156697774_state,P2: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ A3 @ ( collec394671971739345689_state @ P2 ) )
      = ( P2 @ A3 ) ) ).

% mem_Collect_eq
thf(fact_47_mem__Collect__eq,axiom,
    ! [A3: produc7272280185086996969_state,P2: produc7272280185086996969_state > $o] :
      ( ( member7461423308196221312_state @ A3 @ ( collec906845016635587262_state @ P2 ) )
      = ( P2 @ A3 ) ) ).

% mem_Collect_eq
thf(fact_48_mem__Collect__eq,axiom,
    ! [A3: produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ A3 @ ( collec7475294502966882545on_val @ P2 ) )
      = ( P2 @ A3 ) ) ).

% mem_Collect_eq
thf(fact_49_mem__Collect__eq,axiom,
    ! [A3: state,P2: state > $o] :
      ( ( member_state @ A3 @ ( collect_state @ P2 ) )
      = ( P2 @ A3 ) ) ).

% mem_Collect_eq
thf(fact_50_Collect__mem__eq,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ A6 ) )
      = A6 ) ).

% Collect_mem_eq
thf(fact_51_Collect__mem__eq,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ A6 ) )
      = A6 ) ).

% Collect_mem_eq
thf(fact_52_Collect__mem__eq,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ A6 ) )
      = A6 ) ).

% Collect_mem_eq
thf(fact_53_Collect__mem__eq,axiom,
    ! [A6: set_state] :
      ( ( collect_state
        @ ^ [X5: state] : ( member_state @ X5 @ A6 ) )
      = A6 ) ).

% Collect_mem_eq
thf(fact_54_Collect__cong,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
          = ( Q @ X4 ) )
     => ( ( collec906845016635587262_state @ P2 )
        = ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_cong
thf(fact_55_Collect__cong,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X4: produc9003781588162623004on_val] :
          ( ( P2 @ X4 )
          = ( Q @ X4 ) )
     => ( ( collec7475294502966882545on_val @ P2 )
        = ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_cong
thf(fact_56_Collect__cong,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
          = ( Q @ X4 ) )
     => ( ( collect_state @ P2 )
        = ( collect_state @ Q ) ) ) ).

% Collect_cong
thf(fact_57_binary__same,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( binary @ A6 )
     => ( ( intuitionistic @ B4 )
       => ( ord_le2494988322063910608_state @ ( wand @ A6 @ B4 ) @ ( cwand @ A6 @ B4 ) ) ) ) ).

% binary_same
thf(fact_58_PartialSA_Omono__propI,axiom,
    ! [P2: state > $o] :
      ( ! [X4: state,Y3: state] :
          ( ( ( greater @ Y3 @ X4 )
            & ( P2 @ X4 ) )
         => ( P2 @ Y3 ) )
     => ( sep_mono_prop_state @ plus @ P2 ) ) ).

% PartialSA.mono_propI
thf(fact_59_PartialSA_Omono__prop__def,axiom,
    ! [P2: state > $o] :
      ( ( sep_mono_prop_state @ plus @ P2 )
      = ( ! [X5: state,Y4: state] :
            ( ( ( greater @ Y4 @ X5 )
              & ( P2 @ X5 ) )
           => ( P2 @ Y4 ) ) ) ) ).

% PartialSA.mono_prop_def
thf(fact_60_PartialSA_Ointuitionistic__def,axiom,
    ! [A6: state > $o] :
      ( ( packag8361946002163212404_state @ plus @ A6 )
      = ( ! [Phi3: state,Phi4: state] :
            ( ( ( greater @ Phi3 @ Phi4 )
              & ( A6 @ Phi4 ) )
           => ( A6 @ Phi3 ) ) ) ) ).

% PartialSA.intuitionistic_def
thf(fact_61_PartialSA_Ominus__sum,axiom,
    ! [A3: state,B2: state,C: state,X2: state] :
      ( ( ( some_state @ A3 )
        = ( plus @ B2 @ C ) )
     => ( ( greater @ X2 @ A3 )
       => ( ( minus @ X2 @ A3 )
          = ( minus @ ( minus @ X2 @ B2 ) @ C ) ) ) ) ).

% PartialSA.minus_sum
thf(fact_62_PartialSA_Ominus__some,axiom,
    ! [A3: state,B2: state] :
      ( ( greater @ A3 @ B2 )
     => ( ( some_state @ A3 )
        = ( plus @ B2 @ ( minus @ A3 @ B2 ) ) ) ) ).

% PartialSA.minus_some
thf(fact_63_PartialSA_Ominus__bigger,axiom,
    ! [X2: state,A3: state,B2: state] :
      ( ( ( some_state @ X2 )
        = ( plus @ A3 @ B2 ) )
     => ( greater @ ( minus @ X2 @ A3 ) @ B2 ) ) ).

% PartialSA.minus_bigger
thf(fact_64_PartialSA_Ominus__and__plus,axiom,
    ! [Omega: state,Omega2: state,R: state,A3: state] :
      ( ( ( some_state @ Omega )
        = ( plus @ Omega2 @ R ) )
     => ( ( greater @ Omega2 @ A3 )
       => ( ( some_state @ ( minus @ Omega @ A3 ) )
          = ( plus @ ( minus @ Omega2 @ A3 ) @ R ) ) ) ) ).

% PartialSA.minus_and_plus
thf(fact_65_PartialSA_Oprove__last__completeness,axiom,
    ! [A4: state,A3: state,Nf1: state,F2: state] :
      ( ( greater @ A4 @ A3 )
     => ( ( ( some_state @ A3 )
          = ( plus @ Nf1 @ F2 ) )
       => ( greater @ ( minus @ A4 @ Nf1 ) @ F2 ) ) ) ).

% PartialSA.prove_last_completeness
thf(fact_66_PartialSA_Oadd__set__commm,axiom,
    ( add_set
    = ( ^ [A: set_state,B5: set_state] : ( add_set @ B5 @ A ) ) ) ).

% PartialSA.add_set_commm
thf(fact_67_PartialSA_Oadd__set__asso,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( add_set @ ( add_set @ A6 @ B4 ) @ C3 )
      = ( add_set @ A6 @ ( add_set @ B4 @ C3 ) ) ) ).

% PartialSA.add_set_asso
thf(fact_68_w__in__scaled,axiom,
    ! [W: state] : ( member_state @ W @ ( scaled @ W ) ) ).

% w_in_scaled
thf(fact_69_PartialSA_Ogreater__minus__trans,axiom,
    ! [Y: state,X2: state,A3: state] :
      ( ( greater @ Y @ X2 )
     => ( ( greater @ X2 @ A3 )
       => ( greater @ ( minus @ Y @ A3 ) @ ( minus @ X2 @ A3 ) ) ) ) ).

% PartialSA.greater_minus_trans
thf(fact_70_PartialSA_Ominus__smaller,axiom,
    ! [X2: state,A3: state] :
      ( ( greater @ X2 @ A3 )
     => ( greater @ X2 @ ( minus @ X2 @ A3 ) ) ) ).

% PartialSA.minus_smaller
thf(fact_71_PartialSA_Ominus__default,axiom,
    ! [B2: state,A3: state] :
      ( ~ ( greater @ B2 @ A3 )
     => ( ( minus @ B2 @ A3 )
        = B2 ) ) ).

% PartialSA.minus_default
thf(fact_72_PartialSA_Opure__def,axiom,
    ! [A3: state] :
      ( ( sep_pure_state @ plus @ A3 )
      = ( ( some_state @ A3 )
        = ( plus @ A3 @ A3 ) ) ) ).

% PartialSA.pure_def
thf(fact_73_PartialSA_Opure__stable,axiom,
    ! [A3: state,B2: state,C: state] :
      ( ( sep_pure_state @ plus @ A3 )
     => ( ( sep_pure_state @ plus @ B2 )
       => ( ( ( some_state @ C )
            = ( plus @ A3 @ B2 ) )
         => ( sep_pure_state @ plus @ C ) ) ) ) ).

% PartialSA.pure_stable
thf(fact_74_PartialSA_Opure__smaller,axiom,
    ! [A3: state,B2: state] :
      ( ( sep_pure_state @ plus @ A3 )
     => ( ( greater @ A3 @ B2 )
       => ( sep_pure_state @ plus @ B2 ) ) ) ).

% PartialSA.pure_smaller
thf(fact_75_PartialSA_Oadd__set__elem,axiom,
    ! [Phi: state,A6: set_state,B4: set_state] :
      ( ( member_state @ Phi @ ( add_set @ A6 @ B4 ) )
      = ( ? [A2: state,B: state] :
            ( ( ( some_state @ Phi )
              = ( plus @ A2 @ B ) )
            & ( member_state @ A2 @ A6 )
            & ( member_state @ B @ B4 ) ) ) ) ).

% PartialSA.add_set_elem
thf(fact_76_PartialSA_Ox__elem__set__product,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ( member_state @ X2 @ ( add_set @ A6 @ B4 ) )
      = ( ? [A2: state,B: state] :
            ( ( member_state @ A2 @ A6 )
            & ( member_state @ B @ B4 )
            & ( ( some_state @ X2 )
              = ( plus @ A2 @ B ) ) ) ) ) ).

% PartialSA.x_elem_set_product
thf(fact_77_cwand__stronger,axiom,
    ! [A6: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( cwand @ A6 @ B4 ) @ ( wand @ A6 @ B4 ) ) ).

% cwand_stronger
thf(fact_78_subsetI,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X4 @ A6 )
         => ( member7461423308196221312_state @ X4 @ B4 ) )
     => ( ord_le4032880777312351359_state @ A6 @ B4 ) ) ).

% subsetI
thf(fact_79_subsetI,axiom,
    ! [A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X4: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X4 @ A6 )
         => ( member2879030624002546611on_val @ X4 @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A6 @ B4 ) ) ).

% subsetI
thf(fact_80_subsetI,axiom,
    ! [A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X4 @ A6 )
         => ( member6715010751053357271_state @ X4 @ B4 ) )
     => ( ord_le6483787752022044334_state @ A6 @ B4 ) ) ).

% subsetI
thf(fact_81_subsetI,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ A6 )
         => ( member_state @ X4 @ B4 ) )
     => ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ).

% subsetI
thf(fact_82_double__inclusion,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ A6 )
       => ( A6 = B4 ) ) ) ).

% double_inclusion
thf(fact_83_order__refl,axiom,
    ! [X2: set_state] : ( ord_le2494988322063910608_state @ X2 @ X2 ) ).

% order_refl
thf(fact_84_dual__order_Orefl,axiom,
    ! [A3: set_state] : ( ord_le2494988322063910608_state @ A3 @ A3 ) ).

% dual_order.refl
thf(fact_85_PartialSA_Omono__pruner__def,axiom,
    ! [P: state > $o] :
      ( ( packag2456304381420842418_state @ plus @ P )
      = ( ! [Phi3: state,Phi4: state,R2: state] :
            ( ( ( sep_pure_state @ plus @ R2 )
              & ( P @ Phi4 )
              & ( ( some_state @ Phi3 )
                = ( plus @ Phi4 @ R2 ) ) )
           => ( P @ Phi3 ) ) ) ) ).

% PartialSA.mono_pruner_def
thf(fact_86_sep__algebra_Omono__prop_Ocong,axiom,
    sep_mono_prop_state = sep_mono_prop_state ).

% sep_algebra.mono_prop.cong
thf(fact_87_package__logic_Ointuitionistic_Ocong,axiom,
    packag8361946002163212404_state = packag8361946002163212404_state ).

% package_logic.intuitionistic.cong
thf(fact_88_PartialSA_OminusI,axiom,
    ! [B2: state,A3: state,X2: state] :
      ( ( ( some_state @ B2 )
        = ( plus @ A3 @ X2 ) )
     => ( ( greater @ X2 @ ( core @ B2 ) )
       => ( X2
          = ( minus @ B2 @ A3 ) ) ) ) ).

% PartialSA.minusI
thf(fact_89_PartialSA_Ominus__equiv__def,axiom,
    ! [B2: state,A3: state] :
      ( ( greater @ B2 @ A3 )
     => ( ( ( some_state @ B2 )
          = ( plus @ A3 @ ( minus @ B2 @ A3 ) ) )
        & ( greater @ ( minus @ B2 @ A3 ) @ ( core @ B2 ) ) ) ) ).

% PartialSA.minus_equiv_def
thf(fact_90_sep__algebra_Opure_Ocong,axiom,
    sep_pure_state = sep_pure_state ).

% sep_algebra.pure.cong
thf(fact_91_PartialSA_Ox__elem__set__product__splus,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ( member_state @ X2 @ ( add_set @ A6 @ B4 ) )
      = ( ? [A2: state,B: state] :
            ( ( member_state @ A2 @ A6 )
            & ( member_state @ B @ B4 )
            & ( ( some_state @ X2 )
              = ( sep_splus_state @ plus @ ( some_state @ A2 ) @ ( some_state @ B ) ) ) ) ) ) ).

% PartialSA.x_elem_set_product_splus
thf(fact_92_package__logic_Omono__pruner_Ocong,axiom,
    packag2456304381420842418_state = packag2456304381420842418_state ).

% package_logic.mono_pruner.cong
thf(fact_93_sep__algebra_Osplus_Ocong,axiom,
    sep_splus_state = sep_splus_state ).

% sep_algebra.splus.cong
thf(fact_94_PartialSA_Ocore__mono,axiom,
    ! [A3: state,B2: state] :
      ( ( greater @ A3 @ B2 )
     => ( greater @ ( core @ A3 ) @ ( core @ B2 ) ) ) ).

% PartialSA.core_mono
thf(fact_95_PartialSA_Ominus__core,axiom,
    ! [A3: state,B2: state] :
      ( ( core @ ( minus @ A3 @ B2 ) )
      = ( core @ A3 ) ) ).

% PartialSA.minus_core
thf(fact_96_PartialSA_Ominus__core__weaker,axiom,
    ! [A3: state,B2: state] :
      ( ( core @ ( minus @ A3 @ B2 ) )
      = ( minus @ ( core @ A3 ) @ ( core @ B2 ) ) ) ).

% PartialSA.minus_core_weaker
thf(fact_97_PartialSA_Osplus__comm,axiom,
    ! [A3: option_state,B2: option_state] :
      ( ( sep_splus_state @ plus @ A3 @ B2 )
      = ( sep_splus_state @ plus @ B2 @ A3 ) ) ).

% PartialSA.splus_comm
thf(fact_98_PartialSA_Osplus__asso,axiom,
    ! [A3: option_state,B2: option_state,C: option_state] :
      ( ( sep_splus_state @ plus @ ( sep_splus_state @ plus @ A3 @ B2 ) @ C )
      = ( sep_splus_state @ plus @ A3 @ ( sep_splus_state @ plus @ B2 @ C ) ) ) ).

% PartialSA.splus_asso
thf(fact_99_core__is__smaller,axiom,
    ( some_state
    = ( ^ [X5: state] : ( plus @ X5 @ ( core @ X5 ) ) ) ) ).

% core_is_smaller
thf(fact_100_core__is__pure,axiom,
    ! [X2: state] :
      ( ( some_state @ ( core @ X2 ) )
      = ( plus @ ( core @ X2 ) @ ( core @ X2 ) ) ) ).

% core_is_pure
thf(fact_101_cancellative,axiom,
    ! [A3: state,B2: state,X2: state,Y: state] :
      ( ( ( some_state @ A3 )
        = ( plus @ B2 @ X2 ) )
     => ( ( ( some_state @ A3 )
          = ( plus @ B2 @ Y ) )
       => ( ( ( core @ X2 )
            = ( core @ Y ) )
         => ( X2 = Y ) ) ) ) ).

% cancellative
thf(fact_102_core__sum,axiom,
    ! [C: state,A3: state,B2: state] :
      ( ( ( some_state @ C )
        = ( plus @ A3 @ B2 ) )
     => ( ( some_state @ ( core @ C ) )
        = ( plus @ ( core @ A3 ) @ ( core @ B2 ) ) ) ) ).

% core_sum
thf(fact_103_core__max,axiom,
    ! [X2: state,C: state] :
      ( ( ( some_state @ X2 )
        = ( plus @ X2 @ C ) )
     => ? [R3: state] :
          ( ( some_state @ ( core @ X2 ) )
          = ( plus @ C @ R3 ) ) ) ).

% core_max
thf(fact_104_PartialSA_Osmaller__compatible__core,axiom,
    ! [Y: state,X2: state] :
      ( ( greater @ Y @ X2 )
     => ( defined @ X2 @ ( core @ Y ) ) ) ).

% PartialSA.smaller_compatible_core
thf(fact_105_PartialSA_Osplus__develop,axiom,
    ! [A3: state,B2: state,C: state,D: state] :
      ( ( ( some_state @ A3 )
        = ( plus @ B2 @ C ) )
     => ( ( plus @ A3 @ D )
        = ( sep_splus_state @ plus @ ( sep_splus_state @ plus @ ( some_state @ B2 ) @ ( some_state @ C ) ) @ ( some_state @ D ) ) ) ) ).

% PartialSA.splus_develop
thf(fact_106_PartialSA_Osplus_Osimps_I3_J,axiom,
    ! [A3: state,B2: state] :
      ( ( sep_splus_state @ plus @ ( some_state @ A3 ) @ ( some_state @ B2 ) )
      = ( plus @ A3 @ B2 ) ) ).

% PartialSA.splus.simps(3)
thf(fact_107_PartialSA_Oextract__core,axiom,
    ! [B2: state,A3: state,X2: state] :
      ( ( ( ( some_state @ B2 )
          = ( plus @ A3 @ X2 ) )
        & ( greater @ X2 @ ( core @ B2 ) ) )
     => ( ( core @ X2 )
        = ( core @ B2 ) ) ) ).

% PartialSA.extract_core
thf(fact_108_PartialSA_Ominus__exists,axiom,
    ! [B2: state,A3: state] :
      ( ( greater @ B2 @ A3 )
     => ? [X4: state] :
          ( ( ( some_state @ B2 )
            = ( plus @ A3 @ X4 ) )
          & ( greater @ X4 @ ( core @ B2 ) ) ) ) ).

% PartialSA.minus_exists
thf(fact_109_PartialSA_Ominus__unique,axiom,
    ! [B2: state,A3: state,X2: state,Y: state] :
      ( ( ( ( some_state @ B2 )
          = ( plus @ A3 @ X2 ) )
        & ( greater @ X2 @ ( core @ B2 ) ) )
     => ( ( ( ( some_state @ B2 )
            = ( plus @ A3 @ Y ) )
          & ( greater @ Y @ ( core @ B2 ) ) )
       => ( X2 = Y ) ) ) ).

% PartialSA.minus_unique
thf(fact_110_PartialSA_Osmaller__than__core,axiom,
    ! [Y: state,X2: state,Z: state] :
      ( ( greater @ Y @ X2 )
     => ( ( ( some_state @ Z )
          = ( plus @ X2 @ ( core @ Y ) ) )
       => ( ( core @ Z )
          = ( core @ Y ) ) ) ) ).

% PartialSA.smaller_than_core
thf(fact_111_PartialSA_Obigger__core__sum__defined,axiom,
    ! [A3: state,B2: state] :
      ( ( greater @ ( core @ A3 ) @ B2 )
     => ( ( some_state @ A3 )
        = ( plus @ A3 @ B2 ) ) ) ).

% PartialSA.bigger_core_sum_defined
thf(fact_112_PartialSA_Ogreater__than__sum__exists,axiom,
    ! [A3: state,B2: state,B1: state,B22: state] :
      ( ( greater @ A3 @ B2 )
     => ( ( ( some_state @ B2 )
          = ( plus @ B1 @ B22 ) )
       => ? [R3: state] :
            ( ( ( some_state @ A3 )
              = ( plus @ R3 @ B22 ) )
            & ( greater @ ( core @ R3 ) @ ( core @ A3 ) )
            & ( greater @ R3 @ B1 ) ) ) ) ).

% PartialSA.greater_than_sum_exists
thf(fact_113_PartialSA_Ominus__equiv__def__any__elem,axiom,
    ! [X2: state,A3: state,B2: state] :
      ( ( ( some_state @ X2 )
        = ( plus @ A3 @ B2 ) )
     => ( ( some_state @ ( minus @ X2 @ A3 ) )
        = ( plus @ B2 @ ( core @ X2 ) ) ) ) ).

% PartialSA.minus_equiv_def_any_elem
thf(fact_114_order__antisym__conv,axiom,
    ! [Y: set_state,X2: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X2 )
     => ( ( ord_le2494988322063910608_state @ X2 @ Y )
        = ( X2 = Y ) ) ) ).

% order_antisym_conv
thf(fact_115_ord__le__eq__subst,axiom,
    ! [A3: set_state,B2: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ B2 )
     => ( ( ( F @ B2 )
          = C )
       => ( ! [X4: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X4 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A3 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_116_ord__eq__le__subst,axiom,
    ! [A3: set_state,F: set_state > set_state,B2: set_state,C: set_state] :
      ( ( A3
        = ( F @ B2 ) )
     => ( ( ord_le2494988322063910608_state @ B2 @ C )
       => ( ! [X4: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X4 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A3 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_117_order__eq__refl,axiom,
    ! [X2: set_state,Y: set_state] :
      ( ( X2 = Y )
     => ( ord_le2494988322063910608_state @ X2 @ Y ) ) ).

% order_eq_refl
thf(fact_118_order__subst2,axiom,
    ! [A3: set_state,B2: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ B2 )
     => ( ( ord_le2494988322063910608_state @ ( F @ B2 ) @ C )
       => ( ! [X4: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X4 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A3 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_119_order__subst1,axiom,
    ! [A3: set_state,F: set_state > set_state,B2: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ ( F @ B2 ) )
     => ( ( ord_le2494988322063910608_state @ B2 @ C )
       => ( ! [X4: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X4 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A3 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_120_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_state,Z2: set_state] : ( Y5 = Z2 ) )
    = ( ^ [A2: set_state,B: set_state] :
          ( ( ord_le2494988322063910608_state @ A2 @ B )
          & ( ord_le2494988322063910608_state @ B @ A2 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_121_antisym,axiom,
    ! [A3: set_state,B2: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ B2 )
     => ( ( ord_le2494988322063910608_state @ B2 @ A3 )
       => ( A3 = B2 ) ) ) ).

% antisym
thf(fact_122_dual__order_Otrans,axiom,
    ! [B2: set_state,A3: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ B2 @ A3 )
     => ( ( ord_le2494988322063910608_state @ C @ B2 )
       => ( ord_le2494988322063910608_state @ C @ A3 ) ) ) ).

% dual_order.trans
thf(fact_123_dual__order_Oantisym,axiom,
    ! [B2: set_state,A3: set_state] :
      ( ( ord_le2494988322063910608_state @ B2 @ A3 )
     => ( ( ord_le2494988322063910608_state @ A3 @ B2 )
       => ( A3 = B2 ) ) ) ).

% dual_order.antisym
thf(fact_124_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y5: set_state,Z2: set_state] : ( Y5 = Z2 ) )
    = ( ^ [A2: set_state,B: set_state] :
          ( ( ord_le2494988322063910608_state @ B @ A2 )
          & ( ord_le2494988322063910608_state @ A2 @ B ) ) ) ) ).

% dual_order.eq_iff
thf(fact_125_order__trans,axiom,
    ! [X2: set_state,Y: set_state,Z: set_state] :
      ( ( ord_le2494988322063910608_state @ X2 @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ Z )
       => ( ord_le2494988322063910608_state @ X2 @ Z ) ) ) ).

% order_trans
thf(fact_126_order_Otrans,axiom,
    ! [A3: set_state,B2: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ B2 )
     => ( ( ord_le2494988322063910608_state @ B2 @ C )
       => ( ord_le2494988322063910608_state @ A3 @ C ) ) ) ).

% order.trans
thf(fact_127_order__antisym,axiom,
    ! [X2: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X2 @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ X2 )
       => ( X2 = Y ) ) ) ).

% order_antisym
thf(fact_128_ord__le__eq__trans,axiom,
    ! [A3: set_state,B2: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ B2 )
     => ( ( B2 = C )
       => ( ord_le2494988322063910608_state @ A3 @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_129_ord__eq__le__trans,axiom,
    ! [A3: set_state,B2: set_state,C: set_state] :
      ( ( A3 = B2 )
     => ( ( ord_le2494988322063910608_state @ B2 @ C )
       => ( ord_le2494988322063910608_state @ A3 @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_130_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_state,Z2: set_state] : ( Y5 = Z2 ) )
    = ( ^ [X5: set_state,Y4: set_state] :
          ( ( ord_le2494988322063910608_state @ X5 @ Y4 )
          & ( ord_le2494988322063910608_state @ Y4 @ X5 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_131_Collect__mono__iff,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P2 ) @ ( collec906845016635587262_state @ Q ) )
      = ( ! [X5: produc7272280185086996969_state] :
            ( ( P2 @ X5 )
           => ( Q @ X5 ) ) ) ) ).

% Collect_mono_iff
thf(fact_132_Collect__mono__iff,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P2 ) @ ( collec7475294502966882545on_val @ Q ) )
      = ( ! [X5: produc9003781588162623004on_val] :
            ( ( P2 @ X5 )
           => ( Q @ X5 ) ) ) ) ).

% Collect_mono_iff
thf(fact_133_Collect__mono__iff,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ ( collect_state @ P2 ) @ ( collect_state @ Q ) )
      = ( ! [X5: state] :
            ( ( P2 @ X5 )
           => ( Q @ X5 ) ) ) ) ).

% Collect_mono_iff
thf(fact_134_set__eq__subset,axiom,
    ( ( ^ [Y5: set_state,Z2: set_state] : ( Y5 = Z2 ) )
    = ( ^ [A: set_state,B5: set_state] :
          ( ( ord_le2494988322063910608_state @ A @ B5 )
          & ( ord_le2494988322063910608_state @ B5 @ A ) ) ) ) ).

% set_eq_subset
thf(fact_135_subset__trans,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
       => ( ord_le2494988322063910608_state @ A6 @ C3 ) ) ) ).

% subset_trans
thf(fact_136_Collect__mono,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
         => ( Q @ X4 ) )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P2 ) @ ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_mono
thf(fact_137_Collect__mono,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X4: produc9003781588162623004on_val] :
          ( ( P2 @ X4 )
         => ( Q @ X4 ) )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P2 ) @ ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_mono
thf(fact_138_Collect__mono,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
         => ( Q @ X4 ) )
     => ( ord_le2494988322063910608_state @ ( collect_state @ P2 ) @ ( collect_state @ Q ) ) ) ).

% Collect_mono
thf(fact_139_subset__refl,axiom,
    ! [A6: set_state] : ( ord_le2494988322063910608_state @ A6 @ A6 ) ).

% subset_refl
thf(fact_140_subset__iff,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
        ! [T: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ T @ A )
         => ( member7461423308196221312_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_141_subset__iff,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
        ! [T: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ T @ A )
         => ( member2879030624002546611on_val @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_142_subset__iff,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
        ! [T: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ T @ A )
         => ( member6715010751053357271_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_143_subset__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A: set_state,B5: set_state] :
        ! [T: state] :
          ( ( member_state @ T @ A )
         => ( member_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_144_equalityD2,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( A6 = B4 )
     => ( ord_le2494988322063910608_state @ B4 @ A6 ) ) ).

% equalityD2
thf(fact_145_equalityD1,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( A6 = B4 )
     => ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ).

% equalityD1
thf(fact_146_subset__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
        ! [X5: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X5 @ A )
         => ( member7461423308196221312_state @ X5 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_147_subset__eq,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
        ! [X5: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X5 @ A )
         => ( member2879030624002546611on_val @ X5 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_148_subset__eq,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
        ! [X5: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X5 @ A )
         => ( member6715010751053357271_state @ X5 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_149_subset__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A: set_state,B5: set_state] :
        ! [X5: state] :
          ( ( member_state @ X5 @ A )
         => ( member_state @ X5 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_150_equalityE,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( A6 = B4 )
     => ~ ( ( ord_le2494988322063910608_state @ A6 @ B4 )
         => ~ ( ord_le2494988322063910608_state @ B4 @ A6 ) ) ) ).

% equalityE
thf(fact_151_subsetD,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A6 @ B4 )
     => ( ( member7461423308196221312_state @ C @ A6 )
       => ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_152_subsetD,axiom,
    ! [A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,C: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A6 @ B4 )
     => ( ( member2879030624002546611on_val @ C @ A6 )
       => ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% subsetD
thf(fact_153_subsetD,axiom,
    ! [A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,C: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A6 @ B4 )
     => ( ( member6715010751053357271_state @ C @ A6 )
       => ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_154_subsetD,axiom,
    ! [A6: set_state,B4: set_state,C: state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ( member_state @ C @ A6 )
       => ( member_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_155_in__mono,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,X2: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A6 @ B4 )
     => ( ( member7461423308196221312_state @ X2 @ A6 )
       => ( member7461423308196221312_state @ X2 @ B4 ) ) ) ).

% in_mono
thf(fact_156_in__mono,axiom,
    ! [A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,X2: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A6 @ B4 )
     => ( ( member2879030624002546611on_val @ X2 @ A6 )
       => ( member2879030624002546611on_val @ X2 @ B4 ) ) ) ).

% in_mono
thf(fact_157_in__mono,axiom,
    ! [A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,X2: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A6 @ B4 )
     => ( ( member6715010751053357271_state @ X2 @ A6 )
       => ( member6715010751053357271_state @ X2 @ B4 ) ) ) ).

% in_mono
thf(fact_158_in__mono,axiom,
    ! [A6: set_state,B4: set_state,X2: state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ( member_state @ X2 @ A6 )
       => ( member_state @ X2 @ B4 ) ) ) ).

% in_mono
thf(fact_159_PartialSA_Omono__pure__cond__def,axiom,
    ! [B2: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ B2 )
      = ( ! [Phi4: state] :
            ( ( B2 @ Phi4 )
            = ( B2 @ ( core @ Phi4 ) ) )
        & ! [Phi3: state,Phi4: state,R2: state] :
            ( ( ( sep_pure_state @ plus @ R2 )
              & ( ( some_state @ Phi3 )
                = ( plus @ Phi4 @ R2 ) )
              & ~ ( B2 @ Phi4 ) )
           => ~ ( B2 @ Phi3 ) ) ) ) ).

% PartialSA.mono_pure_cond_def
thf(fact_160_PartialSA_Omono__pure__condI,axiom,
    ! [B2: state > $o] :
      ( ! [Phi5: state] :
          ( ( B2 @ Phi5 )
          = ( B2 @ ( core @ Phi5 ) ) )
     => ( ! [Phi5: state,Phi6: state,R3: state] :
            ( ( ( sep_pure_state @ plus @ R3 )
              & ( ( some_state @ Phi6 )
                = ( plus @ Phi5 @ R3 ) )
              & ~ ( B2 @ Phi5 ) )
           => ~ ( B2 @ Phi6 ) )
       => ( packag6595153354952283300_state @ plus @ core @ B2 ) ) ) ).

% PartialSA.mono_pure_condI
thf(fact_161_PartialSA_Omax__projection__prop__pure__core,axiom,
    sep_ma8214210560313151521_state @ plus @ ( sep_pure_state @ plus ) @ core ).

% PartialSA.max_projection_prop_pure_core
thf(fact_162_PartialSA_Obigger__the,axiom,
    ! [A3: state,X: state,Y: state,X2: state] :
      ( ( ( some_state @ A3 )
        = ( plus @ X @ Y ) )
     => ( ( greater @ X @ X2 )
       => ( greater @ ( the_state @ ( plus @ ( core @ A3 ) @ X ) ) @ ( the_state @ ( plus @ ( core @ A3 ) @ X2 ) ) ) ) ) ).

% PartialSA.bigger_the
thf(fact_163_minus__def,axiom,
    ( minus
    = ( sep_minus_state @ plus @ core ) ) ).

% minus_def
thf(fact_164_PartialSA_Osplus_Oelims,axiom,
    ! [X2: option_state,Xa2: option_state,Y: option_state] :
      ( ( ( sep_splus_state @ plus @ X2 @ Xa2 )
        = Y )
     => ( ( ( X2 = none_state )
         => ( Y != none_state ) )
       => ( ( ? [V: state] :
                ( X2
                = ( some_state @ V ) )
           => ( ( Xa2 = none_state )
             => ( Y != none_state ) ) )
         => ~ ! [A7: state] :
                ( ( X2
                  = ( some_state @ A7 ) )
               => ! [B6: state] :
                    ( ( Xa2
                      = ( some_state @ B6 ) )
                   => ( Y
                     != ( plus @ A7 @ B6 ) ) ) ) ) ) ) ).

% PartialSA.splus.elims
thf(fact_165_PartialSA_Osplus_Osimps_I2_J,axiom,
    ! [V2: state] :
      ( ( sep_splus_state @ plus @ ( some_state @ V2 ) @ none_state )
      = none_state ) ).

% PartialSA.splus.simps(2)
thf(fact_166_Greatest__equality,axiom,
    ! [P2: set_state > $o,X2: set_state] :
      ( ( P2 @ X2 )
     => ( ! [Y3: set_state] :
            ( ( P2 @ Y3 )
           => ( ord_le2494988322063910608_state @ Y3 @ X2 ) )
       => ( ( order_2642746146112740183_state @ P2 )
          = X2 ) ) ) ).

% Greatest_equality
thf(fact_167_GreatestI2__order,axiom,
    ! [P2: set_state > $o,X2: set_state,Q: set_state > $o] :
      ( ( P2 @ X2 )
     => ( ! [Y3: set_state] :
            ( ( P2 @ Y3 )
           => ( ord_le2494988322063910608_state @ Y3 @ X2 ) )
       => ( ! [X4: set_state] :
              ( ( P2 @ X4 )
             => ( ! [Y6: set_state] :
                    ( ( P2 @ Y6 )
                   => ( ord_le2494988322063910608_state @ Y6 @ X4 ) )
               => ( Q @ X4 ) ) )
         => ( Q @ ( order_2642746146112740183_state @ P2 ) ) ) ) ) ).

% GreatestI2_order
thf(fact_168_PartialSA_Oequiv__stable__sum,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_equiv_state @ plus @ A6 @ B4 )
     => ( sep_equiv_state @ plus @ ( add_set @ A6 @ C3 ) @ ( add_set @ B4 @ C3 ) ) ) ).

% PartialSA.equiv_stable_sum
thf(fact_169_not__None__eq,axiom,
    ! [X2: option_state] :
      ( ( X2 != none_state )
      = ( ? [Y4: state] :
            ( X2
            = ( some_state @ Y4 ) ) ) ) ).

% not_None_eq
thf(fact_170_not__None__eq,axiom,
    ! [X2: option_val] :
      ( ( X2 != none_val )
      = ( ? [Y4: val] :
            ( X2
            = ( some_val @ Y4 ) ) ) ) ).

% not_None_eq
thf(fact_171_not__Some__eq,axiom,
    ! [X2: option_state] :
      ( ( ! [Y4: state] :
            ( X2
           != ( some_state @ Y4 ) ) )
      = ( X2 = none_state ) ) ).

% not_Some_eq
thf(fact_172_not__Some__eq,axiom,
    ! [X2: option_val] :
      ( ( ! [Y4: val] :
            ( X2
           != ( some_val @ Y4 ) ) )
      = ( X2 = none_val ) ) ).

% not_Some_eq
thf(fact_173_option_Ocollapse,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( ( some_state @ ( the_state @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_174_option_Ocollapse,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( ( some_val @ ( the_val @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_175_sep__algebra_Omax__projection__prop_Ocong,axiom,
    sep_ma8214210560313151521_state = sep_ma8214210560313151521_state ).

% sep_algebra.max_projection_prop.cong
thf(fact_176_package__logic_Omono__pure__cond_Ocong,axiom,
    packag6595153354952283300_state = packag6595153354952283300_state ).

% package_logic.mono_pure_cond.cong
thf(fact_177_sep__algebra_Ominus_Ocong,axiom,
    sep_minus_state = sep_minus_state ).

% sep_algebra.minus.cong
thf(fact_178_sep__algebra_Oequiv_Ocong,axiom,
    sep_equiv_state = sep_equiv_state ).

% sep_algebra.equiv.cong
thf(fact_179_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_180_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_181_option_Oexhaust__sel,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( Option
        = ( some_state @ ( the_state @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_182_option_Oexhaust__sel,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( Option
        = ( some_val @ ( the_val @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_183_option_Odistinct_I1_J,axiom,
    ! [X22: state] :
      ( none_state
     != ( some_state @ X22 ) ) ).

% option.distinct(1)
thf(fact_184_option_Odistinct_I1_J,axiom,
    ! [X22: val] :
      ( none_val
     != ( some_val @ X22 ) ) ).

% option.distinct(1)
thf(fact_185_option_OdiscI,axiom,
    ! [Option: option_state,X22: state] :
      ( ( Option
        = ( some_state @ X22 ) )
     => ( Option != none_state ) ) ).

% option.discI
thf(fact_186_option_OdiscI,axiom,
    ! [Option: option_val,X22: val] :
      ( ( Option
        = ( some_val @ X22 ) )
     => ( Option != none_val ) ) ).

% option.discI
thf(fact_187_option_Oexhaust,axiom,
    ! [Y: option_state] :
      ( ( Y != none_state )
     => ~ ! [X23: state] :
            ( Y
           != ( some_state @ X23 ) ) ) ).

% option.exhaust
thf(fact_188_option_Oexhaust,axiom,
    ! [Y: option_val] :
      ( ( Y != none_val )
     => ~ ! [X23: val] :
            ( Y
           != ( some_val @ X23 ) ) ) ).

% option.exhaust
thf(fact_189_split__option__ex,axiom,
    ( ( ^ [P3: option_state > $o] :
        ? [X6: option_state] : ( P3 @ X6 ) )
    = ( ^ [P4: option_state > $o] :
          ( ( P4 @ none_state )
          | ? [X5: state] : ( P4 @ ( some_state @ X5 ) ) ) ) ) ).

% split_option_ex
thf(fact_190_split__option__ex,axiom,
    ( ( ^ [P3: option_val > $o] :
        ? [X6: option_val] : ( P3 @ X6 ) )
    = ( ^ [P4: option_val > $o] :
          ( ( P4 @ none_val )
          | ? [X5: val] : ( P4 @ ( some_val @ X5 ) ) ) ) ) ).

% split_option_ex
thf(fact_191_split__option__all,axiom,
    ( ( ^ [P3: option_state > $o] :
        ! [X6: option_state] : ( P3 @ X6 ) )
    = ( ^ [P4: option_state > $o] :
          ( ( P4 @ none_state )
          & ! [X5: state] : ( P4 @ ( some_state @ X5 ) ) ) ) ) ).

% split_option_all
thf(fact_192_split__option__all,axiom,
    ( ( ^ [P3: option_val > $o] :
        ! [X6: option_val] : ( P3 @ X6 ) )
    = ( ^ [P4: option_val > $o] :
          ( ( P4 @ none_val )
          & ! [X5: val] : ( P4 @ ( some_val @ X5 ) ) ) ) ) ).

% split_option_all
thf(fact_193_combine__options__cases,axiom,
    ! [X2: option_state,P2: option_state > option_state > $o,Y: option_state] :
      ( ( ( X2 = none_state )
       => ( P2 @ X2 @ Y ) )
     => ( ( ( Y = none_state )
         => ( P2 @ X2 @ Y ) )
       => ( ! [A7: state,B6: state] :
              ( ( X2
                = ( some_state @ A7 ) )
             => ( ( Y
                  = ( some_state @ B6 ) )
               => ( P2 @ X2 @ Y ) ) )
         => ( P2 @ X2 @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_194_combine__options__cases,axiom,
    ! [X2: option_state,P2: option_state > option_val > $o,Y: option_val] :
      ( ( ( X2 = none_state )
       => ( P2 @ X2 @ Y ) )
     => ( ( ( Y = none_val )
         => ( P2 @ X2 @ Y ) )
       => ( ! [A7: state,B6: val] :
              ( ( X2
                = ( some_state @ A7 ) )
             => ( ( Y
                  = ( some_val @ B6 ) )
               => ( P2 @ X2 @ Y ) ) )
         => ( P2 @ X2 @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_195_combine__options__cases,axiom,
    ! [X2: option_val,P2: option_val > option_state > $o,Y: option_state] :
      ( ( ( X2 = none_val )
       => ( P2 @ X2 @ Y ) )
     => ( ( ( Y = none_state )
         => ( P2 @ X2 @ Y ) )
       => ( ! [A7: val,B6: state] :
              ( ( X2
                = ( some_val @ A7 ) )
             => ( ( Y
                  = ( some_state @ B6 ) )
               => ( P2 @ X2 @ Y ) ) )
         => ( P2 @ X2 @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_196_combine__options__cases,axiom,
    ! [X2: option_val,P2: option_val > option_val > $o,Y: option_val] :
      ( ( ( X2 = none_val )
       => ( P2 @ X2 @ Y ) )
     => ( ( ( Y = none_val )
         => ( P2 @ X2 @ Y ) )
       => ( ! [A7: val,B6: val] :
              ( ( X2
                = ( some_val @ A7 ) )
             => ( ( Y
                  = ( some_val @ B6 ) )
               => ( P2 @ X2 @ Y ) ) )
         => ( P2 @ X2 @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_197_option_Osel,axiom,
    ! [X22: state] :
      ( ( the_state @ ( some_state @ X22 ) )
      = X22 ) ).

% option.sel
thf(fact_198_option_Osel,axiom,
    ! [X22: val] :
      ( ( the_val @ ( some_val @ X22 ) )
      = X22 ) ).

% option.sel
thf(fact_199_PartialSA_Ompp__invo,axiom,
    ! [P2: state > $o,F: state > state,X2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( F @ ( F @ X2 ) )
        = ( F @ X2 ) ) ) ).

% PartialSA.mpp_invo
thf(fact_200_PartialSA_Ompp__prop,axiom,
    ! [P2: state > $o,F: state > state,X2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( P2 @ ( F @ X2 ) ) ) ).

% PartialSA.mpp_prop
thf(fact_201_PartialSA_Oasso3,axiom,
    ! [A3: state,B2: state,C: state,Bc: state] :
      ( ( ( plus @ A3 @ B2 )
        = none_state )
     => ( ( ( plus @ B2 @ C )
          = ( some_state @ Bc ) )
       => ( ( plus @ A3 @ Bc )
          = none_state ) ) ) ).

% PartialSA.asso3
thf(fact_202_asso2,axiom,
    ! [A3: state,B2: state,Ab: state,C: state] :
      ( ( ( ( plus @ A3 @ B2 )
          = ( some_state @ Ab ) )
        & ( ( plus @ B2 @ C )
          = none_state ) )
     => ( ( plus @ Ab @ C )
        = none_state ) ) ).

% asso2
thf(fact_203_PartialSA_Odefined__def,axiom,
    ( defined
    = ( ^ [A2: state,B: state] :
          ( ( plus @ A2 @ B )
         != none_state ) ) ) ).

% PartialSA.defined_def
thf(fact_204_PartialSA_Osplus_Osimps_I1_J,axiom,
    ! [Uu: option_state] :
      ( ( sep_splus_state @ plus @ none_state @ Uu )
      = none_state ) ).

% PartialSA.splus.simps(1)
thf(fact_205_PartialSA_Omax__projection__prop__def,axiom,
    ! [P2: state > $o,F: state > state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
      = ( ! [X5: state] :
            ( ( greater @ X5 @ ( F @ X5 ) )
            & ( P2 @ ( F @ X5 ) )
            & ! [P5: state] :
                ( ( ( P2 @ P5 )
                  & ( greater @ X5 @ P5 ) )
               => ( greater @ ( F @ X5 ) @ P5 ) ) ) ) ) ).

% PartialSA.max_projection_prop_def
thf(fact_206_PartialSA_Omax__projection__propI,axiom,
    ! [F: state > state,P2: state > $o] :
      ( ! [X4: state] : ( greater @ X4 @ ( F @ X4 ) )
     => ( ! [X4: state] : ( P2 @ ( F @ X4 ) )
       => ( ! [X4: state,P6: state] :
              ( ( ( P2 @ P6 )
                & ( greater @ X4 @ P6 ) )
             => ( greater @ ( F @ X4 ) @ P6 ) )
         => ( sep_ma8214210560313151521_state @ plus @ P2 @ F ) ) ) ) ).

% PartialSA.max_projection_propI
thf(fact_207_PartialSA_Ompp__smaller,axiom,
    ! [P2: state > $o,F: state > state,X2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( greater @ X2 @ ( F @ X2 ) ) ) ).

% PartialSA.mpp_smaller
thf(fact_208_PartialSA_Ompp__mono,axiom,
    ! [P2: state > $o,F: state > state,A3: state,B2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( greater @ A3 @ B2 )
       => ( greater @ ( F @ A3 ) @ ( F @ B2 ) ) ) ) ).

% PartialSA.mpp_mono
thf(fact_209_PartialSA_OmppI,axiom,
    ! [P2: state > $o,F: state > state,A3: state,X2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( greater @ A3 @ X2 )
       => ( ( P2 @ X2 )
         => ( ( greater @ X2 @ ( F @ A3 ) )
           => ( X2
              = ( F @ A3 ) ) ) ) ) ) ).

% PartialSA.mppI
thf(fact_210_PartialSA_Omax__projection__propE_I3_J,axiom,
    ! [P2: state > $o,F: state > state,P: state,X2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( ( P2 @ P )
          & ( greater @ X2 @ P ) )
       => ( greater @ ( F @ X2 ) @ P ) ) ) ).

% PartialSA.max_projection_propE(3)
thf(fact_211_PartialSA_Ompp__compatible,axiom,
    ! [P2: state > $o,F: state > state,A3: state,B2: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( defined @ A3 @ B2 )
       => ( defined @ ( F @ A3 ) @ ( F @ B2 ) ) ) ) ).

% PartialSA.mpp_compatible
thf(fact_212_PartialSA_Omono__prop__set__equiv,axiom,
    ! [P2: state > $o,A6: set_state,B4: set_state] :
      ( ( sep_mono_prop_state @ plus @ P2 )
     => ( ( sep_equiv_state @ plus @ A6 @ B4 )
       => ( ( sep_setify_state @ P2 @ A6 )
          = ( sep_setify_state @ P2 @ B4 ) ) ) ) ).

% PartialSA.mono_prop_set_equiv
thf(fact_213_PartialSA_Omono__pure__cond__conj,axiom,
    ! [Pc: state > $o,B2: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ Pc )
     => ( ( packag6595153354952283300_state @ plus @ core @ B2 )
       => ( packag6595153354952283300_state @ plus @ core @ ( packag1330488657391168505_state @ Pc @ B2 ) ) ) ) ).

% PartialSA.mono_pure_cond_conj
thf(fact_214_PartialSA_Oequiv__up__closed__subset,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_up_closed_state @ plus @ A6 )
     => ( ( sep_equiv_state @ plus @ B4 @ C3 )
       => ( ( ord_le2494988322063910608_state @ B4 @ A6 )
          = ( ord_le2494988322063910608_state @ C3 @ A6 ) ) ) ) ).

% PartialSA.equiv_up_closed_subset
thf(fact_215_empty__heap__def,axiom,
    ( empty_7512026568161686585ar_val
    = ( ^ [Hl: produc1457211279475724562t_char] : none_val ) ) ).

% empty_heap_def
thf(fact_216_compatible__options_Oelims_I2_J,axiom,
    ! [X2: option_state,Xa2: option_state] :
      ( ( compat2278460363914054422_state @ X2 @ Xa2 )
     => ( ! [A7: state] :
            ( ( X2
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( A7 != B6 ) ) )
       => ( ( X2 != none_state )
         => ( Xa2 = none_state ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_217_compatible__options_Oelims_I2_J,axiom,
    ! [X2: option_val,Xa2: option_val] :
      ( ( compat7209469420100717861ns_val @ X2 @ Xa2 )
     => ( ! [A7: val] :
            ( ( X2
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( A7 != B6 ) ) )
       => ( ( X2 != none_val )
         => ( Xa2 = none_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_218_compatible__options_Oelims_I1_J,axiom,
    ! [X2: option_state,Xa2: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X2 @ Xa2 )
        = Y )
     => ( ! [A7: state] :
            ( ( X2
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( Y
                  = ( A7 != B6 ) ) ) )
       => ( ( ( X2 = none_state )
           => ~ Y )
         => ~ ( ( Xa2 = none_state )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_219_compatible__options_Oelims_I1_J,axiom,
    ! [X2: option_val,Xa2: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X2 @ Xa2 )
        = Y )
     => ( ! [A7: val] :
            ( ( X2
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( Y
                  = ( A7 != B6 ) ) ) )
       => ( ( ( X2 = none_val )
           => ~ Y )
         => ~ ( ( Xa2 = none_val )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_220_PartialSA_OequivI,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( greater_set @ A6 @ B4 )
     => ( ( greater_set @ B4 @ A6 )
       => ( sep_equiv_state @ plus @ A6 @ B4 ) ) ) ).

% PartialSA.equivI
thf(fact_221_PartialSA_Osetify__def,axiom,
    ( sep_setify_state
    = ( ^ [P4: state > $o,A: set_state] :
        ! [X5: state] :
          ( ( member_state @ X5 @ A )
         => ( P4 @ X5 ) ) ) ) ).

% PartialSA.setify_def
thf(fact_222_PartialSA_Osucc__set__trans,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( greater_set @ A6 @ B4 )
     => ( ( greater_set @ B4 @ C3 )
       => ( greater_set @ A6 @ C3 ) ) ) ).

% PartialSA.succ_set_trans
thf(fact_223_PartialSA_Olarger__set__refl,axiom,
    ! [A6: set_state] : ( greater_set @ A6 @ A6 ) ).

% PartialSA.larger_set_refl
thf(fact_224_PartialSA_Obool__conj__def,axiom,
    ( packag1330488657391168505_state
    = ( ^ [A2: state > $o,B: state > $o,X5: state] :
          ( ( A2 @ X5 )
          & ( B @ X5 ) ) ) ) ).

% PartialSA.bool_conj_def
thf(fact_225_sep__algebra_Oup__closed_Ocong,axiom,
    sep_up_closed_state = sep_up_closed_state ).

% sep_algebra.up_closed.cong
thf(fact_226_PartialSA_Oup__closed__bigger__subset,axiom,
    ! [B4: set_state,A6: set_state] :
      ( ( sep_up_closed_state @ plus @ B4 )
     => ( ( greater_set @ A6 @ B4 )
       => ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ) ).

% PartialSA.up_closed_bigger_subset
thf(fact_227_PartialSA_Ogreater__setI,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ! [A7: state] :
          ( ( member_state @ A7 @ A6 )
         => ? [X3: state] :
              ( ( member_state @ X3 @ B4 )
              & ( greater @ A7 @ X3 ) ) )
     => ( greater_set @ A6 @ B4 ) ) ).

% PartialSA.greater_setI
thf(fact_228_PartialSA_Ogreater__set__def,axiom,
    ( greater_set
    = ( ^ [A: set_state,B5: set_state] :
        ! [X5: state] :
          ( ( member_state @ X5 @ A )
         => ? [Y4: state] :
              ( ( member_state @ Y4 @ B5 )
              & ( greater @ X5 @ Y4 ) ) ) ) ) ).

% PartialSA.greater_set_def
thf(fact_229_PartialSA_Omono__prop__set,axiom,
    ! [A6: set_state,B4: set_state,P2: state > $o] :
      ( ( greater_set @ A6 @ B4 )
     => ( ( sep_setify_state @ P2 @ B4 )
       => ( ( sep_mono_prop_state @ plus @ P2 )
         => ( sep_setify_state @ P2 @ A6 ) ) ) ) ).

% PartialSA.mono_prop_set
thf(fact_230_PartialSA_Obigger__set,axiom,
    ! [A8: set_state,A6: set_state,B4: set_state] :
      ( ( greater_set @ A8 @ A6 )
     => ( greater_set @ ( add_set @ A8 @ B4 ) @ ( add_set @ A6 @ B4 ) ) ) ).

% PartialSA.bigger_set
thf(fact_231_compatible__options_Osimps_I1_J,axiom,
    ! [A3: state,B2: state] :
      ( ( compat2278460363914054422_state @ ( some_state @ A3 ) @ ( some_state @ B2 ) )
      = ( A3 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_232_compatible__options_Osimps_I1_J,axiom,
    ! [A3: val,B2: val] :
      ( ( compat7209469420100717861ns_val @ ( some_val @ A3 ) @ ( some_val @ B2 ) )
      = ( A3 = B2 ) ) ).

% compatible_options.simps(1)
thf(fact_233_compatible__options_Oelims_I3_J,axiom,
    ! [X2: option_state,Xa2: option_state] :
      ( ~ ( compat2278460363914054422_state @ X2 @ Xa2 )
     => ~ ! [A7: state] :
            ( ( X2
              = ( some_state @ A7 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( A7 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_234_compatible__options_Oelims_I3_J,axiom,
    ! [X2: option_val,Xa2: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X2 @ Xa2 )
     => ~ ! [A7: val] :
            ( ( X2
              = ( some_val @ A7 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( A7 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_235_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_state] : ( compat2278460363914054422_state @ Uu @ none_state ) ).

% compatible_options.simps(3)
thf(fact_236_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_val] : ( compat7209469420100717861ns_val @ Uu @ none_val ) ).

% compatible_options.simps(3)
thf(fact_237_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_state] : ( compat2278460363914054422_state @ none_state @ Uv ) ).

% compatible_options.simps(2)
thf(fact_238_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_val] : ( compat7209469420100717861ns_val @ none_val @ Uv ) ).

% compatible_options.simps(2)
thf(fact_239_PartialSA_Osub__bigger,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( greater_set @ A6 @ B4 ) ) ).

% PartialSA.sub_bigger
thf(fact_240_PartialSA_Oup__closedI,axiom,
    ! [A6: set_state] :
      ( ! [Phi6: state,Phi5: state] :
          ( ( ( greater @ Phi6 @ Phi5 )
            & ( member_state @ Phi5 @ A6 ) )
         => ( member_state @ Phi6 @ A6 ) )
     => ( sep_up_closed_state @ plus @ A6 ) ) ).

% PartialSA.up_closedI
thf(fact_241_PartialSA_Oup__closed__def,axiom,
    ! [A6: set_state] :
      ( ( sep_up_closed_state @ plus @ A6 )
      = ( ! [Phi3: state] :
            ( ? [X5: state] :
                ( ( member_state @ X5 @ A6 )
                & ( greater @ Phi3 @ X5 ) )
           => ( member_state @ Phi3 @ A6 ) ) ) ) ).

% PartialSA.up_closed_def
thf(fact_242_PartialSA_Oup__closed__sum,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A6 )
     => ( sep_up_closed_state @ plus @ ( add_set @ A6 @ B4 ) ) ) ).

% PartialSA.up_closed_sum
thf(fact_243_PartialSA_Oup__close__equiv,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A6 )
     => ( ( sep_up_closed_state @ plus @ B4 )
       => ( ( sep_equiv_state @ plus @ A6 @ B4 )
          = ( A6 = B4 ) ) ) ) ).

% PartialSA.up_close_equiv
thf(fact_244_PartialSA_Oequiv__def,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( sep_equiv_state @ plus @ A6 @ B4 )
      = ( ( greater_set @ A6 @ B4 )
        & ( greater_set @ B4 @ A6 ) ) ) ).

% PartialSA.equiv_def
thf(fact_245_PartialSA_Oupper__closure__up__closed,axiom,
    ! [A6: set_state] : ( sep_up_closed_state @ plus @ ( sep_up1246176804924251236_state @ plus @ A6 ) ) ).

% PartialSA.upper_closure_up_closed
thf(fact_246_PartialSA_Oup__closed__plus__UNIV,axiom,
    ! [A6: set_state] : ( sep_up_closed_state @ plus @ ( add_set @ A6 @ top_top_set_state ) ) ).

% PartialSA.up_closed_plus_UNIV
thf(fact_247_sep__algebra_Omono__prop__set__equiv,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_mono_prop_state @ Plus @ P2 )
       => ( ( sep_equiv_state @ Plus @ A6 @ B4 )
         => ( ( sep_setify_state @ P2 @ A6 )
            = ( sep_setify_state @ P2 @ B4 ) ) ) ) ) ).

% sep_algebra.mono_prop_set_equiv
thf(fact_248__092_060open_062pgte_Apwrite_A_092_060alpha_062_A_092_060and_062_Apgte_Apwrite_A_092_060beta_062_092_060close_062,axiom,
    ( ( pgte @ pwrite @ alpha )
    & ( pgte @ pwrite @ beta ) ) ).

% \<open>pgte pwrite \<alpha> \<and> pgte pwrite \<beta>\<close>
thf(fact_249_greater__set__def,axiom,
    ( greater_set
    = ( sep_gr7105985528888466643_state @ plus ) ) ).

% greater_set_def
thf(fact_250_package__logic_Omono__pruner__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,P: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8699728003424501129er_val @ Plus @ P )
        = ( ! [Phi3: val,Phi4: val,R2: val] :
              ( ( ( sep_pure_val @ Plus @ R2 )
                & ( P @ Phi4 )
                & ( ( some_val @ Phi3 )
                  = ( Plus @ Phi4 @ R2 ) ) )
             => ( P @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pruner_def
thf(fact_251_package__logic_Omono__pruner__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,P: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2456304381420842418_state @ Plus @ P )
        = ( ! [Phi3: state,Phi4: state,R2: state] :
              ( ( ( sep_pure_state @ Plus @ R2 )
                & ( P @ Phi4 )
                & ( ( some_state @ Phi3 )
                  = ( Plus @ Phi4 @ R2 ) ) )
             => ( P @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pruner_def
thf(fact_252_package__logic_Omono__pure__cond__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B2: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6714868506247462167nd_val @ Plus @ Core @ B2 )
        = ( ! [Phi4: val] :
              ( ( B2 @ Phi4 )
              = ( B2 @ ( Core @ Phi4 ) ) )
          & ! [Phi3: val,Phi4: val,R2: val] :
              ( ( ( sep_pure_val @ Plus @ R2 )
                & ( ( some_val @ Phi3 )
                  = ( Plus @ Phi4 @ R2 ) )
                & ~ ( B2 @ Phi4 ) )
             => ~ ( B2 @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pure_cond_def
thf(fact_253_package__logic_Omono__pure__cond__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B2: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6595153354952283300_state @ Plus @ Core @ B2 )
        = ( ! [Phi4: state] :
              ( ( B2 @ Phi4 )
              = ( B2 @ ( Core @ Phi4 ) ) )
          & ! [Phi3: state,Phi4: state,R2: state] :
              ( ( ( sep_pure_state @ Plus @ R2 )
                & ( ( some_state @ Phi3 )
                  = ( Plus @ Phi4 @ R2 ) )
                & ~ ( B2 @ Phi4 ) )
             => ~ ( B2 @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pure_cond_def
thf(fact_254_package__logic_Omono__pure__condI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B2: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [Phi5: val] :
            ( ( B2 @ Phi5 )
            = ( B2 @ ( Core @ Phi5 ) ) )
       => ( ! [Phi5: val,Phi6: val,R3: val] :
              ( ( ( sep_pure_val @ Plus @ R3 )
                & ( ( some_val @ Phi6 )
                  = ( Plus @ Phi5 @ R3 ) )
                & ~ ( B2 @ Phi5 ) )
             => ~ ( B2 @ Phi6 ) )
         => ( packag6714868506247462167nd_val @ Plus @ Core @ B2 ) ) ) ) ).

% package_logic.mono_pure_condI
thf(fact_255_package__logic_Omono__pure__condI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B2: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [Phi5: state] :
            ( ( B2 @ Phi5 )
            = ( B2 @ ( Core @ Phi5 ) ) )
       => ( ! [Phi5: state,Phi6: state,R3: state] :
              ( ( ( sep_pure_state @ Plus @ R3 )
                & ( ( some_state @ Phi6 )
                  = ( Plus @ Phi5 @ R3 ) )
                & ~ ( B2 @ Phi5 ) )
             => ~ ( B2 @ Phi6 ) )
         => ( packag6595153354952283300_state @ Plus @ Core @ B2 ) ) ) ) ).

% package_logic.mono_pure_condI
thf(fact_256_UNIV__I,axiom,
    ! [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ top_to174962084833059535_state ) ).

% UNIV_I
thf(fact_257_UNIV__I,axiom,
    ! [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ top_to1561438921946393474on_val ) ).

% UNIV_I
thf(fact_258_UNIV__I,axiom,
    ! [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ top_to1744471583079920734_state ) ).

% UNIV_I
thf(fact_259_UNIV__I,axiom,
    ! [X2: state] : ( member_state @ X2 @ top_top_set_state ) ).

% UNIV_I
thf(fact_260_calculation_I3_J,axiom,
    ( ( ppos @ p )
    & ( pgte @ pwrite @ p ) ) ).

% calculation(3)
thf(fact_261_sep__algebra_OequivI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
       => ( ( sep_gr7105985528888466643_state @ Plus @ B4 @ A6 )
         => ( sep_equiv_state @ Plus @ A6 @ B4 ) ) ) ) ).

% sep_algebra.equivI
thf(fact_262_sep__algebra_Oequiv__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_equiv_state @ Plus @ A6 @ B4 )
        = ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
          & ( sep_gr7105985528888466643_state @ Plus @ B4 @ A6 ) ) ) ) ).

% sep_algebra.equiv_def
thf(fact_263_UNIV__witness,axiom,
    ? [X4: produc7272280185086996969_state] : ( member7461423308196221312_state @ X4 @ top_to174962084833059535_state ) ).

% UNIV_witness
thf(fact_264_UNIV__witness,axiom,
    ? [X4: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X4 @ top_to1561438921946393474on_val ) ).

% UNIV_witness
thf(fact_265_UNIV__witness,axiom,
    ? [X4: produc3882902684156697774_state] : ( member6715010751053357271_state @ X4 @ top_to1744471583079920734_state ) ).

% UNIV_witness
thf(fact_266_UNIV__witness,axiom,
    ? [X4: state] : ( member_state @ X4 @ top_top_set_state ) ).

% UNIV_witness
thf(fact_267_UNIV__eq__I,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ! [X4: produc7272280185086996969_state] : ( member7461423308196221312_state @ X4 @ A6 )
     => ( top_to174962084833059535_state = A6 ) ) ).

% UNIV_eq_I
thf(fact_268_UNIV__eq__I,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ! [X4: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X4 @ A6 )
     => ( top_to1561438921946393474on_val = A6 ) ) ).

% UNIV_eq_I
thf(fact_269_UNIV__eq__I,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ! [X4: produc3882902684156697774_state] : ( member6715010751053357271_state @ X4 @ A6 )
     => ( top_to1744471583079920734_state = A6 ) ) ).

% UNIV_eq_I
thf(fact_270_UNIV__eq__I,axiom,
    ! [A6: set_state] :
      ( ! [X4: state] : ( member_state @ X4 @ A6 )
     => ( top_top_set_state = A6 ) ) ).

% UNIV_eq_I
thf(fact_271_sep__algebra_Ogreater__set_Ocong,axiom,
    sep_gr7105985528888466643_state = sep_gr7105985528888466643_state ).

% sep_algebra.greater_set.cong
thf(fact_272_sep__algebra_Olarger__set__refl,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( sep_gr7105985528888466643_state @ Plus @ A6 @ A6 ) ) ).

% sep_algebra.larger_set_refl
thf(fact_273_package__logic_Ostable__unit,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( Stable @ Unit ) ) ).

% package_logic.stable_unit
thf(fact_274_sep__algebra_Osucc__set__trans,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
       => ( ( sep_gr7105985528888466643_state @ Plus @ B4 @ C3 )
         => ( sep_gr7105985528888466643_state @ Plus @ A6 @ C3 ) ) ) ) ).

% sep_algebra.succ_set_trans
thf(fact_275_package__logic_Ounit__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( Core @ Unit )
        = Unit ) ) ).

% package_logic.unit_core
thf(fact_276_sep__algebra_Ocommutative,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( Plus @ A3 @ B2 )
        = ( Plus @ B2 @ A3 ) ) ) ).

% sep_algebra.commutative
thf(fact_277_package__logic_Oaxioms_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( sep_algebra_state @ Plus @ Core ) ) ).

% package_logic.axioms(1)
thf(fact_278_sep__algebra_Osub__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ord_le2494988322063910608_state @ A6 @ B4 )
       => ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 ) ) ) ).

% sep_algebra.sub_bigger
thf(fact_279_sep__algebra_Oupper__closure_Ocong,axiom,
    sep_up1246176804924251236_state = sep_up1246176804924251236_state ).

% sep_algebra.upper_closure.cong
thf(fact_280_sep__algebra_Oupper__closure__up__closed,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( sep_up_closed_state @ Plus @ ( sep_up1246176804924251236_state @ Plus @ A6 ) ) ) ).

% sep_algebra.upper_closure_up_closed
thf(fact_281_sep__algebra_Oasso1,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,Ab: val,C: val,Bc: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( Plus @ A3 @ B2 )
            = ( some_val @ Ab ) )
          & ( ( Plus @ B2 @ C )
            = ( some_val @ Bc ) ) )
       => ( ( Plus @ Ab @ C )
          = ( Plus @ A3 @ Bc ) ) ) ) ).

% sep_algebra.asso1
thf(fact_282_sep__algebra_Oasso1,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,Ab: state,C: state,Bc: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( Plus @ A3 @ B2 )
            = ( some_state @ Ab ) )
          & ( ( Plus @ B2 @ C )
            = ( some_state @ Bc ) ) )
       => ( ( Plus @ Ab @ C )
          = ( Plus @ A3 @ Bc ) ) ) ) ).

% sep_algebra.asso1
thf(fact_283_sep__algebra_Ocore__max,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X2 )
          = ( Plus @ X2 @ C ) )
       => ? [R3: val] :
            ( ( some_val @ ( Core @ X2 ) )
            = ( Plus @ C @ R3 ) ) ) ) ).

% sep_algebra.core_max
thf(fact_284_sep__algebra_Ocore__max,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X2 )
          = ( Plus @ X2 @ C ) )
       => ? [R3: state] :
            ( ( some_state @ ( Core @ X2 ) )
            = ( Plus @ C @ R3 ) ) ) ) ).

% sep_algebra.core_max
thf(fact_285_sep__algebra_Ocore__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,C: val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ C )
          = ( Plus @ A3 @ B2 ) )
       => ( ( some_val @ ( Core @ C ) )
          = ( Plus @ ( Core @ A3 ) @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.core_sum
thf(fact_286_sep__algebra_Ocore__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,C: state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ C )
          = ( Plus @ A3 @ B2 ) )
       => ( ( some_state @ ( Core @ C ) )
          = ( Plus @ ( Core @ A3 ) @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.core_sum
thf(fact_287_sep__algebra_Opositivity,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( Plus @ A3 @ B2 )
          = ( some_val @ C ) )
       => ( ( ( some_val @ C )
            = ( Plus @ C @ C ) )
         => ( ( some_val @ A3 )
            = ( Plus @ A3 @ A3 ) ) ) ) ) ).

% sep_algebra.positivity
thf(fact_288_sep__algebra_Opositivity,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( Plus @ A3 @ B2 )
          = ( some_state @ C ) )
       => ( ( ( some_state @ C )
            = ( Plus @ C @ C ) )
         => ( ( some_state @ A3 )
            = ( Plus @ A3 @ A3 ) ) ) ) ) ).

% sep_algebra.positivity
thf(fact_289_sep__algebra_Ocancellative,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,X2: val,Y: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A3 )
          = ( Plus @ B2 @ X2 ) )
       => ( ( ( some_val @ A3 )
            = ( Plus @ B2 @ Y ) )
         => ( ( ( Core @ X2 )
              = ( Core @ Y ) )
           => ( X2 = Y ) ) ) ) ) ).

% sep_algebra.cancellative
thf(fact_290_sep__algebra_Ocancellative,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,X2: state,Y: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A3 )
          = ( Plus @ B2 @ X2 ) )
       => ( ( ( some_state @ A3 )
            = ( Plus @ B2 @ Y ) )
         => ( ( ( Core @ X2 )
              = ( Core @ Y ) )
           => ( X2 = Y ) ) ) ) ) ).

% sep_algebra.cancellative
thf(fact_291_sep__algebra_Ocore__is__pure,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( some_val @ ( Core @ X2 ) )
        = ( Plus @ ( Core @ X2 ) @ ( Core @ X2 ) ) ) ) ).

% sep_algebra.core_is_pure
thf(fact_292_sep__algebra_Ocore__is__pure,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( some_state @ ( Core @ X2 ) )
        = ( Plus @ ( Core @ X2 ) @ ( Core @ X2 ) ) ) ) ).

% sep_algebra.core_is_pure
thf(fact_293_sep__algebra_Ocore__is__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( some_val @ X2 )
        = ( Plus @ X2 @ ( Core @ X2 ) ) ) ) ).

% sep_algebra.core_is_smaller
thf(fact_294_sep__algebra_Ocore__is__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( some_state @ X2 )
        = ( Plus @ X2 @ ( Core @ X2 ) ) ) ) ).

% sep_algebra.core_is_smaller
thf(fact_295_package__logic_Ostable__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,B2: val,X2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( Stable @ A3 )
       => ( ( Stable @ B2 )
         => ( ( ( some_val @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( Stable @ X2 ) ) ) ) ) ).

% package_logic.stable_sum
thf(fact_296_package__logic_Ostable__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state,X2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( Stable @ A3 )
       => ( ( Stable @ B2 )
         => ( ( ( some_state @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( Stable @ X2 ) ) ) ) ) ).

% package_logic.stable_sum
thf(fact_297_package__logic_Ounit__neutral,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( some_val @ A3 )
        = ( Plus @ A3 @ Unit ) ) ) ).

% package_logic.unit_neutral
thf(fact_298_package__logic_Ounit__neutral,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( some_state @ A3 )
        = ( Plus @ A3 @ Unit ) ) ) ).

% package_logic.unit_neutral
thf(fact_299_top__greatest,axiom,
    ! [A3: set_state] : ( ord_le2494988322063910608_state @ A3 @ top_top_set_state ) ).

% top_greatest
thf(fact_300_top_Oextremum__unique,axiom,
    ! [A3: set_state] :
      ( ( ord_le2494988322063910608_state @ top_top_set_state @ A3 )
      = ( A3 = top_top_set_state ) ) ).

% top.extremum_unique
thf(fact_301_top_Oextremum__uniqueI,axiom,
    ! [A3: set_state] :
      ( ( ord_le2494988322063910608_state @ top_top_set_state @ A3 )
     => ( A3 = top_top_set_state ) ) ).

% top.extremum_uniqueI
thf(fact_302_sep__algebra_Ominus__core__weaker,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( Core @ ( sep_minus_state @ Plus @ Core @ A3 @ B2 ) )
        = ( sep_minus_state @ Plus @ Core @ ( Core @ A3 ) @ ( Core @ B2 ) ) ) ) ).

% sep_algebra.minus_core_weaker
thf(fact_303_sep__algebra_Ominus__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( Core @ ( sep_minus_state @ Plus @ Core @ A3 @ B2 ) )
        = ( Core @ A3 ) ) ) ).

% sep_algebra.minus_core
thf(fact_304_sep__algebra_Osplus__asso,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: option_state,B2: option_state,C: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ ( sep_splus_state @ Plus @ A3 @ B2 ) @ C )
        = ( sep_splus_state @ Plus @ A3 @ ( sep_splus_state @ Plus @ B2 @ C ) ) ) ) ).

% sep_algebra.splus_asso
thf(fact_305_sep__algebra_Osplus__comm,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: option_state,B2: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ A3 @ B2 )
        = ( sep_splus_state @ Plus @ B2 @ A3 ) ) ) ).

% sep_algebra.splus_comm
thf(fact_306_sep__algebra_Oup__closed__bigger__subset,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B4: set_state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ B4 )
       => ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
         => ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ) ) ).

% sep_algebra.up_closed_bigger_subset
thf(fact_307_multiply__order,axiom,
    ! [P: prat,A3: state,B2: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( greater @ A3 @ B2 )
       => ( greater @ ( multiply @ P @ A3 ) @ ( multiply @ P @ B2 ) ) ) ) ).

% multiply_order
thf(fact_308_sep__algebra_Ompp__prop,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( P2 @ ( F @ X2 ) ) ) ) ).

% sep_algebra.mpp_prop
thf(fact_309_sep__algebra_Ompp__invo,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( ( F @ ( F @ X2 ) )
          = ( F @ X2 ) ) ) ) ).

% sep_algebra.mpp_invo
thf(fact_310_sep__algebra_Osetify__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_setify_state @ P2 @ A6 )
        = ( ! [X5: state] :
              ( ( member_state @ X5 @ A6 )
             => ( P2 @ X5 ) ) ) ) ) ).

% sep_algebra.setify_def
thf(fact_311_subset__UNIV,axiom,
    ! [A6: set_state] : ( ord_le2494988322063910608_state @ A6 @ top_top_set_state ) ).

% subset_UNIV
thf(fact_312_package__logic_Obool__conj__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state > $o,B2: state > $o,X2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag1330488657391168505_state @ A3 @ B2 @ X2 )
        = ( ( A3 @ X2 )
          & ( B2 @ X2 ) ) ) ) ).

% package_logic.bool_conj_def
thf(fact_313_sep__algebra_Omono__prop__set,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state,P2: state > $o] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
       => ( ( sep_setify_state @ P2 @ B4 )
         => ( ( sep_mono_prop_state @ Plus @ P2 )
           => ( sep_setify_state @ P2 @ A6 ) ) ) ) ) ).

% sep_algebra.mono_prop_set
thf(fact_314_sep__algebra__def,axiom,
    ( sep_algebra_val
    = ( ^ [Plus2: val > val > option_val,Core2: val > val] :
          ( ! [A2: val,B: val] :
              ( ( Plus2 @ A2 @ B )
              = ( Plus2 @ B @ A2 ) )
          & ! [A2: val,B: val,Ab2: val,C2: val,Bc2: val] :
              ( ( ( ( Plus2 @ A2 @ B )
                  = ( some_val @ Ab2 ) )
                & ( ( Plus2 @ B @ C2 )
                  = ( some_val @ Bc2 ) ) )
             => ( ( Plus2 @ Ab2 @ C2 )
                = ( Plus2 @ A2 @ Bc2 ) ) )
          & ! [A2: val,B: val,Ab2: val,C2: val] :
              ( ( ( ( Plus2 @ A2 @ B )
                  = ( some_val @ Ab2 ) )
                & ( ( Plus2 @ B @ C2 )
                  = none_val ) )
             => ( ( Plus2 @ Ab2 @ C2 )
                = none_val ) )
          & ! [X5: val] :
              ( ( some_val @ X5 )
              = ( Plus2 @ X5 @ ( Core2 @ X5 ) ) )
          & ! [X5: val] :
              ( ( some_val @ ( Core2 @ X5 ) )
              = ( Plus2 @ ( Core2 @ X5 ) @ ( Core2 @ X5 ) ) )
          & ! [X5: val,C2: val] :
              ( ( ( some_val @ X5 )
                = ( Plus2 @ X5 @ C2 ) )
             => ? [R2: val] :
                  ( ( some_val @ ( Core2 @ X5 ) )
                  = ( Plus2 @ C2 @ R2 ) ) )
          & ! [C2: val,A2: val,B: val] :
              ( ( ( some_val @ C2 )
                = ( Plus2 @ A2 @ B ) )
             => ( ( some_val @ ( Core2 @ C2 ) )
                = ( Plus2 @ ( Core2 @ A2 ) @ ( Core2 @ B ) ) ) )
          & ! [A2: val,B: val,C2: val] :
              ( ( ( Plus2 @ A2 @ B )
                = ( some_val @ C2 ) )
             => ( ( ( some_val @ C2 )
                  = ( Plus2 @ C2 @ C2 ) )
               => ( ( some_val @ A2 )
                  = ( Plus2 @ A2 @ A2 ) ) ) )
          & ! [A2: val,B: val,X5: val,Y4: val] :
              ( ( ( some_val @ A2 )
                = ( Plus2 @ B @ X5 ) )
             => ( ( ( some_val @ A2 )
                  = ( Plus2 @ B @ Y4 ) )
               => ( ( ( Core2 @ X5 )
                    = ( Core2 @ Y4 ) )
                 => ( X5 = Y4 ) ) ) ) ) ) ) ).

% sep_algebra_def
thf(fact_315_sep__algebra__def,axiom,
    ( sep_algebra_state
    = ( ^ [Plus2: state > state > option_state,Core2: state > state] :
          ( ! [A2: state,B: state] :
              ( ( Plus2 @ A2 @ B )
              = ( Plus2 @ B @ A2 ) )
          & ! [A2: state,B: state,Ab2: state,C2: state,Bc2: state] :
              ( ( ( ( Plus2 @ A2 @ B )
                  = ( some_state @ Ab2 ) )
                & ( ( Plus2 @ B @ C2 )
                  = ( some_state @ Bc2 ) ) )
             => ( ( Plus2 @ Ab2 @ C2 )
                = ( Plus2 @ A2 @ Bc2 ) ) )
          & ! [A2: state,B: state,Ab2: state,C2: state] :
              ( ( ( ( Plus2 @ A2 @ B )
                  = ( some_state @ Ab2 ) )
                & ( ( Plus2 @ B @ C2 )
                  = none_state ) )
             => ( ( Plus2 @ Ab2 @ C2 )
                = none_state ) )
          & ! [X5: state] :
              ( ( some_state @ X5 )
              = ( Plus2 @ X5 @ ( Core2 @ X5 ) ) )
          & ! [X5: state] :
              ( ( some_state @ ( Core2 @ X5 ) )
              = ( Plus2 @ ( Core2 @ X5 ) @ ( Core2 @ X5 ) ) )
          & ! [X5: state,C2: state] :
              ( ( ( some_state @ X5 )
                = ( Plus2 @ X5 @ C2 ) )
             => ? [R2: state] :
                  ( ( some_state @ ( Core2 @ X5 ) )
                  = ( Plus2 @ C2 @ R2 ) ) )
          & ! [C2: state,A2: state,B: state] :
              ( ( ( some_state @ C2 )
                = ( Plus2 @ A2 @ B ) )
             => ( ( some_state @ ( Core2 @ C2 ) )
                = ( Plus2 @ ( Core2 @ A2 ) @ ( Core2 @ B ) ) ) )
          & ! [A2: state,B: state,C2: state] :
              ( ( ( Plus2 @ A2 @ B )
                = ( some_state @ C2 ) )
             => ( ( ( some_state @ C2 )
                  = ( Plus2 @ C2 @ C2 ) )
               => ( ( some_state @ A2 )
                  = ( Plus2 @ A2 @ A2 ) ) ) )
          & ! [A2: state,B: state,X5: state,Y4: state] :
              ( ( ( some_state @ A2 )
                = ( Plus2 @ B @ X5 ) )
             => ( ( ( some_state @ A2 )
                  = ( Plus2 @ B @ Y4 ) )
               => ( ( ( Core2 @ X5 )
                    = ( Core2 @ Y4 ) )
                 => ( X5 = Y4 ) ) ) ) ) ) ) ).

% sep_algebra_def
thf(fact_316_sep__algebra_Ointro,axiom,
    ! [Plus: val > val > option_val,Core: val > val] :
      ( ! [A7: val,B6: val] :
          ( ( Plus @ A7 @ B6 )
          = ( Plus @ B6 @ A7 ) )
     => ( ! [A7: val,B6: val,Ab3: val,C4: val,Bc3: val] :
            ( ( ( ( Plus @ A7 @ B6 )
                = ( some_val @ Ab3 ) )
              & ( ( Plus @ B6 @ C4 )
                = ( some_val @ Bc3 ) ) )
           => ( ( Plus @ Ab3 @ C4 )
              = ( Plus @ A7 @ Bc3 ) ) )
       => ( ! [A7: val,B6: val,Ab3: val,C4: val] :
              ( ( ( ( Plus @ A7 @ B6 )
                  = ( some_val @ Ab3 ) )
                & ( ( Plus @ B6 @ C4 )
                  = none_val ) )
             => ( ( Plus @ Ab3 @ C4 )
                = none_val ) )
         => ( ! [X4: val] :
                ( ( some_val @ X4 )
                = ( Plus @ X4 @ ( Core @ X4 ) ) )
           => ( ! [X4: val] :
                  ( ( some_val @ ( Core @ X4 ) )
                  = ( Plus @ ( Core @ X4 ) @ ( Core @ X4 ) ) )
             => ( ! [X4: val,C4: val] :
                    ( ( ( some_val @ X4 )
                      = ( Plus @ X4 @ C4 ) )
                   => ? [R4: val] :
                        ( ( some_val @ ( Core @ X4 ) )
                        = ( Plus @ C4 @ R4 ) ) )
               => ( ! [C4: val,A7: val,B6: val] :
                      ( ( ( some_val @ C4 )
                        = ( Plus @ A7 @ B6 ) )
                     => ( ( some_val @ ( Core @ C4 ) )
                        = ( Plus @ ( Core @ A7 ) @ ( Core @ B6 ) ) ) )
                 => ( ! [A7: val,B6: val,C4: val] :
                        ( ( ( Plus @ A7 @ B6 )
                          = ( some_val @ C4 ) )
                       => ( ( ( some_val @ C4 )
                            = ( Plus @ C4 @ C4 ) )
                         => ( ( some_val @ A7 )
                            = ( Plus @ A7 @ A7 ) ) ) )
                   => ( ! [A7: val,B6: val,X4: val,Y3: val] :
                          ( ( ( some_val @ A7 )
                            = ( Plus @ B6 @ X4 ) )
                         => ( ( ( some_val @ A7 )
                              = ( Plus @ B6 @ Y3 ) )
                           => ( ( ( Core @ X4 )
                                = ( Core @ Y3 ) )
                             => ( X4 = Y3 ) ) ) )
                     => ( sep_algebra_val @ Plus @ Core ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.intro
thf(fact_317_sep__algebra_Ointro,axiom,
    ! [Plus: state > state > option_state,Core: state > state] :
      ( ! [A7: state,B6: state] :
          ( ( Plus @ A7 @ B6 )
          = ( Plus @ B6 @ A7 ) )
     => ( ! [A7: state,B6: state,Ab3: state,C4: state,Bc3: state] :
            ( ( ( ( Plus @ A7 @ B6 )
                = ( some_state @ Ab3 ) )
              & ( ( Plus @ B6 @ C4 )
                = ( some_state @ Bc3 ) ) )
           => ( ( Plus @ Ab3 @ C4 )
              = ( Plus @ A7 @ Bc3 ) ) )
       => ( ! [A7: state,B6: state,Ab3: state,C4: state] :
              ( ( ( ( Plus @ A7 @ B6 )
                  = ( some_state @ Ab3 ) )
                & ( ( Plus @ B6 @ C4 )
                  = none_state ) )
             => ( ( Plus @ Ab3 @ C4 )
                = none_state ) )
         => ( ! [X4: state] :
                ( ( some_state @ X4 )
                = ( Plus @ X4 @ ( Core @ X4 ) ) )
           => ( ! [X4: state] :
                  ( ( some_state @ ( Core @ X4 ) )
                  = ( Plus @ ( Core @ X4 ) @ ( Core @ X4 ) ) )
             => ( ! [X4: state,C4: state] :
                    ( ( ( some_state @ X4 )
                      = ( Plus @ X4 @ C4 ) )
                   => ? [R4: state] :
                        ( ( some_state @ ( Core @ X4 ) )
                        = ( Plus @ C4 @ R4 ) ) )
               => ( ! [C4: state,A7: state,B6: state] :
                      ( ( ( some_state @ C4 )
                        = ( Plus @ A7 @ B6 ) )
                     => ( ( some_state @ ( Core @ C4 ) )
                        = ( Plus @ ( Core @ A7 ) @ ( Core @ B6 ) ) ) )
                 => ( ! [A7: state,B6: state,C4: state] :
                        ( ( ( Plus @ A7 @ B6 )
                          = ( some_state @ C4 ) )
                       => ( ( ( some_state @ C4 )
                            = ( Plus @ C4 @ C4 ) )
                         => ( ( some_state @ A7 )
                            = ( Plus @ A7 @ A7 ) ) ) )
                   => ( ! [A7: state,B6: state,X4: state,Y3: state] :
                          ( ( ( some_state @ A7 )
                            = ( Plus @ B6 @ X4 ) )
                         => ( ( ( some_state @ A7 )
                              = ( Plus @ B6 @ Y3 ) )
                           => ( ( ( Core @ X4 )
                                = ( Core @ Y3 ) )
                             => ( X4 = Y3 ) ) ) )
                     => ( sep_algebra_state @ Plus @ Core ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.intro
thf(fact_318_sep__algebra_Oasso3,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val,Bc: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( Plus @ A3 @ B2 )
          = none_val )
       => ( ( ( Plus @ B2 @ C )
            = ( some_val @ Bc ) )
         => ( ( Plus @ A3 @ Bc )
            = none_val ) ) ) ) ).

% sep_algebra.asso3
thf(fact_319_sep__algebra_Oasso3,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state,Bc: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( Plus @ A3 @ B2 )
          = none_state )
       => ( ( ( Plus @ B2 @ C )
            = ( some_state @ Bc ) )
         => ( ( Plus @ A3 @ Bc )
            = none_state ) ) ) ) ).

% sep_algebra.asso3
thf(fact_320_sep__algebra_Oasso2,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,Ab: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( Plus @ A3 @ B2 )
            = ( some_val @ Ab ) )
          & ( ( Plus @ B2 @ C )
            = none_val ) )
       => ( ( Plus @ Ab @ C )
          = none_val ) ) ) ).

% sep_algebra.asso2
thf(fact_321_sep__algebra_Oasso2,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,Ab: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( Plus @ A3 @ B2 )
            = ( some_state @ Ab ) )
          & ( ( Plus @ B2 @ C )
            = none_state ) )
       => ( ( Plus @ Ab @ C )
          = none_state ) ) ) ).

% sep_algebra.asso2
thf(fact_322_PartialSA_Osep__algebra__axioms,axiom,
    sep_algebra_state @ plus @ core ).

% PartialSA.sep_algebra_axioms
thf(fact_323_sep__algebra_Ominus__equiv__def__any__elem,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X2 )
          = ( Plus @ A3 @ B2 ) )
       => ( ( some_val @ ( sep_minus_val @ Plus @ Core @ X2 @ A3 ) )
          = ( Plus @ B2 @ ( Core @ X2 ) ) ) ) ) ).

% sep_algebra.minus_equiv_def_any_elem
thf(fact_324_sep__algebra_Ominus__equiv__def__any__elem,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X2 )
          = ( Plus @ A3 @ B2 ) )
       => ( ( some_state @ ( sep_minus_state @ Plus @ Core @ X2 @ A3 ) )
          = ( Plus @ B2 @ ( Core @ X2 ) ) ) ) ) ).

% sep_algebra.minus_equiv_def_any_elem
thf(fact_325_sep__algebra_Osplus_Osimps_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_splus_val @ Plus @ ( some_val @ A3 ) @ ( some_val @ B2 ) )
        = ( Plus @ A3 @ B2 ) ) ) ).

% sep_algebra.splus.simps(3)
thf(fact_326_sep__algebra_Osplus_Osimps_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ ( some_state @ A3 ) @ ( some_state @ B2 ) )
        = ( Plus @ A3 @ B2 ) ) ) ).

% sep_algebra.splus.simps(3)
thf(fact_327_sep__algebra_Osplus__develop,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val,D: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A3 )
          = ( Plus @ B2 @ C ) )
       => ( ( Plus @ A3 @ D )
          = ( sep_splus_val @ Plus @ ( sep_splus_val @ Plus @ ( some_val @ B2 ) @ ( some_val @ C ) ) @ ( some_val @ D ) ) ) ) ) ).

% sep_algebra.splus_develop
thf(fact_328_sep__algebra_Osplus__develop,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state,D: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A3 )
          = ( Plus @ B2 @ C ) )
       => ( ( Plus @ A3 @ D )
          = ( sep_splus_state @ Plus @ ( sep_splus_state @ Plus @ ( some_state @ B2 ) @ ( some_state @ C ) ) @ ( some_state @ D ) ) ) ) ) ).

% sep_algebra.splus_develop
thf(fact_329_sep__algebra_Opure__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_pure_val @ Plus @ A3 )
        = ( ( some_val @ A3 )
          = ( Plus @ A3 @ A3 ) ) ) ) ).

% sep_algebra.pure_def
thf(fact_330_sep__algebra_Opure__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_pure_state @ Plus @ A3 )
        = ( ( some_state @ A3 )
          = ( Plus @ A3 @ A3 ) ) ) ) ).

% sep_algebra.pure_def
thf(fact_331_sep__algebra_Opure__stable,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_pure_val @ Plus @ A3 )
       => ( ( sep_pure_val @ Plus @ B2 )
         => ( ( ( some_val @ C )
              = ( Plus @ A3 @ B2 ) )
           => ( sep_pure_val @ Plus @ C ) ) ) ) ) ).

% sep_algebra.pure_stable
thf(fact_332_sep__algebra_Opure__stable,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_pure_state @ Plus @ A3 )
       => ( ( sep_pure_state @ Plus @ B2 )
         => ( ( ( some_state @ C )
              = ( Plus @ A3 @ B2 ) )
           => ( sep_pure_state @ Plus @ C ) ) ) ) ) ).

% sep_algebra.pure_stable
thf(fact_333_sep__algebra_Osplus_Osimps_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Uu: option_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_splus_val @ Plus @ none_val @ Uu )
        = none_val ) ) ).

% sep_algebra.splus.simps(1)
thf(fact_334_sep__algebra_Osplus_Osimps_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Uu: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ none_state @ Uu )
        = none_state ) ) ).

% sep_algebra.splus.simps(1)
thf(fact_335_sep__algebra_Omax__projection__prop__pure__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( sep_ma8214210560313151521_state @ Plus @ ( sep_pure_state @ Plus ) @ Core ) ) ).

% sep_algebra.max_projection_prop_pure_core
thf(fact_336_sep__algebra_Oup__close__equiv,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ A6 )
       => ( ( sep_up_closed_state @ Plus @ B4 )
         => ( ( sep_equiv_state @ Plus @ A6 @ B4 )
            = ( A6 = B4 ) ) ) ) ) ).

% sep_algebra.up_close_equiv
thf(fact_337_package__logic_Omono__pure__cond__conj,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Pc: state > $o,B2: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6595153354952283300_state @ Plus @ Core @ Pc )
       => ( ( packag6595153354952283300_state @ Plus @ Core @ B2 )
         => ( packag6595153354952283300_state @ Plus @ Core @ ( packag1330488657391168505_state @ Pc @ B2 ) ) ) ) ) ).

% package_logic.mono_pure_cond_conj
thf(fact_338_sep__algebra_Osplus_Osimps_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,V2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_splus_val @ Plus @ ( some_val @ V2 ) @ none_val )
        = none_val ) ) ).

% sep_algebra.splus.simps(2)
thf(fact_339_sep__algebra_Osplus_Osimps_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,V2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ ( some_state @ V2 ) @ none_state )
        = none_state ) ) ).

% sep_algebra.splus.simps(2)
thf(fact_340_sep__algebra_Osplus_Oelims,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: option_val,Xa2: option_val,Y: option_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( sep_splus_val @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ( ( X2 = none_val )
           => ( Y != none_val ) )
         => ( ( ? [V: val] :
                  ( X2
                  = ( some_val @ V ) )
             => ( ( Xa2 = none_val )
               => ( Y != none_val ) ) )
           => ~ ! [A7: val] :
                  ( ( X2
                    = ( some_val @ A7 ) )
                 => ! [B6: val] :
                      ( ( Xa2
                        = ( some_val @ B6 ) )
                     => ( Y
                       != ( Plus @ A7 @ B6 ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.elims
thf(fact_341_sep__algebra_Osplus_Oelims,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: option_state,Xa2: option_state,Y: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( sep_splus_state @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ( ( X2 = none_state )
           => ( Y != none_state ) )
         => ( ( ? [V: state] :
                  ( X2
                  = ( some_state @ V ) )
             => ( ( Xa2 = none_state )
               => ( Y != none_state ) ) )
           => ~ ! [A7: state] :
                  ( ( X2
                    = ( some_state @ A7 ) )
                 => ! [B6: state] :
                      ( ( Xa2
                        = ( some_state @ B6 ) )
                     => ( Y
                       != ( Plus @ A7 @ B6 ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.elims
thf(fact_342_sep__algebra_Oequiv__up__closed__subset,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ A6 )
       => ( ( sep_equiv_state @ Plus @ B4 @ C3 )
         => ( ( ord_le2494988322063910608_state @ B4 @ A6 )
            = ( ord_le2494988322063910608_state @ C3 @ A6 ) ) ) ) ) ).

% sep_algebra.equiv_up_closed_subset
thf(fact_343__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_O_A_092_060lbrakk_062a_A_124_D_124_Amultiply_Ap_Aw_059_Appos_Ap_A_092_060and_062_Apgte_Apwrite_Ap_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [P6: prat] :
        ( ( defined @ a2 @ ( multiply @ P6 @ w ) )
       => ~ ( ( ppos @ P6 )
            & ( pgte @ pwrite @ P6 ) ) ) ).

% \<open>\<And>thesis. (\<And>p. \<lbrakk>a |#| multiply p w; ppos p \<and> pgte pwrite p\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_344_asm0,axiom,
    ( ( ppos @ alpha )
    & ( ppos @ beta )
    & ( ( padd @ alpha @ beta )
      = pwrite ) ) ).

% asm0
thf(fact_345_non__scalable__instantiate,axiom,
    ! [W: state,A3: state] :
      ( ~ ( scalable @ W @ A3 )
     => ? [P6: prat] :
          ( ( ppos @ P6 )
          & ( pgte @ pwrite @ P6 )
          & ( defined @ A3 @ ( multiply @ P6 @ W ) ) ) ) ).

% non_scalable_instantiate
thf(fact_346_package__logic__def,axiom,
    ( package_logic_state
    = ( ^ [Plus2: state > state > option_state,Core2: state > state,Unit2: state,Stable2: state > $o] :
          ( ( sep_algebra_state @ Plus2 @ Core2 )
          & ( packag2647621270594721818_state @ Plus2 @ Unit2 @ Stable2 ) ) ) ) ).

% package_logic_def
thf(fact_347_package__logic_Ointro,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( packag2647621270594721818_state @ Plus @ Unit @ Stable )
       => ( package_logic_state @ Plus @ Core @ Unit @ Stable ) ) ) ).

% package_logic.intro
thf(fact_348_multiply__sem__assertion_Oelims,axiom,
    ! [X2: prat,Xa2: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X2 @ Xa2 )
        = Y )
     => ( Y
        = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X2 ) @ Xa2 ) ) ) ) ).

% multiply_sem_assertion.elims
thf(fact_349_multiply__sem__assertion_Osimps,axiom,
    ( multip8064567061438756306ertion
    = ( ^ [P5: prat,P4: set_state] : ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ P5 ) @ P4 ) ) ) ) ).

% multiply_sem_assertion.simps
thf(fact_350_image__eqI,axiom,
    ! [B2: state,F: state > state,X2: state,A6: set_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member_state @ X2 @ A6 )
       => ( member_state @ B2 @ ( image_state_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_351_image__eqI,axiom,
    ! [B2: produc3882902684156697774_state,F: state > produc3882902684156697774_state,X2: state,A6: set_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member_state @ X2 @ A6 )
       => ( member6715010751053357271_state @ B2 @ ( image_5311902671526399277_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_352_image__eqI,axiom,
    ! [B2: state,F: produc3882902684156697774_state > state,X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member6715010751053357271_state @ X2 @ A6 )
       => ( member_state @ B2 @ ( image_6759111139246981411_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_353_image__eqI,axiom,
    ! [B2: produc7272280185086996969_state,F: state > produc7272280185086996969_state,X2: state,A6: set_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member_state @ X2 @ A6 )
       => ( member7461423308196221312_state @ B2 @ ( image_632992669292831658_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_354_image__eqI,axiom,
    ! [B2: state,F: produc7272280185086996969_state > state,X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member7461423308196221312_state @ X2 @ A6 )
       => ( member_state @ B2 @ ( image_2710133271811360426_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_355_image__eqI,axiom,
    ! [B2: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state,X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member6715010751053357271_state @ X2 @ A6 )
       => ( member6715010751053357271_state @ B2 @ ( image_508898238547643525_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_356_image__eqI,axiom,
    ! [B2: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state,X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member7461423308196221312_state @ X2 @ A6 )
       => ( member6715010751053357271_state @ B2 @ ( image_7466395622266389182_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_357_image__eqI,axiom,
    ! [B2: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state,X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member6715010751053357271_state @ X2 @ A6 )
       => ( member7461423308196221312_state @ B2 @ ( image_4364510454419742290_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_358_image__eqI,axiom,
    ! [B2: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state,X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member7461423308196221312_state @ X2 @ A6 )
       => ( member7461423308196221312_state @ B2 @ ( image_3064086290059306969_state @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_359_image__eqI,axiom,
    ! [B2: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val,X2: state,A6: set_state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( ( member_state @ X2 @ A6 )
       => ( member2879030624002546611on_val @ B2 @ ( image_4772210114854293981on_val @ F @ A6 ) ) ) ) ).

% image_eqI
thf(fact_360_imageI,axiom,
    ! [X2: state,A6: set_state,F: state > state] :
      ( ( member_state @ X2 @ A6 )
     => ( member_state @ ( F @ X2 ) @ ( image_state_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_361_imageI,axiom,
    ! [X2: state,A6: set_state,F: state > produc3882902684156697774_state] :
      ( ( member_state @ X2 @ A6 )
     => ( member6715010751053357271_state @ ( F @ X2 ) @ ( image_5311902671526399277_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_362_imageI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( member_state @ ( F @ X2 ) @ ( image_6759111139246981411_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_363_imageI,axiom,
    ! [X2: state,A6: set_state,F: state > produc7272280185086996969_state] :
      ( ( member_state @ X2 @ A6 )
     => ( member7461423308196221312_state @ ( F @ X2 ) @ ( image_632992669292831658_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_364_imageI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( member_state @ ( F @ X2 ) @ ( image_2710133271811360426_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_365_imageI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( member6715010751053357271_state @ ( F @ X2 ) @ ( image_508898238547643525_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_366_imageI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc3882902684156697774_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( member6715010751053357271_state @ ( F @ X2 ) @ ( image_7466395622266389182_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_367_imageI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc7272280185086996969_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( member7461423308196221312_state @ ( F @ X2 ) @ ( image_4364510454419742290_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_368_imageI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( member7461423308196221312_state @ ( F @ X2 ) @ ( image_3064086290059306969_state @ F @ A6 ) ) ) ).

% imageI
thf(fact_369_imageI,axiom,
    ! [X2: state,A6: set_state,F: state > produc9003781588162623004on_val] :
      ( ( member_state @ X2 @ A6 )
     => ( member2879030624002546611on_val @ ( F @ X2 ) @ ( image_4772210114854293981on_val @ F @ A6 ) ) ) ).

% imageI
thf(fact_370_image__iff,axiom,
    ! [Z: state,F: state > state,A6: set_state] :
      ( ( member_state @ Z @ ( image_state_state @ F @ A6 ) )
      = ( ? [X5: state] :
            ( ( member_state @ X5 @ A6 )
            & ( Z
              = ( F @ X5 ) ) ) ) ) ).

% image_iff
thf(fact_371_bex__imageD,axiom,
    ! [F: state > state,A6: set_state,P2: state > $o] :
      ( ? [X3: state] :
          ( ( member_state @ X3 @ ( image_state_state @ F @ A6 ) )
          & ( P2 @ X3 ) )
     => ? [X4: state] :
          ( ( member_state @ X4 @ A6 )
          & ( P2 @ ( F @ X4 ) ) ) ) ).

% bex_imageD
thf(fact_372_image__cong,axiom,
    ! [M: set_state,N: set_state,F: state > state,G: state > state] :
      ( ( M = N )
     => ( ! [X4: state] :
            ( ( member_state @ X4 @ N )
           => ( ( F @ X4 )
              = ( G @ X4 ) ) )
       => ( ( image_state_state @ F @ M )
          = ( image_state_state @ G @ N ) ) ) ) ).

% image_cong
thf(fact_373_ball__imageD,axiom,
    ! [F: state > state,A6: set_state,P2: state > $o] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ ( image_state_state @ F @ A6 ) )
         => ( P2 @ X4 ) )
     => ! [X3: state] :
          ( ( member_state @ X3 @ A6 )
         => ( P2 @ ( F @ X3 ) ) ) ) ).

% ball_imageD
thf(fact_374_rev__image__eqI,axiom,
    ! [X2: state,A6: set_state,B2: state,F: state > state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member_state @ B2 @ ( image_state_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_375_rev__image__eqI,axiom,
    ! [X2: state,A6: set_state,B2: produc3882902684156697774_state,F: state > produc3882902684156697774_state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member6715010751053357271_state @ B2 @ ( image_5311902671526399277_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_376_rev__image__eqI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B2: state,F: produc3882902684156697774_state > state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member_state @ B2 @ ( image_6759111139246981411_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_377_rev__image__eqI,axiom,
    ! [X2: state,A6: set_state,B2: produc7272280185086996969_state,F: state > produc7272280185086996969_state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member7461423308196221312_state @ B2 @ ( image_632992669292831658_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_378_rev__image__eqI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B2: state,F: produc7272280185086996969_state > state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member_state @ B2 @ ( image_2710133271811360426_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_379_rev__image__eqI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B2: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member6715010751053357271_state @ B2 @ ( image_508898238547643525_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_380_rev__image__eqI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B2: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member6715010751053357271_state @ B2 @ ( image_7466395622266389182_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_381_rev__image__eqI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B2: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member7461423308196221312_state @ B2 @ ( image_4364510454419742290_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_382_rev__image__eqI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B2: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member7461423308196221312_state @ B2 @ ( image_3064086290059306969_state @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_383_rev__image__eqI,axiom,
    ! [X2: state,A6: set_state,B2: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val] :
      ( ( member_state @ X2 @ A6 )
     => ( ( B2
          = ( F @ X2 ) )
       => ( member2879030624002546611on_val @ B2 @ ( image_4772210114854293981on_val @ F @ A6 ) ) ) ) ).

% rev_image_eqI
thf(fact_384_top__set__def,axiom,
    ( top_to174962084833059535_state
    = ( collec906845016635587262_state @ top_to3660658859742706806tate_o ) ) ).

% top_set_def
thf(fact_385_top__set__def,axiom,
    ( top_to1561438921946393474on_val
    = ( collec7475294502966882545on_val @ top_to9203468014822947715_val_o ) ) ).

% top_set_def
thf(fact_386_top__set__def,axiom,
    ( top_top_set_state
    = ( collect_state @ top_top_state_o ) ) ).

% top_set_def
thf(fact_387_rangeI,axiom,
    ! [F: state > state,X2: state] : ( member_state @ ( F @ X2 ) @ ( image_state_state @ F @ top_top_set_state ) ) ).

% rangeI
thf(fact_388_rangeI,axiom,
    ! [F: state > produc7272280185086996969_state,X2: state] : ( member7461423308196221312_state @ ( F @ X2 ) @ ( image_632992669292831658_state @ F @ top_top_set_state ) ) ).

% rangeI
thf(fact_389_rangeI,axiom,
    ! [F: state > produc9003781588162623004on_val,X2: state] : ( member2879030624002546611on_val @ ( F @ X2 ) @ ( image_4772210114854293981on_val @ F @ top_top_set_state ) ) ).

% rangeI
thf(fact_390_rangeI,axiom,
    ! [F: state > produc3882902684156697774_state,X2: state] : ( member6715010751053357271_state @ ( F @ X2 ) @ ( image_5311902671526399277_state @ F @ top_top_set_state ) ) ).

% rangeI
thf(fact_391_range__eqI,axiom,
    ! [B2: state,F: state > state,X2: state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( member_state @ B2 @ ( image_state_state @ F @ top_top_set_state ) ) ) ).

% range_eqI
thf(fact_392_range__eqI,axiom,
    ! [B2: produc7272280185086996969_state,F: state > produc7272280185086996969_state,X2: state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( member7461423308196221312_state @ B2 @ ( image_632992669292831658_state @ F @ top_top_set_state ) ) ) ).

% range_eqI
thf(fact_393_range__eqI,axiom,
    ! [B2: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val,X2: state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( member2879030624002546611on_val @ B2 @ ( image_4772210114854293981on_val @ F @ top_top_set_state ) ) ) ).

% range_eqI
thf(fact_394_range__eqI,axiom,
    ! [B2: produc3882902684156697774_state,F: state > produc3882902684156697774_state,X2: state] :
      ( ( B2
        = ( F @ X2 ) )
     => ( member6715010751053357271_state @ B2 @ ( image_5311902671526399277_state @ F @ top_top_set_state ) ) ) ).

% range_eqI
thf(fact_395_subset__image__iff,axiom,
    ! [B4: set_state,F: state > state,A6: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A6 ) )
      = ( ? [AA: set_state] :
            ( ( ord_le2494988322063910608_state @ AA @ A6 )
            & ( B4
              = ( image_state_state @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_396_image__subset__iff,axiom,
    ! [F: state > state,A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A6 ) @ B4 )
      = ( ! [X5: state] :
            ( ( member_state @ X5 @ A6 )
           => ( member_state @ ( F @ X5 ) @ B4 ) ) ) ) ).

% image_subset_iff
thf(fact_397_subset__imageE,axiom,
    ! [B4: set_state,F: state > state,A6: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A6 ) )
     => ~ ! [C5: set_state] :
            ( ( ord_le2494988322063910608_state @ C5 @ A6 )
           => ( B4
             != ( image_state_state @ F @ C5 ) ) ) ) ).

% subset_imageE
thf(fact_398_image__subsetI,axiom,
    ! [A6: set_state,F: state > state,B4: set_state] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ A6 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_399_image__subsetI,axiom,
    ! [A6: set_state,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ A6 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_400_image__subsetI,axiom,
    ! [A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state,B4: set_state] :
      ( ! [X4: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X4 @ A6 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_6759111139246981411_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_401_image__subsetI,axiom,
    ! [A6: set_state,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ A6 )
         => ( member7461423308196221312_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_402_image__subsetI,axiom,
    ! [A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X4 @ A6 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_403_image__subsetI,axiom,
    ! [A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X4 @ A6 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_508898238547643525_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_404_image__subsetI,axiom,
    ! [A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X4 @ A6 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_405_image__subsetI,axiom,
    ! [A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X4 @ A6 )
         => ( member7461423308196221312_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_4364510454419742290_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_406_image__subsetI,axiom,
    ! [A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X4 @ A6 )
         => ( member7461423308196221312_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_407_image__subsetI,axiom,
    ! [A6: set_state,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X4: state] :
          ( ( member_state @ X4 @ A6 )
         => ( member2879030624002546611on_val @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ A6 ) @ B4 ) ) ).

% image_subsetI
thf(fact_408_image__mono,axiom,
    ! [A6: set_state,B4: set_state,F: state > state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A6 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_mono
thf(fact_409_range__subsetD,axiom,
    ! [F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,I: state] :
      ( ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ top_top_set_state ) @ B4 )
     => ( member7461423308196221312_state @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_410_range__subsetD,axiom,
    ! [F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,I: state] :
      ( ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ top_top_set_state ) @ B4 )
     => ( member2879030624002546611on_val @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_411_range__subsetD,axiom,
    ! [F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,I: state] :
      ( ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ top_top_set_state ) @ B4 )
     => ( member6715010751053357271_state @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_412_range__subsetD,axiom,
    ! [F: state > state,B4: set_state,I: state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ top_top_set_state ) @ B4 )
     => ( member_state @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_413_package__logic__axioms__def,axiom,
    ( packag2647621270594721818_state
    = ( ^ [Plus2: state > state > option_state,Unit2: state,Stable2: state > $o] :
          ( ! [A2: state] :
              ( ( some_state @ A2 )
              = ( Plus2 @ A2 @ Unit2 ) )
          & ! [A2: state,B: state,X5: state] :
              ( ( Stable2 @ A2 )
             => ( ( Stable2 @ B )
               => ( ( ( some_state @ X5 )
                    = ( Plus2 @ A2 @ B ) )
                 => ( Stable2 @ X5 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_414_package__logic__axioms__def,axiom,
    ( packag6139878888743580961ms_val
    = ( ^ [Plus2: val > val > option_val,Unit2: val,Stable2: val > $o] :
          ( ! [A2: val] :
              ( ( some_val @ A2 )
              = ( Plus2 @ A2 @ Unit2 ) )
          & ! [A2: val,B: val,X5: val] :
              ( ( Stable2 @ A2 )
             => ( ( Stable2 @ B )
               => ( ( ( some_val @ X5 )
                    = ( Plus2 @ A2 @ B ) )
                 => ( Stable2 @ X5 ) ) ) )
          & ( Stable2 @ Unit2 ) ) ) ) ).

% package_logic_axioms_def
thf(fact_415_package__logic__axioms_Ointro,axiom,
    ! [Plus: state > state > option_state,Unit: state,Stable: state > $o] :
      ( ! [A7: state] :
          ( ( some_state @ A7 )
          = ( Plus @ A7 @ Unit ) )
     => ( ! [A7: state,B6: state,X4: state] :
            ( ( Stable @ A7 )
           => ( ( Stable @ B6 )
             => ( ( ( some_state @ X4 )
                  = ( Plus @ A7 @ B6 ) )
               => ( Stable @ X4 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag2647621270594721818_state @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_416_package__logic__axioms_Ointro,axiom,
    ! [Plus: val > val > option_val,Unit: val,Stable: val > $o] :
      ( ! [A7: val] :
          ( ( some_val @ A7 )
          = ( Plus @ A7 @ Unit ) )
     => ( ! [A7: val,B6: val,X4: val] :
            ( ( Stable @ A7 )
           => ( ( Stable @ B6 )
             => ( ( ( some_val @ X4 )
                  = ( Plus @ A7 @ B6 ) )
               => ( Stable @ X4 ) ) ) )
       => ( ( Stable @ Unit )
         => ( packag6139878888743580961ms_val @ Plus @ Unit @ Stable ) ) ) ) ).

% package_logic_axioms.intro
thf(fact_417_package__logic_Oaxioms_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( packag2647621270594721818_state @ Plus @ Unit @ Stable ) ) ).

% package_logic.axioms(2)
thf(fact_418_combinable__def,axiom,
    ( combinable
    = ( ^ [P4: set_state] :
        ! [Alpha: prat,Beta: prat] :
          ( ( ( ppos @ Alpha )
            & ( ppos @ Beta )
            & ( pgte @ pwrite @ ( padd @ Alpha @ Beta ) ) )
         => ( ord_le2494988322063910608_state @ ( add_set @ ( multip8064567061438756306ertion @ Alpha @ P4 ) @ ( multip8064567061438756306ertion @ Beta @ P4 ) ) @ ( multip8064567061438756306ertion @ ( padd @ Alpha @ Beta ) @ P4 ) ) ) ) ) ).

% combinable_def
thf(fact_419_combinableI,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ! [A7: prat,B6: prat] :
          ( ( ( ppos @ A7 )
            & ( ppos @ B6 )
            & ( ( padd @ A7 @ B6 )
              = pwrite ) )
         => ( ord_le2494988322063910608_state @ ( add_set @ ( multip8064567061438756306ertion @ A7 @ ( cwand @ A6 @ B4 ) ) @ ( multip8064567061438756306ertion @ B6 @ ( cwand @ A6 @ B4 ) ) ) @ ( cwand @ A6 @ B4 ) ) )
     => ( combinable @ ( cwand @ A6 @ B4 ) ) ) ).

% combinableI
thf(fact_420_all__subset__image,axiom,
    ! [F: state > state,A6: set_state,P2: set_state > $o] :
      ( ( ! [B5: set_state] :
            ( ( ord_le2494988322063910608_state @ B5 @ ( image_state_state @ F @ A6 ) )
           => ( P2 @ B5 ) ) )
      = ( ! [B5: set_state] :
            ( ( ord_le2494988322063910608_state @ B5 @ A6 )
           => ( P2 @ ( image_state_state @ F @ B5 ) ) ) ) ) ).

% all_subset_image
thf(fact_421_multiply__twice,axiom,
    ! [A3: prat,B2: prat,X2: state] :
      ( ( ( pgte @ pwrite @ A3 )
        & ( pgte @ pwrite @ B2 ) )
     => ( ( multiply @ A3 @ ( multiply @ B2 @ X2 ) )
        = ( multiply @ ( pmult @ A3 @ B2 ) @ X2 ) ) ) ).

% multiply_twice
thf(fact_422_sep__algebra_Oup__closed__plus__UNIV,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( sep_up_closed_state @ Plus @ ( sep_add_set_state @ Plus @ A6 @ top_top_set_state ) ) ) ).

% sep_algebra.up_closed_plus_UNIV
thf(fact_423_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ X2 @ ( sep_ad3908482799505143387_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ A2 @ A6 )
              & ( member7461423308196221312_state @ B @ B4 )
              & ( ( some_P6297086604321900740_state @ X2 )
                = ( sep_sp9219505543755390023_state @ Plus @ ( some_P6297086604321900740_state @ A2 ) @ ( some_P6297086604321900740_state @ B ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_424_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ X2 @ ( sep_ad8320153009520438926on_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ A2 @ A6 )
              & ( member2879030624002546611on_val @ B @ B4 )
              & ( ( some_P2581650809551911671on_val @ X2 )
                = ( sep_sp4146280900173761658on_val @ Plus @ ( some_P2581650809551911671on_val @ A2 ) @ ( some_P2581650809551911671on_val @ B ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_425_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ X2 @ ( sep_ad8203089552910907580_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ A2 @ A6 )
              & ( member6715010751053357271_state @ B @ B4 )
              & ( ( some_P5383513176685068947_state @ X2 )
                = ( sep_sp7584349535955199440_state @ Plus @ ( some_P5383513176685068947_state @ A2 ) @ ( some_P5383513176685068947_state @ B ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_426_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val,A6: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ X2 @ ( sep_add_set_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: val,B: val] :
              ( ( member_val @ A2 @ A6 )
              & ( member_val @ B @ B4 )
              & ( ( some_val @ X2 )
                = ( sep_splus_val @ Plus @ ( some_val @ A2 ) @ ( some_val @ B ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_427_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ X2 @ ( sep_add_set_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: state,B: state] :
              ( ( member_state @ A2 @ A6 )
              & ( member_state @ B @ B4 )
              & ( ( some_state @ X2 )
                = ( sep_splus_state @ Plus @ ( some_state @ A2 ) @ ( some_state @ B ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_428_get__h__multiply,axiom,
    ! [P: prat,X2: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_h @ ( multiply @ P @ X2 ) )
        = ( get_h @ X2 ) ) ) ).

% get_h_multiply
thf(fact_429_sep__algebra_Osplus_Ocases,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: produc5122021904355189735on_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ! [Uu2: option_val] :
            ( X2
           != ( produc904852209897547607on_val @ none_val @ Uu2 ) )
       => ( ! [V: val] :
              ( X2
             != ( produc904852209897547607on_val @ ( some_val @ V ) @ none_val ) )
         => ~ ! [A7: val,B6: val] :
                ( X2
               != ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) ) ) ) ) ).

% sep_algebra.splus.cases
thf(fact_430_sep__algebra_Osplus_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: produc3142500478612311029_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [Uu2: option_state] :
            ( X2
           != ( produc9160152616361873709_state @ none_state @ Uu2 ) )
       => ( ! [V: state] :
              ( X2
             != ( produc9160152616361873709_state @ ( some_state @ V ) @ none_state ) )
         => ~ ! [A7: state,B6: state] :
                ( X2
               != ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) ) ).

% sep_algebra.splus.cases
thf(fact_431_sep__algebra_Oadd__set_Ocong,axiom,
    sep_add_set_state = sep_add_set_state ).

% sep_algebra.add_set.cong
thf(fact_432_ssubsetI,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [Pi: state,H: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi @ H ) @ A6 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi @ H ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_433_ssubsetI,axiom,
    ! [A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [Pi: state,H: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi @ H ) @ A6 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi @ H ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_434_ssubsetI,axiom,
    ! [A6: set_Pr1688445902015331925_state,B4: set_Pr1688445902015331925_state] :
      ( ! [Pi: option_state,H: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi @ H ) @ A6 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi @ H ) @ B4 ) )
     => ( ord_le6423325748750870005_state @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_435_ssubsetI,axiom,
    ! [A6: set_Pr6039890582625207499_state,B4: set_Pr6039890582625207499_state] :
      ( ! [Pi: prat,H: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi @ H ) @ A6 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi @ H ) @ B4 ) )
     => ( ord_le262197048489888875_state @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_436_ssubsetI,axiom,
    ! [A6: set_Pr6847263425858009217_state,B4: set_Pr6847263425858009217_state] :
      ( ! [Pi: prat,H: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi @ H ) @ A6 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi @ H ) @ B4 ) )
     => ( ord_le5761494056910127137_state @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_437_ssubsetI,axiom,
    ! [A6: set_Pr2507339680178222706t_char,B4: set_Pr2507339680178222706t_char] :
      ( ! [Pi: nat,H: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi @ H ) @ A6 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi @ H ) @ B4 ) )
     => ( ord_le6315511645215477266t_char @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_438_ssubsetI,axiom,
    ! [A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi @ H ) @ A6 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi @ H ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A6 @ B4 ) ) ).

% ssubsetI
thf(fact_439_core__defined_I1_J,axiom,
    ! [Phi: state] :
      ( ( get_h @ ( core @ Phi ) )
      = ( get_h @ Phi ) ) ).

% core_defined(1)
thf(fact_440_sep__algebra_Oadd__set__commm,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_add_set_state @ Plus @ A6 @ B4 )
        = ( sep_add_set_state @ Plus @ B4 @ A6 ) ) ) ).

% sep_algebra.add_set_commm
thf(fact_441_sep__algebra_Oadd__set__asso,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_add_set_state @ Plus @ ( sep_add_set_state @ Plus @ A6 @ B4 ) @ C3 )
        = ( sep_add_set_state @ Plus @ A6 @ ( sep_add_set_state @ Plus @ B4 @ C3 ) ) ) ) ).

% sep_algebra.add_set_asso
thf(fact_442_None__notin__image__Some,axiom,
    ! [A6: set_state] :
      ~ ( member_option_state @ none_state @ ( image_6076465424260689483_state @ some_state @ A6 ) ) ).

% None_notin_image_Some
thf(fact_443_None__notin__image__Some,axiom,
    ! [A6: set_val] :
      ~ ( member_option_val @ none_val @ ( image_val_option_val @ some_val @ A6 ) ) ).

% None_notin_image_Some
thf(fact_444_compatible__options_Ocases,axiom,
    ! [X2: produc3142500478612311029_state] :
      ( ! [A7: state,B6: state] :
          ( X2
         != ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
     => ( ! [Uv2: option_state] :
            ( X2
           != ( produc9160152616361873709_state @ none_state @ Uv2 ) )
       => ~ ! [Uu2: option_state] :
              ( X2
             != ( produc9160152616361873709_state @ Uu2 @ none_state ) ) ) ) ).

% compatible_options.cases
thf(fact_445_compatible__options_Ocases,axiom,
    ! [X2: produc5122021904355189735on_val] :
      ( ! [A7: val,B6: val] :
          ( X2
         != ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
     => ( ! [Uv2: option_val] :
            ( X2
           != ( produc904852209897547607on_val @ none_val @ Uv2 ) )
       => ~ ! [Uu2: option_val] :
              ( X2
             != ( produc904852209897547607on_val @ Uu2 @ none_val ) ) ) ) ).

% compatible_options.cases
thf(fact_446_PartialSA_Osplus_Ocases,axiom,
    ! [X2: produc3142500478612311029_state] :
      ( ! [Uu2: option_state] :
          ( X2
         != ( produc9160152616361873709_state @ none_state @ Uu2 ) )
     => ( ! [V: state] :
            ( X2
           != ( produc9160152616361873709_state @ ( some_state @ V ) @ none_state ) )
       => ~ ! [A7: state,B6: state] :
              ( X2
             != ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) ).

% PartialSA.splus.cases
thf(fact_447_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ X2 @ ( sep_ad3908482799505143387_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ A2 @ A6 )
              & ( member7461423308196221312_state @ B @ B4 )
              & ( ( some_P6297086604321900740_state @ X2 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_448_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ X2 @ ( sep_ad8320153009520438926on_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ A2 @ A6 )
              & ( member2879030624002546611on_val @ B @ B4 )
              & ( ( some_P2581650809551911671on_val @ X2 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_449_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ X2 @ ( sep_ad8203089552910907580_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ A2 @ A6 )
              & ( member6715010751053357271_state @ B @ B4 )
              & ( ( some_P5383513176685068947_state @ X2 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_450_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val,A6: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ X2 @ ( sep_add_set_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: val,B: val] :
              ( ( member_val @ A2 @ A6 )
              & ( member_val @ B @ B4 )
              & ( ( some_val @ X2 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_451_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ X2 @ ( sep_add_set_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: state,B: state] :
              ( ( member_state @ A2 @ A6 )
              & ( member_state @ B @ B4 )
              & ( ( some_state @ X2 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_452_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Phi: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ Phi @ ( sep_ad3908482799505143387_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B: produc7272280185086996969_state] :
              ( ( ( some_P6297086604321900740_state @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( member7461423308196221312_state @ A2 @ A6 )
              & ( member7461423308196221312_state @ B @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_453_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Phi: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ Phi @ ( sep_ad8320153009520438926on_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B: produc9003781588162623004on_val] :
              ( ( ( some_P2581650809551911671on_val @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( member2879030624002546611on_val @ A2 @ A6 )
              & ( member2879030624002546611on_val @ B @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_454_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Phi: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ Phi @ ( sep_ad8203089552910907580_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B: produc3882902684156697774_state] :
              ( ( ( some_P5383513176685068947_state @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( member6715010751053357271_state @ A2 @ A6 )
              & ( member6715010751053357271_state @ B @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_455_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Phi: val,A6: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ Phi @ ( sep_add_set_val @ Plus @ A6 @ B4 ) )
        = ( ? [A2: val,B: val] :
              ( ( ( some_val @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( member_val @ A2 @ A6 )
              & ( member_val @ B @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_456_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Phi: state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ Phi @ ( sep_add_set_state @ Plus @ A6 @ B4 ) )
        = ( ? [A2: state,B: state] :
              ( ( ( some_state @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( member_state @ A2 @ A6 )
              & ( member_state @ B @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_457_add__set__def,axiom,
    ( add_set
    = ( sep_add_set_state @ plus ) ) ).

% add_set_def
thf(fact_458_notin__range__Some,axiom,
    ! [X2: option_val] :
      ( ( ~ ( member_option_val @ X2 @ ( image_val_option_val @ some_val @ top_top_set_val ) ) )
      = ( X2 = none_val ) ) ).

% notin_range_Some
thf(fact_459_notin__range__Some,axiom,
    ! [X2: option_state] :
      ( ( ~ ( member_option_state @ X2 @ ( image_6076465424260689483_state @ some_state @ top_top_set_state ) ) )
      = ( X2 = none_state ) ) ).

% notin_range_Some
thf(fact_460_sep__algebra_Oup__closed__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ A6 )
       => ( sep_up_closed_state @ Plus @ ( sep_add_set_state @ Plus @ A6 @ B4 ) ) ) ) ).

% sep_algebra.up_closed_sum
thf(fact_461_sep__algebra_Obigger__set,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A8: set_state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_gr7105985528888466643_state @ Plus @ A8 @ A6 )
       => ( sep_gr7105985528888466643_state @ Plus @ ( sep_add_set_state @ Plus @ A8 @ B4 ) @ ( sep_add_set_state @ Plus @ A6 @ B4 ) ) ) ) ).

% sep_algebra.bigger_set
thf(fact_462_sep__algebra_Oequiv__stable__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state,C3: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_equiv_state @ Plus @ A6 @ B4 )
       => ( sep_equiv_state @ Plus @ ( sep_add_set_state @ Plus @ A6 @ C3 ) @ ( sep_add_set_state @ Plus @ B4 @ C3 ) ) ) ) ).

% sep_algebra.equiv_stable_sum
thf(fact_463_r3,axiom,
    ( ( ( get_h @ ( r @ a2 @ w ) )
      = ( get_h @ w ) )
    & ( ( get_m @ ( r @ a2 @ w ) )
      = ( comp_min_mask @ ( get_m @ a2 ) @ ( get_m @ w ) ) ) ) ).

% r3
thf(fact_464_r1,axiom,
    ( ( ( get_h @ ( r @ a2 @ wa ) )
      = ( get_h @ wa ) )
    & ( ( get_m @ ( r @ a2 @ wa ) )
      = ( comp_min_mask @ ( get_m @ a2 ) @ ( get_m @ wa ) ) ) ) ).

% r1
thf(fact_465_get__m__smaller,axiom,
    ! [P: prat,A3: state,Hl2: produc1457211279475724562t_char] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_m @ ( multiply @ P @ A3 ) @ Hl2 )
        = ( pmult @ P @ ( get_m @ A3 @ Hl2 ) ) ) ) ).

% get_m_smaller
thf(fact_466_sep__algebra_Osplus_Opelims,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: option_val,Xa2: option_val,Y: option_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( sep_splus_val @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ X2 @ Xa2 ) )
         => ( ( ( X2 = none_val )
             => ( ( Y = none_val )
               => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) ) )
           => ( ! [V: val] :
                  ( ( X2
                    = ( some_val @ V ) )
                 => ( ( Xa2 = none_val )
                   => ( ( Y = none_val )
                     => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ ( some_val @ V ) @ none_val ) ) ) ) )
             => ~ ! [A7: val] :
                    ( ( X2
                      = ( some_val @ A7 ) )
                   => ! [B6: val] :
                        ( ( Xa2
                          = ( some_val @ B6 ) )
                       => ( ( Y
                            = ( Plus @ A7 @ B6 ) )
                         => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.pelims
thf(fact_467_sep__algebra_Osplus_Opelims,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: option_state,Xa2: option_state,Y: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( sep_splus_state @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ X2 @ Xa2 ) )
         => ( ( ( X2 = none_state )
             => ( ( Y = none_state )
               => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
           => ( ! [V: state] :
                  ( ( X2
                    = ( some_state @ V ) )
                 => ( ( Xa2 = none_state )
                   => ( ( Y = none_state )
                     => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ V ) @ none_state ) ) ) ) )
             => ~ ! [A7: state] :
                    ( ( X2
                      = ( some_state @ A7 ) )
                   => ! [B6: state] :
                        ( ( Xa2
                          = ( some_state @ B6 ) )
                       => ( ( Y
                            = ( Plus @ A7 @ B6 ) )
                         => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.pelims
thf(fact_468_relChain__def,axiom,
    ( bNF_Ca2815325664443363616_state
    = ( ^ [R2: set_Pr1688445902015331925_state,As: option_state > set_state] :
        ! [I2: option_state,J: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ I2 @ J ) @ R2 )
         => ( ord_le2494988322063910608_state @ ( As @ I2 ) @ ( As @ J ) ) ) ) ) ).

% relChain_def
thf(fact_469_image__Fpow__mono,axiom,
    ! [F: state > state,A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A6 ) @ B4 )
     => ( ord_le5175021213330142598_state @ ( image_2476256681063834599_state @ ( image_state_state @ F ) @ ( finite_Fpow_state @ A6 ) ) @ ( finite_Fpow_state @ B4 ) ) ) ).

% image_Fpow_mono
thf(fact_470_state__ext,axiom,
    ! [A3: state,B2: state] :
      ( ( ( get_h @ A3 )
        = ( get_h @ B2 ) )
     => ( ( ( get_m @ A3 )
          = ( get_m @ B2 ) )
       => ( A3 = B2 ) ) ) ).

% state_ext
thf(fact_471_Fpow__mono,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ord_le5175021213330142598_state @ ( finite_Fpow_state @ A6 ) @ ( finite_Fpow_state @ B4 ) ) ) ).

% Fpow_mono
thf(fact_472_larger__implies__greater__mask__hl,axiom,
    ! [A3: state,B2: state,Hl2: produc1457211279475724562t_char] :
      ( ( greater @ A3 @ B2 )
     => ( pgte @ ( get_m @ A3 @ Hl2 ) @ ( get_m @ B2 @ Hl2 ) ) ) ).

% larger_implies_greater_mask_hl
thf(fact_473_non__scalable__R__charact,axiom,
    ! [W: state,A3: state] :
      ( ~ ( scalable @ W @ A3 )
     => ( ( ( get_m @ ( r @ A3 @ W ) )
          = ( comp_min_mask @ ( get_m @ A3 ) @ ( get_m @ W ) ) )
        & ( ( get_h @ ( r @ A3 @ W ) )
          = ( get_h @ W ) ) ) ) ).

% non_scalable_R_charact
thf(fact_474_PartialSA_Osplus_Opelims,axiom,
    ! [X2: option_state,Xa2: option_state,Y: option_state] :
      ( ( ( sep_splus_state @ plus @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ X2 @ Xa2 ) )
       => ( ( ( X2 = none_state )
           => ( ( Y = none_state )
             => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
         => ( ! [V: state] :
                ( ( X2
                  = ( some_state @ V ) )
               => ( ( Xa2 = none_state )
                 => ( ( Y = none_state )
                   => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ V ) @ none_state ) ) ) ) )
           => ~ ! [A7: state] :
                  ( ( X2
                    = ( some_state @ A7 ) )
                 => ! [B6: state] :
                      ( ( Xa2
                        = ( some_state @ B6 ) )
                     => ( ( Y
                          = ( plus @ A7 @ B6 ) )
                       => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) ) ) ) ) ) ).

% PartialSA.splus.pelims
thf(fact_475_compatible__options_Opelims_I2_J,axiom,
    ! [X2: option_state,Xa2: option_state] :
      ( ( compat2278460363914054422_state @ X2 @ Xa2 )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X2 @ Xa2 ) )
       => ( ! [A7: state] :
              ( ( X2
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
                   => ( A7 != B6 ) ) ) )
         => ( ( ( X2 = none_state )
             => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) )
           => ~ ( ( Xa2 = none_state )
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X2 @ none_state ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_476_compatible__options_Opelims_I2_J,axiom,
    ! [X2: option_val,Xa2: option_val] :
      ( ( compat7209469420100717861ns_val @ X2 @ Xa2 )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X2 @ Xa2 ) )
       => ( ! [A7: val] :
              ( ( X2
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
                   => ( A7 != B6 ) ) ) )
         => ( ( ( X2 = none_val )
             => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) )
           => ~ ( ( Xa2 = none_val )
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X2 @ none_val ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_477_compatible__options_Opelims_I1_J,axiom,
    ! [X2: option_state,Xa2: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X2 @ Xa2 ) )
       => ( ! [A7: state] :
              ( ( X2
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( Y
                      = ( A7 = B6 ) )
                   => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) ) ) ) )
         => ( ( ( X2 = none_state )
             => ( Y
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
           => ~ ( ( Xa2 = none_state )
               => ( Y
                 => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X2 @ none_state ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_478_compatible__options_Opelims_I1_J,axiom,
    ! [X2: option_val,Xa2: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X2 @ Xa2 ) )
       => ( ! [A7: val] :
              ( ( X2
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( Y
                      = ( A7 = B6 ) )
                   => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) ) ) ) )
         => ( ( ( X2 = none_val )
             => ( Y
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) ) )
           => ~ ( ( Xa2 = none_val )
               => ( Y
                 => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X2 @ none_val ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_479_R__def,axiom,
    ( r
    = ( ^ [A2: state,W2: state] : ( if_state @ ( scalable @ W2 @ A2 ) @ W2 @ ( abs_state @ ( produc74620467203698198on_val @ ( comp_min_mask @ ( get_m @ A2 ) @ ( get_m @ W2 ) ) @ ( get_h @ W2 ) ) ) ) ) ) ).

% R_def
thf(fact_480_compatible__options_Opelims_I3_J,axiom,
    ! [X2: option_state,Xa2: option_state] :
      ( ~ ( compat2278460363914054422_state @ X2 @ Xa2 )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X2 @ Xa2 ) )
       => ~ ! [A7: state] :
              ( ( X2
                = ( some_state @ A7 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A7 ) @ ( some_state @ B6 ) ) )
                   => ( A7 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_481_compatible__options_Opelims_I3_J,axiom,
    ! [X2: option_val,Xa2: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X2 @ Xa2 )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X2 @ Xa2 ) )
       => ~ ! [A7: val] :
              ( ( X2
                = ( some_val @ A7 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A7 ) @ ( some_val @ B6 ) ) )
                   => ( A7 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_482_subrelI,axiom,
    ! [R: set_Pr4231240917283394591_state,S: set_Pr4231240917283394591_state] :
      ( ! [X4: state,Y3: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X4 @ Y3 ) @ R )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X4 @ Y3 ) @ S ) )
     => ( ord_le4032880777312351359_state @ R @ S ) ) ).

% subrelI
thf(fact_483_subrelI,axiom,
    ! [R: set_Pr2391701600042252046_state,S: set_Pr2391701600042252046_state] :
      ( ! [X4: state,Y3: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X4 @ Y3 ) @ R )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X4 @ Y3 ) @ S ) )
     => ( ord_le6483787752022044334_state @ R @ S ) ) ).

% subrelI
thf(fact_484_subrelI,axiom,
    ! [R: set_Pr1688445902015331925_state,S: set_Pr1688445902015331925_state] :
      ( ! [X4: option_state,Y3: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X4 @ Y3 ) @ R )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X4 @ Y3 ) @ S ) )
     => ( ord_le6423325748750870005_state @ R @ S ) ) ).

% subrelI
thf(fact_485_subrelI,axiom,
    ! [R: set_Pr6039890582625207499_state,S: set_Pr6039890582625207499_state] :
      ( ! [X4: prat,Y3: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X4 @ Y3 ) @ R )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X4 @ Y3 ) @ S ) )
     => ( ord_le262197048489888875_state @ R @ S ) ) ).

% subrelI
thf(fact_486_subrelI,axiom,
    ! [R: set_Pr6847263425858009217_state,S: set_Pr6847263425858009217_state] :
      ( ! [X4: prat,Y3: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X4 @ Y3 ) @ R )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X4 @ Y3 ) @ S ) )
     => ( ord_le5761494056910127137_state @ R @ S ) ) ).

% subrelI
thf(fact_487_subrelI,axiom,
    ! [R: set_Pr2507339680178222706t_char,S: set_Pr2507339680178222706t_char] :
      ( ! [X4: nat,Y3: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X4 @ Y3 ) @ R )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X4 @ Y3 ) @ S ) )
     => ( ord_le6315511645215477266t_char @ R @ S ) ) ).

% subrelI
thf(fact_488_subrelI,axiom,
    ! [R: set_Pr7649655576376376530on_val,S: set_Pr7649655576376376530on_val] :
      ( ! [X4: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X4 @ Y3 ) @ R )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X4 @ Y3 ) @ S ) )
     => ( ord_le6900622908513426738on_val @ R @ S ) ) ).

% subrelI
thf(fact_489_get__m__smaller__mask,axiom,
    ! [P: prat,A3: state] :
      ( ( pgte @ pwrite @ P )
     => ( ( get_m @ ( multiply @ P @ A3 ) )
        = ( multiply_mask @ P @ ( get_m @ A3 ) ) ) ) ).

% get_m_smaller_mask
thf(fact_490_valid__state_Ocases,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
          ( X2
         != ( produc74620467203698198on_val @ Pi @ H ) ) ).

% valid_state.cases
thf(fact_491_add__states_Ocases,axiom,
    ! [X2: produc1317171644805857433on_val] :
      ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val,Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
          ( X2
         != ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi @ H ) @ ( produc74620467203698198on_val @ Pi2 @ H2 ) ) ) ).

% add_states.cases
thf(fact_492_mult__write__mask,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ pwrite @ Pi3 )
      = Pi3 ) ).

% mult_write_mask
thf(fact_493_multiply__mask__def,axiom,
    ( multiply_mask
    = ( ^ [P5: prat,Pi4: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char] : ( pmult @ P5 @ ( Pi4 @ Hl ) ) ) ) ).

% multiply_mask_def
thf(fact_494_multiply_Oelims,axiom,
    ! [X2: prat,Xa2: state,Y: state] :
      ( ( ( multiply @ X2 @ Xa2 )
        = Y )
     => ( Y
        = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X2 @ ( get_m @ Xa2 ) ) @ ( get_h @ Xa2 ) ) ) ) ) ).

% multiply.elims
thf(fact_495_multiply_Osimps,axiom,
    ( multiply
    = ( ^ [P5: prat,Phi4: state] : ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ P5 @ ( get_m @ Phi4 ) ) @ ( get_h @ Phi4 ) ) ) ) ) ).

% multiply.simps
thf(fact_496_binary__def,axiom,
    ( binary
    = ( ^ [A: set_state] :
        ! [X5: state] :
          ( ( member_state @ X5 @ A )
         => ( member_state @ ( abs_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ X5 ) ) @ ( get_h @ X5 ) ) ) @ A ) ) ) ) ).

% binary_def
thf(fact_497_multiply__valid,axiom,
    ! [P: prat,Phi: state] :
      ( ( pgte @ pwrite @ P )
     => ( valid_state @ ( produc74620467203698198on_val @ ( multiply_mask @ P @ ( get_m @ Phi ) ) @ ( get_h @ Phi ) ) ) ) ).

% multiply_valid
thf(fact_498_core__def,axiom,
    ( core
    = ( ^ [Phi4: state] : ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ ( get_h @ Phi4 ) ) ) ) ) ).

% core_def
thf(fact_499_multiply_Opelims,axiom,
    ! [X2: prat,Xa2: state,Y: state] :
      ( ( ( multiply @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X2 @ Xa2 ) )
       => ~ ( ( Y
              = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X2 @ ( get_m @ Xa2 ) ) @ ( get_h @ Xa2 ) ) ) )
           => ~ ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X2 @ Xa2 ) ) ) ) ) ).

% multiply.pelims
thf(fact_500_these__image__Some__eq,axiom,
    ! [A6: set_state] :
      ( ( these_state @ ( image_6076465424260689483_state @ some_state @ A6 ) )
      = A6 ) ).

% these_image_Some_eq
thf(fact_501_these__image__Some__eq,axiom,
    ! [A6: set_val] :
      ( ( these_val @ ( image_val_option_val @ some_val @ A6 ) )
      = A6 ) ).

% these_image_Some_eq
thf(fact_502_multiply__sem__assertion_Opelims,axiom,
    ! [X2: prat,Xa2: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X2 @ Xa2 ) )
       => ~ ( ( Y
              = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X2 ) @ Xa2 ) ) )
           => ~ ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X2 @ Xa2 ) ) ) ) ) ).

% multiply_sem_assertion.pelims
thf(fact_503_valid__pre__unit,axiom,
    valid_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ).

% valid_pre_unit
thf(fact_504_multiply_Ocases,axiom,
    ! [X2: produc4844402304972151915_state] :
      ~ ! [P6: prat,Phi5: state] :
          ( X2
         != ( produc6205719116230455971_state @ P6 @ Phi5 ) ) ).

% multiply.cases
thf(fact_505_multiply__sem__assertion_Ocases,axiom,
    ! [X2: produc6251377953716854561_state] :
      ~ ! [P6: prat,P7: set_state] :
          ( X2
         != ( produc9080284787853255769_state @ P6 @ P7 ) ) ).

% multiply_sem_assertion.cases
thf(fact_506_in__these__eq,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_op8023886964038656367_state] :
      ( ( member7461423308196221312_state @ X2 @ ( these_4347185934205712492_state @ A6 ) )
      = ( member3894984953261475024_state @ ( some_P6297086604321900740_state @ X2 ) @ A6 ) ) ).

% in_these_eq
thf(fact_507_in__these__eq,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_op6240181410663953058on_val] :
      ( ( member2879030624002546611on_val @ X2 @ ( these_3919539662624406175on_val @ A6 ) )
      = ( member4602090469187516291on_val @ ( some_P2581650809551911671on_val @ X2 ) @ A6 ) ) ).

% in_these_eq
thf(fact_508_in__these__eq,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_op3387789762728285652_state] :
      ( ( member6715010751053357271_state @ X2 @ ( these_7452845017025203435_state @ A6 ) )
      = ( member5919342556599141533_state @ ( some_P5383513176685068947_state @ X2 ) @ A6 ) ) ).

% in_these_eq
thf(fact_509_in__these__eq,axiom,
    ! [X2: state,A6: set_option_state] :
      ( ( member_state @ X2 @ ( these_state @ A6 ) )
      = ( member_option_state @ ( some_state @ X2 ) @ A6 ) ) ).

% in_these_eq
thf(fact_510_in__these__eq,axiom,
    ! [X2: val,A6: set_option_val] :
      ( ( member_val @ X2 @ ( these_val @ A6 ) )
      = ( member_option_val @ ( some_val @ X2 ) @ A6 ) ) ).

% in_these_eq
thf(fact_511_valid__bin,axiom,
    ! [A3: state] : ( valid_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ A3 ) ) @ ( get_h @ A3 ) ) ) ).

% valid_bin
thf(fact_512_core__defined_I2_J,axiom,
    ! [Phi: state] :
      ( ( get_m @ ( core @ Phi ) )
      = empty_3446695950879338768t_char ) ).

% core_defined(2)
thf(fact_513_unit__def,axiom,
    ( unit
    = ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ) ) ).

% unit_def
thf(fact_514_get__h__m,axiom,
    ( rep_state
    = ( ^ [X5: state] : ( produc74620467203698198on_val @ ( get_m @ X5 ) @ ( get_h @ X5 ) ) ) ) ).

% get_h_m
thf(fact_515_image__Pow__mono,axiom,
    ! [F: state > state,A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A6 ) @ B4 )
     => ( ord_le5175021213330142598_state @ ( image_2476256681063834599_state @ ( image_state_state @ F ) @ ( pow_state @ A6 ) ) @ ( pow_state @ B4 ) ) ) ).

% image_Pow_mono
thf(fact_516_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_517_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_518_binary__mask__def,axiom,
    ( binary_mask
    = ( ^ [Pi4: produc1457211279475724562t_char > prat,L: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( Pi4 @ L )
            = pwrite )
          @ pwrite
          @ pnone ) ) ) ).

% binary_mask_def
thf(fact_519_insert__absorb2,axiom,
    ! [X2: state,A6: set_state] :
      ( ( insert_state @ X2 @ ( insert_state @ X2 @ A6 ) )
      = ( insert_state @ X2 @ A6 ) ) ).

% insert_absorb2
thf(fact_520_insert__iff,axiom,
    ! [A3: state,B2: state,A6: set_state] :
      ( ( member_state @ A3 @ ( insert_state @ B2 @ A6 ) )
      = ( ( A3 = B2 )
        | ( member_state @ A3 @ A6 ) ) ) ).

% insert_iff
thf(fact_521_insert__iff,axiom,
    ! [A3: produc7272280185086996969_state,B2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ B2 @ A6 ) )
      = ( ( A3 = B2 )
        | ( member7461423308196221312_state @ A3 @ A6 ) ) ) ).

% insert_iff
thf(fact_522_insert__iff,axiom,
    ! [A3: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ B2 @ A6 ) )
      = ( ( A3 = B2 )
        | ( member2879030624002546611on_val @ A3 @ A6 ) ) ) ).

% insert_iff
thf(fact_523_insert__iff,axiom,
    ! [A3: produc3882902684156697774_state,B2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ B2 @ A6 ) )
      = ( ( A3 = B2 )
        | ( member6715010751053357271_state @ A3 @ A6 ) ) ) ).

% insert_iff
thf(fact_524_insertCI,axiom,
    ! [A3: state,B4: set_state,B2: state] :
      ( ( ~ ( member_state @ A3 @ B4 )
       => ( A3 = B2 ) )
     => ( member_state @ A3 @ ( insert_state @ B2 @ B4 ) ) ) ).

% insertCI
thf(fact_525_insertCI,axiom,
    ! [A3: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,B2: produc7272280185086996969_state] :
      ( ( ~ ( member7461423308196221312_state @ A3 @ B4 )
       => ( A3 = B2 ) )
     => ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ B2 @ B4 ) ) ) ).

% insertCI
thf(fact_526_insertCI,axiom,
    ! [A3: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val] :
      ( ( ~ ( member2879030624002546611on_val @ A3 @ B4 )
       => ( A3 = B2 ) )
     => ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ B2 @ B4 ) ) ) ).

% insertCI
thf(fact_527_insertCI,axiom,
    ! [A3: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,B2: produc3882902684156697774_state] :
      ( ( ~ ( member6715010751053357271_state @ A3 @ B4 )
       => ( A3 = B2 ) )
     => ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ B2 @ B4 ) ) ) ).

% insertCI
thf(fact_528_insert__image,axiom,
    ! [X2: state,A6: set_state,F: state > state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( insert_state @ ( F @ X2 ) @ ( image_state_state @ F @ A6 ) )
        = ( image_state_state @ F @ A6 ) ) ) ).

% insert_image
thf(fact_529_insert__image,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( insert_state @ ( F @ X2 ) @ ( image_2710133271811360426_state @ F @ A6 ) )
        = ( image_2710133271811360426_state @ F @ A6 ) ) ) ).

% insert_image
thf(fact_530_insert__image,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,F: produc9003781588162623004on_val > state] :
      ( ( member2879030624002546611on_val @ X2 @ A6 )
     => ( ( insert_state @ ( F @ X2 ) @ ( image_1205529093420515805_state @ F @ A6 ) )
        = ( image_1205529093420515805_state @ F @ A6 ) ) ) ).

% insert_image
thf(fact_531_insert__image,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( insert_state @ ( F @ X2 ) @ ( image_6759111139246981411_state @ F @ A6 ) )
        = ( image_6759111139246981411_state @ F @ A6 ) ) ) ).

% insert_image
thf(fact_532_image__insert,axiom,
    ! [F: state > state,A3: state,B4: set_state] :
      ( ( image_state_state @ F @ ( insert_state @ A3 @ B4 ) )
      = ( insert_state @ ( F @ A3 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_insert
thf(fact_533_insert__subset,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( insert175804457004744729_state @ X2 @ A6 ) @ B4 )
      = ( ( member7461423308196221312_state @ X2 @ B4 )
        & ( ord_le4032880777312351359_state @ A6 @ B4 ) ) ) ).

% insert_subset
thf(fact_534_insert__subset,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ ( insert3030518898131756108on_val @ X2 @ A6 ) @ B4 )
      = ( ( member2879030624002546611on_val @ X2 @ B4 )
        & ( ord_le6900622908513426738on_val @ A6 @ B4 ) ) ) ).

% insert_subset
thf(fact_535_insert__subset,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ ( insert94804854012721790_state @ X2 @ A6 ) @ B4 )
      = ( ( member6715010751053357271_state @ X2 @ B4 )
        & ( ord_le6483787752022044334_state @ A6 @ B4 ) ) ) ).

% insert_subset
thf(fact_536_insert__subset,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( insert_state @ X2 @ A6 ) @ B4 )
      = ( ( member_state @ X2 @ B4 )
        & ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ) ).

% insert_subset
thf(fact_537_Pow__UNIV,axiom,
    ( ( pow_state @ top_top_set_state )
    = top_to5262587396890829782_state ) ).

% Pow_UNIV
thf(fact_538_PowI,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( member_set_state @ A6 @ ( pow_state @ B4 ) ) ) ).

% PowI
thf(fact_539_Pow__iff,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( member_set_state @ A6 @ ( pow_state @ B4 ) )
      = ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ).

% Pow_iff
thf(fact_540_these__insert__None,axiom,
    ! [A6: set_option_state] :
      ( ( these_state @ ( insert_option_state @ none_state @ A6 ) )
      = ( these_state @ A6 ) ) ).

% these_insert_None
thf(fact_541_these__insert__None,axiom,
    ! [A6: set_option_val] :
      ( ( these_val @ ( insert_option_val @ none_val @ A6 ) )
      = ( these_val @ A6 ) ) ).

% these_insert_None
thf(fact_542_these__insert__Some,axiom,
    ! [X2: state,A6: set_option_state] :
      ( ( these_state @ ( insert_option_state @ ( some_state @ X2 ) @ A6 ) )
      = ( insert_state @ X2 @ ( these_state @ A6 ) ) ) ).

% these_insert_Some
thf(fact_543_these__insert__Some,axiom,
    ! [X2: val,A6: set_option_val] :
      ( ( these_val @ ( insert_option_val @ ( some_val @ X2 ) @ A6 ) )
      = ( insert_val @ X2 @ ( these_val @ A6 ) ) ) ).

% these_insert_Some
thf(fact_544_mk__disjoint__insert,axiom,
    ! [A3: state,A6: set_state] :
      ( ( member_state @ A3 @ A6 )
     => ? [B7: set_state] :
          ( ( A6
            = ( insert_state @ A3 @ B7 ) )
          & ~ ( member_state @ A3 @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_545_mk__disjoint__insert,axiom,
    ! [A3: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ A3 @ A6 )
     => ? [B7: set_Pr4231240917283394591_state] :
          ( ( A6
            = ( insert175804457004744729_state @ A3 @ B7 ) )
          & ~ ( member7461423308196221312_state @ A3 @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_546_mk__disjoint__insert,axiom,
    ! [A3: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A3 @ A6 )
     => ? [B7: set_Pr7649655576376376530on_val] :
          ( ( A6
            = ( insert3030518898131756108on_val @ A3 @ B7 ) )
          & ~ ( member2879030624002546611on_val @ A3 @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_547_mk__disjoint__insert,axiom,
    ! [A3: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ A3 @ A6 )
     => ? [B7: set_Pr2391701600042252046_state] :
          ( ( A6
            = ( insert94804854012721790_state @ A3 @ B7 ) )
          & ~ ( member6715010751053357271_state @ A3 @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_548_insert__commute,axiom,
    ! [X2: state,Y: state,A6: set_state] :
      ( ( insert_state @ X2 @ ( insert_state @ Y @ A6 ) )
      = ( insert_state @ Y @ ( insert_state @ X2 @ A6 ) ) ) ).

% insert_commute
thf(fact_549_insert__eq__iff,axiom,
    ! [A3: state,A6: set_state,B2: state,B4: set_state] :
      ( ~ ( member_state @ A3 @ A6 )
     => ( ~ ( member_state @ B2 @ B4 )
       => ( ( ( insert_state @ A3 @ A6 )
            = ( insert_state @ B2 @ B4 ) )
          = ( ( ( A3 = B2 )
             => ( A6 = B4 ) )
            & ( ( A3 != B2 )
             => ? [C6: set_state] :
                  ( ( A6
                    = ( insert_state @ B2 @ C6 ) )
                  & ~ ( member_state @ B2 @ C6 )
                  & ( B4
                    = ( insert_state @ A3 @ C6 ) )
                  & ~ ( member_state @ A3 @ C6 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_550_insert__eq__iff,axiom,
    ! [A3: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B2: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ~ ( member7461423308196221312_state @ A3 @ A6 )
     => ( ~ ( member7461423308196221312_state @ B2 @ B4 )
       => ( ( ( insert175804457004744729_state @ A3 @ A6 )
            = ( insert175804457004744729_state @ B2 @ B4 ) )
          = ( ( ( A3 = B2 )
             => ( A6 = B4 ) )
            & ( ( A3 != B2 )
             => ? [C6: set_Pr4231240917283394591_state] :
                  ( ( A6
                    = ( insert175804457004744729_state @ B2 @ C6 ) )
                  & ~ ( member7461423308196221312_state @ B2 @ C6 )
                  & ( B4
                    = ( insert175804457004744729_state @ A3 @ C6 ) )
                  & ~ ( member7461423308196221312_state @ A3 @ C6 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_551_insert__eq__iff,axiom,
    ! [A3: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ A3 @ A6 )
     => ( ~ ( member2879030624002546611on_val @ B2 @ B4 )
       => ( ( ( insert3030518898131756108on_val @ A3 @ A6 )
            = ( insert3030518898131756108on_val @ B2 @ B4 ) )
          = ( ( ( A3 = B2 )
             => ( A6 = B4 ) )
            & ( ( A3 != B2 )
             => ? [C6: set_Pr7649655576376376530on_val] :
                  ( ( A6
                    = ( insert3030518898131756108on_val @ B2 @ C6 ) )
                  & ~ ( member2879030624002546611on_val @ B2 @ C6 )
                  & ( B4
                    = ( insert3030518898131756108on_val @ A3 @ C6 ) )
                  & ~ ( member2879030624002546611on_val @ A3 @ C6 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_552_insert__eq__iff,axiom,
    ! [A3: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B2: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ~ ( member6715010751053357271_state @ A3 @ A6 )
     => ( ~ ( member6715010751053357271_state @ B2 @ B4 )
       => ( ( ( insert94804854012721790_state @ A3 @ A6 )
            = ( insert94804854012721790_state @ B2 @ B4 ) )
          = ( ( ( A3 = B2 )
             => ( A6 = B4 ) )
            & ( ( A3 != B2 )
             => ? [C6: set_Pr2391701600042252046_state] :
                  ( ( A6
                    = ( insert94804854012721790_state @ B2 @ C6 ) )
                  & ~ ( member6715010751053357271_state @ B2 @ C6 )
                  & ( B4
                    = ( insert94804854012721790_state @ A3 @ C6 ) )
                  & ~ ( member6715010751053357271_state @ A3 @ C6 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_553_insert__absorb,axiom,
    ! [A3: state,A6: set_state] :
      ( ( member_state @ A3 @ A6 )
     => ( ( insert_state @ A3 @ A6 )
        = A6 ) ) ).

% insert_absorb
thf(fact_554_insert__absorb,axiom,
    ! [A3: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ A3 @ A6 )
     => ( ( insert175804457004744729_state @ A3 @ A6 )
        = A6 ) ) ).

% insert_absorb
thf(fact_555_insert__absorb,axiom,
    ! [A3: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A3 @ A6 )
     => ( ( insert3030518898131756108on_val @ A3 @ A6 )
        = A6 ) ) ).

% insert_absorb
thf(fact_556_insert__absorb,axiom,
    ! [A3: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ A3 @ A6 )
     => ( ( insert94804854012721790_state @ A3 @ A6 )
        = A6 ) ) ).

% insert_absorb
thf(fact_557_insert__ident,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ~ ( member_state @ X2 @ A6 )
     => ( ~ ( member_state @ X2 @ B4 )
       => ( ( ( insert_state @ X2 @ A6 )
            = ( insert_state @ X2 @ B4 ) )
          = ( A6 = B4 ) ) ) ) ).

% insert_ident
thf(fact_558_insert__ident,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ~ ( member7461423308196221312_state @ X2 @ A6 )
     => ( ~ ( member7461423308196221312_state @ X2 @ B4 )
       => ( ( ( insert175804457004744729_state @ X2 @ A6 )
            = ( insert175804457004744729_state @ X2 @ B4 ) )
          = ( A6 = B4 ) ) ) ) ).

% insert_ident
thf(fact_559_insert__ident,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X2 @ A6 )
     => ( ~ ( member2879030624002546611on_val @ X2 @ B4 )
       => ( ( ( insert3030518898131756108on_val @ X2 @ A6 )
            = ( insert3030518898131756108on_val @ X2 @ B4 ) )
          = ( A6 = B4 ) ) ) ) ).

% insert_ident
thf(fact_560_insert__ident,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ~ ( member6715010751053357271_state @ X2 @ A6 )
     => ( ~ ( member6715010751053357271_state @ X2 @ B4 )
       => ( ( ( insert94804854012721790_state @ X2 @ A6 )
            = ( insert94804854012721790_state @ X2 @ B4 ) )
          = ( A6 = B4 ) ) ) ) ).

% insert_ident
thf(fact_561_Set_Oset__insert,axiom,
    ! [X2: state,A6: set_state] :
      ( ( member_state @ X2 @ A6 )
     => ~ ! [B7: set_state] :
            ( ( A6
              = ( insert_state @ X2 @ B7 ) )
           => ( member_state @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_562_Set_Oset__insert,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ~ ! [B7: set_Pr4231240917283394591_state] :
            ( ( A6
              = ( insert175804457004744729_state @ X2 @ B7 ) )
           => ( member7461423308196221312_state @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_563_Set_Oset__insert,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X2 @ A6 )
     => ~ ! [B7: set_Pr7649655576376376530on_val] :
            ( ( A6
              = ( insert3030518898131756108on_val @ X2 @ B7 ) )
           => ( member2879030624002546611on_val @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_564_Set_Oset__insert,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ~ ! [B7: set_Pr2391701600042252046_state] :
            ( ( A6
              = ( insert94804854012721790_state @ X2 @ B7 ) )
           => ( member6715010751053357271_state @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_565_insertI2,axiom,
    ! [A3: state,B4: set_state,B2: state] :
      ( ( member_state @ A3 @ B4 )
     => ( member_state @ A3 @ ( insert_state @ B2 @ B4 ) ) ) ).

% insertI2
thf(fact_566_insertI2,axiom,
    ! [A3: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,B2: produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ A3 @ B4 )
     => ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ B2 @ B4 ) ) ) ).

% insertI2
thf(fact_567_insertI2,axiom,
    ! [A3: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,B2: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ A3 @ B4 )
     => ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ B2 @ B4 ) ) ) ).

% insertI2
thf(fact_568_insertI2,axiom,
    ! [A3: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,B2: produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ A3 @ B4 )
     => ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ B2 @ B4 ) ) ) ).

% insertI2
thf(fact_569_insertI1,axiom,
    ! [A3: state,B4: set_state] : ( member_state @ A3 @ ( insert_state @ A3 @ B4 ) ) ).

% insertI1
thf(fact_570_insertI1,axiom,
    ! [A3: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] : ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ A3 @ B4 ) ) ).

% insertI1
thf(fact_571_insertI1,axiom,
    ! [A3: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] : ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ A3 @ B4 ) ) ).

% insertI1
thf(fact_572_insertI1,axiom,
    ! [A3: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] : ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ A3 @ B4 ) ) ).

% insertI1
thf(fact_573_insertE,axiom,
    ! [A3: state,B2: state,A6: set_state] :
      ( ( member_state @ A3 @ ( insert_state @ B2 @ A6 ) )
     => ( ( A3 != B2 )
       => ( member_state @ A3 @ A6 ) ) ) ).

% insertE
thf(fact_574_insertE,axiom,
    ! [A3: produc7272280185086996969_state,B2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ B2 @ A6 ) )
     => ( ( A3 != B2 )
       => ( member7461423308196221312_state @ A3 @ A6 ) ) ) ).

% insertE
thf(fact_575_insertE,axiom,
    ! [A3: produc9003781588162623004on_val,B2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ B2 @ A6 ) )
     => ( ( A3 != B2 )
       => ( member2879030624002546611on_val @ A3 @ A6 ) ) ) ).

% insertE
thf(fact_576_insertE,axiom,
    ! [A3: produc3882902684156697774_state,B2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ B2 @ A6 ) )
     => ( ( A3 != B2 )
       => ( member6715010751053357271_state @ A3 @ A6 ) ) ) ).

% insertE
thf(fact_577_Rep__state__inject,axiom,
    ! [X2: state,Y: state] :
      ( ( ( rep_state @ X2 )
        = ( rep_state @ Y ) )
      = ( X2 = Y ) ) ).

% Rep_state_inject
thf(fact_578_insert__UNIV,axiom,
    ! [X2: state] :
      ( ( insert_state @ X2 @ top_top_set_state )
      = top_top_set_state ) ).

% insert_UNIV
thf(fact_579_insert__mono,axiom,
    ! [C3: set_state,D2: set_state,A3: state] :
      ( ( ord_le2494988322063910608_state @ C3 @ D2 )
     => ( ord_le2494988322063910608_state @ ( insert_state @ A3 @ C3 ) @ ( insert_state @ A3 @ D2 ) ) ) ).

% insert_mono
thf(fact_580_subset__insert,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ~ ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( ord_le4032880777312351359_state @ A6 @ ( insert175804457004744729_state @ X2 @ B4 ) )
        = ( ord_le4032880777312351359_state @ A6 @ B4 ) ) ) ).

% subset_insert
thf(fact_581_subset__insert,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X2 @ A6 )
     => ( ( ord_le6900622908513426738on_val @ A6 @ ( insert3030518898131756108on_val @ X2 @ B4 ) )
        = ( ord_le6900622908513426738on_val @ A6 @ B4 ) ) ) ).

% subset_insert
thf(fact_582_subset__insert,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ~ ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( ord_le6483787752022044334_state @ A6 @ ( insert94804854012721790_state @ X2 @ B4 ) )
        = ( ord_le6483787752022044334_state @ A6 @ B4 ) ) ) ).

% subset_insert
thf(fact_583_subset__insert,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ~ ( member_state @ X2 @ A6 )
     => ( ( ord_le2494988322063910608_state @ A6 @ ( insert_state @ X2 @ B4 ) )
        = ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ) ).

% subset_insert
thf(fact_584_subset__insertI,axiom,
    ! [B4: set_state,A3: state] : ( ord_le2494988322063910608_state @ B4 @ ( insert_state @ A3 @ B4 ) ) ).

% subset_insertI
thf(fact_585_subset__insertI2,axiom,
    ! [A6: set_state,B4: set_state,B2: state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ord_le2494988322063910608_state @ A6 @ ( insert_state @ B2 @ B4 ) ) ) ).

% subset_insertI2
thf(fact_586_PowD,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( member_set_state @ A6 @ ( pow_state @ B4 ) )
     => ( ord_le2494988322063910608_state @ A6 @ B4 ) ) ).

% PowD
thf(fact_587_PartialSA_Ounit__core,axiom,
    ( ( core @ unit )
    = unit ) ).

% PartialSA.unit_core
thf(fact_588_PartialSA_Ounit__smaller,axiom,
    ! [Phi: state] : ( greater @ Phi @ unit ) ).

% PartialSA.unit_smaller
thf(fact_589_unit__charact_I1_J,axiom,
    ( ( get_h @ unit )
    = empty_7512026568161686585ar_val ) ).

% unit_charact(1)
thf(fact_590_Rep__state__inverse,axiom,
    ! [X2: state] :
      ( ( abs_state @ ( rep_state @ X2 ) )
      = X2 ) ).

% Rep_state_inverse
thf(fact_591_empty__mask_Osimps,axiom,
    ( empty_3446695950879338768t_char
    = ( ^ [Hl: produc1457211279475724562t_char] : pnone ) ) ).

% empty_mask.simps
thf(fact_592_empty__mask_Oelims,axiom,
    ! [X2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X2 )
        = Y )
     => ( Y = pnone ) ) ).

% empty_mask.elims
thf(fact_593_Pow__mono,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ord_le5175021213330142598_state @ ( pow_state @ A6 ) @ ( pow_state @ B4 ) ) ) ).

% Pow_mono
thf(fact_594_image__Pow__surj,axiom,
    ! [F: state > state,A6: set_state,B4: set_state] :
      ( ( ( image_state_state @ F @ A6 )
        = B4 )
     => ( ( image_2476256681063834599_state @ ( image_state_state @ F ) @ ( pow_state @ A6 ) )
        = ( pow_state @ B4 ) ) ) ).

% image_Pow_surj
thf(fact_595_unit__neutral,axiom,
    ( some_state
    = ( ^ [A2: state] : ( plus @ A2 @ unit ) ) ) ).

% unit_neutral
thf(fact_596_unit__charact_I2_J,axiom,
    ( ( get_m @ unit )
    = empty_3446695950879338768t_char ) ).

% unit_charact(2)
thf(fact_597_empty__mask_Opelims,axiom,
    ! [X2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X2 )
        = Y )
     => ( ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_598_empty__mask_Opelims,axiom,
    ! [X2: produc3142500478612311029_state,Y: prat] :
      ( ( ( empty_5858998862663000819_state @ X2 )
        = Y )
     => ( ( accp_P7183347322223220350_state @ empty_3683758330361983676_state @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P7183347322223220350_state @ empty_3683758330361983676_state @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_599_empty__mask_Opelims,axiom,
    ! [X2: produc4844402304972151915_state,Y: prat] :
      ( ( ( empty_3913122416104905065_state @ X2 )
        = Y )
     => ( ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_600_empty__mask_Opelims,axiom,
    ! [X2: produc6251377953716854561_state,Y: prat] :
      ( ( ( empty_5541330147480151071_state @ X2 )
        = Y )
     => ( ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_601_empty__mask_Opelims,axiom,
    ! [X2: produc9003781588162623004on_val,Y: prat] :
      ( ( ( empty_6102255041883331742on_val @ X2 )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_602_empty__mask_Opelims,axiom,
    ! [X2: produc1457211279475724562t_char > prat,Y: prat] :
      ( ( ( empty_6616431780912394577r_prat @ X2 )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X2 )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X2 ) ) ) ) ).

% empty_mask.pelims
thf(fact_603_plus__def,axiom,
    ( plus
    = ( ^ [A2: state,B: state] : ( if_option_state @ ( compatible @ ( rep_state @ A2 ) @ ( rep_state @ B ) ) @ ( some_state @ ( abs_state @ ( add_states @ ( rep_state @ A2 ) @ ( rep_state @ B ) ) ) ) @ none_state ) ) ) ).

% plus_def
thf(fact_604_insert__subsetI,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,X7: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( ord_le4032880777312351359_state @ X7 @ A6 )
       => ( ord_le4032880777312351359_state @ ( insert175804457004744729_state @ X2 @ X7 ) @ A6 ) ) ) ).

% insert_subsetI
thf(fact_605_insert__subsetI,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,X7: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X2 @ A6 )
     => ( ( ord_le6900622908513426738on_val @ X7 @ A6 )
       => ( ord_le6900622908513426738on_val @ ( insert3030518898131756108on_val @ X2 @ X7 ) @ A6 ) ) ) ).

% insert_subsetI
thf(fact_606_insert__subsetI,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,X7: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( ord_le6483787752022044334_state @ X7 @ A6 )
       => ( ord_le6483787752022044334_state @ ( insert94804854012721790_state @ X2 @ X7 ) @ A6 ) ) ) ).

% insert_subsetI
thf(fact_607_insert__subsetI,axiom,
    ! [X2: state,A6: set_state,X7: set_state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( ord_le2494988322063910608_state @ X7 @ A6 )
       => ( ord_le2494988322063910608_state @ ( insert_state @ X2 @ X7 ) @ A6 ) ) ) ).

% insert_subsetI
thf(fact_608_sep__algebra_Osetify__sum__image,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_setify_state @ P2 @ ( sep_add_set_state @ Plus @ ( image_state_state @ F @ A6 ) @ B4 ) )
        = ( ! [X5: state] :
              ( ( member_state @ X5 @ A6 )
             => ( sep_setify_state @ P2 @ ( sep_add_set_state @ Plus @ ( insert_state @ ( F @ X5 ) @ bot_bot_set_state ) @ B4 ) ) ) ) ) ) ).

% sep_algebra.setify_sum_image
thf(fact_609_PartialSA_Omono__transformer__def,axiom,
    ! [T2: state > state] :
      ( ( packag4817583915586052229_state @ plus @ unit @ T2 )
      = ( ! [Phi4: state,Phi3: state] :
            ( ( greater @ Phi3 @ Phi4 )
           => ( greater @ ( T2 @ Phi3 ) @ ( T2 @ Phi4 ) ) )
        & ( ( T2 @ unit )
          = unit ) ) ) ).

% PartialSA.mono_transformer_def
thf(fact_610_empty__iff,axiom,
    ! [C: produc7272280185086996969_state] :
      ~ ( member7461423308196221312_state @ C @ bot_bo6430881413863817907_state ) ).

% empty_iff
thf(fact_611_empty__iff,axiom,
    ! [C: produc9003781588162623004on_val] :
      ~ ( member2879030624002546611on_val @ C @ bot_bo6722054719108133734on_val ) ).

% empty_iff
thf(fact_612_empty__iff,axiom,
    ! [C: produc3882902684156697774_state] :
      ~ ( member6715010751053357271_state @ C @ bot_bo3524941057552913786_state ) ).

% empty_iff
thf(fact_613_empty__iff,axiom,
    ! [C: state] :
      ~ ( member_state @ C @ bot_bot_set_state ) ).

% empty_iff
thf(fact_614_all__not__in__conv,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( ! [X5: produc7272280185086996969_state] :
            ~ ( member7461423308196221312_state @ X5 @ A6 ) )
      = ( A6 = bot_bo6430881413863817907_state ) ) ).

% all_not_in_conv
thf(fact_615_all__not__in__conv,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ( ! [X5: produc9003781588162623004on_val] :
            ~ ( member2879030624002546611on_val @ X5 @ A6 ) )
      = ( A6 = bot_bo6722054719108133734on_val ) ) ).

% all_not_in_conv
thf(fact_616_all__not__in__conv,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ( ! [X5: produc3882902684156697774_state] :
            ~ ( member6715010751053357271_state @ X5 @ A6 ) )
      = ( A6 = bot_bo3524941057552913786_state ) ) ).

% all_not_in_conv
thf(fact_617_all__not__in__conv,axiom,
    ! [A6: set_state] :
      ( ( ! [X5: state] :
            ~ ( member_state @ X5 @ A6 ) )
      = ( A6 = bot_bot_set_state ) ) ).

% all_not_in_conv
thf(fact_618_Collect__empty__eq,axiom,
    ! [P2: produc7272280185086996969_state > $o] :
      ( ( ( collec906845016635587262_state @ P2 )
        = bot_bo6430881413863817907_state )
      = ( ! [X5: produc7272280185086996969_state] :
            ~ ( P2 @ X5 ) ) ) ).

% Collect_empty_eq
thf(fact_619_Collect__empty__eq,axiom,
    ! [P2: produc9003781588162623004on_val > $o] :
      ( ( ( collec7475294502966882545on_val @ P2 )
        = bot_bo6722054719108133734on_val )
      = ( ! [X5: produc9003781588162623004on_val] :
            ~ ( P2 @ X5 ) ) ) ).

% Collect_empty_eq
thf(fact_620_Collect__empty__eq,axiom,
    ! [P2: state > $o] :
      ( ( ( collect_state @ P2 )
        = bot_bot_set_state )
      = ( ! [X5: state] :
            ~ ( P2 @ X5 ) ) ) ).

% Collect_empty_eq
thf(fact_621_empty__Collect__eq,axiom,
    ! [P2: produc7272280185086996969_state > $o] :
      ( ( bot_bo6430881413863817907_state
        = ( collec906845016635587262_state @ P2 ) )
      = ( ! [X5: produc7272280185086996969_state] :
            ~ ( P2 @ X5 ) ) ) ).

% empty_Collect_eq
thf(fact_622_empty__Collect__eq,axiom,
    ! [P2: produc9003781588162623004on_val > $o] :
      ( ( bot_bo6722054719108133734on_val
        = ( collec7475294502966882545on_val @ P2 ) )
      = ( ! [X5: produc9003781588162623004on_val] :
            ~ ( P2 @ X5 ) ) ) ).

% empty_Collect_eq
thf(fact_623_empty__Collect__eq,axiom,
    ! [P2: state > $o] :
      ( ( bot_bot_set_state
        = ( collect_state @ P2 ) )
      = ( ! [X5: state] :
            ~ ( P2 @ X5 ) ) ) ).

% empty_Collect_eq
thf(fact_624_image__empty,axiom,
    ! [F: state > state] :
      ( ( image_state_state @ F @ bot_bot_set_state )
      = bot_bot_set_state ) ).

% image_empty
thf(fact_625_empty__is__image,axiom,
    ! [F: state > state,A6: set_state] :
      ( ( bot_bot_set_state
        = ( image_state_state @ F @ A6 ) )
      = ( A6 = bot_bot_set_state ) ) ).

% empty_is_image
thf(fact_626_image__is__empty,axiom,
    ! [F: state > state,A6: set_state] :
      ( ( ( image_state_state @ F @ A6 )
        = bot_bot_set_state )
      = ( A6 = bot_bot_set_state ) ) ).

% image_is_empty
thf(fact_627_empty__subsetI,axiom,
    ! [A6: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A6 ) ).

% empty_subsetI
thf(fact_628_subset__empty,axiom,
    ! [A6: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ bot_bot_set_state )
      = ( A6 = bot_bot_set_state ) ) ).

% subset_empty
thf(fact_629_singletonI,axiom,
    ! [A3: produc7272280185086996969_state] : ( member7461423308196221312_state @ A3 @ ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) ) ).

% singletonI
thf(fact_630_singletonI,axiom,
    ! [A3: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ A3 @ ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) ) ).

% singletonI
thf(fact_631_singletonI,axiom,
    ! [A3: produc3882902684156697774_state] : ( member6715010751053357271_state @ A3 @ ( insert94804854012721790_state @ A3 @ bot_bo3524941057552913786_state ) ) ).

% singletonI
thf(fact_632_singletonI,axiom,
    ! [A3: state] : ( member_state @ A3 @ ( insert_state @ A3 @ bot_bot_set_state ) ) ).

% singletonI
thf(fact_633_Pow__singleton__iff,axiom,
    ! [X7: set_state,Y7: set_state] :
      ( ( ( pow_state @ X7 )
        = ( insert_set_state @ Y7 @ bot_bo2271482359692755898_state ) )
      = ( ( X7 = bot_bot_set_state )
        & ( Y7 = bot_bot_set_state ) ) ) ).

% Pow_singleton_iff
thf(fact_634_Pow__empty,axiom,
    ( ( pow_state @ bot_bot_set_state )
    = ( insert_set_state @ bot_bot_set_state @ bot_bo2271482359692755898_state ) ) ).

% Pow_empty
thf(fact_635_these__empty,axiom,
    ( ( these_state @ bot_bo710180891245420500_state )
    = bot_bot_set_state ) ).

% these_empty
thf(fact_636_singleton__insert__inj__eq,axiom,
    ! [B2: state,A3: state,A6: set_state] :
      ( ( ( insert_state @ B2 @ bot_bot_set_state )
        = ( insert_state @ A3 @ A6 ) )
      = ( ( A3 = B2 )
        & ( ord_le2494988322063910608_state @ A6 @ ( insert_state @ B2 @ bot_bot_set_state ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_637_singleton__insert__inj__eq_H,axiom,
    ! [A3: state,A6: set_state,B2: state] :
      ( ( ( insert_state @ A3 @ A6 )
        = ( insert_state @ B2 @ bot_bot_set_state ) )
      = ( ( A3 = B2 )
        & ( ord_le2494988322063910608_state @ A6 @ ( insert_state @ B2 @ bot_bot_set_state ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_638_package__logic_Omono__transformer_Ocong,axiom,
    packag4817583915586052229_state = packag4817583915586052229_state ).

% package_logic.mono_transformer.cong
thf(fact_639_emptyE,axiom,
    ! [A3: produc7272280185086996969_state] :
      ~ ( member7461423308196221312_state @ A3 @ bot_bo6430881413863817907_state ) ).

% emptyE
thf(fact_640_emptyE,axiom,
    ! [A3: produc9003781588162623004on_val] :
      ~ ( member2879030624002546611on_val @ A3 @ bot_bo6722054719108133734on_val ) ).

% emptyE
thf(fact_641_emptyE,axiom,
    ! [A3: produc3882902684156697774_state] :
      ~ ( member6715010751053357271_state @ A3 @ bot_bo3524941057552913786_state ) ).

% emptyE
thf(fact_642_emptyE,axiom,
    ! [A3: state] :
      ~ ( member_state @ A3 @ bot_bot_set_state ) ).

% emptyE
thf(fact_643_equals0D,axiom,
    ! [A6: set_Pr4231240917283394591_state,A3: produc7272280185086996969_state] :
      ( ( A6 = bot_bo6430881413863817907_state )
     => ~ ( member7461423308196221312_state @ A3 @ A6 ) ) ).

% equals0D
thf(fact_644_equals0D,axiom,
    ! [A6: set_Pr7649655576376376530on_val,A3: produc9003781588162623004on_val] :
      ( ( A6 = bot_bo6722054719108133734on_val )
     => ~ ( member2879030624002546611on_val @ A3 @ A6 ) ) ).

% equals0D
thf(fact_645_equals0D,axiom,
    ! [A6: set_Pr2391701600042252046_state,A3: produc3882902684156697774_state] :
      ( ( A6 = bot_bo3524941057552913786_state )
     => ~ ( member6715010751053357271_state @ A3 @ A6 ) ) ).

% equals0D
thf(fact_646_equals0D,axiom,
    ! [A6: set_state,A3: state] :
      ( ( A6 = bot_bot_set_state )
     => ~ ( member_state @ A3 @ A6 ) ) ).

% equals0D
thf(fact_647_equals0I,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ! [Y3: produc7272280185086996969_state] :
          ~ ( member7461423308196221312_state @ Y3 @ A6 )
     => ( A6 = bot_bo6430881413863817907_state ) ) ).

% equals0I
thf(fact_648_equals0I,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ! [Y3: produc9003781588162623004on_val] :
          ~ ( member2879030624002546611on_val @ Y3 @ A6 )
     => ( A6 = bot_bo6722054719108133734on_val ) ) ).

% equals0I
thf(fact_649_equals0I,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ! [Y3: produc3882902684156697774_state] :
          ~ ( member6715010751053357271_state @ Y3 @ A6 )
     => ( A6 = bot_bo3524941057552913786_state ) ) ).

% equals0I
thf(fact_650_equals0I,axiom,
    ! [A6: set_state] :
      ( ! [Y3: state] :
          ~ ( member_state @ Y3 @ A6 )
     => ( A6 = bot_bot_set_state ) ) ).

% equals0I
thf(fact_651_ex__in__conv,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( ? [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ A6 ) )
      = ( A6 != bot_bo6430881413863817907_state ) ) ).

% ex_in_conv
thf(fact_652_ex__in__conv,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ( ? [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ A6 ) )
      = ( A6 != bot_bo6722054719108133734on_val ) ) ).

% ex_in_conv
thf(fact_653_ex__in__conv,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ( ? [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ A6 ) )
      = ( A6 != bot_bo3524941057552913786_state ) ) ).

% ex_in_conv
thf(fact_654_ex__in__conv,axiom,
    ! [A6: set_state] :
      ( ( ? [X5: state] : ( member_state @ X5 @ A6 ) )
      = ( A6 != bot_bot_set_state ) ) ).

% ex_in_conv
thf(fact_655_subset__emptyI,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ~ ( member7461423308196221312_state @ X4 @ A6 )
     => ( ord_le4032880777312351359_state @ A6 @ bot_bo6430881413863817907_state ) ) ).

% subset_emptyI
thf(fact_656_subset__emptyI,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ! [X4: produc9003781588162623004on_val] :
          ~ ( member2879030624002546611on_val @ X4 @ A6 )
     => ( ord_le6900622908513426738on_val @ A6 @ bot_bo6722054719108133734on_val ) ) ).

% subset_emptyI
thf(fact_657_subset__emptyI,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ! [X4: produc3882902684156697774_state] :
          ~ ( member6715010751053357271_state @ X4 @ A6 )
     => ( ord_le6483787752022044334_state @ A6 @ bot_bo3524941057552913786_state ) ) ).

% subset_emptyI
thf(fact_658_subset__emptyI,axiom,
    ! [A6: set_state] :
      ( ! [X4: state] :
          ~ ( member_state @ X4 @ A6 )
     => ( ord_le2494988322063910608_state @ A6 @ bot_bot_set_state ) ) ).

% subset_emptyI
thf(fact_659_bot_Oextremum,axiom,
    ! [A3: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A3 ) ).

% bot.extremum
thf(fact_660_bot_Oextremum__unique,axiom,
    ! [A3: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ bot_bot_set_state )
      = ( A3 = bot_bot_set_state ) ) ).

% bot.extremum_unique
thf(fact_661_bot_Oextremum__uniqueI,axiom,
    ! [A3: set_state] :
      ( ( ord_le2494988322063910608_state @ A3 @ bot_bot_set_state )
     => ( A3 = bot_bot_set_state ) ) ).

% bot.extremum_uniqueI
thf(fact_662_PartialSA_Obigger__singleton,axiom,
    ! [Phi2: state,Phi: state] :
      ( ( greater @ Phi2 @ Phi )
     => ( greater_set @ ( insert_state @ Phi2 @ bot_bot_set_state ) @ ( insert_state @ Phi @ bot_bot_set_state ) ) ) ).

% PartialSA.bigger_singleton
thf(fact_663_empty__not__UNIV,axiom,
    bot_bot_set_state != top_top_set_state ).

% empty_not_UNIV
thf(fact_664_singletonD,axiom,
    ! [B2: produc7272280185086996969_state,A3: produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ B2 @ ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) )
     => ( B2 = A3 ) ) ).

% singletonD
thf(fact_665_singletonD,axiom,
    ! [B2: produc9003781588162623004on_val,A3: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ B2 @ ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) )
     => ( B2 = A3 ) ) ).

% singletonD
thf(fact_666_singletonD,axiom,
    ! [B2: produc3882902684156697774_state,A3: produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ B2 @ ( insert94804854012721790_state @ A3 @ bot_bo3524941057552913786_state ) )
     => ( B2 = A3 ) ) ).

% singletonD
thf(fact_667_singletonD,axiom,
    ! [B2: state,A3: state] :
      ( ( member_state @ B2 @ ( insert_state @ A3 @ bot_bot_set_state ) )
     => ( B2 = A3 ) ) ).

% singletonD
thf(fact_668_singleton__iff,axiom,
    ! [B2: produc7272280185086996969_state,A3: produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ B2 @ ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) )
      = ( B2 = A3 ) ) ).

% singleton_iff
thf(fact_669_singleton__iff,axiom,
    ! [B2: produc9003781588162623004on_val,A3: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ B2 @ ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) )
      = ( B2 = A3 ) ) ).

% singleton_iff
thf(fact_670_singleton__iff,axiom,
    ! [B2: produc3882902684156697774_state,A3: produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ B2 @ ( insert94804854012721790_state @ A3 @ bot_bo3524941057552913786_state ) )
      = ( B2 = A3 ) ) ).

% singleton_iff
thf(fact_671_singleton__iff,axiom,
    ! [B2: state,A3: state] :
      ( ( member_state @ B2 @ ( insert_state @ A3 @ bot_bot_set_state ) )
      = ( B2 = A3 ) ) ).

% singleton_iff
thf(fact_672_doubleton__eq__iff,axiom,
    ! [A3: state,B2: state,C: state,D: state] :
      ( ( ( insert_state @ A3 @ ( insert_state @ B2 @ bot_bot_set_state ) )
        = ( insert_state @ C @ ( insert_state @ D @ bot_bot_set_state ) ) )
      = ( ( ( A3 = C )
          & ( B2 = D ) )
        | ( ( A3 = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_673_insert__not__empty,axiom,
    ! [A3: state,A6: set_state] :
      ( ( insert_state @ A3 @ A6 )
     != bot_bot_set_state ) ).

% insert_not_empty
thf(fact_674_singleton__inject,axiom,
    ! [A3: state,B2: state] :
      ( ( ( insert_state @ A3 @ bot_bot_set_state )
        = ( insert_state @ B2 @ bot_bot_set_state ) )
     => ( A3 = B2 ) ) ).

% singleton_inject
thf(fact_675_PartialSA_Osetify__sum,axiom,
    ! [P2: state > $o,A6: set_state,B4: set_state] :
      ( ( sep_setify_state @ P2 @ ( add_set @ A6 @ B4 ) )
      = ( ! [X5: state] :
            ( ( member_state @ X5 @ A6 )
           => ( sep_setify_state @ P2 @ ( add_set @ ( insert_state @ X5 @ bot_bot_set_state ) @ B4 ) ) ) ) ) ).

% PartialSA.setify_sum
thf(fact_676_Pow__bottom,axiom,
    ! [B4: set_state] : ( member_set_state @ bot_bot_set_state @ ( pow_state @ B4 ) ) ).

% Pow_bottom
thf(fact_677_PartialSA_Oempty__set__sum,axiom,
    ! [A6: set_state] :
      ( ( add_set @ bot_bot_set_state @ A6 )
      = bot_bot_set_state ) ).

% PartialSA.empty_set_sum
thf(fact_678_PartialSA_Osum__then__singleton,axiom,
    ! [A3: state,B2: state,C: state] :
      ( ( ( some_state @ A3 )
        = ( plus @ B2 @ C ) )
      = ( ( insert_state @ A3 @ bot_bot_set_state )
        = ( add_set @ ( insert_state @ B2 @ bot_bot_set_state ) @ ( insert_state @ C @ bot_bot_set_state ) ) ) ) ).

% PartialSA.sum_then_singleton
thf(fact_679_these__not__empty__eq,axiom,
    ! [B4: set_option_val] :
      ( ( ( these_val @ B4 )
       != bot_bot_set_val )
      = ( ( B4 != bot_bo5906790151302476563on_val )
        & ( B4
         != ( insert_option_val @ none_val @ bot_bo5906790151302476563on_val ) ) ) ) ).

% these_not_empty_eq
thf(fact_680_these__not__empty__eq,axiom,
    ! [B4: set_option_state] :
      ( ( ( these_state @ B4 )
       != bot_bot_set_state )
      = ( ( B4 != bot_bo710180891245420500_state )
        & ( B4
         != ( insert_option_state @ none_state @ bot_bo710180891245420500_state ) ) ) ) ).

% these_not_empty_eq
thf(fact_681_these__empty__eq,axiom,
    ! [B4: set_option_val] :
      ( ( ( these_val @ B4 )
        = bot_bot_set_val )
      = ( ( B4 = bot_bo5906790151302476563on_val )
        | ( B4
          = ( insert_option_val @ none_val @ bot_bo5906790151302476563on_val ) ) ) ) ).

% these_empty_eq
thf(fact_682_these__empty__eq,axiom,
    ! [B4: set_option_state] :
      ( ( ( these_state @ B4 )
        = bot_bot_set_state )
      = ( ( B4 = bot_bo710180891245420500_state )
        | ( B4
          = ( insert_option_state @ none_state @ bot_bo710180891245420500_state ) ) ) ) ).

% these_empty_eq
thf(fact_683_PartialSA_Osetify__sum__image,axiom,
    ! [P2: state > $o,F: state > state,A6: set_state,B4: set_state] :
      ( ( sep_setify_state @ P2 @ ( add_set @ ( image_state_state @ F @ A6 ) @ B4 ) )
      = ( ! [X5: state] :
            ( ( member_state @ X5 @ A6 )
           => ( sep_setify_state @ P2 @ ( add_set @ ( insert_state @ ( F @ X5 ) @ bot_bot_set_state ) @ B4 ) ) ) ) ) ).

% PartialSA.setify_sum_image
thf(fact_684_subset__singletonD,axiom,
    ! [A6: set_state,X2: state] :
      ( ( ord_le2494988322063910608_state @ A6 @ ( insert_state @ X2 @ bot_bot_set_state ) )
     => ( ( A6 = bot_bot_set_state )
        | ( A6
          = ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ).

% subset_singletonD
thf(fact_685_subset__singleton__iff,axiom,
    ! [X7: set_state,A3: state] :
      ( ( ord_le2494988322063910608_state @ X7 @ ( insert_state @ A3 @ bot_bot_set_state ) )
      = ( ( X7 = bot_bot_set_state )
        | ( X7
          = ( insert_state @ A3 @ bot_bot_set_state ) ) ) ) ).

% subset_singleton_iff
thf(fact_686_sep__algebra_Oempty__set__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_add_set_state @ Plus @ bot_bot_set_state @ A6 )
        = bot_bot_set_state ) ) ).

% sep_algebra.empty_set_sum
thf(fact_687_range__eq__singletonD,axiom,
    ! [F: state > state,A3: state,X2: state] :
      ( ( ( image_state_state @ F @ top_top_set_state )
        = ( insert_state @ A3 @ bot_bot_set_state ) )
     => ( ( F @ X2 )
        = A3 ) ) ).

% range_eq_singletonD
thf(fact_688_sep__algebra_Osum__then__singleton,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A3 )
          = ( Plus @ B2 @ C ) )
        = ( ( insert_val @ A3 @ bot_bot_set_val )
          = ( sep_add_set_val @ Plus @ ( insert_val @ B2 @ bot_bot_set_val ) @ ( insert_val @ C @ bot_bot_set_val ) ) ) ) ) ).

% sep_algebra.sum_then_singleton
thf(fact_689_sep__algebra_Osum__then__singleton,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A3 )
          = ( Plus @ B2 @ C ) )
        = ( ( insert_state @ A3 @ bot_bot_set_state )
          = ( sep_add_set_state @ Plus @ ( insert_state @ B2 @ bot_bot_set_state ) @ ( insert_state @ C @ bot_bot_set_state ) ) ) ) ) ).

% sep_algebra.sum_then_singleton
thf(fact_690_sep__algebra_Osetify__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_setify_state @ P2 @ ( sep_add_set_state @ Plus @ A6 @ B4 ) )
        = ( ! [X5: state] :
              ( ( member_state @ X5 @ A6 )
             => ( sep_setify_state @ P2 @ ( sep_add_set_state @ Plus @ ( insert_state @ X5 @ bot_bot_set_state ) @ B4 ) ) ) ) ) ) ).

% sep_algebra.setify_sum
thf(fact_691_PartialSA_Ovalid__package__setI,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( defined @ A7 @ U )
            & ( greater @ ( core @ A7 ) @ ( core @ U ) )
            & ( packag4817583915586052229_state @ plus @ unit @ T3 )
            & ( greater @ A7 @ ( core @ ( T3 @ F ) ) ) ) )
     => ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F ) ) ).

% PartialSA.valid_package_setI
thf(fact_692_the__elem__eq,axiom,
    ! [X2: state] :
      ( ( the_elem_state @ ( insert_state @ X2 @ bot_bot_set_state ) )
      = X2 ) ).

% the_elem_eq
thf(fact_693_is__singletonI,axiom,
    ! [X2: state] : ( is_singleton_state @ ( insert_state @ X2 @ bot_bot_set_state ) ) ).

% is_singletonI
thf(fact_694_the__elem__image__unique,axiom,
    ! [A6: set_state,F: state > state,X2: state] :
      ( ( A6 != bot_bot_set_state )
     => ( ! [Y3: state] :
            ( ( member_state @ Y3 @ A6 )
           => ( ( F @ Y3 )
              = ( F @ X2 ) ) )
       => ( ( the_elem_state @ ( image_state_state @ F @ A6 ) )
          = ( F @ X2 ) ) ) ) ).

% the_elem_image_unique
thf(fact_695_Set_Ois__empty__def,axiom,
    ( is_empty_state
    = ( ^ [A: set_state] : ( A = bot_bot_set_state ) ) ) ).

% Set.is_empty_def
thf(fact_696_bot__set__def,axiom,
    ( bot_bo6430881413863817907_state
    = ( collec906845016635587262_state @ bot_bo4916705512949510546tate_o ) ) ).

% bot_set_def
thf(fact_697_bot__set__def,axiom,
    ( bot_bo6722054719108133734on_val
    = ( collec7475294502966882545on_val @ bot_bo6370234372831922335_val_o ) ) ).

% bot_set_def
thf(fact_698_bot__set__def,axiom,
    ( bot_bot_set_state
    = ( collect_state @ bot_bot_state_o ) ) ).

% bot_set_def
thf(fact_699_package__logic_Ovalid__package__set_Ocong,axiom,
    packag3877571396724326311_state = packag3877571396724326311_state ).

% package_logic.valid_package_set.cong
thf(fact_700_is__singleton__the__elem,axiom,
    ( is_singleton_state
    = ( ^ [A: set_state] :
          ( A
          = ( insert_state @ ( the_elem_state @ A ) @ bot_bot_set_state ) ) ) ) ).

% is_singleton_the_elem
thf(fact_701_is__singletonI_H,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( A6 != bot_bo6430881413863817907_state )
     => ( ! [X4: produc7272280185086996969_state,Y3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X4 @ A6 )
           => ( ( member7461423308196221312_state @ Y3 @ A6 )
             => ( X4 = Y3 ) ) )
       => ( is_sin5735034780885272053_state @ A6 ) ) ) ).

% is_singletonI'
thf(fact_702_is__singletonI_H,axiom,
    ! [A6: set_Pr7649655576376376530on_val] :
      ( ( A6 != bot_bo6722054719108133734on_val )
     => ( ! [X4: produc9003781588162623004on_val,Y3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X4 @ A6 )
           => ( ( member2879030624002546611on_val @ Y3 @ A6 )
             => ( X4 = Y3 ) ) )
       => ( is_sin1022367449962840616on_val @ A6 ) ) ) ).

% is_singletonI'
thf(fact_703_is__singletonI_H,axiom,
    ! [A6: set_Pr2391701600042252046_state] :
      ( ( A6 != bot_bo3524941057552913786_state )
     => ( ! [X4: produc3882902684156697774_state,Y3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X4 @ A6 )
           => ( ( member6715010751053357271_state @ Y3 @ A6 )
             => ( X4 = Y3 ) ) )
       => ( is_sin8914544035436372898_state @ A6 ) ) ) ).

% is_singletonI'
thf(fact_704_is__singletonI_H,axiom,
    ! [A6: set_state] :
      ( ( A6 != bot_bot_set_state )
     => ( ! [X4: state,Y3: state] :
            ( ( member_state @ X4 @ A6 )
           => ( ( member_state @ Y3 @ A6 )
             => ( X4 = Y3 ) ) )
       => ( is_singleton_state @ A6 ) ) ) ).

% is_singletonI'
thf(fact_705_is__singletonE,axiom,
    ! [A6: set_state] :
      ( ( is_singleton_state @ A6 )
     => ~ ! [X4: state] :
            ( A6
           != ( insert_state @ X4 @ bot_bot_set_state ) ) ) ).

% is_singletonE
thf(fact_706_is__singleton__def,axiom,
    ( is_singleton_state
    = ( ^ [A: set_state] :
        ? [X5: state] :
          ( A
          = ( insert_state @ X5 @ bot_bot_set_state ) ) ) ) ).

% is_singleton_def
thf(fact_707_upper__bounded__smaller,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,A3: prat,P: prat] :
      ( ( upper_bounded @ Pi3 @ A3 )
     => ( upper_bounded @ ( multiply_mask @ P @ Pi3 ) @ ( pmult @ P @ A3 ) ) ) ).

% upper_bounded_smaller
thf(fact_708_add__masks_Opelims,axiom,
    ! [X2: produc1457211279475724562t_char > prat,Xa2: produc1457211279475724562t_char > prat,Xb2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X2 @ Xa2 @ Xb2 )
        = Y )
     => ( ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X2 @ ( produc2591414526589101846t_char @ Xa2 @ Xb2 ) ) )
       => ~ ( ( Y
              = ( padd @ ( X2 @ Xb2 ) @ ( Xa2 @ Xb2 ) ) )
           => ~ ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X2 @ ( produc2591414526589101846t_char @ Xa2 @ Xb2 ) ) ) ) ) ) ).

% add_masks.pelims
thf(fact_709_valid__stateI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
      ( ( valid_mask @ Pi3 )
     => ( ! [Hl3: produc1457211279475724562t_char] :
            ( ( ppos @ ( Pi3 @ Hl3 ) )
           => ( ( H3 @ Hl3 )
             != none_val ) )
       => ( valid_state @ ( produc74620467203698198on_val @ Pi3 @ H3 ) ) ) ) ).

% valid_stateI
thf(fact_710_valid__mult,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,P: prat] :
      ( ( valid_mask @ Pi3 )
     => ( ( pgte @ pwrite @ P )
       => ( valid_mask @ ( multiply_mask @ P @ Pi3 ) ) ) ) ).

% valid_mult
thf(fact_711_valid__sum_I2_J,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A3 )
     => ( ( valid_mask @ B2 )
       => ( ( upper_bounded @ A3 @ Ma )
         => ( ( upper_bounded @ B2 @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( upper_bounded @ ( add_ma6586698345353345811t_char @ A3 @ B2 ) @ ( padd @ Ma @ Mb ) ) ) ) ) ) ) ).

% valid_sum(2)
thf(fact_712_valid__sum_I1_J,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A3 )
     => ( ( valid_mask @ B2 )
       => ( ( upper_bounded @ A3 @ Ma )
         => ( ( upper_bounded @ B2 @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( valid_mask @ ( add_ma6586698345353345811t_char @ A3 @ B2 ) ) ) ) ) ) ) ).

% valid_sum(1)
thf(fact_713_upper__valid,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A3 )
     => ( ( A3
          = ( add_ma6586698345353345811t_char @ B2 @ C ) )
       => ( ( valid_mask @ B2 )
          & ( valid_mask @ C ) ) ) ) ).

% upper_valid
thf(fact_714_add__masks__asso,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( add_ma6586698345353345811t_char @ ( add_ma6586698345353345811t_char @ A3 @ B2 ) @ C )
      = ( add_ma6586698345353345811t_char @ A3 @ ( add_ma6586698345353345811t_char @ B2 @ C ) ) ) ).

% add_masks_asso
thf(fact_715_add__masks__comm,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [A2: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat] : ( add_ma6586698345353345811t_char @ B @ A2 ) ) ) ).

% add_masks_comm
thf(fact_716_upper__valid__aux,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A3 )
     => ( ( A3
          = ( add_ma6586698345353345811t_char @ B2 @ C ) )
       => ( valid_mask @ B2 ) ) ) ).

% upper_valid_aux
thf(fact_717_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_718_compatible__same__mask,axiom,
    ! [A3: produc1457211279475724562t_char > prat,W: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ ( add_ma6586698345353345811t_char @ A3 @ W ) )
     => ( W
        = ( comp_min_mask @ A3 @ W ) ) ) ).

% compatible_same_mask
thf(fact_719_valid__mask__add__comp__min,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A3 )
     => ( ( valid_mask @ B2 )
       => ( valid_mask @ ( add_ma6586698345353345811t_char @ ( comp_min_mask @ B2 @ A3 ) @ B2 ) ) ) ) ).

% valid_mask_add_comp_min
thf(fact_720_mult__distr__masks,axiom,
    ! [A3: prat,B2: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ A3 @ ( add_ma6586698345353345811t_char @ B2 @ C ) )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A3 @ B2 ) @ ( multiply_mask @ A3 @ C ) ) ) ).

% mult_distr_masks
thf(fact_721_add__masks_Oelims,axiom,
    ! [X2: produc1457211279475724562t_char > prat,Xa2: produc1457211279475724562t_char > prat,Xb2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X2 @ Xa2 @ Xb2 )
        = Y )
     => ( Y
        = ( padd @ ( X2 @ Xb2 ) @ ( Xa2 @ Xb2 ) ) ) ) ).

% add_masks.elims
thf(fact_722_add__masks_Osimps,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [Pi5: produc1457211279475724562t_char > prat,Pi4: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char] : ( padd @ ( Pi5 @ Hl ) @ ( Pi4 @ Hl ) ) ) ) ).

% add_masks.simps
thf(fact_723_valid__empty,axiom,
    valid_mask @ empty_3446695950879338768t_char ).

% valid_empty
thf(fact_724_minus__empty,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( Pi3
      = ( add_ma6586698345353345811t_char @ Pi3 @ empty_3446695950879338768t_char ) ) ).

% minus_empty
thf(fact_725_upper__boundedI,axiom,
    ! [P: prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ P @ ( Pi3 @ Hl3 ) )
     => ( upper_bounded @ Pi3 @ P ) ) ).

% upper_boundedI
thf(fact_726_upper__bounded__def,axiom,
    ( upper_bounded
    = ( ^ [Pi4: produc1457211279475724562t_char > prat,P5: prat] :
        ! [Hl: produc1457211279475724562t_char] : ( pgte @ P5 @ ( Pi4 @ Hl ) ) ) ) ).

% upper_bounded_def
thf(fact_727_upper__bounded__bigger,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,A3: prat,B2: prat] :
      ( ( upper_bounded @ Pi3 @ A3 )
     => ( ( pgte @ B2 @ A3 )
       => ( upper_bounded @ Pi3 @ B2 ) ) ) ).

% upper_bounded_bigger
thf(fact_728_valid__state__decompose,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ A3 @ B2 ) @ H3 ) )
     => ( valid_state @ ( produc74620467203698198on_val @ A3 @ H3 ) ) ) ).

% valid_state_decompose
thf(fact_729_mult__add__states,axiom,
    ! [A3: prat,B2: prat,Pi3: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ ( padd @ A3 @ B2 ) @ Pi3 )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A3 @ Pi3 ) @ ( multiply_mask @ B2 @ Pi3 ) ) ) ).

% mult_add_states
thf(fact_730_valid__multiply,axiom,
    ! [A3: produc1457211279475724562t_char > prat,Ma: prat,P: prat] :
      ( ( valid_mask @ A3 )
     => ( ( upper_bounded @ A3 @ Ma )
       => ( ( pgte @ pwrite @ ( pmult @ Ma @ P ) )
         => ( valid_mask @ ( multiply_mask @ P @ A3 ) ) ) ) ) ).

% valid_multiply
thf(fact_731_plus__charact_I1_J,axiom,
    ! [A3: state,B2: state,X2: state] :
      ( ( ( plus @ A3 @ B2 )
        = ( some_state @ X2 ) )
     => ( ( get_m @ X2 )
        = ( add_ma6586698345353345811t_char @ ( get_m @ A3 ) @ ( get_m @ B2 ) ) ) ) ).

% plus_charact(1)
thf(fact_732_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_733_valid__maskI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat] :
      ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi3 @ Hl3 ) )
     => ( ! [F3: list_char] :
            ( ( Pi3 @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
            = pnone )
       => ( valid_mask @ Pi3 ) ) ) ).

% valid_maskI
thf(fact_734_valid__mask_Osimps,axiom,
    ( valid_mask
    = ( ^ [Pi4: produc1457211279475724562t_char > prat] :
          ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi4 @ Hl ) )
          & ! [F4: list_char] :
              ( ( Pi4 @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
              = pnone ) ) ) ) ).

% valid_mask.simps
thf(fact_735_valid__mask_Oelims_I1_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X2 )
        = Y )
     => ( Y
        = ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl ) )
          & ! [F4: list_char] :
              ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
              = pnone ) ) ) ) ).

% valid_mask.elims(1)
thf(fact_736_compatible__heaps__def,axiom,
    ( compatible_heaps
    = ( ^ [H4: produc1457211279475724562t_char > option_val,H5: produc1457211279475724562t_char > option_val] :
        ! [Hl: produc1457211279475724562t_char] : ( compat7209469420100717861ns_val @ ( H4 @ Hl ) @ ( H5 @ Hl ) ) ) ) ).

% compatible_heaps_def
thf(fact_737_compatible__heapsI,axiom,
    ! [H3: produc1457211279475724562t_char > option_val,H6: produc1457211279475724562t_char > option_val] :
      ( ! [Hl3: produc1457211279475724562t_char,A7: val,B6: val] :
          ( ( ( H3 @ Hl3 )
            = ( some_val @ A7 ) )
         => ( ( ( H6 @ Hl3 )
              = ( some_val @ B6 ) )
           => ( A7 = B6 ) ) )
     => ( compatible_heaps @ H3 @ H6 ) ) ).

% compatible_heapsI
thf(fact_738_compatibleI,axiom,
    ! [A3: state,B2: state] :
      ( ( compatible_heaps @ ( get_h @ A3 ) @ ( get_h @ B2 ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ A3 ) @ ( get_m @ B2 ) ) )
       => ( defined @ A3 @ B2 ) ) ) ).

% compatibleI
thf(fact_739_valid__mask_Oelims_I3_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X2 )
     => ~ ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl3 ) )
          & ! [F3: list_char] :
              ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
              = pnone ) ) ) ).

% valid_mask.elims(3)
thf(fact_740_valid__mask_Oelims_I2_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X2 )
     => ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl4 ) )
        & ! [F5: list_char] :
            ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F5 ) )
            = pnone ) ) ) ).

% valid_mask.elims(2)
thf(fact_741_valid__mask_Opelims_I1_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X2 )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 )
       => ~ ( ( Y
              = ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl ) )
                & ! [F4: list_char] :
                    ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
                    = pnone ) ) )
           => ~ ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 ) ) ) ) ).

% valid_mask.pelims(1)
thf(fact_742_valid__mask_Opelims_I2_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X2 )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 )
           => ~ ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl4 ) )
                & ! [F5: list_char] :
                    ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F5 ) )
                    = pnone ) ) ) ) ) ).

% valid_mask.pelims(2)
thf(fact_743_valid__mask_Opelims_I3_J,axiom,
    ! [X2: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X2 )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X2 )
           => ( ! [Hl3: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X2 @ Hl3 ) )
              & ! [F3: list_char] :
                  ( ( X2 @ ( produc120197956887798346t_char @ null_nat @ F3 ) )
                  = pnone ) ) ) ) ) ).

% valid_mask.pelims(3)
thf(fact_744_valid__null__def,axiom,
    ( valid_null
    = ( ^ [Pi4: produc1457211279475724562t_char > prat] :
        ! [F4: list_char] :
          ( ( Pi4 @ ( produc120197956887798346t_char @ null_nat @ F4 ) )
          = pnone ) ) ) ).

% valid_null_def
thf(fact_745_add__masks__equiv__valid__null,axiom,
    ! [A3: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat] :
      ( ( valid_null @ ( add_ma6586698345353345811t_char @ A3 @ B2 ) )
      = ( ( valid_null @ A3 )
        & ( valid_null @ B2 ) ) ) ).

% add_masks_equiv_valid_null
thf(fact_746_valid__state_Osimps,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ Pi3 @ H3 ) )
      = ( ( valid_mask @ Pi3 )
        & ( valid_heap @ Pi3 @ H3 ) ) ) ).

% valid_state.simps
thf(fact_747_valid__state_Oelims_I1_J,axiom,
    ! [X2: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X2 )
        = Y )
     => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
            ( ( X2
              = ( produc74620467203698198on_val @ Pi @ H ) )
           => ( Y
              = ( ~ ( ( valid_mask @ Pi )
                    & ( valid_heap @ Pi @ H ) ) ) ) ) ) ).

% valid_state.elims(1)
thf(fact_748_valid__state_Oelims_I2_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ( valid_state @ X2 )
     => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
            ( ( X2
              = ( produc74620467203698198on_val @ Pi @ H ) )
           => ~ ( ( valid_mask @ Pi )
                & ( valid_heap @ Pi @ H ) ) ) ) ).

% valid_state.elims(2)
thf(fact_749_valid__state_Oelims_I3_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X2 )
     => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
            ( ( X2
              = ( produc74620467203698198on_val @ Pi @ H ) )
           => ( ( valid_mask @ Pi )
              & ( valid_heap @ Pi @ H ) ) ) ) ).

% valid_state.elims(3)
thf(fact_750_valid__heap__def,axiom,
    ( valid_heap
    = ( ^ [Pi4: produc1457211279475724562t_char > prat,H4: produc1457211279475724562t_char > option_val] :
        ! [Hl: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi4 @ Hl ) )
         => ( ( H4 @ Hl )
           != none_val ) ) ) ) ).

% valid_heap_def
thf(fact_751_valid__heapI,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
      ( ! [Hl3: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi3 @ Hl3 ) )
         => ( ( H3 @ Hl3 )
           != none_val ) )
     => ( valid_heap @ Pi3 @ H3 ) ) ).

% valid_heapI
thf(fact_752_valid__state_Opelims_I1_J,axiom,
    ! [X2: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X2 )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X2 )
       => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
              ( ( X2
                = ( produc74620467203698198on_val @ Pi @ H ) )
             => ( ( Y
                  = ( ( valid_mask @ Pi )
                    & ( valid_heap @ Pi @ H ) ) )
               => ~ ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi @ H ) ) ) ) ) ) ).

% valid_state.pelims(1)
thf(fact_753_valid__state_Opelims_I2_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ( valid_state @ X2 )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X2 )
       => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
              ( ( X2
                = ( produc74620467203698198on_val @ Pi @ H ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi @ H ) )
               => ~ ( ( valid_mask @ Pi )
                    & ( valid_heap @ Pi @ H ) ) ) ) ) ) ).

% valid_state.pelims(2)
thf(fact_754_valid__state_Opelims_I3_J,axiom,
    ! [X2: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X2 )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X2 )
       => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
              ( ( X2
                = ( produc74620467203698198on_val @ Pi @ H ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi @ H ) )
               => ( ( valid_mask @ Pi )
                  & ( valid_heap @ Pi @ H ) ) ) ) ) ) ).

% valid_state.pelims(3)
thf(fact_755_stableI,axiom,
    ! [Phi: state] :
      ( ! [Hl3: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi @ Hl3 ) )
          = ( ( get_h @ Phi @ Hl3 )
           != none_val ) )
     => ( stable @ Phi ) ) ).

% stableI
thf(fact_756_stable__unit,axiom,
    stable @ unit ).

% stable_unit
thf(fact_757_stable__sum,axiom,
    ! [A3: state,B2: state,X2: state] :
      ( ( stable @ A3 )
     => ( ( stable @ B2 )
       => ( ( ( some_state @ X2 )
            = ( plus @ A3 @ B2 ) )
         => ( stable @ X2 ) ) ) ) ).

% stable_sum
thf(fact_758_PartialSA_Opackage__logic__axioms,axiom,
    package_logic_state @ plus @ core @ unit @ stable ).

% PartialSA.package_logic_axioms
thf(fact_759_PartialHeapSA_Ostable__def,axiom,
    ( stable
    = ( ^ [Phi4: state] :
        ! [Hl: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi4 @ Hl ) )
          = ( ( get_h @ Phi4 @ Hl )
           != none_val ) ) ) ) ).

% PartialHeapSA.stable_def
thf(fact_760_PartialSA_Opackage__rhs__connectionI,axiom,
    ! [Phi: state,F: state,Phi2: state,F6: state,S2: set_Pr4231240917283394591_state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state] :
      ( ( ( plus @ Phi @ F )
        = ( plus @ Phi2 @ F6 ) )
     => ( ( stable @ F6 )
       => ( ( defined @ Phi @ F )
         => ( ( greater @ F6 @ F )
           => ( ! [A7: state,U: state,T3: state > state] :
                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
                 => ? [Au: state] :
                      ( ( ( some_state @ Au )
                        = ( plus @ A7 @ U ) )
                      & ( ( defined @ Au @ ( minus @ ( T3 @ F6 ) @ ( T3 @ F ) ) )
                       => ? [A9: state,U2: state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A9 @ ( produc8632743443909064678_state @ U2 @ T3 ) ) @ S3 )
                            & ( greater @ ( core @ A9 ) @ ( core @ A7 ) )
                            & ( ( plus @ Au @ ( minus @ ( T3 @ F6 ) @ ( T3 @ F ) ) )
                              = ( plus @ A9 @ U2 ) )
                            & ( greater @ U2 @ U )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A6 @ A9 @ U2 @ U ) ) ) ) )
             => ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connectionI
thf(fact_761_PartialSA_Opackage__rhs__connection__instantiate,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state,A3: state,U3: state,T2: state > state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
     => ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A3 @ ( produc8632743443909064678_state @ U3 @ T2 ) ) @ S2 )
       => ~ ! [Au2: state] :
              ( ( ( some_state @ Au2 )
                = ( plus @ A3 @ U3 ) )
             => ~ ( ( defined @ Au2 @ ( minus @ ( T2 @ F6 ) @ ( T2 @ F ) ) )
                 => ? [A10: state,U4: state] :
                      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A10 @ ( produc8632743443909064678_state @ U4 @ T2 ) ) @ S3 )
                      & ( greater @ ( core @ A10 ) @ ( core @ A3 ) )
                      & ( ( plus @ Au2 @ ( minus @ ( T2 @ F6 ) @ ( T2 @ F ) ) )
                        = ( plus @ A10 @ U4 ) )
                      & ( greater @ U4 @ U3 )
                      & ( packag8070727096299822599_state @ plus @ core @ Pc @ A6 @ A10 @ U4 @ U3 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connection_instantiate
thf(fact_762_add__states_Opelims,axiom,
    ! [X2: produc9003781588162623004on_val,Xa2: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ X2 @ Xa2 ) )
       => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
              ( ( X2
                = ( produc74620467203698198on_val @ Pi @ H ) )
             => ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
                  ( ( Xa2
                    = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
                 => ( ( Y
                      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi @ Pi2 ) @ ( map_ad2908576761495157028ar_val @ H @ H2 ) ) )
                   => ~ ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi @ H ) @ ( produc74620467203698198on_val @ Pi2 @ H2 ) ) ) ) ) ) ) ) ).

% add_states.pelims
thf(fact_763_valid__mask__full__mask,axiom,
    valid_mask @ full_mask ).

% valid_mask_full_mask
thf(fact_764_compatible__heaps__sum,axiom,
    ! [A3: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A3 @ B2 )
     => ( ( compatible_heaps @ A3 @ C )
       => ( compatible_heaps @ A3 @ ( map_ad2908576761495157028ar_val @ B2 @ C ) ) ) ) ).

% compatible_heaps_sum
thf(fact_765_compatible__heaps__comm,axiom,
    ! [A3: produc1457211279475724562t_char > option_val,B2: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A3 @ B2 )
     => ( ( map_ad2908576761495157028ar_val @ A3 @ B2 )
        = ( map_ad2908576761495157028ar_val @ B2 @ A3 ) ) ) ).

% compatible_heaps_comm
thf(fact_766_package__logic_Opackage__rhs__connection_Ocong,axiom,
    packag2054414653763826108_state = packag2054414653763826108_state ).

% package_logic.package_rhs_connection.cong
thf(fact_767_package__logic_Opackage__sat_Ocong,axiom,
    packag8070727096299822599_state = packag8070727096299822599_state ).

% package_logic.package_sat.cong
thf(fact_768_empty__heap__neutral,axiom,
    ! [A3: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ A3 @ empty_7512026568161686585ar_val )
      = A3 ) ).

% empty_heap_neutral
thf(fact_769_plus__charact_I2_J,axiom,
    ! [A3: state,B2: state,X2: state] :
      ( ( ( plus @ A3 @ B2 )
        = ( some_state @ X2 ) )
     => ( ( get_h @ X2 )
        = ( map_ad2908576761495157028ar_val @ ( get_h @ A3 ) @ ( get_h @ B2 ) ) ) ) ).

% plus_charact(2)
thf(fact_770_add__states_Osimps,axiom,
    ! [Pi3: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val,Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
      ( ( add_states @ ( produc74620467203698198on_val @ Pi3 @ H3 ) @ ( produc74620467203698198on_val @ Pi6 @ H6 ) )
      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi3 @ Pi6 ) @ ( map_ad2908576761495157028ar_val @ H3 @ H6 ) ) ) ).

% add_states.simps
thf(fact_771_add__states_Oelims,axiom,
    ! [X2: produc9003781588162623004on_val,Xa2: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X2 @ Xa2 )
        = Y )
     => ~ ! [Pi: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
            ( ( X2
              = ( produc74620467203698198on_val @ Pi @ H ) )
           => ! [Pi2: produc1457211279475724562t_char > prat,H2: produc1457211279475724562t_char > option_val] :
                ( ( Xa2
                  = ( produc74620467203698198on_val @ Pi2 @ H2 ) )
               => ( Y
                 != ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi @ Pi2 ) @ ( map_ad2908576761495157028ar_val @ H @ H2 ) ) ) ) ) ) ).

% add_states.elims
thf(fact_772_map__add__None,axiom,
    ! [M2: produc1457211279475724562t_char > option_val,N2: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char] :
      ( ( ( map_ad2908576761495157028ar_val @ M2 @ N2 @ K )
        = none_val )
      = ( ( ( N2 @ K )
          = none_val )
        & ( ( M2 @ K )
          = none_val ) ) ) ).

% map_add_None
thf(fact_773_map__add__eq__empty__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( ( map_ad2908576761495157028ar_val @ F @ G )
        = ( ^ [X5: produc1457211279475724562t_char] : none_val ) )
      = ( ( F
          = ( ^ [X5: produc1457211279475724562t_char] : none_val ) )
        & ( G
          = ( ^ [X5: produc1457211279475724562t_char] : none_val ) ) ) ) ).

% map_add_eq_empty_iff
thf(fact_774_map__add__find__right,axiom,
    ! [N2: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,Xx: val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( N2 @ K )
        = ( some_val @ Xx ) )
     => ( ( map_ad2908576761495157028ar_val @ M2 @ N2 @ K )
        = ( some_val @ Xx ) ) ) ).

% map_add_find_right
thf(fact_775_map__add__Some__iff,axiom,
    ! [M2: produc1457211279475724562t_char > option_val,N2: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X2: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M2 @ N2 @ K )
        = ( some_val @ X2 ) )
      = ( ( ( N2 @ K )
          = ( some_val @ X2 ) )
        | ( ( ( N2 @ K )
            = none_val )
          & ( ( M2 @ K )
            = ( some_val @ X2 ) ) ) ) ) ).

% map_add_Some_iff
thf(fact_776_map__add__SomeD,axiom,
    ! [M2: produc1457211279475724562t_char > option_val,N2: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X2: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M2 @ N2 @ K )
        = ( some_val @ X2 ) )
     => ( ( ( N2 @ K )
          = ( some_val @ X2 ) )
        | ( ( ( N2 @ K )
            = none_val )
          & ( ( M2 @ K )
            = ( some_val @ X2 ) ) ) ) ) ).

% map_add_SomeD
thf(fact_777_full__mask__def,axiom,
    ( full_mask
    = ( ^ [Hl: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( produc6204653154488278070t_char @ Hl )
            = null_nat )
          @ pnone
          @ pwrite ) ) ) ).

% full_mask_def
thf(fact_778_PartialSA_Opackage__sat__def,axiom,
    ! [Pc: state > $o,A6: aassertion_state,A4: state,U5: state,U3: state] :
      ( ( packag8070727096299822599_state @ plus @ core @ Pc @ A6 @ A4 @ U5 @ U3 )
      = ( ( Pc @ ( core @ A4 ) )
       => ? [X5: state] :
            ( ( ( some_state @ X5 )
              = ( plus @ ( core @ A4 ) @ ( minus @ U5 @ U3 ) ) )
            & ( package_sat_state @ plus @ A6 @ X5 ) ) ) ) ).

% PartialSA.package_sat_def
thf(fact_779_PartialSA_Opackage__satI,axiom,
    ! [Pc: state > $o,A4: state,U5: state,U3: state,A6: aassertion_state] :
      ( ( ( Pc @ ( core @ A4 ) )
       => ? [X3: state] :
            ( ( ( some_state @ X3 )
              = ( plus @ ( core @ A4 ) @ ( minus @ U5 @ U3 ) ) )
            & ( package_sat_state @ plus @ A6 @ X3 ) ) )
     => ( packag8070727096299822599_state @ plus @ core @ Pc @ A6 @ A4 @ U5 @ U3 ) ) ).

% PartialSA.package_satI
thf(fact_780_package__logic_Opackage__satI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Pc: val > $o,A4: val,U5: val,U3: val,A6: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Pc @ ( Core @ A4 ) )
         => ? [X3: val] :
              ( ( ( some_val @ X3 )
                = ( Plus @ ( Core @ A4 ) @ ( sep_minus_val @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_val @ Plus @ A6 @ X3 ) ) )
       => ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A6 @ A4 @ U5 @ U3 ) ) ) ).

% package_logic.package_satI
thf(fact_781_package__logic_Opackage__satI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Pc: state > $o,A4: state,U5: state,U3: state,A6: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Pc @ ( Core @ A4 ) )
         => ? [X3: state] :
              ( ( ( some_state @ X3 )
                = ( Plus @ ( Core @ A4 ) @ ( sep_minus_state @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_state @ Plus @ A6 @ X3 ) ) )
       => ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A6 @ A4 @ U5 @ U3 ) ) ) ).

% package_logic.package_satI
thf(fact_782_package__logic_Osat_Ocong,axiom,
    package_sat_state = package_sat_state ).

% package_logic.sat.cong
thf(fact_783_package__logic_Opackage__sat__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Pc: val > $o,A6: aassertion_val,A4: val,U5: val,U3: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A6 @ A4 @ U5 @ U3 )
        = ( ( Pc @ ( Core @ A4 ) )
         => ? [X5: val] :
              ( ( ( some_val @ X5 )
                = ( Plus @ ( Core @ A4 ) @ ( sep_minus_val @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_val @ Plus @ A6 @ X5 ) ) ) ) ) ).

% package_logic.package_sat_def
thf(fact_784_package__logic_Opackage__sat__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Pc: state > $o,A6: aassertion_state,A4: state,U5: state,U3: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A6 @ A4 @ U5 @ U3 )
        = ( ( Pc @ ( Core @ A4 ) )
         => ? [X5: state] :
              ( ( ( some_state @ X5 )
                = ( Plus @ ( Core @ A4 ) @ ( sep_minus_state @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_state @ Plus @ A6 @ X5 ) ) ) ) ) ).

% package_logic.package_sat_def
thf(fact_785_package__logic_Ois__footprint__generalI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A6: aassertion_val,R5: val > val > val,W: val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: val,B6: val] :
            ( ( ( package_sat_val @ Plus @ A6 @ A7 )
              & ( ( some_val @ B6 )
                = ( Plus @ A7 @ ( R5 @ A7 @ W ) ) ) )
           => ( package_sat_val @ Plus @ B4 @ B6 ) )
       => ( packag4897621287243763553al_val @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ).

% package_logic.is_footprint_generalI
thf(fact_786_package__logic_Ois__footprint__generalI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,R5: state > state > state,W: state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,B6: state] :
            ( ( ( package_sat_state @ Plus @ A6 @ A7 )
              & ( ( some_state @ B6 )
                = ( Plus @ A7 @ ( R5 @ A7 @ W ) ) ) )
           => ( package_sat_state @ Plus @ B4 @ B6 ) )
       => ( packag6192661653625646554_state @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ).

% package_logic.is_footprint_generalI
thf(fact_787_package__logic_Ois__footprint__standardI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A6: aassertion_val,W: val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: val,B6: val] :
            ( ( ( package_sat_val @ Plus @ A6 @ A7 )
              & ( ( some_val @ B6 )
                = ( Plus @ A7 @ W ) ) )
           => ( package_sat_val @ Plus @ B4 @ B6 ) )
       => ( packag685230357167683994rd_val @ Plus @ W @ A6 @ B4 ) ) ) ).

% package_logic.is_footprint_standardI
thf(fact_788_package__logic_Ois__footprint__standardI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,W: state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,B6: state] :
            ( ( ( package_sat_state @ Plus @ A6 @ A7 )
              & ( ( some_state @ B6 )
                = ( Plus @ A7 @ W ) ) )
           => ( package_sat_state @ Plus @ B4 @ B6 ) )
       => ( packag7096211993527611489_state @ Plus @ W @ A6 @ B4 ) ) ) ).

% package_logic.is_footprint_standardI
thf(fact_789_package__logic_Ois__footprint__general__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,W: val,R5: val > val > val,A6: aassertion_val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag4897621287243763553al_val @ Plus @ W @ R5 @ A6 @ B4 )
        = ( ! [A2: val,B: val] :
              ( ( ( package_sat_val @ Plus @ A6 @ A2 )
                & ( ( some_val @ B )
                  = ( Plus @ A2 @ ( R5 @ A2 @ W ) ) ) )
             => ( package_sat_val @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.is_footprint_general_def
thf(fact_790_package__logic_Ois__footprint__general__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,W: state,R5: state > state > state,A6: aassertion_state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6192661653625646554_state @ Plus @ W @ R5 @ A6 @ B4 )
        = ( ! [A2: state,B: state] :
              ( ( ( package_sat_state @ Plus @ A6 @ A2 )
                & ( ( some_state @ B )
                  = ( Plus @ A2 @ ( R5 @ A2 @ W ) ) ) )
             => ( package_sat_state @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.is_footprint_general_def
thf(fact_791_package__logic_Ois__footprint__standard__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,W: val,A6: aassertion_val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag685230357167683994rd_val @ Plus @ W @ A6 @ B4 )
        = ( ! [A2: val,B: val] :
              ( ( ( package_sat_val @ Plus @ A6 @ A2 )
                & ( ( some_val @ B )
                  = ( Plus @ A2 @ W ) ) )
             => ( package_sat_val @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.is_footprint_standard_def
thf(fact_792_package__logic_Ois__footprint__standard__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,W: state,A6: aassertion_state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7096211993527611489_state @ Plus @ W @ A6 @ B4 )
        = ( ! [A2: state,B: state] :
              ( ( ( package_sat_state @ Plus @ A6 @ A2 )
                & ( ( some_state @ B )
                  = ( Plus @ A2 @ W ) ) )
             => ( package_sat_state @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.is_footprint_standard_def
thf(fact_793_package__logic_Ois__footprint__general_Ocong,axiom,
    packag6192661653625646554_state = packag6192661653625646554_state ).

% package_logic.is_footprint_general.cong
thf(fact_794_package__logic_Ois__footprint__standard_Ocong,axiom,
    packag7096211993527611489_state = packag7096211993527611489_state ).

% package_logic.is_footprint_standard.cong
thf(fact_795_PartialSA_Ois__footprint__standard__def,axiom,
    ! [W: state,A6: aassertion_state,B4: aassertion_state] :
      ( ( packag7096211993527611489_state @ plus @ W @ A6 @ B4 )
      = ( ! [A2: state,B: state] :
            ( ( ( package_sat_state @ plus @ A6 @ A2 )
              & ( ( some_state @ B )
                = ( plus @ A2 @ W ) ) )
           => ( package_sat_state @ plus @ B4 @ B ) ) ) ) ).

% PartialSA.is_footprint_standard_def
thf(fact_796_PartialSA_Ois__footprint__general__def,axiom,
    ! [W: state,R5: state > state > state,A6: aassertion_state,B4: aassertion_state] :
      ( ( packag6192661653625646554_state @ plus @ W @ R5 @ A6 @ B4 )
      = ( ! [A2: state,B: state] :
            ( ( ( package_sat_state @ plus @ A6 @ A2 )
              & ( ( some_state @ B )
                = ( plus @ A2 @ ( R5 @ A2 @ W ) ) ) )
           => ( package_sat_state @ plus @ B4 @ B ) ) ) ) ).

% PartialSA.is_footprint_general_def
thf(fact_797_PartialSA_Ois__footprint__standardI,axiom,
    ! [A6: aassertion_state,W: state,B4: aassertion_state] :
      ( ! [A7: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A6 @ A7 )
            & ( ( some_state @ B6 )
              = ( plus @ A7 @ W ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag7096211993527611489_state @ plus @ W @ A6 @ B4 ) ) ).

% PartialSA.is_footprint_standardI
thf(fact_798_PartialSA_Ois__footprint__generalI,axiom,
    ! [A6: aassertion_state,R5: state > state > state,W: state,B4: aassertion_state] :
      ( ! [A7: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A6 @ A7 )
            & ( ( some_state @ B6 )
              = ( plus @ A7 @ ( R5 @ A7 @ W ) ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag6192661653625646554_state @ plus @ W @ R5 @ A6 @ B4 ) ) ).

% PartialSA.is_footprint_generalI
thf(fact_799_PartialSA_Owf__assertion__and__the,axiom,
    ! [A3: state,B2: state,A6: aassertion_state] :
      ( ( defined @ ( core @ A3 ) @ B2 )
     => ( ( package_sat_state @ plus @ A6 @ B2 )
       => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
         => ( package_sat_state @ plus @ A6 @ ( the_state @ ( plus @ ( core @ A3 ) @ B2 ) ) ) ) ) ) ).

% PartialSA.wf_assertion_and_the
thf(fact_800_PartialSA_Owf__assertion__sat__larger__pure,axiom,
    ! [A6: aassertion_state,Phi: state,Phi2: state,R: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ A6 )
     => ( ( package_sat_state @ plus @ A6 @ Phi )
       => ( ( ( some_state @ Phi2 )
            = ( plus @ Phi @ R ) )
         => ( ( sep_pure_state @ plus @ R )
           => ( package_sat_state @ plus @ A6 @ Phi2 ) ) ) ) ) ).

% PartialSA.wf_assertion_sat_larger_pure
thf(fact_801_package__logic_Owf__assertion__sat__larger__pure,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A6: aassertion_val,Phi: val,Phi2: val,R: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ A6 )
       => ( ( package_sat_val @ Plus @ A6 @ Phi )
         => ( ( ( some_val @ Phi2 )
              = ( Plus @ Phi @ R ) )
           => ( ( sep_pure_val @ Plus @ R )
             => ( package_sat_val @ Plus @ A6 @ Phi2 ) ) ) ) ) ) ).

% package_logic.wf_assertion_sat_larger_pure
thf(fact_802_package__logic_Owf__assertion__sat__larger__pure,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,Phi: state,Phi2: state,R: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
       => ( ( package_sat_state @ Plus @ A6 @ Phi )
         => ( ( ( some_state @ Phi2 )
              = ( Plus @ Phi @ R ) )
           => ( ( sep_pure_state @ Plus @ R )
             => ( package_sat_state @ Plus @ A6 @ Phi2 ) ) ) ) ) ) ).

% package_logic.wf_assertion_sat_larger_pure
thf(fact_803_PartialSA_Opackage__rhs__proof,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( stable @ F )
             => ( ( defined @ Phi @ F )
               => ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
                  & ( packag3877571396724326311_state @ plus @ core @ unit @ S3 @ F6 ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs_proof
thf(fact_804_package__logic_Owf__assertion_Ocong,axiom,
    packag7298478212905792770_state = packag7298478212905792770_state ).

% package_logic.wf_assertion.cong
thf(fact_805_package__logic_Opackage__rhs_Ocong,axiom,
    packag3171892606229212990_state = packag3171892606229212990_state ).

% package_logic.package_rhs.cong
thf(fact_806_package__logic_Opackage__rhs__proof,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
       => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
           => ( ( packag6595153354952283300_state @ Plus @ Core @ Pc )
             => ( ( Stable @ F )
               => ( ( sep_defined_state @ Plus @ Phi @ F )
                 => ( ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
                    & ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S3 @ F6 ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs_proof
thf(fact_807_PartialSA_Osat__star__exists__bigger,axiom,
    ! [A6: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ A6 @ B4 ) @ Phi )
     => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
       => ( ( packag7298478212905792770_state @ plus @ core @ B4 )
         => ? [A7: state,B6: state] :
              ( ( greater @ ( core @ A7 ) @ ( core @ Phi ) )
              & ( greater @ ( core @ B6 ) @ ( core @ Phi ) )
              & ( ( some_state @ Phi )
                = ( plus @ A7 @ B6 ) )
              & ( package_sat_state @ plus @ A6 @ A7 )
              & ( package_sat_state @ plus @ B4 @ B6 ) ) ) ) ) ).

% PartialSA.sat_star_exists_bigger
thf(fact_808_PartialSA_OAImp,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,B2: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ ( packag1330488657391168505_state @ Pc @ B2 ) @ A6 @ Phi2 @ F6 @ S3 )
     => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aImp_state @ B2 @ A6 ) @ Phi2 @ F6 @ S3 ) ) ).

% PartialSA.AImp
thf(fact_809_PartialSA_Ogeneral__completeness,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state,A6: aassertion_state,Phi: state,Phi2: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ! [X4: state] :
              ( ( ( some_state @ X4 )
                = ( plus @ A7 @ ( T3 @ F ) ) )
             => ( package_sat_state @ plus @ A6 @ X4 ) ) )
     => ( ( ( some_state @ Phi )
          = ( plus @ Phi2 @ F ) )
       => ( ( stable @ F )
         => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ unit )
           => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
             => ? [X_1: set_Pr4231240917283394591_state] :
                  ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ unit @ S2
                  @ ^ [Uu3: state] : $true
                  @ A6
                  @ Phi2
                  @ F
                  @ X_1 ) ) ) ) ) ) ).

% PartialSA.general_completeness
thf(fact_810_aassertion_Oinject_I1_J,axiom,
    ! [X11: aassertion_state,X12: aassertion_state,Y11: aassertion_state,Y12: aassertion_state] :
      ( ( ( aStar_state @ X11 @ X12 )
        = ( aStar_state @ Y11 @ Y12 ) )
      = ( ( X11 = Y11 )
        & ( X12 = Y12 ) ) ) ).

% aassertion.inject(1)
thf(fact_811_aassertion_Oinject_I2_J,axiom,
    ! [X21: state > $o,X222: aassertion_state,Y21: state > $o,Y22: aassertion_state] :
      ( ( ( aImp_state @ X21 @ X222 )
        = ( aImp_state @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% aassertion.inject(2)
thf(fact_812_image__ident,axiom,
    ! [Y7: set_state] :
      ( ( image_state_state
        @ ^ [X5: state] : X5
        @ Y7 )
      = Y7 ) ).

% image_ident
thf(fact_813_Collect__const,axiom,
    ! [P2: $o] :
      ( ( P2
       => ( ( collec906845016635587262_state
            @ ^ [S4: produc7272280185086996969_state] : P2 )
          = top_to174962084833059535_state ) )
      & ( ~ P2
       => ( ( collec906845016635587262_state
            @ ^ [S4: produc7272280185086996969_state] : P2 )
          = bot_bo6430881413863817907_state ) ) ) ).

% Collect_const
thf(fact_814_Collect__const,axiom,
    ! [P2: $o] :
      ( ( P2
       => ( ( collec7475294502966882545on_val
            @ ^ [S4: produc9003781588162623004on_val] : P2 )
          = top_to1561438921946393474on_val ) )
      & ( ~ P2
       => ( ( collec7475294502966882545on_val
            @ ^ [S4: produc9003781588162623004on_val] : P2 )
          = bot_bo6722054719108133734on_val ) ) ) ).

% Collect_const
thf(fact_815_Collect__const,axiom,
    ! [P2: $o] :
      ( ( P2
       => ( ( collect_state
            @ ^ [S4: state] : P2 )
          = top_top_set_state ) )
      & ( ~ P2
       => ( ( collect_state
            @ ^ [S4: state] : P2 )
          = bot_bot_set_state ) ) ) ).

% Collect_const
thf(fact_816_singleton__conv,axiom,
    ! [A3: produc7272280185086996969_state] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] : ( X5 = A3 ) )
      = ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) ) ).

% singleton_conv
thf(fact_817_singleton__conv,axiom,
    ! [A3: produc9003781588162623004on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] : ( X5 = A3 ) )
      = ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) ) ).

% singleton_conv
thf(fact_818_singleton__conv,axiom,
    ! [A3: state] :
      ( ( collect_state
        @ ^ [X5: state] : ( X5 = A3 ) )
      = ( insert_state @ A3 @ bot_bot_set_state ) ) ).

% singleton_conv
thf(fact_819_singleton__conv2,axiom,
    ! [A3: produc7272280185086996969_state] :
      ( ( collec906845016635587262_state
        @ ( ^ [Y5: produc7272280185086996969_state,Z2: produc7272280185086996969_state] : ( Y5 = Z2 )
          @ A3 ) )
      = ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) ) ).

% singleton_conv2
thf(fact_820_singleton__conv2,axiom,
    ! [A3: produc9003781588162623004on_val] :
      ( ( collec7475294502966882545on_val
        @ ( ^ [Y5: produc9003781588162623004on_val,Z2: produc9003781588162623004on_val] : ( Y5 = Z2 )
          @ A3 ) )
      = ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) ) ).

% singleton_conv2
thf(fact_821_singleton__conv2,axiom,
    ! [A3: state] :
      ( ( collect_state
        @ ( ^ [Y5: state,Z2: state] : ( Y5 = Z2 )
          @ A3 ) )
      = ( insert_state @ A3 @ bot_bot_set_state ) ) ).

% singleton_conv2
thf(fact_822_empty__map__add,axiom,
    ! [M2: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val
        @ ^ [X5: produc1457211279475724562t_char] : none_val
        @ M2 )
      = M2 ) ).

% empty_map_add
thf(fact_823_map__add__empty,axiom,
    ! [M2: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ M2
        @ ^ [X5: produc1457211279475724562t_char] : none_val )
      = M2 ) ).

% map_add_empty
thf(fact_824_empty__eq__map__add__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( ( ^ [X5: produc1457211279475724562t_char] : none_val )
        = ( map_ad2908576761495157028ar_val @ F @ G ) )
      = ( ( F
          = ( ^ [X5: produc1457211279475724562t_char] : none_val ) )
        & ( G
          = ( ^ [X5: produc1457211279475724562t_char] : none_val ) ) ) ) ).

% empty_eq_map_add_iff
thf(fact_825_range__constant,axiom,
    ! [X2: state] :
      ( ( image_state_state
        @ ^ [Uu3: state] : X2
        @ top_top_set_state )
      = ( insert_state @ X2 @ bot_bot_set_state ) ) ).

% range_constant
thf(fact_826_pred__subset__eq2,axiom,
    ! [R5: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le6704609105599929480tate_o
        @ ^ [X5: state,Y4: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: state,Y4: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le4032880777312351359_state @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_827_pred__subset__eq2,axiom,
    ! [R5: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le1106678366802930969tate_o
        @ ^ [X5: state,Y4: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: state,Y4: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le6483787752022044334_state @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_828_pred__subset__eq2,axiom,
    ! [R5: set_Pr1688445902015331925_state,S2: set_Pr1688445902015331925_state] :
      ( ( ord_le2052508915978315794tate_o
        @ ^ [X5: option_state,Y4: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: option_state,Y4: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le6423325748750870005_state @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_829_pred__subset__eq2,axiom,
    ! [R5: set_Pr6039890582625207499_state,S2: set_Pr6039890582625207499_state] :
      ( ( ord_le9040380983013460636tate_o
        @ ^ [X5: prat,Y4: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: prat,Y4: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le262197048489888875_state @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_830_pred__subset__eq2,axiom,
    ! [R5: set_Pr6847263425858009217_state,S2: set_Pr6847263425858009217_state] :
      ( ( ord_le8830457724327557734tate_o
        @ ^ [X5: prat,Y4: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: prat,Y4: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le5761494056910127137_state @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_831_pred__subset__eq2,axiom,
    ! [R5: set_Pr2507339680178222706t_char,S2: set_Pr2507339680178222706t_char] :
      ( ( ord_le2712619360209801397char_o
        @ ^ [X5: nat,Y4: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: nat,Y4: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le6315511645215477266t_char @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_832_pred__subset__eq2,axiom,
    ! [R5: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le3852884270828607079_val_o
        @ ^ [X5: produc1457211279475724562t_char > prat,Y4: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X5 @ Y4 ) @ R5 )
        @ ^ [X5: produc1457211279475724562t_char > prat,Y4: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X5 @ Y4 ) @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R5 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_833_range__composition,axiom,
    ! [F: state > state,G: state > state] :
      ( ( image_state_state
        @ ^ [X5: state] : ( F @ ( G @ X5 ) )
        @ top_top_set_state )
      = ( image_state_state @ F @ ( image_state_state @ G @ top_top_set_state ) ) ) ).

% range_composition
thf(fact_834_rangeE,axiom,
    ! [B2: state,F: state > state] :
      ( ( member_state @ B2 @ ( image_state_state @ F @ top_top_set_state ) )
     => ~ ! [X4: state] :
            ( B2
           != ( F @ X4 ) ) ) ).

% rangeE
thf(fact_835_rangeE,axiom,
    ! [B2: produc7272280185086996969_state,F: state > produc7272280185086996969_state] :
      ( ( member7461423308196221312_state @ B2 @ ( image_632992669292831658_state @ F @ top_top_set_state ) )
     => ~ ! [X4: state] :
            ( B2
           != ( F @ X4 ) ) ) ).

% rangeE
thf(fact_836_rangeE,axiom,
    ! [B2: produc9003781588162623004on_val,F: state > produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ B2 @ ( image_4772210114854293981on_val @ F @ top_top_set_state ) )
     => ~ ! [X4: state] :
            ( B2
           != ( F @ X4 ) ) ) ).

% rangeE
thf(fact_837_rangeE,axiom,
    ! [B2: produc3882902684156697774_state,F: state > produc3882902684156697774_state] :
      ( ( member6715010751053357271_state @ B2 @ ( image_5311902671526399277_state @ F @ top_top_set_state ) )
     => ~ ! [X4: state] :
            ( B2
           != ( F @ X4 ) ) ) ).

% rangeE
thf(fact_838_insert__Collect,axiom,
    ! [A3: produc7272280185086996969_state,P2: produc7272280185086996969_state > $o] :
      ( ( insert175804457004744729_state @ A3 @ ( collec906845016635587262_state @ P2 ) )
      = ( collec906845016635587262_state
        @ ^ [U6: produc7272280185086996969_state] :
            ( ( U6 != A3 )
           => ( P2 @ U6 ) ) ) ) ).

% insert_Collect
thf(fact_839_insert__Collect,axiom,
    ! [A3: produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( insert3030518898131756108on_val @ A3 @ ( collec7475294502966882545on_val @ P2 ) )
      = ( collec7475294502966882545on_val
        @ ^ [U6: produc9003781588162623004on_val] :
            ( ( U6 != A3 )
           => ( P2 @ U6 ) ) ) ) ).

% insert_Collect
thf(fact_840_insert__Collect,axiom,
    ! [A3: state,P2: state > $o] :
      ( ( insert_state @ A3 @ ( collect_state @ P2 ) )
      = ( collect_state
        @ ^ [U6: state] :
            ( ( U6 != A3 )
           => ( P2 @ U6 ) ) ) ) ).

% insert_Collect
thf(fact_841_insert__compr,axiom,
    ( insert94804854012721790_state
    = ( ^ [A2: produc3882902684156697774_state,B5: set_Pr2391701600042252046_state] :
          ( collec394671971739345689_state
          @ ^ [X5: produc3882902684156697774_state] :
              ( ( X5 = A2 )
              | ( member6715010751053357271_state @ X5 @ B5 ) ) ) ) ) ).

% insert_compr
thf(fact_842_insert__compr,axiom,
    ( insert175804457004744729_state
    = ( ^ [A2: produc7272280185086996969_state,B5: set_Pr4231240917283394591_state] :
          ( collec906845016635587262_state
          @ ^ [X5: produc7272280185086996969_state] :
              ( ( X5 = A2 )
              | ( member7461423308196221312_state @ X5 @ B5 ) ) ) ) ) ).

% insert_compr
thf(fact_843_insert__compr,axiom,
    ( insert3030518898131756108on_val
    = ( ^ [A2: produc9003781588162623004on_val,B5: set_Pr7649655576376376530on_val] :
          ( collec7475294502966882545on_val
          @ ^ [X5: produc9003781588162623004on_val] :
              ( ( X5 = A2 )
              | ( member2879030624002546611on_val @ X5 @ B5 ) ) ) ) ) ).

% insert_compr
thf(fact_844_insert__compr,axiom,
    ( insert_state
    = ( ^ [A2: state,B5: set_state] :
          ( collect_state
          @ ^ [X5: state] :
              ( ( X5 = A2 )
              | ( member_state @ X5 @ B5 ) ) ) ) ) ).

% insert_compr
thf(fact_845_Compr__image__eq,axiom,
    ! [F: state > state,A6: set_state,P2: state > $o] :
      ( ( collect_state
        @ ^ [X5: state] :
            ( ( member_state @ X5 @ ( image_state_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_state_state @ F
        @ ( collect_state
          @ ^ [X5: state] :
              ( ( member_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_846_Compr__image__eq,axiom,
    ! [F: state > produc3882902684156697774_state,A6: set_state,P2: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X5 @ ( image_5311902671526399277_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_5311902671526399277_state @ F
        @ ( collect_state
          @ ^ [X5: state] :
              ( ( member_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_847_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > state,A6: set_Pr2391701600042252046_state,P2: state > $o] :
      ( ( collect_state
        @ ^ [X5: state] :
            ( ( member_state @ X5 @ ( image_6759111139246981411_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_6759111139246981411_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X5: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_848_Compr__image__eq,axiom,
    ! [F: state > produc7272280185086996969_state,A6: set_state,P2: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ ( image_632992669292831658_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_632992669292831658_state @ F
        @ ( collect_state
          @ ^ [X5: state] :
              ( ( member_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_849_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > state,A6: set_Pr4231240917283394591_state,P2: state > $o] :
      ( ( collect_state
        @ ^ [X5: state] :
            ( ( member_state @ X5 @ ( image_2710133271811360426_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_2710133271811360426_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_850_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X5 @ ( image_508898238547643525_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_508898238547643525_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X5: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_851_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > produc3882902684156697774_state,A6: set_Pr4231240917283394591_state,P2: produc3882902684156697774_state > $o] :
      ( ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X5 @ ( image_7466395622266389182_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_7466395622266389182_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_852_Compr__image__eq,axiom,
    ! [F: produc3882902684156697774_state > produc7272280185086996969_state,A6: set_Pr2391701600042252046_state,P2: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ ( image_4364510454419742290_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_4364510454419742290_state @ F
        @ ( collec394671971739345689_state
          @ ^ [X5: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_853_Compr__image__eq,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ ( image_3064086290059306969_state @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_3064086290059306969_state @ F
        @ ( collec906845016635587262_state
          @ ^ [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_854_Compr__image__eq,axiom,
    ! [F: state > produc9003781588162623004on_val,A6: set_state,P2: produc9003781588162623004on_val > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X5 @ ( image_4772210114854293981on_val @ F @ A6 ) )
            & ( P2 @ X5 ) ) )
      = ( image_4772210114854293981on_val @ F
        @ ( collect_state
          @ ^ [X5: state] :
              ( ( member_state @ X5 @ A6 )
              & ( P2 @ ( F @ X5 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_855_image__image,axiom,
    ! [F: state > state,G: state > state,A6: set_state] :
      ( ( image_state_state @ F @ ( image_state_state @ G @ A6 ) )
      = ( image_state_state
        @ ^ [X5: state] : ( F @ ( G @ X5 ) )
        @ A6 ) ) ).

% image_image
thf(fact_856_imageE,axiom,
    ! [B2: state,F: state > state,A6: set_state] :
      ( ( member_state @ B2 @ ( image_state_state @ F @ A6 ) )
     => ~ ! [X4: state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_857_imageE,axiom,
    ! [B2: state,F: produc3882902684156697774_state > state,A6: set_Pr2391701600042252046_state] :
      ( ( member_state @ B2 @ ( image_6759111139246981411_state @ F @ A6 ) )
     => ~ ! [X4: produc3882902684156697774_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member6715010751053357271_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_858_imageE,axiom,
    ! [B2: produc3882902684156697774_state,F: state > produc3882902684156697774_state,A6: set_state] :
      ( ( member6715010751053357271_state @ B2 @ ( image_5311902671526399277_state @ F @ A6 ) )
     => ~ ! [X4: state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_859_imageE,axiom,
    ! [B2: state,F: produc7272280185086996969_state > state,A6: set_Pr4231240917283394591_state] :
      ( ( member_state @ B2 @ ( image_2710133271811360426_state @ F @ A6 ) )
     => ~ ! [X4: produc7272280185086996969_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member7461423308196221312_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_860_imageE,axiom,
    ! [B2: produc7272280185086996969_state,F: state > produc7272280185086996969_state,A6: set_state] :
      ( ( member7461423308196221312_state @ B2 @ ( image_632992669292831658_state @ F @ A6 ) )
     => ~ ! [X4: state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_861_imageE,axiom,
    ! [B2: produc3882902684156697774_state,F: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ B2 @ ( image_508898238547643525_state @ F @ A6 ) )
     => ~ ! [X4: produc3882902684156697774_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member6715010751053357271_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_862_imageE,axiom,
    ! [B2: produc7272280185086996969_state,F: produc3882902684156697774_state > produc7272280185086996969_state,A6: set_Pr2391701600042252046_state] :
      ( ( member7461423308196221312_state @ B2 @ ( image_4364510454419742290_state @ F @ A6 ) )
     => ~ ! [X4: produc3882902684156697774_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member6715010751053357271_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_863_imageE,axiom,
    ! [B2: produc3882902684156697774_state,F: produc7272280185086996969_state > produc3882902684156697774_state,A6: set_Pr4231240917283394591_state] :
      ( ( member6715010751053357271_state @ B2 @ ( image_7466395622266389182_state @ F @ A6 ) )
     => ~ ! [X4: produc7272280185086996969_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member7461423308196221312_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_864_imageE,axiom,
    ! [B2: produc7272280185086996969_state,F: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ B2 @ ( image_3064086290059306969_state @ F @ A6 ) )
     => ~ ! [X4: produc7272280185086996969_state] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member7461423308196221312_state @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_865_imageE,axiom,
    ! [B2: state,F: produc9003781588162623004on_val > state,A6: set_Pr7649655576376376530on_val] :
      ( ( member_state @ B2 @ ( image_1205529093420515805_state @ F @ A6 ) )
     => ~ ! [X4: produc9003781588162623004on_val] :
            ( ( B2
              = ( F @ X4 ) )
           => ~ ( member2879030624002546611on_val @ X4 @ A6 ) ) ) ).

% imageE
thf(fact_866_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > state,B4: set_state] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_867_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_868_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
         => ( member7461423308196221312_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_869_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_870_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_871_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
         => ( member7461423308196221312_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_872_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X4: state] :
          ( ( P2 @ X4 )
         => ( member2879030624002546611on_val @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_873_image__Collect__subsetI,axiom,
    ! [P2: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > state,B4: set_state] :
      ( ! [X4: produc9003781588162623004on_val] :
          ( ( P2 @ X4 )
         => ( member_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_1205529093420515805_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_874_image__Collect__subsetI,axiom,
    ! [P2: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X4: produc9003781588162623004on_val] :
          ( ( P2 @ X4 )
         => ( member6715010751053357271_state @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_4494208899119068747_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_875_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X4: produc7272280185086996969_state] :
          ( ( P2 @ X4 )
         => ( member2879030624002546611on_val @ ( F @ X4 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_3393013468800240652on_val @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_876_Pow__def,axiom,
    ( pow_state
    = ( ^ [A: set_state] :
          ( collect_set_state
          @ ^ [B5: set_state] : ( ord_le2494988322063910608_state @ B5 @ A ) ) ) ) ).

% Pow_def
thf(fact_877_pred__subset__eq,axiom,
    ! [R5: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le7281427340513060550tate_o
        @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ R5 )
        @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ S2 ) )
      = ( ord_le4032880777312351359_state @ R5 @ S2 ) ) ).

% pred_subset_eq
thf(fact_878_pred__subset__eq,axiom,
    ! [R5: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le6140313152057869779_val_o
        @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ R5 )
        @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R5 @ S2 ) ) ).

% pred_subset_eq
thf(fact_879_pred__subset__eq,axiom,
    ! [R5: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le8077393285996101039tate_o
        @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ R5 )
        @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ S2 ) )
      = ( ord_le6483787752022044334_state @ R5 @ S2 ) ) ).

% pred_subset_eq
thf(fact_880_pred__subset__eq,axiom,
    ! [R5: set_state,S2: set_state] :
      ( ( ord_less_eq_state_o
        @ ^ [X5: state] : ( member_state @ X5 @ R5 )
        @ ^ [X5: state] : ( member_state @ X5 @ S2 ) )
      = ( ord_le2494988322063910608_state @ R5 @ S2 ) ) ).

% pred_subset_eq
thf(fact_881_aassertion_Odistinct_I1_J,axiom,
    ! [X11: aassertion_state,X12: aassertion_state,X21: state > $o,X222: aassertion_state] :
      ( ( aStar_state @ X11 @ X12 )
     != ( aImp_state @ X21 @ X222 ) ) ).

% aassertion.distinct(1)
thf(fact_882_sep__algebra_Odefined_Ocong,axiom,
    sep_defined_state = sep_defined_state ).

% sep_algebra.defined.cong
thf(fact_883_less__eq__set__def,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( ord_le7281427340513060550tate_o
          @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ A )
          @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_884_less__eq__set__def,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
          ( ord_le6140313152057869779_val_o
          @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ A )
          @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_885_less__eq__set__def,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
          ( ord_le8077393285996101039tate_o
          @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ A )
          @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_886_less__eq__set__def,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A: set_state,B5: set_state] :
          ( ord_less_eq_state_o
          @ ^ [X5: state] : ( member_state @ X5 @ A )
          @ ^ [X5: state] : ( member_state @ X5 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_887_Collect__subset,axiom,
    ! [A6: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X5 @ A6 )
            & ( P2 @ X5 ) ) )
      @ A6 ) ).

% Collect_subset
thf(fact_888_Collect__subset,axiom,
    ! [A6: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ A6 )
            & ( P2 @ X5 ) ) )
      @ A6 ) ).

% Collect_subset
thf(fact_889_Collect__subset,axiom,
    ! [A6: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X5 @ A6 )
            & ( P2 @ X5 ) ) )
      @ A6 ) ).

% Collect_subset
thf(fact_890_Collect__subset,axiom,
    ! [A6: set_state,P2: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X5: state] :
            ( ( member_state @ X5 @ A6 )
            & ( P2 @ X5 ) ) )
      @ A6 ) ).

% Collect_subset
thf(fact_891_prop__restrict,axiom,
    ! [X2: produc3882902684156697774_state,Z3: set_Pr2391701600042252046_state,X7: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ X2 @ Z3 )
     => ( ( ord_le6483787752022044334_state @ Z3
          @ ( collec394671971739345689_state
            @ ^ [X5: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X5 @ X7 )
                & ( P2 @ X5 ) ) ) )
       => ( P2 @ X2 ) ) ) ).

% prop_restrict
thf(fact_892_prop__restrict,axiom,
    ! [X2: produc7272280185086996969_state,Z3: set_Pr4231240917283394591_state,X7: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( member7461423308196221312_state @ X2 @ Z3 )
     => ( ( ord_le4032880777312351359_state @ Z3
          @ ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X5 @ X7 )
                & ( P2 @ X5 ) ) ) )
       => ( P2 @ X2 ) ) ) ).

% prop_restrict
thf(fact_893_prop__restrict,axiom,
    ! [X2: produc9003781588162623004on_val,Z3: set_Pr7649655576376376530on_val,X7: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ X2 @ Z3 )
     => ( ( ord_le6900622908513426738on_val @ Z3
          @ ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X5 @ X7 )
                & ( P2 @ X5 ) ) ) )
       => ( P2 @ X2 ) ) ) ).

% prop_restrict
thf(fact_894_prop__restrict,axiom,
    ! [X2: state,Z3: set_state,X7: set_state,P2: state > $o] :
      ( ( member_state @ X2 @ Z3 )
     => ( ( ord_le2494988322063910608_state @ Z3
          @ ( collect_state
            @ ^ [X5: state] :
                ( ( member_state @ X5 @ X7 )
                & ( P2 @ X5 ) ) ) )
       => ( P2 @ X2 ) ) ) ).

% prop_restrict
thf(fact_895_Collect__restrict,axiom,
    ! [X7: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X5: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X5 @ X7 )
            & ( P2 @ X5 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_896_Collect__restrict,axiom,
    ! [X7: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ X7 )
            & ( P2 @ X5 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_897_Collect__restrict,axiom,
    ! [X7: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X5 @ X7 )
            & ( P2 @ X5 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_898_Collect__restrict,axiom,
    ! [X7: set_state,P2: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X5: state] :
            ( ( member_state @ X5 @ X7 )
            & ( P2 @ X5 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_899_UNIV__def,axiom,
    ( top_to174962084833059535_state
    = ( collec906845016635587262_state
      @ ^ [X5: produc7272280185086996969_state] : $true ) ) ).

% UNIV_def
thf(fact_900_UNIV__def,axiom,
    ( top_to1561438921946393474on_val
    = ( collec7475294502966882545on_val
      @ ^ [X5: produc9003781588162623004on_val] : $true ) ) ).

% UNIV_def
thf(fact_901_UNIV__def,axiom,
    ( top_top_set_state
    = ( collect_state
      @ ^ [X5: state] : $true ) ) ).

% UNIV_def
thf(fact_902_option_Odisc__eq__case_I1_J,axiom,
    ! [Option: option_state] :
      ( ( Option = none_state )
      = ( case_option_o_state @ $true
        @ ^ [Uu3: state] : $false
        @ Option ) ) ).

% option.disc_eq_case(1)
thf(fact_903_option_Odisc__eq__case_I1_J,axiom,
    ! [Option: option_val] :
      ( ( Option = none_val )
      = ( case_option_o_val @ $true
        @ ^ [Uu3: val] : $false
        @ Option ) ) ).

% option.disc_eq_case(1)
thf(fact_904_option_Odisc__eq__case_I2_J,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
      = ( case_option_o_state @ $false
        @ ^ [Uu3: state] : $true
        @ Option ) ) ).

% option.disc_eq_case(2)
thf(fact_905_option_Odisc__eq__case_I2_J,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
      = ( case_option_o_val @ $false
        @ ^ [Uu3: val] : $true
        @ Option ) ) ).

% option.disc_eq_case(2)
thf(fact_906_image__constant,axiom,
    ! [X2: state,A6: set_state,C: state] :
      ( ( member_state @ X2 @ A6 )
     => ( ( image_state_state
          @ ^ [X5: state] : C
          @ A6 )
        = ( insert_state @ C @ bot_bot_set_state ) ) ) ).

% image_constant
thf(fact_907_image__constant,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,C: state] :
      ( ( member7461423308196221312_state @ X2 @ A6 )
     => ( ( image_2710133271811360426_state
          @ ^ [X5: produc7272280185086996969_state] : C
          @ A6 )
        = ( insert_state @ C @ bot_bot_set_state ) ) ) ).

% image_constant
thf(fact_908_image__constant,axiom,
    ! [X2: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,C: state] :
      ( ( member2879030624002546611on_val @ X2 @ A6 )
     => ( ( image_1205529093420515805_state
          @ ^ [X5: produc9003781588162623004on_val] : C
          @ A6 )
        = ( insert_state @ C @ bot_bot_set_state ) ) ) ).

% image_constant
thf(fact_909_image__constant,axiom,
    ! [X2: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,C: state] :
      ( ( member6715010751053357271_state @ X2 @ A6 )
     => ( ( image_6759111139246981411_state
          @ ^ [X5: produc3882902684156697774_state] : C
          @ A6 )
        = ( insert_state @ C @ bot_bot_set_state ) ) ) ).

% image_constant
thf(fact_910_image__constant__conv,axiom,
    ! [A6: set_state,C: state] :
      ( ( ( A6 = bot_bot_set_state )
       => ( ( image_state_state
            @ ^ [X5: state] : C
            @ A6 )
          = bot_bot_set_state ) )
      & ( ( A6 != bot_bot_set_state )
       => ( ( image_state_state
            @ ^ [X5: state] : C
            @ A6 )
          = ( insert_state @ C @ bot_bot_set_state ) ) ) ) ).

% image_constant_conv
thf(fact_911_empty__def,axiom,
    ( bot_bo6430881413863817907_state
    = ( collec906845016635587262_state
      @ ^ [X5: produc7272280185086996969_state] : $false ) ) ).

% empty_def
thf(fact_912_empty__def,axiom,
    ( bot_bo6722054719108133734on_val
    = ( collec7475294502966882545on_val
      @ ^ [X5: produc9003781588162623004on_val] : $false ) ) ).

% empty_def
thf(fact_913_empty__def,axiom,
    ( bot_bot_set_state
    = ( collect_state
      @ ^ [X5: state] : $false ) ) ).

% empty_def
thf(fact_914_Collect__conv__if,axiom,
    ! [P2: produc7272280185086996969_state > $o,A3: produc7272280185086996969_state] :
      ( ( ( P2 @ A3 )
       => ( ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = bot_bo6430881413863817907_state ) ) ) ).

% Collect_conv_if
thf(fact_915_Collect__conv__if,axiom,
    ! [P2: produc9003781588162623004on_val > $o,A3: produc9003781588162623004on_val] :
      ( ( ( P2 @ A3 )
       => ( ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = bot_bo6722054719108133734on_val ) ) ) ).

% Collect_conv_if
thf(fact_916_Collect__conv__if,axiom,
    ! [P2: state > $o,A3: state] :
      ( ( ( P2 @ A3 )
       => ( ( collect_state
            @ ^ [X5: state] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = ( insert_state @ A3 @ bot_bot_set_state ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collect_state
            @ ^ [X5: state] :
                ( ( X5 = A3 )
                & ( P2 @ X5 ) ) )
          = bot_bot_set_state ) ) ) ).

% Collect_conv_if
thf(fact_917_Collect__conv__if2,axiom,
    ! [P2: produc7272280185086996969_state > $o,A3: produc7272280185086996969_state] :
      ( ( ( P2 @ A3 )
       => ( ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = ( insert175804457004744729_state @ A3 @ bot_bo6430881413863817907_state ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = bot_bo6430881413863817907_state ) ) ) ).

% Collect_conv_if2
thf(fact_918_Collect__conv__if2,axiom,
    ! [P2: produc9003781588162623004on_val > $o,A3: produc9003781588162623004on_val] :
      ( ( ( P2 @ A3 )
       => ( ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = ( insert3030518898131756108on_val @ A3 @ bot_bo6722054719108133734on_val ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = bot_bo6722054719108133734on_val ) ) ) ).

% Collect_conv_if2
thf(fact_919_Collect__conv__if2,axiom,
    ! [P2: state > $o,A3: state] :
      ( ( ( P2 @ A3 )
       => ( ( collect_state
            @ ^ [X5: state] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = ( insert_state @ A3 @ bot_bot_set_state ) ) )
      & ( ~ ( P2 @ A3 )
       => ( ( collect_state
            @ ^ [X5: state] :
                ( ( A3 = X5 )
                & ( P2 @ X5 ) ) )
          = bot_bot_set_state ) ) ) ).

% Collect_conv_if2
thf(fact_920_case__optionE,axiom,
    ! [P2: $o,Q: state > $o,X2: option_state] :
      ( ( case_option_o_state @ P2 @ Q @ X2 )
     => ( ( ( X2 = none_state )
         => ~ P2 )
       => ~ ! [Y3: state] :
              ( ( X2
                = ( some_state @ Y3 ) )
             => ~ ( Q @ Y3 ) ) ) ) ).

% case_optionE
thf(fact_921_case__optionE,axiom,
    ! [P2: $o,Q: val > $o,X2: option_val] :
      ( ( case_option_o_val @ P2 @ Q @ X2 )
     => ( ( ( X2 = none_val )
         => ~ P2 )
       => ~ ! [Y3: val] :
              ( ( X2
                = ( some_val @ Y3 ) )
             => ~ ( Q @ Y3 ) ) ) ) ).

% case_optionE
thf(fact_922_Option_Othese__def,axiom,
    ( these_state
    = ( ^ [A: set_option_state] :
          ( image_3532137647693456075_state @ the_state
          @ ( collect_option_state
            @ ^ [X5: option_state] :
                ( ( member_option_state @ X5 @ A )
                & ( X5 != none_state ) ) ) ) ) ) ).

% Option.these_def
thf(fact_923_Option_Othese__def,axiom,
    ( these_val
    = ( ^ [A: set_option_val] :
          ( image_option_val_val @ the_val
          @ ( collect_option_val
            @ ^ [X5: option_val] :
                ( ( member_option_val @ X5 @ A )
                & ( X5 != none_val ) ) ) ) ) ) ).

% Option.these_def
thf(fact_924_map__add__def,axiom,
    ( map_ad2908576761495157028ar_val
    = ( ^ [M1: produc1457211279475724562t_char > option_val,M22: produc1457211279475724562t_char > option_val,X5: produc1457211279475724562t_char] : ( case_o7794706883426356101al_val @ ( M1 @ X5 ) @ some_val @ ( M22 @ X5 ) ) ) ) ).

% map_add_def
thf(fact_925_Some__image__these__eq,axiom,
    ! [A6: set_option_state] :
      ( ( image_6076465424260689483_state @ some_state @ ( these_state @ A6 ) )
      = ( collect_option_state
        @ ^ [X5: option_state] :
            ( ( member_option_state @ X5 @ A6 )
            & ( X5 != none_state ) ) ) ) ).

% Some_image_these_eq
thf(fact_926_Some__image__these__eq,axiom,
    ! [A6: set_option_val] :
      ( ( image_val_option_val @ some_val @ ( these_val @ A6 ) )
      = ( collect_option_val
        @ ^ [X5: option_val] :
            ( ( member_option_val @ X5 @ A6 )
            & ( X5 != none_val ) ) ) ) ).

% Some_image_these_eq
thf(fact_927_PartialSA_Osat_Osimps_I2_J,axiom,
    ! [B2: state > $o,Aa: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aImp_state @ B2 @ Aa ) @ Phi )
      = ( ( B2 @ Phi )
       => ( package_sat_state @ plus @ Aa @ Phi ) ) ) ).

% PartialSA.sat.simps(2)
thf(fact_928_package__logic_Osat_Osimps_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B2: state > $o,A6: aassertion_state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aImp_state @ B2 @ A6 ) @ Phi )
        = ( ( B2 @ Phi )
         => ( package_sat_state @ Plus @ A6 @ Phi ) ) ) ) ).

% package_logic.sat.simps(2)
thf(fact_929_package__logic_Owf__assertion_Osimps_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ ( aStar_state @ A6 @ B4 ) )
        = ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
          & ( packag7298478212905792770_state @ Plus @ Core @ B4 ) ) ) ) ).

% package_logic.wf_assertion.simps(1)
thf(fact_930_package__logic_OAStar,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state,B4: aassertion_state,Phi7: state,F7: state,S5: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
       => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F6 @ S3 @ Pc @ B4 @ Phi7 @ F7 @ S5 )
         => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ ( aStar_state @ A6 @ B4 ) @ Phi7 @ F7 @ S5 ) ) ) ) ).

% package_logic.AStar
thf(fact_931_sep__algebra_Odefined__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_defined_val @ Plus @ A3 @ B2 )
        = ( ( Plus @ A3 @ B2 )
         != none_val ) ) ) ).

% sep_algebra.defined_def
thf(fact_932_sep__algebra_Odefined__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_defined_state @ Plus @ A3 @ B2 )
        = ( ( Plus @ A3 @ B2 )
         != none_state ) ) ) ).

% sep_algebra.defined_def
thf(fact_933_package__logic_Odefined__sum__move,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,B2: val,X2: val,Y: val,A4: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_defined_val @ Plus @ A3 @ B2 )
       => ( ( ( some_val @ B2 )
            = ( Plus @ X2 @ Y ) )
         => ( ( ( some_val @ A4 )
              = ( Plus @ A3 @ X2 ) )
           => ( sep_defined_val @ Plus @ A4 @ Y ) ) ) ) ) ).

% package_logic.defined_sum_move
thf(fact_934_package__logic_Odefined__sum__move,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state,X2: state,Y: state,A4: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_defined_state @ Plus @ A3 @ B2 )
       => ( ( ( some_state @ B2 )
            = ( Plus @ X2 @ Y ) )
         => ( ( ( some_state @ A4 )
              = ( Plus @ A3 @ X2 ) )
           => ( sep_defined_state @ Plus @ A4 @ Y ) ) ) ) ) ).

% package_logic.defined_sum_move
thf(fact_935_defined__def,axiom,
    ( defined
    = ( sep_defined_state @ plus ) ) ).

% defined_def
thf(fact_936_sep__algebra_Ompp__compatible,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( ( sep_defined_state @ Plus @ A3 @ B2 )
         => ( sep_defined_state @ Plus @ ( F @ A3 ) @ ( F @ B2 ) ) ) ) ) ).

% sep_algebra.mpp_compatible
thf(fact_937_PartialSA_Osat_Osimps_I1_J,axiom,
    ! [Aa: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ Aa @ B4 ) @ Phi )
      = ( ? [A2: state,B: state] :
            ( ( ( some_state @ Phi )
              = ( plus @ A2 @ B ) )
            & ( package_sat_state @ plus @ Aa @ A2 )
            & ( package_sat_state @ plus @ B4 @ B ) ) ) ) ).

% PartialSA.sat.simps(1)
thf(fact_938_PartialSA_Owf__assertion_Osimps_I1_J,axiom,
    ! [Aa: aassertion_state,B4: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aStar_state @ Aa @ B4 ) )
      = ( ( packag7298478212905792770_state @ plus @ core @ Aa )
        & ( packag7298478212905792770_state @ plus @ core @ B4 ) ) ) ).

% PartialSA.wf_assertion.simps(1)
thf(fact_939_package__logic_Osat_Osimps_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A6: aassertion_val,B4: aassertion_val,Phi: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ ( aStar_val @ A6 @ B4 ) @ Phi )
        = ( ? [A2: val,B: val] :
              ( ( ( some_val @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( package_sat_val @ Plus @ A6 @ A2 )
              & ( package_sat_val @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.sat.simps(1)
thf(fact_940_package__logic_Osat_Osimps_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aStar_state @ A6 @ B4 ) @ Phi )
        = ( ? [A2: state,B: state] :
              ( ( ( some_state @ Phi )
                = ( Plus @ A2 @ B ) )
              & ( package_sat_state @ Plus @ A6 @ A2 )
              & ( package_sat_state @ Plus @ B4 @ B ) ) ) ) ) ).

% package_logic.sat.simps(1)
thf(fact_941_package__logic_Owf__assertion_Osimps_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B2: state > $o,A6: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ ( aImp_state @ B2 @ A6 ) )
        = ( ( packag6595153354952283300_state @ Plus @ Core @ B2 )
          & ( packag7298478212905792770_state @ Plus @ Core @ A6 ) ) ) ) ).

% package_logic.wf_assertion.simps(2)
thf(fact_942_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,S2: set_Pr4723104092121316667al_val,F: val,A6: aassertion_val,Phi: val,Phi2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: val,U: val,T3: val > val] :
            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A7 @ ( produc303288909735261391al_val @ U @ T3 ) ) @ S2 )
           => ! [X4: val] :
                ( ( ( some_val @ X4 )
                  = ( Plus @ A7 @ ( T3 @ F ) ) )
               => ( package_sat_val @ Plus @ A6 @ X4 ) ) )
       => ( ( ( some_val @ Phi )
            = ( Plus @ Phi2 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag7517340229427718612et_val @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag5732365195153136185on_val @ Plus @ Core @ A6 )
               => ? [X_1: set_Pr4723104092121316667al_val] :
                    ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ Unit @ S2
                    @ ^ [Uu3: val] : $true
                    @ A6
                    @ Phi2
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_943_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state,A6: aassertion_state,Phi: state,Phi2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ! [X4: state] :
                ( ( ( some_state @ X4 )
                  = ( Plus @ A7 @ ( T3 @ F ) ) )
               => ( package_sat_state @ Plus @ A6 @ X4 ) ) )
       => ( ( ( some_state @ Phi )
            = ( Plus @ Phi2 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
               => ? [X_1: set_Pr4231240917283394591_state] :
                    ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ Unit @ S2
                    @ ^ [Uu3: state] : $true
                    @ A6
                    @ Phi2
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_944_package__logic_OAImp,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,B2: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ ( packag1330488657391168505_state @ Pc @ B2 ) @ A6 @ Phi2 @ F6 @ S3 )
       => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ ( aImp_state @ B2 @ A6 ) @ Phi2 @ F6 @ S3 ) ) ) ).

% package_logic.AImp
thf(fact_945_PartialSA_Owf__assertion_Osimps_I2_J,axiom,
    ! [B2: state > $o,Aa: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aImp_state @ B2 @ Aa ) )
      = ( ( packag6595153354952283300_state @ plus @ core @ B2 )
        & ( packag7298478212905792770_state @ plus @ core @ Aa ) ) ) ).

% PartialSA.wf_assertion.simps(2)
thf(fact_946_PartialSA_Opackage__rhs_Ointros_I1_J,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state,Ba2: aassertion_state,Phi7: state,F7: state,S5: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F6 @ S3 @ Pc @ Ba2 @ Phi7 @ F7 @ S5 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aStar_state @ A6 @ Ba2 ) @ Phi7 @ F7 @ S5 ) ) ) ).

% PartialSA.package_rhs.intros(1)
thf(fact_947_PartialSA_OAStar,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state,B4: aassertion_state,Phi7: state,F7: state,S5: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F6 @ S3 @ Pc @ B4 @ Phi7 @ F7 @ S5 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aStar_state @ A6 @ B4 ) @ Phi7 @ F7 @ S5 ) ) ) ).

% PartialSA.AStar
thf(fact_948_package__logic_Owf__assertion__and__the,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state,A6: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_defined_state @ Plus @ ( Core @ A3 ) @ B2 )
       => ( ( package_sat_state @ Plus @ A6 @ B2 )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
           => ( package_sat_state @ Plus @ A6 @ ( the_state @ ( Plus @ ( Core @ A3 ) @ B2 ) ) ) ) ) ) ) ).

% package_logic.wf_assertion_and_the
thf(fact_949_PartialSA_Ocompleteness,axiom,
    ! [B4: aassertion_state,W: state,R5: state > state > state,A6: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag6192661653625646554_state @ plus @ W @ R5 @ A6 @ B4 ) )
       => ( ( ( some_state @ Sigma )
            = ( plus @ Sigma2 @ W ) )
         => ( ! [A7: state] :
                ( ( package_sat_state @ plus @ A6 @ A7 )
               => ( packag4817583915586052229_state @ plus @ unit @ ( R5 @ A7 ) ) )
           => ? [X_1: set_Pr4231240917283394591_state] :
                ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ ( R5 @ A2 ) ) ) )
                      & ( package_sat_state @ plus @ A6 @ A2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% PartialSA.completeness
thf(fact_950_package__logic_Ocompleteness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,R5: val > val > val,A6: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag4897621287243763553al_val @ Plus @ W @ R5 @ A6 @ B4 ) )
         => ( ( ( some_val @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A7: val] :
                  ( ( package_sat_val @ Plus @ A6 @ A7 )
                 => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R5 @ A7 ) ) )
             => ? [X_1: set_Pr4723104092121316667al_val] :
                  ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                  @ ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A2: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ ( R5 @ A2 ) ) ) )
                        & ( package_sat_val @ Plus @ A6 @ A2 ) ) )
                  @ ^ [Uu3: val] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_951_package__logic_Ocompleteness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,R5: state > state > state,A6: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag6192661653625646554_state @ Plus @ W @ R5 @ A6 @ B4 ) )
         => ( ( ( some_state @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A7: state] :
                  ( ( package_sat_state @ Plus @ A6 @ A7 )
                 => ( packag4817583915586052229_state @ Plus @ Unit @ ( R5 @ A7 ) ) )
             => ? [X_1: set_Pr4231240917283394591_state] :
                  ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                  @ ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A2: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ ( R5 @ A2 ) ) ) )
                        & ( package_sat_state @ Plus @ A6 @ A2 ) ) )
                  @ ^ [Uu3: state] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_952_PartialSA_Osoundness,axiom,
    ! [B4: aassertion_state,A6: aassertion_state,S2: set_state,R5: state > state > state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A7: state] :
            ( ( package_sat_state @ plus @ A6 @ A7 )
           => ( member_state @ A7 @ S2 ) )
       => ( ! [A7: state] :
              ( ( member_state @ A7 @ S2 )
             => ( packag4817583915586052229_state @ plus @ unit @ ( R5 @ A7 ) ) )
         => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ ( R5 @ A2 ) ) ) )
                    & ( member_state @ A2 @ S2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ B4 ) )
                | ( packag4152378406607043437_state @ plus @ S3 ) )
             => ( ( stable @ W )
                & ( ( some_state @ Sigma )
                  = ( plus @ Sigma2 @ W ) )
                & ( packag6192661653625646554_state @ plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ).

% PartialSA.soundness
thf(fact_953_PartialSA_Ominus__def,axiom,
    ( minus
    = ( ^ [B: state,A2: state] :
          ( fun_TH8221542053827138557_state @ B
          @ ^ [X5: state] :
              ( ( ( some_state @ B )
                = ( plus @ A2 @ X5 ) )
              & ( greater @ X5 @ ( core @ B ) ) ) ) ) ) ).

% PartialSA.minus_def
thf(fact_954_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,P2: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_3064086290059306969_state @ F @ ( collec906845016635587262_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_955_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc7272280185086996969_state,P2: produc9003781588162623004on_val > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_3204238854701872908_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_956_setcompr__eq__image,axiom,
    ! [F: state > produc7272280185086996969_state,P2: state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_632992669292831658_state @ F @ ( collect_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_957_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc9003781588162623004on_val,P2: produc7272280185086996969_state > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X5: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_3393013468800240652on_val @ F @ ( collec906845016635587262_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_958_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X5: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_4170889944715819327on_val @ F @ ( collec7475294502966882545on_val @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_959_setcompr__eq__image,axiom,
    ! [F: state > produc9003781588162623004on_val,P2: state > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_4772210114854293981on_val @ F @ ( collect_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_960_setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > state,P2: produc7272280185086996969_state > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_2710133271811360426_state @ F @ ( collec906845016635587262_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_961_setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > state,P2: produc9003781588162623004on_val > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_1205529093420515805_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_962_setcompr__eq__image,axiom,
    ! [F: state > state,P2: state > $o] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( P2 @ X5 ) ) )
      = ( image_state_state @ F @ ( collect_state @ P2 ) ) ) ).

% setcompr_eq_image
thf(fact_963_Setcompr__eq__image,axiom,
    ! [F: state > state,A6: set_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member_state @ X5 @ A6 ) ) )
      = ( image_state_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_964_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > state,A6: set_Pr2391701600042252046_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member6715010751053357271_state @ X5 @ A6 ) ) )
      = ( image_6759111139246981411_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_965_Setcompr__eq__image,axiom,
    ! [F: state > produc7272280185086996969_state,A6: set_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member_state @ X5 @ A6 ) ) )
      = ( image_632992669292831658_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_966_Setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > state,A6: set_Pr4231240917283394591_state] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member7461423308196221312_state @ X5 @ A6 ) ) )
      = ( image_2710133271811360426_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_967_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > produc7272280185086996969_state,A6: set_Pr2391701600042252046_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member6715010751053357271_state @ X5 @ A6 ) ) )
      = ( image_4364510454419742290_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_968_Setcompr__eq__image,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: produc7272280185086996969_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member7461423308196221312_state @ X5 @ A6 ) ) )
      = ( image_3064086290059306969_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_969_Setcompr__eq__image,axiom,
    ! [F: state > produc9003781588162623004on_val,A6: set_state] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X5: state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member_state @ X5 @ A6 ) ) )
      = ( image_4772210114854293981on_val @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_970_Setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > state,A6: set_Pr7649655576376376530on_val] :
      ( ( collect_state
        @ ^ [Uu3: state] :
          ? [X5: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member2879030624002546611on_val @ X5 @ A6 ) ) )
      = ( image_1205529093420515805_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_971_Setcompr__eq__image,axiom,
    ! [F: produc3882902684156697774_state > produc9003781588162623004on_val,A6: set_Pr2391701600042252046_state] :
      ( ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [X5: produc3882902684156697774_state] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member6715010751053357271_state @ X5 @ A6 ) ) )
      = ( image_4690842878458256517on_val @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_972_Setcompr__eq__image,axiom,
    ! [F: produc9003781588162623004on_val > produc7272280185086996969_state,A6: set_Pr7649655576376376530on_val] :
      ( ( collec906845016635587262_state
        @ ^ [Uu3: produc7272280185086996969_state] :
          ? [X5: produc9003781588162623004on_val] :
            ( ( Uu3
              = ( F @ X5 ) )
            & ( member2879030624002546611on_val @ X5 @ A6 ) ) )
      = ( image_3204238854701872908_state @ F @ A6 ) ) ).

% Setcompr_eq_image
thf(fact_973_package__logic_Opure__remains_Ocong,axiom,
    packag4152378406607043437_state = packag4152378406607043437_state ).

% package_logic.pure_remains.cong
thf(fact_974_full__SetCompr__eq,axiom,
    ! [F: state > produc7272280185086996969_state] :
      ( ( collec906845016635587262_state
        @ ^ [U6: produc7272280185086996969_state] :
          ? [X5: state] :
            ( U6
            = ( F @ X5 ) ) )
      = ( image_632992669292831658_state @ F @ top_top_set_state ) ) ).

% full_SetCompr_eq
thf(fact_975_full__SetCompr__eq,axiom,
    ! [F: state > produc9003781588162623004on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [U6: produc9003781588162623004on_val] :
          ? [X5: state] :
            ( U6
            = ( F @ X5 ) ) )
      = ( image_4772210114854293981on_val @ F @ top_top_set_state ) ) ).

% full_SetCompr_eq
thf(fact_976_full__SetCompr__eq,axiom,
    ! [F: state > state] :
      ( ( collect_state
        @ ^ [U6: state] :
          ? [X5: state] :
            ( U6
            = ( F @ X5 ) ) )
      = ( image_state_state @ F @ top_top_set_state ) ) ).

% full_SetCompr_eq
thf(fact_977_Rep__state__induct,axiom,
    ! [Y: produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ Y
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi4: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi4 )
              & ( valid_state @ Phi4 ) ) ) )
     => ( ! [X4: state] : ( P2 @ ( rep_state @ X4 ) )
       => ( P2 @ Y ) ) ) ).

% Rep_state_induct
thf(fact_978_Rep__state__cases,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ Y @ ( collec7475294502966882545on_val @ valid_state ) )
     => ~ ! [X4: state] :
            ( Y
           != ( rep_state @ X4 ) ) ) ).

% Rep_state_cases
thf(fact_979_Rep__state,axiom,
    ! [X2: state] :
      ( member2879030624002546611on_val @ ( rep_state @ X2 )
      @ ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [Phi4: produc9003781588162623004on_val] :
            ( ( Uu3 = Phi4 )
            & ( valid_state @ Phi4 ) ) ) ) ).

% Rep_state
thf(fact_980_Abs__state__inject,axiom,
    ! [X2: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ X2
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi4: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi4 )
              & ( valid_state @ Phi4 ) ) ) )
     => ( ( member2879030624002546611on_val @ Y
          @ ( collec7475294502966882545on_val
            @ ^ [Uu3: produc9003781588162623004on_val] :
              ? [Phi4: produc9003781588162623004on_val] :
                ( ( Uu3 = Phi4 )
                & ( valid_state @ Phi4 ) ) ) )
       => ( ( ( abs_state @ X2 )
            = ( abs_state @ Y ) )
          = ( X2 = Y ) ) ) ) ).

% Abs_state_inject
thf(fact_981_Abs__state__induct,axiom,
    ! [P2: state > $o,X2: state] :
      ( ! [Y3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ Y3
            @ ( collec7475294502966882545on_val
              @ ^ [Uu3: produc9003781588162623004on_val] :
                ? [Phi4: produc9003781588162623004on_val] :
                  ( ( Uu3 = Phi4 )
                  & ( valid_state @ Phi4 ) ) ) )
         => ( P2 @ ( abs_state @ Y3 ) ) )
     => ( P2 @ X2 ) ) ).

% Abs_state_induct
thf(fact_982_Abs__state__cases,axiom,
    ! [X2: state] :
      ~ ! [Y3: produc9003781588162623004on_val] :
          ( ( X2
            = ( abs_state @ Y3 ) )
         => ~ ( member2879030624002546611on_val @ Y3 @ ( collec7475294502966882545on_val @ valid_state ) ) ) ).

% Abs_state_cases
thf(fact_983_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( sep_ad8203089552910907580_state @ Plus @ A6 @ B4 )
        = ( collec394671971739345689_state
          @ ^ [Uu3: produc3882902684156697774_state] :
            ? [Phi4: produc3882902684156697774_state,A2: produc3882902684156697774_state,B: produc3882902684156697774_state] :
              ( ( Uu3 = Phi4 )
              & ( member6715010751053357271_state @ A2 @ A6 )
              & ( member6715010751053357271_state @ B @ B4 )
              & ( ( some_P5383513176685068947_state @ Phi4 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_984_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( sep_ad3908482799505143387_state @ Plus @ A6 @ B4 )
        = ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [Phi4: produc7272280185086996969_state,A2: produc7272280185086996969_state,B: produc7272280185086996969_state] :
              ( ( Uu3 = Phi4 )
              & ( member7461423308196221312_state @ A2 @ A6 )
              & ( member7461423308196221312_state @ B @ B4 )
              & ( ( some_P6297086604321900740_state @ Phi4 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_985_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( sep_ad8320153009520438926on_val @ Plus @ A6 @ B4 )
        = ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi4: produc9003781588162623004on_val,A2: produc9003781588162623004on_val,B: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi4 )
              & ( member2879030624002546611on_val @ A2 @ A6 )
              & ( member2879030624002546611on_val @ B @ B4 )
              & ( ( some_P2581650809551911671on_val @ Phi4 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_986_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A6: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_add_set_val @ Plus @ A6 @ B4 )
        = ( collect_val
          @ ^ [Uu3: val] :
            ? [Phi4: val,A2: val,B: val] :
              ( ( Uu3 = Phi4 )
              & ( member_val @ A2 @ A6 )
              & ( member_val @ B @ B4 )
              & ( ( some_val @ Phi4 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_987_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_add_set_state @ Plus @ A6 @ B4 )
        = ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state,A2: state,B: state] :
              ( ( Uu3 = Phi4 )
              & ( member_state @ A2 @ A6 )
              & ( member_state @ B @ B4 )
              & ( ( some_state @ Phi4 )
                = ( Plus @ A2 @ B ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_988_PartialSA_Oadd__set__def,axiom,
    ( add_set
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state,A2: state,B: state] :
              ( ( Uu3 = Phi4 )
              & ( member_state @ A2 @ A )
              & ( member_state @ B @ B5 )
              & ( ( some_state @ Phi4 )
                = ( plus @ A2 @ B ) ) ) ) ) ) ).

% PartialSA.add_set_def
thf(fact_989_Abs__state__inverse,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ Y
        @ ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi4: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi4 )
              & ( valid_state @ Phi4 ) ) ) )
     => ( ( rep_state @ ( abs_state @ Y ) )
        = Y ) ) ).

% Abs_state_inverse
thf(fact_990_package__logic_OAddFromOutside,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,Phi2: val,M2: val,F6: val,S3: set_Pr4723104092121316667al_val,Pc: val > $o,A6: aassertion_val,Phi7: val,F7: val,S5: set_Pr4723104092121316667al_val,F: val,S2: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ Phi )
          = ( Plus @ Phi2 @ M2 ) )
       => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ F6 @ S3 @ Pc @ A6 @ Phi7 @ F7 @ S5 )
         => ( ( Stable @ M2 )
           => ( ( ( some_val @ F6 )
                = ( Plus @ F @ M2 ) )
             => ( ( S3
                  = ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A2: val,U6: val,T4: val > val,R2: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ R2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ S2 )
                        & ( ( some_val @ R2 )
                          = ( Plus @ A2 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F6 ) @ ( T4 @ F ) ) ) )
                        & ( sep_defined_val @ Plus @ R2 @ U6 ) ) ) )
               => ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi7 @ F7 @ S5 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_991_package__logic_OAddFromOutside,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,Phi2: state,M2: state,F6: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi7: state,F7: state,S5: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ Phi )
          = ( Plus @ Phi2 @ M2 ) )
       => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F6 @ S3 @ Pc @ A6 @ Phi7 @ F7 @ S5 )
         => ( ( Stable @ M2 )
           => ( ( ( some_state @ F6 )
                = ( Plus @ F @ M2 ) )
             => ( ( S3
                  = ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A2: state,U6: state,T4: state > state,R2: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ R2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                        & ( ( some_state @ R2 )
                          = ( Plus @ A2 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F6 ) @ ( T4 @ F ) ) ) )
                        & ( sep_defined_state @ Plus @ R2 @ U6 ) ) ) )
               => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi7 @ F7 @ S5 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_992_PartialSA_Oupper__closure__def,axiom,
    ! [A6: set_state] :
      ( ( sep_up1246176804924251236_state @ plus @ A6 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Phi3: state,Phi4: state] :
            ( ( Uu3 = Phi3 )
            & ( greater @ Phi3 @ Phi4 )
            & ( member_state @ Phi4 @ A6 ) ) ) ) ).

% PartialSA.upper_closure_def
thf(fact_993_PartialSA_OAddFromOutside,axiom,
    ! [Phi: state,Phi2: state,M2: state,F6: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi7: state,F7: state,S5: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( ( some_state @ Phi )
        = ( plus @ Phi2 @ M2 ) )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F6 @ S3 @ Pc @ A6 @ Phi7 @ F7 @ S5 )
       => ( ( stable @ M2 )
         => ( ( ( some_state @ F6 )
              = ( plus @ F @ M2 ) )
           => ( ( S3
                = ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state,R2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ R2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                      & ( ( some_state @ R2 )
                        = ( plus @ A2 @ ( minus @ ( T4 @ F6 ) @ ( T4 @ F ) ) ) )
                      & ( defined @ R2 @ U6 ) ) ) )
             => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi7 @ F7 @ S5 ) ) ) ) ) ) ).

% PartialSA.AddFromOutside
thf(fact_994_scaled__def,axiom,
    ( scaled
    = ( ^ [Phi4: state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [P5: prat] :
              ( ( Uu3
                = ( multiply @ P5 @ Phi4 ) )
              & ( ppos @ P5 )
              & ( pgte @ pwrite @ P5 ) ) ) ) ) ).

% scaled_def
thf(fact_995_wand__equiv__def,axiom,
    ( wand
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state] :
              ( ( Uu3 = Phi4 )
              & ( ord_le2494988322063910608_state @ ( add_set @ A @ ( insert_state @ Phi4 @ bot_bot_set_state ) ) @ B5 ) ) ) ) ) ).

% wand_equiv_def
thf(fact_996_package__logic_Osoundness,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Unit: produc7272280185086996969_state,Stable: produc7272280185086996969_state > $o,B4: aasser7019605857572776418_state,A6: aasser7019605857572776418_state,S2: set_Pr4231240917283394591_state,R5: produc7272280185086996969_state > produc7272280185086996969_state > produc7272280185086996969_state,Sigma: produc7272280185086996969_state,Sigma2: produc7272280185086996969_state,W: produc7272280185086996969_state,S3: set_Pr3289333603297600445_state] :
      ( ( packag2204431621656667814_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6254535061403973169_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A6 @ A7 )
             => ( member7461423308196221312_state @ A7 @ S2 ) )
         => ( ! [A7: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ A7 @ S2 )
               => ( packag3884151059541177780_state @ Plus @ Unit @ ( R5 @ A7 ) ) )
           => ( ( packag3630742828623380589_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec7677102015826254172_state
                  @ ^ [Uu3: produc3057782296003698823_state] :
                    ? [A2: produc7272280185086996969_state] :
                      ( ( Uu3
                        = ( produc1904032489304825401_state @ A2 @ ( produc7648782313880683123_state @ Unit @ ( R5 @ A2 ) ) ) )
                      & ( member7461423308196221312_state @ A2 @ S2 ) ) )
                @ ^ [Uu3: produc7272280185086996969_state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1160585701684337059_state @ Plus @ ( packag4865960244449834244_state @ Plus @ B4 ) )
                  | ( packag3875795242785447337_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P6297086604321900740_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag7261830501500456713_state @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_997_package__logic_Osoundness,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Unit: produc9003781588162623004on_val,Stable: produc9003781588162623004on_val > $o,B4: aasser1163550960519286933on_val,A6: aasser1163550960519286933on_val,S2: set_Pr7649655576376376530on_val,R5: produc9003781588162623004on_val > produc9003781588162623004on_val > produc9003781588162623004on_val,Sigma: produc9003781588162623004on_val,Sigma2: produc9003781588162623004on_val,W: produc9003781588162623004on_val,S3: set_Pr1565700067222966883on_val] :
      ( ( packag4549880205214723289on_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5541956234368469604on_val @ Plus @ Core @ B4 )
       => ( ! [A7: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A6 @ A7 )
             => ( member2879030624002546611on_val @ A7 @ S2 ) )
         => ( ! [A7: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ A7 @ S2 )
               => ( packag5955012701910386663on_val @ Plus @ Unit @ ( R5 @ A7 ) ) )
           => ( ( packag6843733491101478048on_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec3787697688312515330on_val
                  @ ^ [Uu3: produc217507841372899885on_val] :
                    ? [A2: produc9003781588162623004on_val] :
                      ( ( Uu3
                        = ( produc6985948203474072671on_val @ A2 @ ( produc6949276712527400972on_val @ Unit @ ( R5 @ A2 ) ) ) )
                      & ( member2879030624002546611on_val @ A2 @ S2 ) ) )
                @ ^ [Uu3: produc9003781588162623004on_val] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1465513459401564630on_val @ Plus @ ( packag3677137384183703351on_val @ Plus @ B4 ) )
                  | ( packag161099568566171125on_val @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P2581650809551911671on_val @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag8228529196479615804on_val @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_998_package__logic_Osoundness,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Unit: produc3882902684156697774_state,Stable: produc3882902684156697774_state > $o,B4: aasser3179708585289803787_state,A6: aasser3179708585289803787_state,S2: set_Pr2391701600042252046_state,R5: produc3882902684156697774_state > produc3882902684156697774_state > produc3882902684156697774_state,Sigma: produc3882902684156697774_state,Sigma2: produc3882902684156697774_state,W: produc3882902684156697774_state,S3: set_Pr5308428015838290133_state] :
      ( ( packag9124413901382861105_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8517968027831007846_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A6 @ A7 )
             => ( member6715010751053357271_state @ A7 @ S2 ) )
         => ( ! [A7: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ A7 @ S2 )
               => ( packag5827594511758291363_state @ Plus @ Unit @ ( R5 @ A7 ) ) )
           => ( ( packag4061699384143886122_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec6806307004801468532_state
                  @ ^ [Uu3: produc6455357576889117855_state] :
                    ? [A2: produc3882902684156697774_state] :
                      ( ( Uu3
                        = ( produc5427679348311974809_state @ A2 @ ( produc3987245858496418492_state @ Unit @ ( R5 @ A2 ) ) ) )
                      & ( member6715010751053357271_state @ A2 @ S2 ) ) )
                @ ^ [Uu3: produc3882902684156697774_state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag1930333982449825652_state @ Plus @ ( packag2518615827549365843_state @ Plus @ B4 ) )
                  | ( packag1386629450763126729_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_P5383513176685068947_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag4438072966337169294_state @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_999_package__logic_Osoundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A6: aassertion_val,S2: set_val,R5: val > val > val,Sigma: val,Sigma2: val,W: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ! [A7: val] :
              ( ( package_sat_val @ Plus @ A6 @ A7 )
             => ( member_val @ A7 @ S2 ) )
         => ( ! [A7: val] :
                ( ( member_val @ A7 @ S2 )
               => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R5 @ A7 ) ) )
           => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A2: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ ( R5 @ A2 ) ) ) )
                      & ( member_val @ A2 @ S2 ) ) )
                @ ^ [Uu3: val] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ B4 ) )
                  | ( packag3202507263771882441al_val @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_val @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag4897621287243763553al_val @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_1000_package__logic_Osoundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A6: aassertion_state,S2: set_state,R5: state > state > state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ! [A7: state] :
              ( ( package_sat_state @ Plus @ A6 @ A7 )
             => ( member_state @ A7 @ S2 ) )
         => ( ! [A7: state] :
                ( ( member_state @ A7 @ S2 )
               => ( packag4817583915586052229_state @ Plus @ Unit @ ( R5 @ A7 ) ) )
           => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ ( R5 @ A2 ) ) ) )
                      & ( member_state @ A2 @ S2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ S3 )
             => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ B4 ) )
                  | ( packag4152378406607043437_state @ Plus @ S3 ) )
               => ( ( Stable @ W )
                  & ( ( some_state @ Sigma )
                    = ( Plus @ Sigma2 @ W ) )
                  & ( packag6192661653625646554_state @ Plus @ W @ R5 @ A6 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_1001_PartialSA_Osoundness__paper,axiom,
    ! [B4: aassertion_state,A6: aassertion_state,S2: set_state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A7: state] :
            ( ( package_sat_state @ plus @ A6 @ A7 )
           => ( member_state @ A7 @ S2 ) )
       => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A2: state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ id_state ) ) )
                  & ( member_state @ A2 @ S2 ) ) )
            @ ^ [Uu3: state] : $true
            @ B4
            @ Sigma2
            @ W
            @ S3 )
         => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ B4 ) )
              | ( packag4152378406607043437_state @ plus @ S3 ) )
           => ( ( stable @ W )
              & ( ( some_state @ Sigma )
                = ( plus @ Sigma2 @ W ) )
              & ( packag7096211993527611489_state @ plus @ W @ A6 @ B4 ) ) ) ) ) ) ).

% PartialSA.soundness_paper
thf(fact_1002_PartialSA_Ocompleteness__paper,axiom,
    ! [B4: aassertion_state,W: state,A6: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag7096211993527611489_state @ plus @ W @ A6 @ B4 ) )
       => ( ( ( some_state @ Sigma )
            = ( plus @ Sigma2 @ W ) )
         => ? [X_1: set_Pr4231240917283394591_state] :
              ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ id_state ) ) )
                    & ( package_sat_state @ plus @ A6 @ A2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ X_1 ) ) ) ) ).

% PartialSA.completeness_paper
thf(fact_1003_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Unit: produc7272280185086996969_state,Stable: produc7272280185086996969_state > $o,B4: aasser7019605857572776418_state,A6: aasser7019605857572776418_state,S2: set_Pr4231240917283394591_state,Sigma: produc7272280185086996969_state,Sigma2: produc7272280185086996969_state,W: produc7272280185086996969_state,S3: set_Pr3289333603297600445_state] :
      ( ( packag2204431621656667814_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6254535061403973169_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A6 @ A7 )
             => ( member7461423308196221312_state @ A7 @ S2 ) )
         => ( ( packag3630742828623380589_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec7677102015826254172_state
                @ ^ [Uu3: produc3057782296003698823_state] :
                  ? [A2: produc7272280185086996969_state] :
                    ( ( Uu3
                      = ( produc1904032489304825401_state @ A2 @ ( produc7648782313880683123_state @ Unit @ id_Pro2933125508726022968_state ) ) )
                    & ( member7461423308196221312_state @ A2 @ S2 ) ) )
              @ ^ [Uu3: produc7272280185086996969_state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1160585701684337059_state @ Plus @ ( packag4865960244449834244_state @ Plus @ B4 ) )
                | ( packag3875795242785447337_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P6297086604321900740_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag8077625386405451152_state @ Plus @ W @ A6 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_1004_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Unit: produc9003781588162623004on_val,Stable: produc9003781588162623004on_val > $o,B4: aasser1163550960519286933on_val,A6: aasser1163550960519286933on_val,S2: set_Pr7649655576376376530on_val,Sigma: produc9003781588162623004on_val,Sigma2: produc9003781588162623004on_val,W: produc9003781588162623004on_val,S3: set_Pr1565700067222966883on_val] :
      ( ( packag4549880205214723289on_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5541956234368469604on_val @ Plus @ Core @ B4 )
       => ( ! [A7: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A6 @ A7 )
             => ( member2879030624002546611on_val @ A7 @ S2 ) )
         => ( ( packag6843733491101478048on_val @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec3787697688312515330on_val
                @ ^ [Uu3: produc217507841372899885on_val] :
                  ? [A2: produc9003781588162623004on_val] :
                    ( ( Uu3
                      = ( produc6985948203474072671on_val @ A2 @ ( produc6949276712527400972on_val @ Unit @ id_Pro1402184692240358763on_val ) ) )
                    & ( member2879030624002546611on_val @ A2 @ S2 ) ) )
              @ ^ [Uu3: produc9003781588162623004on_val] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1465513459401564630on_val @ Plus @ ( packag3677137384183703351on_val @ Plus @ B4 ) )
                | ( packag161099568566171125on_val @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P2581650809551911671on_val @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag6258220590826782659on_val @ Plus @ W @ A6 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_1005_package__logic_Osoundness__paper,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Unit: produc3882902684156697774_state,Stable: produc3882902684156697774_state > $o,B4: aasser3179708585289803787_state,A6: aasser3179708585289803787_state,S2: set_Pr2391701600042252046_state,Sigma: produc3882902684156697774_state,Sigma2: produc3882902684156697774_state,W: produc3882902684156697774_state,S3: set_Pr5308428015838290133_state] :
      ( ( packag9124413901382861105_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8517968027831007846_state @ Plus @ Core @ B4 )
       => ( ! [A7: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A6 @ A7 )
             => ( member6715010751053357271_state @ A7 @ S2 ) )
         => ( ( packag4061699384143886122_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec6806307004801468532_state
                @ ^ [Uu3: produc6455357576889117855_state] :
                  ? [A2: produc3882902684156697774_state] :
                    ( ( Uu3
                      = ( produc5427679348311974809_state @ A2 @ ( produc3987245858496418492_state @ Unit @ id_Pro689249233197853983_state ) ) )
                    & ( member6715010751053357271_state @ A2 @ S2 ) ) )
              @ ^ [Uu3: produc3882902684156697774_state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag1930333982449825652_state @ Plus @ ( packag2518615827549365843_state @ Plus @ B4 ) )
                | ( packag1386629450763126729_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_P5383513176685068947_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag3130788337556013255_state @ Plus @ W @ A6 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_1006_package__logic_Osoundness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A6: aassertion_val,S2: set_val,Sigma: val,Sigma2: val,W: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ! [A7: val] :
              ( ( package_sat_val @ Plus @ A6 @ A7 )
             => ( member_val @ A7 @ S2 ) )
         => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec8300311316619386842al_val
                @ ^ [Uu3: produc2072440392815185925al_val] :
                  ? [A2: val] :
                    ( ( Uu3
                      = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ id_val ) ) )
                    & ( member_val @ A2 @ S2 ) ) )
              @ ^ [Uu3: val] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ B4 ) )
                | ( packag3202507263771882441al_val @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_val @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag685230357167683994rd_val @ Plus @ W @ A6 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_1007_package__logic_Osoundness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A6: aassertion_state,S2: set_state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ! [A7: state] :
              ( ( package_sat_state @ Plus @ A6 @ A7 )
             => ( member_state @ A7 @ S2 ) )
         => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ id_state ) ) )
                    & ( member_state @ A2 @ S2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ S3 )
           => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ B4 ) )
                | ( packag4152378406607043437_state @ Plus @ S3 ) )
             => ( ( Stable @ W )
                & ( ( some_state @ Sigma )
                  = ( Plus @ Sigma2 @ W ) )
                & ( packag7096211993527611489_state @ Plus @ W @ A6 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_1008_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,A6: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag685230357167683994rd_val @ Plus @ W @ A6 @ B4 ) )
         => ( ( ( some_val @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ? [X_1: set_Pr4723104092121316667al_val] :
                ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A2: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ id_val ) ) )
                      & ( package_sat_val @ Plus @ A6 @ A2 ) ) )
                @ ^ [Uu3: val] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_1009_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,A6: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag7096211993527611489_state @ Plus @ W @ A6 @ B4 ) )
         => ( ( ( some_state @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ? [X_1: set_Pr4231240917283394591_state] :
                ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ id_state ) ) )
                      & ( package_sat_state @ Plus @ A6 @ A2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_1010_accp__subset,axiom,
    ! [R1: produc3142500478612311029_state > produc3142500478612311029_state > $o,R22: produc3142500478612311029_state > produc3142500478612311029_state > $o] :
      ( ( ord_le3734019104314464462tate_o @ R1 @ R22 )
     => ( ord_le5366583112655343912tate_o @ ( accp_P7183347322223220350_state @ R22 ) @ ( accp_P7183347322223220350_state @ R1 ) ) ) ).

% accp_subset
thf(fact_1011_accp__subset,axiom,
    ! [R1: produc4844402304972151915_state > produc4844402304972151915_state > $o,R22: produc4844402304972151915_state > produc4844402304972151915_state > $o] :
      ( ( ord_le2599682012455951694tate_o @ R1 @ R22 )
     => ( ord_le5681876185599785522tate_o @ ( accp_P6233459008282737652_state @ R22 ) @ ( accp_P6233459008282737652_state @ R1 ) ) ) ).

% accp_subset
thf(fact_1012_accp__subset,axiom,
    ! [R1: produc6251377953716854561_state > produc6251377953716854561_state > $o,R22: produc6251377953716854561_state > produc6251377953716854561_state > $o] :
      ( ( ord_le249087669307848398tate_o @ R1 @ R22 )
     => ( ord_le8699832056682887676tate_o @ ( accp_P6554740477754186410_state @ R22 ) @ ( accp_P6554740477754186410_state @ R1 ) ) ) ).

% accp_subset
thf(fact_1013_accp__subset,axiom,
    ! [R1: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,R22: produc9003781588162623004on_val > produc9003781588162623004on_val > $o] :
      ( ( ord_le616650860478780142_val_o @ R1 @ R22 )
     => ( ord_le6140313152057869779_val_o @ ( accp_P4405556307444930259on_val @ R22 ) @ ( accp_P4405556307444930259on_val @ R1 ) ) ) ).

% accp_subset
thf(fact_1014_accp__subset,axiom,
    ! [R1: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,R22: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le6723339807950303054prat_o @ R1 @ R22 )
     => ( ord_le2830794348966088778prat_o @ ( accp_P4765339447491148764r_prat @ R22 ) @ ( accp_P4765339447491148764r_prat @ R1 ) ) ) ).

% accp_subset
thf(fact_1015_PartialSA_Ogeneral__soundness,axiom,
    ! [Phi: state,S2: set_Pr2391701600042252046_state,A6: aassertion_state,Phi2: state,F: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ unit
        @ ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [A2: state,T4: state > state] :
              ( ( Uu3
                = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ T4 ) ) )
              & ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A2 @ T4 ) @ S2 ) ) )
        @ ^ [Uu3: state] : $true
        @ A6
        @ Phi2
        @ F
        @ S3 )
     => ( ! [A7: state,T3: state > state] :
            ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A7 @ T3 ) @ S2 )
           => ( packag4817583915586052229_state @ plus @ unit @ T3 ) )
       => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
         => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ A6 ) )
              | ( packag4152378406607043437_state @ plus @ S3 ) )
           => ( ( ( some_state @ Phi )
                = ( plus @ Phi2 @ F ) )
              & ( stable @ F )
              & ! [X3: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ X3 @ S2 )
                 => ( produc3645877548210629341tate_o
                    @ ^ [A2: state,T4: state > state] :
                        ( ( defined @ A2 @ ( T4 @ F ) )
                       => ( package_sat_state @ plus @ A6 @ ( the_state @ ( plus @ A2 @ ( T4 @ F ) ) ) ) )
                    @ X3 ) ) ) ) ) ) ) ).

% PartialSA.general_soundness
thf(fact_1016_PartialSA_Ounder__def,axiom,
    ! [A6: set_state,Omega2: state] :
      ( ( sep_under_state @ plus @ A6 @ Omega2 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Omega3: state] :
            ( ( Uu3 = Omega3 )
            & ( member_state @ Omega3 @ A6 )
            & ( greater @ Omega2 @ Omega3 ) ) ) ) ).

% PartialSA.under_def
thf(fact_1017_ball__empty,axiom,
    ! [P2: state > $o,X3: state] :
      ( ( member_state @ X3 @ bot_bot_set_state )
     => ( P2 @ X3 ) ) ).

% ball_empty
thf(fact_1018_sep__algebra_Ounder_Ocong,axiom,
    sep_under_state = sep_under_state ).

% sep_algebra.under.cong
thf(fact_1019_Ball__def,axiom,
    ( ball_state
    = ( ^ [A: set_state,P4: state > $o] :
        ! [X5: state] :
          ( ( member_state @ X5 @ A )
         => ( P4 @ X5 ) ) ) ) ).

% Ball_def
thf(fact_1020_Ball__def,axiom,
    ( ball_P7403102246598991807_state
    = ( ^ [A: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] :
        ! [X5: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X5 @ A )
         => ( P4 @ X5 ) ) ) ) ).

% Ball_def
thf(fact_1021_Ball__def,axiom,
    ( ball_P2871712132005019634on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] :
        ! [X5: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X5 @ A )
         => ( P4 @ X5 ) ) ) ) ).

% Ball_def
thf(fact_1022_Ball__def,axiom,
    ( ball_P1066487999220904024_state
    = ( ^ [A: set_Pr2391701600042252046_state,P4: produc3882902684156697774_state > $o] :
        ! [X5: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X5 @ A )
         => ( P4 @ X5 ) ) ) ) ).

% Ball_def
thf(fact_1023_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,S2: set_Pr6546617632949187467al_val,A6: aassertion_val,Phi2: val,F: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ Unit
          @ ( collec8300311316619386842al_val
            @ ^ [Uu3: produc2072440392815185925al_val] :
              ? [A2: val,T4: val > val] :
                ( ( Uu3
                  = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ T4 ) ) )
                & ( member331055627401653996al_val @ ( produc303288909735261391al_val @ A2 @ T4 ) @ S2 ) ) )
          @ ^ [Uu3: val] : $true
          @ A6
          @ Phi2
          @ F
          @ S3 )
       => ( ! [A7: val,T3: val > val] :
              ( ( member331055627401653996al_val @ ( produc303288909735261391al_val @ A7 @ T3 ) @ S2 )
             => ( packag4175576287423129206er_val @ Plus @ Unit @ T3 ) )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ A6 )
           => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ A6 ) )
                | ( packag3202507263771882441al_val @ Plus @ S3 ) )
             => ( ( ( some_val @ Phi )
                  = ( Plus @ Phi2 @ F ) )
                & ( Stable @ F )
                & ! [X3: produc5503543764249810261al_val] :
                    ( ( member331055627401653996al_val @ X3 @ S2 )
                   => ( produc7666680587469814684_val_o
                      @ ^ [A2: val,T4: val > val] :
                          ( ( sep_defined_val @ Plus @ A2 @ ( T4 @ F ) )
                         => ( package_sat_val @ Plus @ A6 @ ( the_val @ ( Plus @ A2 @ ( T4 @ F ) ) ) ) )
                      @ X3 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_1024_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,S2: set_Pr2391701600042252046_state,A6: aassertion_state,Phi2: state,F: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ Unit
          @ ( collec906845016635587262_state
            @ ^ [Uu3: produc7272280185086996969_state] :
              ? [A2: state,T4: state > state] :
                ( ( Uu3
                  = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ T4 ) ) )
                & ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A2 @ T4 ) @ S2 ) ) )
          @ ^ [Uu3: state] : $true
          @ A6
          @ Phi2
          @ F
          @ S3 )
       => ( ! [A7: state,T3: state > state] :
              ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A7 @ T3 ) @ S2 )
             => ( packag4817583915586052229_state @ Plus @ Unit @ T3 ) )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
           => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ A6 ) )
                | ( packag4152378406607043437_state @ Plus @ S3 ) )
             => ( ( ( some_state @ Phi )
                  = ( Plus @ Phi2 @ F ) )
                & ( Stable @ F )
                & ! [X3: produc3882902684156697774_state] :
                    ( ( member6715010751053357271_state @ X3 @ S2 )
                   => ( produc3645877548210629341tate_o
                      @ ^ [A2: state,T4: state > state] :
                          ( ( sep_defined_state @ Plus @ A2 @ ( T4 @ F ) )
                         => ( package_sat_state @ Plus @ A6 @ ( the_state @ ( Plus @ A2 @ ( T4 @ F ) ) ) ) )
                      @ X3 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_1025_accp__subset__induct,axiom,
    ! [D2: produc3142500478612311029_state > $o,R5: produc3142500478612311029_state > produc3142500478612311029_state > $o,X2: produc3142500478612311029_state,P2: produc3142500478612311029_state > $o] :
      ( ( ord_le5366583112655343912tate_o @ D2 @ ( accp_P7183347322223220350_state @ R5 ) )
     => ( ! [X4: produc3142500478612311029_state,Z4: produc3142500478612311029_state] :
            ( ( D2 @ X4 )
           => ( ( R5 @ Z4 @ X4 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X2 )
         => ( ! [X4: produc3142500478612311029_state] :
                ( ( D2 @ X4 )
               => ( ! [Z5: produc3142500478612311029_state] :
                      ( ( R5 @ Z5 @ X4 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X4 ) ) )
           => ( P2 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_1026_accp__subset__induct,axiom,
    ! [D2: produc4844402304972151915_state > $o,R5: produc4844402304972151915_state > produc4844402304972151915_state > $o,X2: produc4844402304972151915_state,P2: produc4844402304972151915_state > $o] :
      ( ( ord_le5681876185599785522tate_o @ D2 @ ( accp_P6233459008282737652_state @ R5 ) )
     => ( ! [X4: produc4844402304972151915_state,Z4: produc4844402304972151915_state] :
            ( ( D2 @ X4 )
           => ( ( R5 @ Z4 @ X4 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X2 )
         => ( ! [X4: produc4844402304972151915_state] :
                ( ( D2 @ X4 )
               => ( ! [Z5: produc4844402304972151915_state] :
                      ( ( R5 @ Z5 @ X4 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X4 ) ) )
           => ( P2 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_1027_accp__subset__induct,axiom,
    ! [D2: produc6251377953716854561_state > $o,R5: produc6251377953716854561_state > produc6251377953716854561_state > $o,X2: produc6251377953716854561_state,P2: produc6251377953716854561_state > $o] :
      ( ( ord_le8699832056682887676tate_o @ D2 @ ( accp_P6554740477754186410_state @ R5 ) )
     => ( ! [X4: produc6251377953716854561_state,Z4: produc6251377953716854561_state] :
            ( ( D2 @ X4 )
           => ( ( R5 @ Z4 @ X4 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X2 )
         => ( ! [X4: produc6251377953716854561_state] :
                ( ( D2 @ X4 )
               => ( ! [Z5: produc6251377953716854561_state] :
                      ( ( R5 @ Z5 @ X4 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X4 ) ) )
           => ( P2 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_1028_accp__subset__induct,axiom,
    ! [D2: produc9003781588162623004on_val > $o,R5: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,X2: produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( ord_le6140313152057869779_val_o @ D2 @ ( accp_P4405556307444930259on_val @ R5 ) )
     => ( ! [X4: produc9003781588162623004on_val,Z4: produc9003781588162623004on_val] :
            ( ( D2 @ X4 )
           => ( ( R5 @ Z4 @ X4 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X2 )
         => ( ! [X4: produc9003781588162623004on_val] :
                ( ( D2 @ X4 )
               => ( ! [Z5: produc9003781588162623004on_val] :
                      ( ( R5 @ Z5 @ X4 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X4 ) ) )
           => ( P2 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_1029_accp__subset__induct,axiom,
    ! [D2: ( produc1457211279475724562t_char > prat ) > $o,R5: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,X2: produc1457211279475724562t_char > prat,P2: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le2830794348966088778prat_o @ D2 @ ( accp_P4765339447491148764r_prat @ R5 ) )
     => ( ! [X4: produc1457211279475724562t_char > prat,Z4: produc1457211279475724562t_char > prat] :
            ( ( D2 @ X4 )
           => ( ( R5 @ Z4 @ X4 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X2 )
         => ( ! [X4: produc1457211279475724562t_char > prat] :
                ( ( D2 @ X4 )
               => ( ! [Z5: produc1457211279475724562t_char > prat] :
                      ( ( R5 @ Z5 @ X4 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X4 ) ) )
           => ( P2 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_1030_Collect__case__prod__mono,axiom,
    ! [A6: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,B4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( ord_le3852884270828607079_val_o @ A6 @ B4 )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ A6 ) ) @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_1031_Collect__case__prod__mono,axiom,
    ! [A6: state > ( state > state ) > $o,B4: state > ( state > state ) > $o] :
      ( ( ord_le1106678366802930969tate_o @ A6 @ B4 )
     => ( ord_le6483787752022044334_state @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ A6 ) ) @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_1032_Collect__case__prod__mono,axiom,
    ! [A6: state > produc3882902684156697774_state > $o,B4: state > produc3882902684156697774_state > $o] :
      ( ( ord_le6704609105599929480tate_o @ A6 @ B4 )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ A6 ) ) @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_1033_PartialSA_Opackage__rhs_Ocases,axiom,
    ! [A1: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A1 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
     => ( ! [A11: aassertion_state,Phi6: state,F8: state,S6: set_Pr4231240917283394591_state,B7: aassertion_state] :
            ( ( A52
              = ( aStar_state @ A11 @ B7 ) )
           => ( ( packag3171892606229212990_state @ plus @ core @ stable @ A1 @ A22 @ A32 @ A42 @ A11 @ Phi6 @ F8 @ S6 )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ Phi6 @ F8 @ S6 @ A42 @ B7 @ A62 @ A72 @ A82 ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( A52
                = ( aImp_state @ B6 @ A11 ) )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ A1 @ A22 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A11 @ A62 @ A72 @ A82 ) )
         => ( ! [Witness: produc7272280185086996969_state > state,B7: state > $o] :
                ( ( A52
                  = ( aSem_state @ B7 ) )
               => ( ( A62 = A1 )
                 => ( ( A72 = A22 )
                   => ( ! [A5: state,U7: state,T5: state > state] :
                          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) @ A32 )
                         => ( ( A42 @ A5 )
                           => ( ( greater @ A5 @ ( Witness @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) ) )
                              & ( B7 @ ( Witness @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) ) ) ) ) )
                     => ( A82
                       != ( sup_su3837536599209510219_state
                          @ ( collec906845016635587262_state
                            @ ^ [Uu3: produc7272280185086996969_state] :
                              ? [A2: state,U6: state,T4: state > state] :
                                ( ( Uu3
                                  = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                & ~ ( A42 @ A2 ) ) )
                          @ ( collec906845016635587262_state
                            @ ^ [Uu3: produc7272280185086996969_state] :
                              ? [A2: state,U6: state,T4: state > state] :
                                ( ( Uu3
                                  = ( produc5886875603596089627_state @ ( minus @ A2 @ ( Witness @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ ( Witness @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) @ T4 ) ) )
                                & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                & ( A42 @ A2 ) ) ) ) ) ) ) ) )
           => ~ ! [Phi6: state,M3: state] :
                  ( ( ( some_state @ A1 )
                    = ( plus @ Phi6 @ M3 ) )
                 => ! [F8: state,S6: set_Pr4231240917283394591_state] :
                      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi6 @ F8 @ S6 @ A42 @ A52 @ A62 @ A72 @ A82 )
                     => ( ( stable @ M3 )
                       => ( ( ( some_state @ F8 )
                            = ( plus @ A22 @ M3 ) )
                         => ( S6
                           != ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A2: state,U6: state,T4: state > state,R2: state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ R2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                  & ( ( some_state @ R2 )
                                    = ( plus @ A2 @ ( minus @ ( T4 @ F8 ) @ ( T4 @ A22 ) ) ) )
                                  & ( defined @ R2 @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.cases
thf(fact_1034_PartialSA_Opackage__rhs_Osimps,axiom,
    ! [A1: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A1 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
      = ( ? [Phi4: state,F4: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,A: aassertion_state,Phi3: state,F9: state,S8: set_Pr4231240917283394591_state,B5: aassertion_state,Phi8: state,F10: state,S9: set_Pr4231240917283394591_state] :
            ( ( A1 = Phi4 )
            & ( A22 = F4 )
            & ( A32 = S7 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aStar_state @ A @ B5 ) )
            & ( A62 = Phi8 )
            & ( A72 = F10 )
            & ( A82 = S9 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F4 @ S7 @ Pc2 @ A @ Phi3 @ F9 @ S8 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi3 @ F9 @ S8 @ Pc2 @ B5 @ Phi8 @ F10 @ S9 ) )
        | ? [Phi4: state,F4: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,B: state > $o,A: aassertion_state,Phi3: state,F9: state,S8: set_Pr4231240917283394591_state] :
            ( ( A1 = Phi4 )
            & ( A22 = F4 )
            & ( A32 = S7 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aImp_state @ B @ A ) )
            & ( A62 = Phi3 )
            & ( A72 = F9 )
            & ( A82 = S8 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F4 @ S7 @ ( packag1330488657391168505_state @ Pc2 @ B ) @ A @ Phi3 @ F9 @ S8 ) )
        | ? [S7: set_Pr4231240917283394591_state,Pc2: state > $o,Witness2: produc7272280185086996969_state > state,B5: state > $o,S8: set_Pr4231240917283394591_state,Phi4: state,F4: state] :
            ( ( A1 = Phi4 )
            & ( A22 = F4 )
            & ( A32 = S7 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aSem_state @ B5 ) )
            & ( A62 = Phi4 )
            & ( A72 = F4 )
            & ( A82 = S8 )
            & ! [X5: state,Y4: state,Z6: state > state,Aa2: state] :
                ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X5 @ ( produc8632743443909064678_state @ Y4 @ Z6 ) ) @ S7 )
               => ( ( Pc2 @ X5 )
                 => ( ( Aa2
                      = ( Witness2 @ ( produc5886875603596089627_state @ X5 @ ( produc8632743443909064678_state @ Y4 @ Z6 ) ) ) )
                   => ( ( greater @ X5 @ Aa2 )
                      & ( B5 @ Aa2 ) ) ) ) )
            & ( S8
              = ( sup_su3837536599209510219_state
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S7 )
                      & ~ ( Pc2 @ A2 ) ) )
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state,B: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ ( minus @ A2 @ B ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B ) ) @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S7 )
                      & ( Pc2 @ A2 )
                      & ( B
                        = ( Witness2 @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) ) ) ) )
        | ? [Phi4: state,Phi3: state,M4: state,F9: state,S8: set_Pr4231240917283394591_state,Pc2: state > $o,A: aassertion_state,Phi8: state,F10: state,S9: set_Pr4231240917283394591_state,F4: state,S7: set_Pr4231240917283394591_state] :
            ( ( A1 = Phi4 )
            & ( A22 = F4 )
            & ( A32 = S7 )
            & ( A42 = Pc2 )
            & ( A52 = A )
            & ( A62 = Phi8 )
            & ( A72 = F10 )
            & ( A82 = S9 )
            & ( ( some_state @ Phi4 )
              = ( plus @ Phi3 @ M4 ) )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi3 @ F9 @ S8 @ Pc2 @ A @ Phi8 @ F10 @ S9 )
            & ( stable @ M4 )
            & ( ( some_state @ F9 )
              = ( plus @ F4 @ M4 ) )
            & ( S8
              = ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state,U6: state,T4: state > state,R2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ R2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S7 )
                    & ( ( some_state @ R2 )
                      = ( plus @ A2 @ ( minus @ ( T4 @ F9 ) @ ( T4 @ F4 ) ) ) )
                    & ( defined @ R2 @ U6 ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.simps
thf(fact_1035_UnCI,axiom,
    ! [C: state,B4: set_state,A6: set_state] :
      ( ( ~ ( member_state @ C @ B4 )
       => ( member_state @ C @ A6 ) )
     => ( member_state @ C @ ( sup_sup_set_state @ A6 @ B4 ) ) ) ).

% UnCI
thf(fact_1036_UnCI,axiom,
    ! [C: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( ~ ( member2879030624002546611on_val @ C @ B4 )
       => ( member2879030624002546611on_val @ C @ A6 ) )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A6 @ B4 ) ) ) ).

% UnCI
thf(fact_1037_UnCI,axiom,
    ! [C: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,A6: set_Pr2391701600042252046_state] :
      ( ( ~ ( member6715010751053357271_state @ C @ B4 )
       => ( member6715010751053357271_state @ C @ A6 ) )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A6 @ B4 ) ) ) ).

% UnCI
thf(fact_1038_UnCI,axiom,
    ! [C: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,A6: set_Pr4231240917283394591_state] :
      ( ( ~ ( member7461423308196221312_state @ C @ B4 )
       => ( member7461423308196221312_state @ C @ A6 ) )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ) ).

% UnCI
thf(fact_1039_Un__iff,axiom,
    ! [C: state,A6: set_state,B4: set_state] :
      ( ( member_state @ C @ ( sup_sup_set_state @ A6 @ B4 ) )
      = ( ( member_state @ C @ A6 )
        | ( member_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_1040_Un__iff,axiom,
    ! [C: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A6 @ B4 ) )
      = ( ( member2879030624002546611on_val @ C @ A6 )
        | ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_1041_Un__iff,axiom,
    ! [C: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A6 @ B4 ) )
      = ( ( member6715010751053357271_state @ C @ A6 )
        | ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_1042_Un__iff,axiom,
    ! [C: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
      = ( ( member7461423308196221312_state @ C @ A6 )
        | ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_1043_aassertion_Oinject_I3_J,axiom,
    ! [X32: state > $o,Y32: state > $o] :
      ( ( ( aSem_state @ X32 )
        = ( aSem_state @ Y32 ) )
      = ( X32 = Y32 ) ) ).

% aassertion.inject(3)
thf(fact_1044_Un__empty,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ( sup_su3837536599209510219_state @ A6 @ B4 )
        = bot_bo6430881413863817907_state )
      = ( ( A6 = bot_bo6430881413863817907_state )
        & ( B4 = bot_bo6430881413863817907_state ) ) ) ).

% Un_empty
thf(fact_1045_Un__empty,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ( sup_sup_set_state @ A6 @ B4 )
        = bot_bot_set_state )
      = ( ( A6 = bot_bot_set_state )
        & ( B4 = bot_bot_set_state ) ) ) ).

% Un_empty
thf(fact_1046_Un__subset__iff,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A6 @ B4 ) @ C3 )
      = ( ( ord_le4032880777312351359_state @ A6 @ C3 )
        & ( ord_le4032880777312351359_state @ B4 @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_1047_Un__subset__iff,axiom,
    ! [A6: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A6 @ B4 ) @ C3 )
      = ( ( ord_le2494988322063910608_state @ A6 @ C3 )
        & ( ord_le2494988322063910608_state @ B4 @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_1048_Un__insert__right,axiom,
    ! [A6: set_state,A3: state,B4: set_state] :
      ( ( sup_sup_set_state @ A6 @ ( insert_state @ A3 @ B4 ) )
      = ( insert_state @ A3 @ ( sup_sup_set_state @ A6 @ B4 ) ) ) ).

% Un_insert_right
thf(fact_1049_Un__insert__right,axiom,
    ! [A6: set_Pr4231240917283394591_state,A3: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ ( insert175804457004744729_state @ A3 @ B4 ) )
      = ( insert175804457004744729_state @ A3 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ) ).

% Un_insert_right
thf(fact_1050_Un__insert__left,axiom,
    ! [A3: state,B4: set_state,C3: set_state] :
      ( ( sup_sup_set_state @ ( insert_state @ A3 @ B4 ) @ C3 )
      = ( insert_state @ A3 @ ( sup_sup_set_state @ B4 @ C3 ) ) ) ).

% Un_insert_left
thf(fact_1051_Un__insert__left,axiom,
    ! [A3: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ ( insert175804457004744729_state @ A3 @ B4 ) @ C3 )
      = ( insert175804457004744729_state @ A3 @ ( sup_su3837536599209510219_state @ B4 @ C3 ) ) ) ).

% Un_insert_left
thf(fact_1052_insert__def,axiom,
    ( insert3030518898131756108on_val
    = ( ^ [A2: produc9003781588162623004on_val] :
          ( sup_su7506060154676209150on_val
          @ ( collec7475294502966882545on_val
            @ ^ [X5: produc9003781588162623004on_val] : ( X5 = A2 ) ) ) ) ) ).

% insert_def
thf(fact_1053_insert__def,axiom,
    ( insert_state
    = ( ^ [A2: state] :
          ( sup_sup_set_state
          @ ( collect_state
            @ ^ [X5: state] : ( X5 = A2 ) ) ) ) ) ).

% insert_def
thf(fact_1054_insert__def,axiom,
    ( insert175804457004744729_state
    = ( ^ [A2: produc7272280185086996969_state] :
          ( sup_su3837536599209510219_state
          @ ( collec906845016635587262_state
            @ ^ [X5: produc7272280185086996969_state] : ( X5 = A2 ) ) ) ) ) ).

% insert_def
thf(fact_1055_aassertion_Odistinct_I5_J,axiom,
    ! [X21: state > $o,X222: aassertion_state,X32: state > $o] :
      ( ( aImp_state @ X21 @ X222 )
     != ( aSem_state @ X32 ) ) ).

% aassertion.distinct(5)
thf(fact_1056_aassertion_Odistinct_I3_J,axiom,
    ! [X11: aassertion_state,X12: aassertion_state,X32: state > $o] :
      ( ( aStar_state @ X11 @ X12 )
     != ( aSem_state @ X32 ) ) ).

% aassertion.distinct(3)
thf(fact_1057_Un__def,axiom,
    ( sup_su1984960714304006370_state
    = ( ^ [A: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
          ( collec394671971739345689_state
          @ ^ [X5: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X5 @ A )
              | ( member6715010751053357271_state @ X5 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_1058_Un__def,axiom,
    ( sup_su7506060154676209150on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
          ( collec7475294502966882545on_val
          @ ^ [X5: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ X5 @ A )
              | ( member2879030624002546611on_val @ X5 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_1059_Un__def,axiom,
    ( sup_sup_set_state
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ^ [X5: state] :
              ( ( member_state @ X5 @ A )
              | ( member_state @ X5 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_1060_Un__def,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( collec906845016635587262_state
          @ ^ [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ A )
              | ( member7461423308196221312_state @ X5 @ B5 ) ) ) ) ) ).

% Un_def
thf(fact_1061_Collect__disj__eq,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( collec7475294502966882545on_val
        @ ^ [X5: produc9003781588162623004on_val] :
            ( ( P2 @ X5 )
            | ( Q @ X5 ) ) )
      = ( sup_su7506060154676209150on_val @ ( collec7475294502966882545on_val @ P2 ) @ ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1062_Collect__disj__eq,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ( collect_state
        @ ^ [X5: state] :
            ( ( P2 @ X5 )
            | ( Q @ X5 ) ) )
      = ( sup_sup_set_state @ ( collect_state @ P2 ) @ ( collect_state @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1063_Collect__disj__eq,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( collec906845016635587262_state
        @ ^ [X5: produc7272280185086996969_state] :
            ( ( P2 @ X5 )
            | ( Q @ X5 ) ) )
      = ( sup_su3837536599209510219_state @ ( collec906845016635587262_state @ P2 ) @ ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1064_Un__Pow__subset,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] : ( ord_le8498320074568675253_state @ ( sup_su6129196281181032577_state @ ( pow_Pr3120271928052550924_state @ A6 ) @ ( pow_Pr3120271928052550924_state @ B4 ) ) @ ( pow_Pr3120271928052550924_state @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ) ).

% Un_Pow_subset
thf(fact_1065_subset__Un__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A @ B5 )
          = B5 ) ) ) ).

% subset_Un_eq
thf(fact_1066_subset__Un__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A: set_state,B5: set_state] :
          ( ( sup_sup_set_state @ A @ B5 )
          = B5 ) ) ) ).

% subset_Un_eq
thf(fact_1067_subset__UnE,axiom,
    ! [C3: set_Pr4231240917283394591_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C3 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
     => ~ ! [A12: set_Pr4231240917283394591_state] :
            ( ( ord_le4032880777312351359_state @ A12 @ A6 )
           => ! [B8: set_Pr4231240917283394591_state] :
                ( ( ord_le4032880777312351359_state @ B8 @ B4 )
               => ( C3
                 != ( sup_su3837536599209510219_state @ A12 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_1068_subset__UnE,axiom,
    ! [C3: set_state,A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ C3 @ ( sup_sup_set_state @ A6 @ B4 ) )
     => ~ ! [A12: set_state] :
            ( ( ord_le2494988322063910608_state @ A12 @ A6 )
           => ! [B8: set_state] :
                ( ( ord_le2494988322063910608_state @ B8 @ B4 )
               => ( C3
                 != ( sup_sup_set_state @ A12 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_1069_Un__absorb2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A6: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B4 @ A6 )
     => ( ( sup_su3837536599209510219_state @ A6 @ B4 )
        = A6 ) ) ).

% Un_absorb2
thf(fact_1070_Un__absorb2,axiom,
    ! [B4: set_state,A6: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ A6 )
     => ( ( sup_sup_set_state @ A6 @ B4 )
        = A6 ) ) ).

% Un_absorb2
thf(fact_1071_Un__absorb1,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A6 @ B4 )
     => ( ( sup_su3837536599209510219_state @ A6 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_1072_Un__absorb1,axiom,
    ! [A6: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ B4 )
     => ( ( sup_sup_set_state @ A6 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_1073_Un__upper2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A6: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ B4 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ).

% Un_upper2
thf(fact_1074_Un__upper2,axiom,
    ! [B4: set_state,A6: set_state] : ( ord_le2494988322063910608_state @ B4 @ ( sup_sup_set_state @ A6 @ B4 ) ) ).

% Un_upper2
thf(fact_1075_Un__upper1,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ A6 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ).

% Un_upper1
thf(fact_1076_Un__upper1,axiom,
    ! [A6: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ A6 @ ( sup_sup_set_state @ A6 @ B4 ) ) ).

% Un_upper1
thf(fact_1077_Un__least,axiom,
    ! [A6: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A6 @ C3 )
     => ( ( ord_le4032880777312351359_state @ B4 @ C3 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A6 @ B4 ) @ C3 ) ) ) ).

% Un_least
thf(fact_1078_Un__least,axiom,
    ! [A6: set_state,C3: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ C3 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A6 @ B4 ) @ C3 ) ) ) ).

% Un_least
thf(fact_1079_Un__mono,axiom,
    ! [A6: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,D2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A6 @ C3 )
     => ( ( ord_le4032880777312351359_state @ B4 @ D2 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A6 @ B4 ) @ ( sup_su3837536599209510219_state @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_1080_Un__mono,axiom,
    ! [A6: set_state,C3: set_state,B4: set_state,D2: set_state] :
      ( ( ord_le2494988322063910608_state @ A6 @ C3 )
     => ( ( ord_le2494988322063910608_state @ B4 @ D2 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A6 @ B4 ) @ ( sup_sup_set_state @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_1081_image__Un,axiom,
    ! [F: state > state,A6: set_state,B4: set_state] :
      ( ( image_state_state @ F @ ( sup_sup_set_state @ A6 @ B4 ) )
      = ( sup_sup_set_state @ ( image_state_state @ F @ A6 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_Un
thf(fact_1082_image__Un,axiom,
    ! [F: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( image_3064086290059306969_state @ F @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
      = ( sup_su3837536599209510219_state @ ( image_3064086290059306969_state @ F @ A6 ) @ ( image_3064086290059306969_state @ F @ B4 ) ) ) ).

% image_Un
thf(fact_1083_UnE,axiom,
    ! [C: state,A6: set_state,B4: set_state] :
      ( ( member_state @ C @ ( sup_sup_set_state @ A6 @ B4 ) )
     => ( ~ ( member_state @ C @ A6 )
       => ( member_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_1084_UnE,axiom,
    ! [C: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A6 @ B4 ) )
     => ( ~ ( member2879030624002546611on_val @ C @ A6 )
       => ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% UnE
thf(fact_1085_UnE,axiom,
    ! [C: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A6 @ B4 ) )
     => ( ~ ( member6715010751053357271_state @ C @ A6 )
       => ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_1086_UnE,axiom,
    ! [C: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
     => ( ~ ( member7461423308196221312_state @ C @ A6 )
       => ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% UnE
thf(fact_1087_UnI1,axiom,
    ! [C: state,A6: set_state,B4: set_state] :
      ( ( member_state @ C @ A6 )
     => ( member_state @ C @ ( sup_sup_set_state @ A6 @ B4 ) ) ) ).

% UnI1
thf(fact_1088_UnI1,axiom,
    ! [C: produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ A6 )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A6 @ B4 ) ) ) ).

% UnI1
thf(fact_1089_UnI1,axiom,
    ! [C: produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ A6 )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A6 @ B4 ) ) ) ).

% UnI1
thf(fact_1090_UnI1,axiom,
    ! [C: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ A6 )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ) ).

% UnI1
thf(fact_1091_UnI2,axiom,
    ! [C: state,B4: set_state,A6: set_state] :
      ( ( member_state @ C @ B4 )
     => ( member_state @ C @ ( sup_sup_set_state @ A6 @ B4 ) ) ) ).

% UnI2
thf(fact_1092_UnI2,axiom,
    ! [C: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ C @ B4 )
     => ( member2879030624002546611on_val @ C @ ( sup_su7506060154676209150on_val @ A6 @ B4 ) ) ) ).

% UnI2
thf(fact_1093_UnI2,axiom,
    ! [C: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state,A6: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ C @ B4 )
     => ( member6715010751053357271_state @ C @ ( sup_su1984960714304006370_state @ A6 @ B4 ) ) ) ).

% UnI2
thf(fact_1094_UnI2,axiom,
    ! [C: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state,A6: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ C @ B4 )
     => ( member7461423308196221312_state @ C @ ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ) ).

% UnI2
thf(fact_1095_bex__Un,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( ? [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
            & ( P2 @ X5 ) ) )
      = ( ? [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ A6 )
            & ( P2 @ X5 ) )
        | ? [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ B4 )
            & ( P2 @ X5 ) ) ) ) ).

% bex_Un
thf(fact_1096_ball__Un,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
           => ( P2 @ X5 ) ) )
      = ( ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ A6 )
           => ( P2 @ X5 ) )
        & ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ B4 )
           => ( P2 @ X5 ) ) ) ) ).

% ball_Un
thf(fact_1097_Un__assoc,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ ( sup_su3837536599209510219_state @ A6 @ B4 ) @ C3 )
      = ( sup_su3837536599209510219_state @ A6 @ ( sup_su3837536599209510219_state @ B4 @ C3 ) ) ) ).

% Un_assoc
thf(fact_1098_Un__absorb,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ A6 )
      = A6 ) ).

% Un_absorb
thf(fact_1099_Un__commute,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] : ( sup_su3837536599209510219_state @ B5 @ A ) ) ) ).

% Un_commute
thf(fact_1100_Un__left__absorb,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ ( sup_su3837536599209510219_state @ A6 @ B4 ) )
      = ( sup_su3837536599209510219_state @ A6 @ B4 ) ) ).

% Un_left_absorb
thf(fact_1101_Un__left__commute,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ ( sup_su3837536599209510219_state @ B4 @ C3 ) )
      = ( sup_su3837536599209510219_state @ B4 @ ( sup_su3837536599209510219_state @ A6 @ C3 ) ) ) ).

% Un_left_commute
thf(fact_1102_Un__UNIV__right,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ top_to174962084833059535_state )
      = top_to174962084833059535_state ) ).

% Un_UNIV_right
thf(fact_1103_Un__UNIV__right,axiom,
    ! [A6: set_state] :
      ( ( sup_sup_set_state @ A6 @ top_top_set_state )
      = top_top_set_state ) ).

% Un_UNIV_right
thf(fact_1104_Un__UNIV__left,axiom,
    ! [B4: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ top_to174962084833059535_state @ B4 )
      = top_to174962084833059535_state ) ).

% Un_UNIV_left
thf(fact_1105_Un__UNIV__left,axiom,
    ! [B4: set_state] :
      ( ( sup_sup_set_state @ top_top_set_state @ B4 )
      = top_top_set_state ) ).

% Un_UNIV_left
thf(fact_1106_Un__empty__right,axiom,
    ! [A6: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ A6 @ bot_bo6430881413863817907_state )
      = A6 ) ).

% Un_empty_right
thf(fact_1107_Un__empty__right,axiom,
    ! [A6: set_state] :
      ( ( sup_sup_set_state @ A6 @ bot_bot_set_state )
      = A6 ) ).

% Un_empty_right
thf(fact_1108_Un__empty__left,axiom,
    ! [B4: set_Pr4231240917283394591_state] :
      ( ( sup_su3837536599209510219_state @ bot_bo6430881413863817907_state @ B4 )
      = B4 ) ).

% Un_empty_left
thf(fact_1109_Un__empty__left,axiom,
    ! [B4: set_state] :
      ( ( sup_sup_set_state @ bot_bot_set_state @ B4 )
      = B4 ) ).

% Un_empty_left
thf(fact_1110_singleton__Un__iff,axiom,
    ! [X2: produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state )
        = ( sup_su3837536599209510219_state @ A6 @ B4 ) )
      = ( ( ( A6 = bot_bo6430881413863817907_state )
          & ( B4
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) ) )
        | ( ( A6
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) )
          & ( B4 = bot_bo6430881413863817907_state ) )
        | ( ( A6
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) )
          & ( B4
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1111_singleton__Un__iff,axiom,
    ! [X2: state,A6: set_state,B4: set_state] :
      ( ( ( insert_state @ X2 @ bot_bot_set_state )
        = ( sup_sup_set_state @ A6 @ B4 ) )
      = ( ( ( A6 = bot_bot_set_state )
          & ( B4
            = ( insert_state @ X2 @ bot_bot_set_state ) ) )
        | ( ( A6
            = ( insert_state @ X2 @ bot_bot_set_state ) )
          & ( B4 = bot_bot_set_state ) )
        | ( ( A6
            = ( insert_state @ X2 @ bot_bot_set_state ) )
          & ( B4
            = ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1112_Un__singleton__iff,axiom,
    ! [A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,X2: produc7272280185086996969_state] :
      ( ( ( sup_su3837536599209510219_state @ A6 @ B4 )
        = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) )
      = ( ( ( A6 = bot_bo6430881413863817907_state )
          & ( B4
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) ) )
        | ( ( A6
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) )
          & ( B4 = bot_bo6430881413863817907_state ) )
        | ( ( A6
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) )
          & ( B4
            = ( insert175804457004744729_state @ X2 @ bot_bo6430881413863817907_state ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1113_Un__singleton__iff,axiom,
    ! [A6: set_state,B4: set_state,X2: state] :
      ( ( ( sup_sup_set_state @ A6 @ B4 )
        = ( insert_state @ X2 @ bot_bot_set_state ) )
      = ( ( ( A6 = bot_bot_set_state )
          & ( B4
            = ( insert_state @ X2 @ bot_bot_set_state ) ) )
        | ( ( A6
            = ( insert_state @ X2 @ bot_bot_set_state ) )
          & ( B4 = bot_bot_set_state ) )
        | ( ( A6
            = ( insert_state @ X2 @ bot_bot_set_state ) )
          & ( B4
            = ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1114_insert__is__Un,axiom,
    ( insert175804457004744729_state
    = ( ^ [A2: produc7272280185086996969_state] : ( sup_su3837536599209510219_state @ ( insert175804457004744729_state @ A2 @ bot_bo6430881413863817907_state ) ) ) ) ).

% insert_is_Un
thf(fact_1115_insert__is__Un,axiom,
    ( insert_state
    = ( ^ [A2: state] : ( sup_sup_set_state @ ( insert_state @ A2 @ bot_bot_set_state ) ) ) ) ).

% insert_is_Un
thf(fact_1116_PartialSA_Osat_Osimps_I3_J,axiom,
    ! [A6: state > $o,Phi: state] :
      ( ( package_sat_state @ plus @ ( aSem_state @ A6 ) @ Phi )
      = ( A6 @ Phi ) ) ).

% PartialSA.sat.simps(3)
thf(fact_1117_PartialSA_Osat_Ocases,axiom,
    ! [X2: produc2756261550280135502_state] :
      ( ! [A11: aassertion_state,B7: aassertion_state,Phi5: state] :
          ( X2
         != ( produc6654088501289988998_state @ ( aStar_state @ A11 @ B7 ) @ Phi5 ) )
     => ( ! [B6: state > $o,A11: aassertion_state,Phi5: state] :
            ( X2
           != ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A11 ) @ Phi5 ) )
       => ~ ! [A11: state > $o,Phi5: state] :
              ( X2
             != ( produc6654088501289988998_state @ ( aSem_state @ A11 ) @ Phi5 ) ) ) ) ).

% PartialSA.sat.cases
thf(fact_1118_PartialSA_Owf__assertion_Ocases,axiom,
    ! [X2: aassertion_state] :
      ( ! [A11: aassertion_state,B7: aassertion_state] :
          ( X2
         != ( aStar_state @ A11 @ B7 ) )
     => ( ! [B6: state > $o,A11: aassertion_state] :
            ( X2
           != ( aImp_state @ B6 @ A11 ) )
       => ~ ! [A11: state > $o] :
              ( X2
             != ( aSem_state @ A11 ) ) ) ) ).

% PartialSA.wf_assertion.cases
thf(fact_1119_package__logic_Osat_Osimps_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: state > $o,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aSem_state @ A6 ) @ Phi )
        = ( A6 @ Phi ) ) ) ).

% package_logic.sat.simps(3)
thf(fact_1120_aassertion_Oexhaust,axiom,
    ! [Y: aassertion_state] :
      ( ! [X112: aassertion_state,X122: aassertion_state] :
          ( Y
         != ( aStar_state @ X112 @ X122 ) )
     => ( ! [X212: state > $o,X223: aassertion_state] :
            ( Y
           != ( aImp_state @ X212 @ X223 ) )
       => ~ ! [X33: state > $o] :
              ( Y
             != ( aSem_state @ X33 ) ) ) ) ).

% aassertion.exhaust
thf(fact_1121_package__logic_Owf__assertion_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( X2
           != ( aStar_state @ A11 @ B7 ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( X2
             != ( aImp_state @ B6 @ A11 ) )
         => ~ ! [A11: state > $o] :
                ( X2
               != ( aSem_state @ A11 ) ) ) ) ) ).

% package_logic.wf_assertion.cases
thf(fact_1122_package__logic_Osat_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: produc2756261550280135502_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A11: aassertion_state,B7: aassertion_state,Phi5: state] :
            ( X2
           != ( produc6654088501289988998_state @ ( aStar_state @ A11 @ B7 ) @ Phi5 ) )
       => ( ! [B6: state > $o,A11: aassertion_state,Phi5: state] :
              ( X2
             != ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A11 ) @ Phi5 ) )
         => ~ ! [A11: state > $o,Phi5: state] :
                ( X2
               != ( produc6654088501289988998_state @ ( aSem_state @ A11 ) @ Phi5 ) ) ) ) ) ).

% package_logic.sat.cases
thf(fact_1123_package__logic_Owf__assertion_Osimps_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ ( aSem_state @ A6 ) )
        = ( packag2456304381420842418_state @ Plus @ A6 ) ) ) ).

% package_logic.wf_assertion.simps(3)
thf(fact_1124_PartialSA_Owf__assertion_Osimps_I3_J,axiom,
    ! [A6: state > $o] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aSem_state @ A6 ) )
      = ( packag2456304381420842418_state @ plus @ A6 ) ) ).

% PartialSA.wf_assertion.simps(3)
thf(fact_1125_PartialSA_Ovalid__package__set__def,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
      = ( ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A2: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,T4: state > state] :
                      ( ( defined @ A2 @ U6 )
                      & ( greater @ ( core @ A2 ) @ ( core @ U6 ) )
                      & ( packag4817583915586052229_state @ plus @ unit @ T4 )
                      & ( greater @ A2 @ ( core @ ( T4 @ F ) ) ) ) )
              @ X5 ) ) ) ) ).

% PartialSA.valid_package_set_def
thf(fact_1126_package__logic_Opure__remains__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr523392378426063460_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag9013619817833129428_state @ Plus @ S2 )
        = ( ! [X5: produc4357056439811976324_state] :
              ( ( member5752234768399382829_state @ X5 @ S2 )
             => ( produc8801812494870056711tate_o
                @ ^ [A2: state] :
                    ( produc1745419677418529872tate_o
                    @ ^ [U6: state,P5: produc3882902684156697774_state] : ( sep_pure_state @ Plus @ A2 ) )
                @ X5 ) ) ) ) ) ).

% package_logic.pure_remains_def
thf(fact_1127_package__logic_Opure__remains__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag4152378406607043437_state @ Plus @ S2 )
        = ( ! [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ S2 )
             => ( produc1745419677418529872tate_o
                @ ^ [A2: state] :
                    ( produc3645877548210629341tate_o
                    @ ^ [U6: state,P5: state > state] : ( sep_pure_state @ Plus @ A2 ) )
                @ X5 ) ) ) ) ) ).

% package_logic.pure_remains_def
thf(fact_1128_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr523392378426063460_state] :
      ( ( packag9013619817833129428_state @ plus @ S2 )
      = ( ! [X5: produc4357056439811976324_state] :
            ( ( member5752234768399382829_state @ X5 @ S2 )
           => ( produc8801812494870056711tate_o
              @ ^ [A2: state] :
                  ( produc1745419677418529872tate_o
                  @ ^ [U6: state,P5: produc3882902684156697774_state] : ( sep_pure_state @ plus @ A2 ) )
              @ X5 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_1129_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr4231240917283394591_state] :
      ( ( packag4152378406607043437_state @ plus @ S2 )
      = ( ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A2: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,P5: state > state] : ( sep_pure_state @ plus @ A2 ) )
              @ X5 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_1130_PartialSA_Osat_Oelims_I1_J,axiom,
    ! [X2: aassertion_state,Xa2: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X2 @ Xa2 )
        = Y )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ( Y
              = ( ~ ? [A2: state,B: state] :
                      ( ( ( some_state @ Xa2 )
                        = ( plus @ A2 @ B ) )
                      & ( package_sat_state @ plus @ A11 @ A2 )
                      & ( package_sat_state @ plus @ B7 @ B ) ) ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ( Y
                = ( ~ ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A11 @ Xa2 ) ) ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ( Y
                  = ( ~ ( A11 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.elims(1)
thf(fact_1131_PartialSA_Osat_Oelims_I2_J,axiom,
    ! [X2: aassertion_state,Xa2: state] :
      ( ( package_sat_state @ plus @ X2 @ Xa2 )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ~ ? [A7: state,B6: state] :
                  ( ( ( some_state @ Xa2 )
                    = ( plus @ A7 @ B6 ) )
                  & ( package_sat_state @ plus @ A11 @ A7 )
                  & ( package_sat_state @ plus @ B7 @ B6 ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ~ ( ( B6 @ Xa2 )
                 => ( package_sat_state @ plus @ A11 @ Xa2 ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ~ ( A11 @ Xa2 ) ) ) ) ) ).

% PartialSA.sat.elims(2)
thf(fact_1132_PartialSA_Osat_Oelims_I3_J,axiom,
    ! [X2: aassertion_state,Xa2: state] :
      ( ~ ( package_sat_state @ plus @ X2 @ Xa2 )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ? [A5: state,B9: state] :
                ( ( ( some_state @ Xa2 )
                  = ( plus @ A5 @ B9 ) )
                & ( package_sat_state @ plus @ A11 @ A5 )
                & ( package_sat_state @ plus @ B7 @ B9 ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ( ( B6 @ Xa2 )
               => ( package_sat_state @ plus @ A11 @ Xa2 ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ( A11 @ Xa2 ) ) ) ) ) ).

% PartialSA.sat.elims(3)
thf(fact_1133_package__logic_Osat_Oelims_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X2: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_val @ Plus @ X2 @ Xa2 )
       => ( ! [A11: aassertion_val,B7: aassertion_val] :
              ( ( X2
                = ( aStar_val @ A11 @ B7 ) )
             => ? [A5: val,B9: val] :
                  ( ( ( some_val @ Xa2 )
                    = ( Plus @ A5 @ B9 ) )
                  & ( package_sat_val @ Plus @ A11 @ A5 )
                  & ( package_sat_val @ Plus @ B7 @ B9 ) ) )
         => ( ! [B6: val > $o,A11: aassertion_val] :
                ( ( X2
                  = ( aImp_val @ B6 @ A11 ) )
               => ( ( B6 @ Xa2 )
                 => ( package_sat_val @ Plus @ A11 @ Xa2 ) ) )
           => ~ ! [A11: val > $o] :
                  ( ( X2
                    = ( aSem_val @ A11 ) )
                 => ( A11 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(3)
thf(fact_1134_package__logic_Osat_Oelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_state @ Plus @ X2 @ Xa2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ? [A5: state,B9: state] :
                  ( ( ( some_state @ Xa2 )
                    = ( Plus @ A5 @ B9 ) )
                  & ( package_sat_state @ Plus @ A11 @ A5 )
                  & ( package_sat_state @ Plus @ B7 @ B9 ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( B6 @ Xa2 )
                 => ( package_sat_state @ Plus @ A11 @ Xa2 ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( A11 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(3)
thf(fact_1135_package__logic_Osat_Oelims_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X2: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ X2 @ Xa2 )
       => ( ! [A11: aassertion_val,B7: aassertion_val] :
              ( ( X2
                = ( aStar_val @ A11 @ B7 ) )
             => ~ ? [A7: val,B6: val] :
                    ( ( ( some_val @ Xa2 )
                      = ( Plus @ A7 @ B6 ) )
                    & ( package_sat_val @ Plus @ A11 @ A7 )
                    & ( package_sat_val @ Plus @ B7 @ B6 ) ) )
         => ( ! [B6: val > $o,A11: aassertion_val] :
                ( ( X2
                  = ( aImp_val @ B6 @ A11 ) )
               => ~ ( ( B6 @ Xa2 )
                   => ( package_sat_val @ Plus @ A11 @ Xa2 ) ) )
           => ~ ! [A11: val > $o] :
                  ( ( X2
                    = ( aSem_val @ A11 ) )
                 => ~ ( A11 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(2)
thf(fact_1136_package__logic_Osat_Oelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ X2 @ Xa2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ~ ? [A7: state,B6: state] :
                    ( ( ( some_state @ Xa2 )
                      = ( Plus @ A7 @ B6 ) )
                    & ( package_sat_state @ Plus @ A11 @ A7 )
                    & ( package_sat_state @ Plus @ B7 @ B6 ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ~ ( ( B6 @ Xa2 )
                   => ( package_sat_state @ Plus @ A11 @ Xa2 ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ~ ( A11 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(2)
thf(fact_1137_package__logic_Osat_Oelims_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X2: aassertion_val,Xa2: val,Y: $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_val @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ! [A11: aassertion_val,B7: aassertion_val] :
              ( ( X2
                = ( aStar_val @ A11 @ B7 ) )
             => ( Y
                = ( ~ ? [A2: val,B: val] :
                        ( ( ( some_val @ Xa2 )
                          = ( Plus @ A2 @ B ) )
                        & ( package_sat_val @ Plus @ A11 @ A2 )
                        & ( package_sat_val @ Plus @ B7 @ B ) ) ) ) )
         => ( ! [B6: val > $o,A11: aassertion_val] :
                ( ( X2
                  = ( aImp_val @ B6 @ A11 ) )
               => ( Y
                  = ( ~ ( ( B6 @ Xa2 )
                       => ( package_sat_val @ Plus @ A11 @ Xa2 ) ) ) ) )
           => ~ ! [A11: val > $o] :
                  ( ( X2
                    = ( aSem_val @ A11 ) )
                 => ( Y
                    = ( ~ ( A11 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.elims(1)
thf(fact_1138_package__logic_Osat_Oelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state,Xa2: state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_state @ Plus @ X2 @ Xa2 )
          = Y )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( Y
                = ( ~ ? [A2: state,B: state] :
                        ( ( ( some_state @ Xa2 )
                          = ( Plus @ A2 @ B ) )
                        & ( package_sat_state @ Plus @ A11 @ A2 )
                        & ( package_sat_state @ Plus @ B7 @ B ) ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( Y
                  = ( ~ ( ( B6 @ Xa2 )
                       => ( package_sat_state @ Plus @ A11 @ Xa2 ) ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( Y
                    = ( ~ ( A11 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.elims(1)
thf(fact_1139_PartialSA_OASem,axiom,
    ! [S2: set_Pr4231240917283394591_state,Pc: state > $o,Witness3: produc7272280185086996969_state > state,B4: state > $o,S3: set_Pr4231240917283394591_state,Phi: state,F: state] :
      ( ! [A7: state,U: state,T3: state > state,B6: state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( Pc @ A7 )
           => ( ( B6
                = ( Witness3 @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) ) )
             => ( ( greater @ A7 @ B6 )
                & ( B4 @ B6 ) ) ) ) )
     => ( ( S3
          = ( sup_su3837536599209510219_state
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A2: state,U6: state,T4: state > state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                  & ~ ( Pc @ A2 ) ) )
            @ ( collec906845016635587262_state
              @ ^ [Uu3: produc7272280185086996969_state] :
                ? [A2: state,U6: state,T4: state > state,B: state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ ( minus @ A2 @ B ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B ) ) @ T4 ) ) )
                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                  & ( Pc @ A2 )
                  & ( B
                    = ( Witness3 @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) ) ) )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aSem_state @ B4 ) @ Phi @ F @ S3 ) ) ) ).

% PartialSA.ASem
thf(fact_1140_PartialSA_Opackage__rhs__connection__def,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A6: aassertion_state,Phi2: state,F6: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi2 @ F6 @ S3 )
      = ( ( greater @ F6 @ F )
        & ( defined @ Phi @ F )
        & ( ( plus @ Phi @ F )
          = ( plus @ Phi2 @ F6 ) )
        & ( stable @ F6 )
        & ! [X5: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X5 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A2: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,T4: state > state] :
                    ? [Au3: state] :
                      ( ( ( some_state @ Au3 )
                        = ( plus @ A2 @ U6 ) )
                      & ( ( defined @ Au3 @ ( minus @ ( T4 @ F6 ) @ ( T4 @ F ) ) )
                       => ? [A13: state,U8: state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A13 @ ( produc8632743443909064678_state @ U8 @ T4 ) ) @ S3 )
                            & ( greater @ ( core @ A13 ) @ ( core @ A2 ) )
                            & ( ( plus @ Au3 @ ( minus @ ( T4 @ F6 ) @ ( T4 @ F ) ) )
                              = ( plus @ A13 @ U8 ) )
                            & ( greater @ U8 @ U6 )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A6 @ A13 @ U8 @ U6 ) ) ) ) )
              @ X5 ) ) ) ) ).

% PartialSA.package_rhs_connection_def
thf(fact_1141_package__logic_Owf__assertion_Oelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( packag7298478212905792770_state @ Plus @ Core @ X2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( packag7298478212905792770_state @ Plus @ Core @ A11 )
                & ( packag7298478212905792770_state @ Plus @ Core @ B7 ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                  & ( packag7298478212905792770_state @ Plus @ Core @ A11 ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( packag2456304381420842418_state @ Plus @ A11 ) ) ) ) ) ) ).

% package_logic.wf_assertion.elims(3)
thf(fact_1142_package__logic_Owf__assertion_Oelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ X2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ~ ( ( packag7298478212905792770_state @ Plus @ Core @ A11 )
                  & ( packag7298478212905792770_state @ Plus @ Core @ B7 ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ~ ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                    & ( packag7298478212905792770_state @ Plus @ Core @ A11 ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ~ ( packag2456304381420842418_state @ Plus @ A11 ) ) ) ) ) ) ).

% package_logic.wf_assertion.elims(2)
thf(fact_1143_package__logic_Owf__assertion_Oelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X2: aassertion_state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( packag7298478212905792770_state @ Plus @ Core @ X2 )
          = Y )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( Y
                = ( ~ ( ( packag7298478212905792770_state @ Plus @ Core @ A11 )
                      & ( packag7298478212905792770_state @ Plus @ Core @ B7 ) ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( Y
                  = ( ~ ( ( packag6595153354952283300_state @ Plus @ Core @ B6 )
                        & ( packag7298478212905792770_state @ Plus @ Core @ A11 ) ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( Y
                    = ( ~ ( packag2456304381420842418_state @ Plus @ A11 ) ) ) ) ) ) ) ) ).

% package_logic.wf_assertion.elims(1)
thf(fact_1144_PartialSA_Owf__assertion_Oelims_I1_J,axiom,
    ! [X2: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X2 )
        = Y )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ( Y
              = ( ~ ( ( packag7298478212905792770_state @ plus @ core @ A11 )
                    & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ( Y
                = ( ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ( Y
                  = ( ~ ( packag2456304381420842418_state @ plus @ A11 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(1)
thf(fact_1145_PartialSA_Owf__assertion_Oelims_I2_J,axiom,
    ! [X2: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X2 )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ~ ( ( packag7298478212905792770_state @ plus @ core @ A11 )
                & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                  & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ~ ( packag2456304381420842418_state @ plus @ A11 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(2)
thf(fact_1146_PartialSA_Owf__assertion_Oelims_I3_J,axiom,
    ! [X2: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X2 )
     => ( ! [A11: aassertion_state,B7: aassertion_state] :
            ( ( X2
              = ( aStar_state @ A11 @ B7 ) )
           => ( ( packag7298478212905792770_state @ plus @ core @ A11 )
              & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) )
       => ( ! [B6: state > $o,A11: aassertion_state] :
              ( ( X2
                = ( aImp_state @ B6 @ A11 ) )
             => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) )
         => ~ ! [A11: state > $o] :
                ( ( X2
                  = ( aSem_state @ A11 ) )
               => ( packag2456304381420842418_state @ plus @ A11 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(3)
thf(fact_1147_PartialSA_Ocompleteness__aux,axiom,
    ! [S2: set_Pr4231240917283394591_state,F1: state > state > ( state > state ) > state,F2: state > state > ( state > state ) > state,Pc: state > $o,A6: aassertion_state,F: state,Phi: state] :
      ( ! [A7: state,U: state,T3: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
         => ( ( greater @ ( core @ ( F1 @ A7 @ U @ T3 ) ) @ ( core @ A7 ) )
            & ( ( some_state @ A7 )
              = ( plus @ ( F1 @ A7 @ U @ T3 ) @ ( F2 @ A7 @ U @ T3 ) ) )
            & ( ( Pc @ ( core @ A7 ) )
             => ( package_sat_state @ plus @ A6 @ ( the_state @ ( plus @ ( core @ A7 ) @ ( F1 @ A7 @ U @ T3 ) ) ) ) ) ) )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A6 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( ( stable @ F )
                & ( defined @ Phi @ F ) )
             => ? [S6: set_Pr4231240917283394591_state] :
                  ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A6 @ Phi @ F @ S6 )
                  & ! [X3: produc7272280185086996969_state] :
                      ( ( member7461423308196221312_state @ X3 @ S6 )
                     => ( produc1745419677418529872tate_o
                        @ ^ [A13: state] :
                            ( produc3645877548210629341tate_o
                            @ ^ [U8: state,T4: state > state] :
                              ? [A2: state,U6: state] :
                                ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                                & ( greater @ A13 @ ( F2 @ A2 @ U6 @ T4 ) )
                                & ( ( core @ A13 )
                                  = ( core @ A2 ) ) ) )
                        @ X3 ) ) ) ) ) ) ) ) ).

% PartialSA.completeness_aux
thf(fact_1148_le__sup__iff,axiom,
    ! [X2: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ X2 @ Y ) @ Z )
      = ( ( ord_le4032880777312351359_state @ X2 @ Z )
        & ( ord_le4032880777312351359_state @ Y @ Z ) ) ) ).

% le_sup_iff
thf(fact_1149_le__sup__iff,axiom,
    ! [X2: set_state,Y: set_state,Z: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X2 @ Y ) @ Z )
      = ( ( ord_le2494988322063910608_state @ X2 @ Z )
        & ( ord_le2494988322063910608_state @ Y @ Z ) ) ) ).

% le_sup_iff
thf(fact_1150_sup_Obounded__iff,axiom,
    ! [B2: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,A3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B2 @ C ) @ A3 )
      = ( ( ord_le4032880777312351359_state @ B2 @ A3 )
        & ( ord_le4032880777312351359_state @ C @ A3 ) ) ) ).

% sup.bounded_iff
thf(fact_1151_sup_Obounded__iff,axiom,
    ! [B2: set_state,C: set_state,A3: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B2 @ C ) @ A3 )
      = ( ( ord_le2494988322063910608_state @ B2 @ A3 )
        & ( ord_le2494988322063910608_state @ C @ A3 ) ) ) ).

% sup.bounded_iff
thf(fact_1152_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A1: val,A22: val,A32: set_Pr4723104092121316667al_val,A42: val > $o,A52: aassertion_val,A62: val,A72: val,A82: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A11: aassertion_val,Phi6: val,F8: val,S6: set_Pr4723104092121316667al_val,B7: aassertion_val] :
              ( ( A52
                = ( aStar_val @ A11 @ B7 ) )
             => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ A42 @ A11 @ Phi6 @ F8 @ S6 )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi6 @ F8 @ S6 @ A42 @ B7 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: val > $o,A11: aassertion_val] :
                ( ( A52
                  = ( aImp_val @ B6 @ A11 ) )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ ( packag6750194596558674946nj_val @ A42 @ B6 ) @ A11 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness: produc2072440392815185925al_val > val,B7: val > $o] :
                  ( ( A52
                    = ( aSem_val @ B7 ) )
                 => ( ( A62 = A1 )
                   => ( ( A72 = A22 )
                     => ( ! [A5: val,U7: val,T5: val > val] :
                            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A5 @ ( produc303288909735261391al_val @ U7 @ T5 ) ) @ A32 )
                           => ( ( A42 @ A5 )
                             => ( ( sep_greater_val @ Plus @ A5 @ ( Witness @ ( produc7187740677493149823al_val @ A5 @ ( produc303288909735261391al_val @ U7 @ T5 ) ) ) )
                                & ( B7 @ ( Witness @ ( produc7187740677493149823al_val @ A5 @ ( produc303288909735261391al_val @ U7 @ T5 ) ) ) ) ) ) )
                       => ( A82
                         != ( sup_su4800132526891881063al_val
                            @ ( collec8300311316619386842al_val
                              @ ^ [Uu3: produc2072440392815185925al_val] :
                                ? [A2: val,U6: val,T4: val > val] :
                                  ( ( Uu3
                                    = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                                  & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ A32 )
                                  & ~ ( A42 @ A2 ) ) )
                            @ ( collec8300311316619386842al_val
                              @ ^ [Uu3: produc2072440392815185925al_val] :
                                ? [A2: val,U6: val,T4: val > val] :
                                  ( ( Uu3
                                    = ( produc7187740677493149823al_val @ ( sep_minus_val @ Plus @ Core @ A2 @ ( Witness @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) ) ) @ ( produc303288909735261391al_val @ ( the_val @ ( Plus @ U6 @ ( Witness @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) ) ) ) @ T4 ) ) )
                                  & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ A32 )
                                  & ( A42 @ A2 ) ) ) ) ) ) ) ) )
             => ~ ! [Phi6: val,M3: val] :
                    ( ( ( some_val @ A1 )
                      = ( Plus @ Phi6 @ M3 ) )
                   => ! [F8: val,S6: set_Pr4723104092121316667al_val] :
                        ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi6 @ F8 @ S6 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M3 )
                         => ( ( ( some_val @ F8 )
                              = ( Plus @ A22 @ M3 ) )
                           => ( S6
                             != ( collec8300311316619386842al_val
                                @ ^ [Uu3: produc2072440392815185925al_val] :
                                  ? [A2: val,U6: val,T4: val > val,R2: val] :
                                    ( ( Uu3
                                      = ( produc7187740677493149823al_val @ R2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                                    & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ A32 )
                                    & ( ( some_val @ R2 )
                                      = ( Plus @ A2 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F8 ) @ ( T4 @ A22 ) ) ) )
                                    & ( sep_defined_val @ Plus @ R2 @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_1153_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A1: state,A22: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A11: aassertion_state,Phi6: state,F8: state,S6: set_Pr4231240917283394591_state,B7: aassertion_state] :
              ( ( A52
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ A42 @ A11 @ Phi6 @ F8 @ S6 )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi6 @ F8 @ S6 @ A42 @ B7 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( A52
                  = ( aImp_state @ B6 @ A11 ) )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A1 @ A22 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A11 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness: produc7272280185086996969_state > state,B7: state > $o] :
                  ( ( A52
                    = ( aSem_state @ B7 ) )
                 => ( ( A62 = A1 )
                   => ( ( A72 = A22 )
                     => ( ! [A5: state,U7: state,T5: state > state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) @ A32 )
                           => ( ( A42 @ A5 )
                             => ( ( sep_greater_state @ Plus @ A5 @ ( Witness @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) ) )
                                & ( B7 @ ( Witness @ ( produc5886875603596089627_state @ A5 @ ( produc8632743443909064678_state @ U7 @ T5 ) ) ) ) ) ) )
                       => ( A82
                         != ( sup_su3837536599209510219_state
                            @ ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A2: state,U6: state,T4: state > state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                  & ~ ( A42 @ A2 ) ) )
                            @ ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A2: state,U6: state,T4: state > state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ ( sep_minus_state @ Plus @ Core @ A2 @ ( Witness @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) @ ( produc8632743443909064678_state @ ( the_state @ ( Plus @ U6 @ ( Witness @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) @ T4 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                  & ( A42 @ A2 ) ) ) ) ) ) ) ) )
             => ~ ! [Phi6: state,M3: state] :
                    ( ( ( some_state @ A1 )
                      = ( Plus @ Phi6 @ M3 ) )
                   => ! [F8: state,S6: set_Pr4231240917283394591_state] :
                        ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi6 @ F8 @ S6 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M3 )
                         => ( ( ( some_state @ F8 )
                              = ( Plus @ A22 @ M3 ) )
                           => ( S6
                             != ( collec906845016635587262_state
                                @ ^ [Uu3: produc7272280185086996969_state] :
                                  ? [A2: state,U6: state,T4: state > state,R2: state] :
                                    ( ( Uu3
                                      = ( produc5886875603596089627_state @ R2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                    & ( ( some_state @ R2 )
                                      = ( Plus @ A2 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F8 ) @ ( T4 @ A22 ) ) ) )
                                    & ( sep_defined_state @ Plus @ R2 @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_1154_sup__set__def,axiom,
    ( sup_su1984960714304006370_state
    = ( ^ [A: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
          ( collec394671971739345689_state
          @ ( sup_su1130956725435522171tate_o
            @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ A )
            @ ^ [X5: produc3882902684156697774_state] : ( member6715010751053357271_state @ X5 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_1155_sup__set__def,axiom,
    ( sup_su7506060154676209150on_val
    = ( ^ [A: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
          ( collec7475294502966882545on_val
          @ ( sup_su3200866414790943751_val_o
            @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ A )
            @ ^ [X5: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X5 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_1156_sup__set__def,axiom,
    ( sup_sup_set_state
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ( sup_sup_state_o
            @ ^ [X5: state] : ( member_state @ X5 @ A )
            @ ^ [X5: state] : ( member_state @ X5 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_1157_sup__set__def,axiom,
    ( sup_su3837536599209510219_state
    = ( ^ [A: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( collec906845016635587262_state
          @ ( sup_su4345871077856951546tate_o
            @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ A )
            @ ^ [X5: produc7272280185086996969_state] : ( member7461423308196221312_state @ X5 @ B5 ) ) ) ) ) ).

% sup_set_def
thf(fact_1158_sep__algebra_Ogreater__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A3 @ B2 )
        = ( ? [C2: val] :
              ( ( some_val @ A3 )
              = ( Plus @ B2 @ C2 ) ) ) ) ) ).

% sep_algebra.greater_def
thf(fact_1159_sep__algebra_Ogreater__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
        = ( ? [C2: state] :
              ( ( some_state @ A3 )
              = ( Plus @ B2 @ C2 ) ) ) ) ) ).

% sep_algebra.greater_def
thf(fact_1160_sep__algebra_Oextract__core,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( some_val @ B2 )
            = ( Plus @ A3 @ X2 ) )
          & ( sep_greater_val @ Plus @ X2 @ ( Core @ B2 ) ) )
       => ( ( Core @ X2 )
          = ( Core @ B2 ) ) ) ) ).

% sep_algebra.extract_core
thf(fact_1161_sep__algebra_Oextract__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( some_state @ B2 )
            = ( Plus @ A3 @ X2 ) )
          & ( sep_greater_state @ Plus @ X2 @ ( Core @ B2 ) ) )
       => ( ( Core @ X2 )
          = ( Core @ B2 ) ) ) ) ).

% sep_algebra.extract_core
thf(fact_1162_sep__algebra_Ominus__exists,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ B2 @ A3 )
       => ? [X4: val] :
            ( ( ( some_val @ B2 )
              = ( Plus @ A3 @ X4 ) )
            & ( sep_greater_val @ Plus @ X4 @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.minus_exists
thf(fact_1163_sep__algebra_Ominus__exists,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ B2 @ A3 )
       => ? [X4: state] :
            ( ( ( some_state @ B2 )
              = ( Plus @ A3 @ X4 ) )
            & ( sep_greater_state @ Plus @ X4 @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.minus_exists
thf(fact_1164_sep__algebra_Ominus__unique,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val,X2: val,Y: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( some_val @ B2 )
            = ( Plus @ A3 @ X2 ) )
          & ( sep_greater_val @ Plus @ X2 @ ( Core @ B2 ) ) )
       => ( ( ( ( some_val @ B2 )
              = ( Plus @ A3 @ Y ) )
            & ( sep_greater_val @ Plus @ Y @ ( Core @ B2 ) ) )
         => ( X2 = Y ) ) ) ) ).

% sep_algebra.minus_unique
thf(fact_1165_sep__algebra_Ominus__unique,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state,X2: state,Y: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( some_state @ B2 )
            = ( Plus @ A3 @ X2 ) )
          & ( sep_greater_state @ Plus @ X2 @ ( Core @ B2 ) ) )
       => ( ( ( ( some_state @ B2 )
              = ( Plus @ A3 @ Y ) )
            & ( sep_greater_state @ Plus @ Y @ ( Core @ B2 ) ) )
         => ( X2 = Y ) ) ) ) ).

% sep_algebra.minus_unique
thf(fact_1166_sep__algebra_Ogreater__equiv,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A3 @ B2 )
        = ( ? [C2: val] :
              ( ( some_val @ A3 )
              = ( Plus @ C2 @ B2 ) ) ) ) ) ).

% sep_algebra.greater_equiv
thf(fact_1167_sep__algebra_Ogreater__equiv,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
        = ( ? [C2: state] :
              ( ( some_state @ A3 )
              = ( Plus @ C2 @ B2 ) ) ) ) ) ).

% sep_algebra.greater_equiv
thf(fact_1168_sep__algebra_Oaddition__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A4: val,A3: val,X: val,B2: val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A4 @ A3 )
       => ( ( ( some_val @ X )
            = ( Plus @ A4 @ B2 ) )
         => ( ( ( some_val @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( sep_greater_val @ Plus @ X @ X2 ) ) ) ) ) ).

% sep_algebra.addition_bigger
thf(fact_1169_sep__algebra_Oaddition__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A4: state,A3: state,X: state,B2: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A4 @ A3 )
       => ( ( ( some_state @ X )
            = ( Plus @ A4 @ B2 ) )
         => ( ( ( some_state @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( sep_greater_state @ Plus @ X @ X2 ) ) ) ) ) ).

% sep_algebra.addition_bigger
thf(fact_1170_sep__algebra_Osmaller__than__core,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Y: val,X2: val,Z: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ Y @ X2 )
       => ( ( ( some_val @ Z )
            = ( Plus @ X2 @ ( Core @ Y ) ) )
         => ( ( Core @ Z )
            = ( Core @ Y ) ) ) ) ) ).

% sep_algebra.smaller_than_core
thf(fact_1171_sep__algebra_Osmaller__than__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,X2: state,Z: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ X2 )
       => ( ( ( some_state @ Z )
            = ( Plus @ X2 @ ( Core @ Y ) ) )
         => ( ( Core @ Z )
            = ( Core @ Y ) ) ) ) ) ).

% sep_algebra.smaller_than_core
thf(fact_1172_sep__algebra_Obigger__sum__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,C: val,A3: val,B2: val,A4: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ C )
          = ( Plus @ A3 @ B2 ) )
       => ( ( sep_greater_val @ Plus @ A3 @ A4 )
         => ? [B3: val] :
              ( ( sep_greater_val @ Plus @ B3 @ B2 )
              & ( ( some_val @ C )
                = ( Plus @ A4 @ B3 ) ) ) ) ) ) ).

% sep_algebra.bigger_sum_smaller
thf(fact_1173_sep__algebra_Obigger__sum__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,C: state,A3: state,B2: state,A4: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ C )
          = ( Plus @ A3 @ B2 ) )
       => ( ( sep_greater_state @ Plus @ A3 @ A4 )
         => ? [B3: state] :
              ( ( sep_greater_state @ Plus @ B3 @ B2 )
              & ( ( some_state @ C )
                = ( Plus @ A4 @ B3 ) ) ) ) ) ) ).

% sep_algebra.bigger_sum_smaller
thf(fact_1174_greater__def,axiom,
    ( greater
    = ( sep_greater_state @ plus ) ) ).

% greater_def
thf(fact_1175_package__logic_Obigger__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,A3: val,B2: val,Phi2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ Phi )
          = ( Plus @ A3 @ B2 ) )
       => ( ( sep_greater_val @ Plus @ Phi2 @ Phi )
         => ? [B3: val] :
              ( ( sep_greater_val @ Plus @ B3 @ B2 )
              & ( ( some_val @ Phi2 )
                = ( Plus @ A3 @ B3 ) ) ) ) ) ) ).

% package_logic.bigger_sum
thf(fact_1176_package__logic_Obigger__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,A3: state,B2: state,Phi2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ Phi )
          = ( Plus @ A3 @ B2 ) )
       => ( ( sep_greater_state @ Plus @ Phi2 @ Phi )
         => ? [B3: state] :
              ( ( sep_greater_state @ Plus @ B3 @ B2 )
              & ( ( some_state @ Phi2 )
                = ( Plus @ A3 @ B3 ) ) ) ) ) ) ).

% package_logic.bigger_sum
thf(fact_1177_package__logic_Obigger__core__sum__defined,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,B2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ ( Core @ A3 ) @ B2 )
       => ( ( some_val @ A3 )
          = ( Plus @ A3 @ B2 ) ) ) ) ).

% package_logic.bigger_core_sum_defined
thf(fact_1178_package__logic_Obigger__core__sum__defined,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ ( Core @ A3 ) @ B2 )
       => ( ( some_state @ A3 )
          = ( Plus @ A3 @ B2 ) ) ) ) ).

% package_logic.bigger_core_sum_defined
thf(fact_1179_package__logic_Ogreater__than__sum__exists,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,B2: val,B1: val,B22: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A3 @ B2 )
       => ( ( ( some_val @ B2 )
            = ( Plus @ B1 @ B22 ) )
         => ? [R3: val] :
              ( ( ( some_val @ A3 )
                = ( Plus @ R3 @ B22 ) )
              & ( sep_greater_val @ Plus @ ( Core @ R3 ) @ ( Core @ A3 ) )
              & ( sep_greater_val @ Plus @ R3 @ B1 ) ) ) ) ) ).

% package_logic.greater_than_sum_exists
thf(fact_1180_package__logic_Ogreater__than__sum__exists,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state,B1: state,B22: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
       => ( ( ( some_state @ B2 )
            = ( Plus @ B1 @ B22 ) )
         => ? [R3: state] :
              ( ( ( some_state @ A3 )
                = ( Plus @ R3 @ B22 ) )
              & ( sep_greater_state @ Plus @ ( Core @ R3 ) @ ( Core @ A3 ) )
              & ( sep_greater_state @ Plus @ R3 @ B1 ) ) ) ) ) ).

% package_logic.greater_than_sum_exists
thf(fact_1181_sep__algebra_Osucc__refl,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( sep_greater_state @ Plus @ A3 @ A3 ) ) ).

% sep_algebra.succ_refl
thf(fact_1182_sep__algebra_Osucc__trans,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
       => ( ( sep_greater_state @ Plus @ B2 @ C )
         => ( sep_greater_state @ Plus @ A3 @ C ) ) ) ) ).

% sep_algebra.succ_trans
thf(fact_1183_sep__algebra_Osucc__antisym,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
       => ( ( sep_greater_state @ Plus @ B2 @ A3 )
         => ( A3 = B2 ) ) ) ) ).

% sep_algebra.succ_antisym
thf(fact_1184_sep__algebra_Ogreater_Ocong,axiom,
    sep_greater_state = sep_greater_state ).

% sep_algebra.greater.cong
thf(fact_1185_package__logic_Ounit__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( sep_greater_state @ Plus @ Phi @ Unit ) ) ).

% package_logic.unit_smaller
thf(fact_1186_package__logic_Ocore__mono,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
       => ( sep_greater_state @ Plus @ ( Core @ A3 ) @ ( Core @ B2 ) ) ) ) ).

% package_logic.core_mono
thf(fact_1187_sep__algebra_Ogreater__minus__trans,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,X2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ X2 )
       => ( ( sep_greater_state @ Plus @ X2 @ A3 )
         => ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ Y @ A3 ) @ ( sep_minus_state @ Plus @ Core @ X2 @ A3 ) ) ) ) ) ).

% sep_algebra.greater_minus_trans
thf(fact_1188_sep__algebra_Ominus__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ X2 @ A3 )
       => ( sep_greater_state @ Plus @ X2 @ ( sep_minus_state @ Plus @ Core @ X2 @ A3 ) ) ) ) ).

% sep_algebra.minus_smaller
thf(fact_1189_sep__algebra_Ominus__default,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ~ ( sep_greater_state @ Plus @ B2 @ A3 )
       => ( ( sep_minus_state @ Plus @ Core @ B2 @ A3 )
          = B2 ) ) ) ).

% sep_algebra.minus_default
thf(fact_1190_sep__algebra_Opure__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_pure_state @ Plus @ A3 )
       => ( ( sep_greater_state @ Plus @ A3 @ B2 )
         => ( sep_pure_state @ Plus @ B2 ) ) ) ) ).

% sep_algebra.pure_smaller
thf(fact_1191_sep__algebra_Osmaller__compatible__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ X2 )
       => ( sep_defined_state @ Plus @ X2 @ ( Core @ Y ) ) ) ) ).

% sep_algebra.smaller_compatible_core
thf(fact_1192_sep__algebra_Osmaller__compatible,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A4: state,B2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_defined_state @ Plus @ A4 @ B2 )
       => ( ( sep_greater_state @ Plus @ A4 @ A3 )
         => ( sep_defined_state @ Plus @ A3 @ B2 ) ) ) ) ).

% sep_algebra.smaller_compatible
thf(fact_1193_sep__algebra_Omax__projection__prop__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
        = ( ! [X5: state] :
              ( ( sep_greater_state @ Plus @ X5 @ ( F @ X5 ) )
              & ( P2 @ ( F @ X5 ) )
              & ! [P5: state] :
                  ( ( ( P2 @ P5 )
                    & ( sep_greater_state @ Plus @ X5 @ P5 ) )
                 => ( sep_greater_state @ Plus @ ( F @ X5 ) @ P5 ) ) ) ) ) ) ).

% sep_algebra.max_projection_prop_def
thf(fact_1194_sep__algebra_Omax__projection__propI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,F: state > state,P2: state > $o] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [X4: state] : ( sep_greater_state @ Plus @ X4 @ ( F @ X4 ) )
       => ( ! [X4: state] : ( P2 @ ( F @ X4 ) )
         => ( ! [X4: state,P6: state] :
                ( ( ( P2 @ P6 )
                  & ( sep_greater_state @ Plus @ X4 @ P6 ) )
               => ( sep_greater_state @ Plus @ ( F @ X4 ) @ P6 ) )
           => ( sep_ma8214210560313151521_state @ Plus @ P2 @ F ) ) ) ) ) ).

% sep_algebra.max_projection_propI
thf(fact_1195_sep__algebra_Ompp__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( sep_greater_state @ Plus @ X2 @ ( F @ X2 ) ) ) ) ).

% sep_algebra.mpp_smaller
thf(fact_1196_sep__algebra_Ompp__mono,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( ( sep_greater_state @ Plus @ A3 @ B2 )
         => ( sep_greater_state @ Plus @ ( F @ A3 ) @ ( F @ B2 ) ) ) ) ) ).

% sep_algebra.mpp_mono
thf(fact_1197_sep__algebra_OmppI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,A3: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( ( sep_greater_state @ Plus @ A3 @ X2 )
         => ( ( P2 @ X2 )
           => ( ( sep_greater_state @ Plus @ X2 @ ( F @ A3 ) )
             => ( X2
                = ( F @ A3 ) ) ) ) ) ) ) ).

% sep_algebra.mppI
thf(fact_1198_sep__algebra_Omax__projection__propE_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o,F: state > state,P: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_ma8214210560313151521_state @ Plus @ P2 @ F )
       => ( ( ( P2 @ P )
            & ( sep_greater_state @ Plus @ X2 @ P ) )
         => ( sep_greater_state @ Plus @ ( F @ X2 ) @ P ) ) ) ) ).

% sep_algebra.max_projection_propE(3)
thf(fact_1199_sep__algebra_Oup__closedI,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ! [Phi6: produc7272280185086996969_state,Phi5: produc7272280185086996969_state] :
            ( ( ( sep_gr1233117237951779860_state @ Plus @ Phi6 @ Phi5 )
              & ( member7461423308196221312_state @ Phi5 @ A6 ) )
           => ( member7461423308196221312_state @ Phi6 @ A6 ) )
       => ( sep_up5671800011468993857_state @ Plus @ A6 ) ) ) ).

% sep_algebra.up_closedI
thf(fact_1200_sep__algebra_Oup__closedI,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ! [Phi6: produc9003781588162623004on_val,Phi5: produc9003781588162623004on_val] :
            ( ( ( sep_gr8124549141218502215on_val @ Plus @ Phi6 @ Phi5 )
              & ( member2879030624002546611on_val @ Phi5 @ A6 ) )
           => ( member2879030624002546611on_val @ Phi6 @ A6 ) )
       => ( sep_up3467202520194525556on_val @ Plus @ A6 ) ) ) ).

% sep_algebra.up_closedI
thf(fact_1201_sep__algebra_Oup__closedI,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ! [Phi6: produc3882902684156697774_state,Phi5: produc3882902684156697774_state] :
            ( ( ( sep_gr6114829331755084611_state @ Plus @ Phi6 @ Phi5 )
              & ( member6715010751053357271_state @ Phi5 @ A6 ) )
           => ( member6715010751053357271_state @ Phi6 @ A6 ) )
       => ( sep_up2356903840689987414_state @ Plus @ A6 ) ) ) ).

% sep_algebra.up_closedI
thf(fact_1202_sep__algebra_Oup__closedI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [Phi6: state,Phi5: state] :
            ( ( ( sep_greater_state @ Plus @ Phi6 @ Phi5 )
              & ( member_state @ Phi5 @ A6 ) )
           => ( member_state @ Phi6 @ A6 ) )
       => ( sep_up_closed_state @ Plus @ A6 ) ) ) ).

% sep_algebra.up_closedI
thf(fact_1203_sep__algebra_Oup__closed__def,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( sep_up5671800011468993857_state @ Plus @ A6 )
        = ( ! [Phi3: produc7272280185086996969_state] :
              ( ? [X5: produc7272280185086996969_state] :
                  ( ( member7461423308196221312_state @ X5 @ A6 )
                  & ( sep_gr1233117237951779860_state @ Plus @ Phi3 @ X5 ) )
             => ( member7461423308196221312_state @ Phi3 @ A6 ) ) ) ) ) ).

% sep_algebra.up_closed_def
thf(fact_1204_sep__algebra_Oup__closed__def,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( sep_up3467202520194525556on_val @ Plus @ A6 )
        = ( ! [Phi3: produc9003781588162623004on_val] :
              ( ? [X5: produc9003781588162623004on_val] :
                  ( ( member2879030624002546611on_val @ X5 @ A6 )
                  & ( sep_gr8124549141218502215on_val @ Plus @ Phi3 @ X5 ) )
             => ( member2879030624002546611on_val @ Phi3 @ A6 ) ) ) ) ) ).

% sep_algebra.up_closed_def
thf(fact_1205_sep__algebra_Oup__closed__def,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( sep_up2356903840689987414_state @ Plus @ A6 )
        = ( ! [Phi3: produc3882902684156697774_state] :
              ( ? [X5: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ X5 @ A6 )
                  & ( sep_gr6114829331755084611_state @ Plus @ Phi3 @ X5 ) )
             => ( member6715010751053357271_state @ Phi3 @ A6 ) ) ) ) ) ).

% sep_algebra.up_closed_def
thf(fact_1206_sep__algebra_Oup__closed__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ A6 )
        = ( ! [Phi3: state] :
              ( ? [X5: state] :
                  ( ( member_state @ X5 @ A6 )
                  & ( sep_greater_state @ Plus @ Phi3 @ X5 ) )
             => ( member_state @ Phi3 @ A6 ) ) ) ) ) ).

% sep_algebra.up_closed_def
thf(fact_1207_sep__algebra_Ogreater__set__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 )
        = ( ! [X5: state] :
              ( ( member_state @ X5 @ A6 )
             => ? [Y4: state] :
                  ( ( member_state @ Y4 @ B4 )
                  & ( sep_greater_state @ Plus @ X5 @ Y4 ) ) ) ) ) ) ).

% sep_algebra.greater_set_def
thf(fact_1208_sep__algebra_Ogreater__setI,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ! [A7: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ A7 @ A6 )
           => ? [X3: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X3 @ B4 )
                & ( sep_gr1233117237951779860_state @ Plus @ A7 @ X3 ) ) )
       => ( sep_gr2254073943460739586_state @ Plus @ A6 @ B4 ) ) ) ).

% sep_algebra.greater_setI
thf(fact_1209_sep__algebra_Ogreater__setI,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ! [A7: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ A7 @ A6 )
           => ? [X3: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X3 @ B4 )
                & ( sep_gr8124549141218502215on_val @ Plus @ A7 @ X3 ) ) )
       => ( sep_gr6201018273107925045on_val @ Plus @ A6 @ B4 ) ) ) ).

% sep_algebra.greater_setI
thf(fact_1210_sep__algebra_Ogreater__setI,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ! [A7: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ A7 @ A6 )
           => ? [X3: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X3 @ B4 )
                & ( sep_gr6114829331755084611_state @ Plus @ A7 @ X3 ) ) )
       => ( sep_gr851398640268573909_state @ Plus @ A6 @ B4 ) ) ) ).

% sep_algebra.greater_setI
thf(fact_1211_sep__algebra_Ogreater__setI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [A7: state] :
            ( ( member_state @ A7 @ A6 )
           => ? [X3: state] :
                ( ( member_state @ X3 @ B4 )
                & ( sep_greater_state @ Plus @ A7 @ X3 ) ) )
       => ( sep_gr7105985528888466643_state @ Plus @ A6 @ B4 ) ) ) ).

% sep_algebra.greater_setI
thf(fact_1212_package__logic_Omono__transformer__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,T2: state > state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag4817583915586052229_state @ Plus @ Unit @ T2 )
        = ( ! [Phi4: state,Phi3: state] :
              ( ( sep_greater_state @ Plus @ Phi3 @ Phi4 )
             => ( sep_greater_state @ Plus @ ( T2 @ Phi3 ) @ ( T2 @ Phi4 ) ) )
          & ( ( T2 @ Unit )
            = Unit ) ) ) ) ).

% package_logic.mono_transformer_def
thf(fact_1213_sep__algebra_Omono__propI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [X4: state,Y3: state] :
            ( ( ( sep_greater_state @ Plus @ Y3 @ X4 )
              & ( P2 @ X4 ) )
           => ( P2 @ Y3 ) )
       => ( sep_mono_prop_state @ Plus @ P2 ) ) ) ).

% sep_algebra.mono_propI
thf(fact_1214_sep__algebra_Omono__prop__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,P2: state > $o] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_mono_prop_state @ Plus @ P2 )
        = ( ! [X5: state,Y4: state] :
              ( ( ( sep_greater_state @ Plus @ Y4 @ X5 )
                & ( P2 @ X5 ) )
             => ( P2 @ Y4 ) ) ) ) ) ).

% sep_algebra.mono_prop_def
thf(fact_1215_package__logic_Ointuitionistic__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8361946002163212404_state @ Plus @ A6 )
        = ( ! [Phi3: state,Phi4: state] :
              ( ( ( sep_greater_state @ Plus @ Phi3 @ Phi4 )
                & ( A6 @ Phi4 ) )
             => ( A6 @ Phi3 ) ) ) ) ) ).

% package_logic.intuitionistic_def
thf(fact_1216_package__logic_Obigger__the,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,X: val,Y: val,X2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ A3 )
          = ( Plus @ X @ Y ) )
       => ( ( sep_greater_val @ Plus @ X @ X2 )
         => ( sep_greater_val @ Plus @ ( the_val @ ( Plus @ ( Core @ A3 ) @ X ) ) @ ( the_val @ ( Plus @ ( Core @ A3 ) @ X2 ) ) ) ) ) ) ).

% package_logic.bigger_the
thf(fact_1217_package__logic_Obigger__the,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,X: state,Y: state,X2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ A3 )
          = ( Plus @ X @ Y ) )
       => ( ( sep_greater_state @ Plus @ X @ X2 )
         => ( sep_greater_state @ Plus @ ( the_state @ ( Plus @ ( Core @ A3 ) @ X ) ) @ ( the_state @ ( Plus @ ( Core @ A3 ) @ X2 ) ) ) ) ) ) ).

% package_logic.bigger_the
thf(fact_1218_sep__algebra_Ominus__equiv__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ B2 @ A3 )
       => ( ( ( some_val @ B2 )
            = ( Plus @ A3 @ ( sep_minus_val @ Plus @ Core @ B2 @ A3 ) ) )
          & ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ B2 @ A3 ) @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.minus_equiv_def
thf(fact_1219_sep__algebra_Ominus__equiv__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ B2 @ A3 )
       => ( ( ( some_state @ B2 )
            = ( Plus @ A3 @ ( sep_minus_state @ Plus @ Core @ B2 @ A3 ) ) )
          & ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ B2 @ A3 ) @ ( Core @ B2 ) ) ) ) ) ).

% sep_algebra.minus_equiv_def
thf(fact_1220_sep__algebra_Ominus__and__plus,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Omega: val,Omega2: val,R: val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ Omega )
          = ( Plus @ Omega2 @ R ) )
       => ( ( sep_greater_val @ Plus @ Omega2 @ A3 )
         => ( ( some_val @ ( sep_minus_val @ Plus @ Core @ Omega @ A3 ) )
            = ( Plus @ ( sep_minus_val @ Plus @ Core @ Omega2 @ A3 ) @ R ) ) ) ) ) ).

% sep_algebra.minus_and_plus
thf(fact_1221_sep__algebra_Ominus__and__plus,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Omega: state,Omega2: state,R: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ Omega )
          = ( Plus @ Omega2 @ R ) )
       => ( ( sep_greater_state @ Plus @ Omega2 @ A3 )
         => ( ( some_state @ ( sep_minus_state @ Plus @ Core @ Omega @ A3 ) )
            = ( Plus @ ( sep_minus_state @ Plus @ Core @ Omega2 @ A3 ) @ R ) ) ) ) ) ).

% sep_algebra.minus_and_plus
thf(fact_1222_sep__algebra_Ominus__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X2: val,A3: val,B2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X2 )
          = ( Plus @ A3 @ B2 ) )
       => ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ X2 @ A3 ) @ B2 ) ) ) ).

% sep_algebra.minus_bigger
thf(fact_1223_sep__algebra_Ominus__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X2: state,A3: state,B2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X2 )
          = ( Plus @ A3 @ B2 ) )
       => ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ X2 @ A3 ) @ B2 ) ) ) ).

% sep_algebra.minus_bigger
thf(fact_1224_sep__algebra_Ominus__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,B2: val,C: val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A3 )
          = ( Plus @ B2 @ C ) )
       => ( ( sep_greater_val @ Plus @ X2 @ A3 )
         => ( ( sep_minus_val @ Plus @ Core @ X2 @ A3 )
            = ( sep_minus_val @ Plus @ Core @ ( sep_minus_val @ Plus @ Core @ X2 @ B2 ) @ C ) ) ) ) ) ).

% sep_algebra.minus_sum
thf(fact_1225_sep__algebra_Ominus__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,B2: state,C: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A3 )
          = ( Plus @ B2 @ C ) )
       => ( ( sep_greater_state @ Plus @ X2 @ A3 )
         => ( ( sep_minus_state @ Plus @ Core @ X2 @ A3 )
            = ( sep_minus_state @ Plus @ Core @ ( sep_minus_state @ Plus @ Core @ X2 @ B2 ) @ C ) ) ) ) ) ).

% sep_algebra.minus_sum
thf(fact_1226_sep__algebra_OminusI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ B2 )
          = ( Plus @ A3 @ X2 ) )
       => ( ( sep_greater_val @ Plus @ X2 @ ( Core @ B2 ) )
         => ( X2
            = ( sep_minus_val @ Plus @ Core @ B2 @ A3 ) ) ) ) ) ).

% sep_algebra.minusI
thf(fact_1227_sep__algebra_OminusI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ B2 )
          = ( Plus @ A3 @ X2 ) )
       => ( ( sep_greater_state @ Plus @ X2 @ ( Core @ B2 ) )
         => ( X2
            = ( sep_minus_state @ Plus @ Core @ B2 @ A3 ) ) ) ) ) ).

% sep_algebra.minusI
thf(fact_1228_package__logic_Oprove__last__completeness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: val,A3: val,Nf1: val,F2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A4 @ A3 )
       => ( ( ( some_val @ A3 )
            = ( Plus @ Nf1 @ F2 ) )
         => ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ A4 @ Nf1 ) @ F2 ) ) ) ) ).

% package_logic.prove_last_completeness
thf(fact_1229_package__logic_Oprove__last__completeness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: state,A3: state,Nf1: state,F2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A4 @ A3 )
       => ( ( ( some_state @ A3 )
            = ( Plus @ Nf1 @ F2 ) )
         => ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ A4 @ Nf1 ) @ F2 ) ) ) ) ).

% package_logic.prove_last_completeness
thf(fact_1230_package__logic_Ominus__some,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,B2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A3 @ B2 )
       => ( ( some_val @ A3 )
          = ( Plus @ B2 @ ( sep_minus_val @ Plus @ Core @ A3 @ B2 ) ) ) ) ) ).

% package_logic.minus_some
thf(fact_1231_package__logic_Ominus__some,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,B2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A3 @ B2 )
       => ( ( some_state @ A3 )
          = ( Plus @ B2 @ ( sep_minus_state @ Plus @ Core @ A3 @ B2 ) ) ) ) ) ).

% package_logic.minus_some
thf(fact_1232_sep__algebra_Osmaller__pure__sum__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Y: val,A3: val,B2: val,X2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ Y @ A3 )
       => ( ( sep_greater_val @ Plus @ Y @ B2 )
         => ( ( ( some_val @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( ( sep_pure_val @ Plus @ B2 )
             => ( sep_greater_val @ Plus @ Y @ X2 ) ) ) ) ) ) ).

% sep_algebra.smaller_pure_sum_smaller
thf(fact_1233_sep__algebra_Osmaller__pure__sum__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,A3: state,B2: state,X2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ A3 )
       => ( ( sep_greater_state @ Plus @ Y @ B2 )
         => ( ( ( some_state @ X2 )
              = ( Plus @ A3 @ B2 ) )
           => ( ( sep_pure_state @ Plus @ B2 )
             => ( sep_greater_state @ Plus @ Y @ X2 ) ) ) ) ) ) ).

% sep_algebra.smaller_pure_sum_smaller
thf(fact_1234_sep__algebra_Oupper__closure__def,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( sep_up6452048470549419908_state @ Plus @ A6 )
        = ( collec394671971739345689_state
          @ ^ [Uu3: produc3882902684156697774_state] :
            ? [Phi3: produc3882902684156697774_state,Phi4: produc3882902684156697774_state] :
              ( ( Uu3 = Phi3 )
              & ( sep_gr6114829331755084611_state @ Plus @ Phi3 @ Phi4 )
              & ( member6715010751053357271_state @ Phi4 @ A6 ) ) ) ) ) ).

% sep_algebra.upper_closure_def
thf(fact_1235_sep__algebra_Oupper__closure__def,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( sep_up6054414863798424979_state @ Plus @ A6 )
        = ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [Phi3: produc7272280185086996969_state,Phi4: produc7272280185086996969_state] :
              ( ( Uu3 = Phi3 )
              & ( sep_gr1233117237951779860_state @ Plus @ Phi3 @ Phi4 )
              & ( member7461423308196221312_state @ Phi4 @ A6 ) ) ) ) ) ).

% sep_algebra.upper_closure_def
thf(fact_1236_sep__algebra_Oupper__closure__def,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( sep_up7144661806627585478on_val @ Plus @ A6 )
        = ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi3: produc9003781588162623004on_val,Phi4: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi3 )
              & ( sep_gr8124549141218502215on_val @ Plus @ Phi3 @ Phi4 )
              & ( member2879030624002546611on_val @ Phi4 @ A6 ) ) ) ) ) ).

% sep_algebra.upper_closure_def
thf(fact_1237_sep__algebra_Oupper__closure__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up1246176804924251236_state @ Plus @ A6 )
        = ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi3: state,Phi4: state] :
              ( ( Uu3 = Phi3 )
              & ( sep_greater_state @ Plus @ Phi3 @ Phi4 )
              & ( member_state @ Phi4 @ A6 ) ) ) ) ) ).

% sep_algebra.upper_closure_def
thf(fact_1238_Pow__insert,axiom,
    ! [A3: state,A6: set_state] :
      ( ( pow_state @ ( insert_state @ A3 @ A6 ) )
      = ( sup_su4188871578264421970_state @ ( pow_state @ A6 ) @ ( image_2476256681063834599_state @ ( insert_state @ A3 ) @ ( pow_state @ A6 ) ) ) ) ).

% Pow_insert
thf(fact_1239_sep__algebra_Ounder__def,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A6: set_Pr2391701600042252046_state,Omega2: produc3882902684156697774_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( sep_un1732284790778891013_state @ Plus @ A6 @ Omega2 )
        = ( collec394671971739345689_state
          @ ^ [Uu3: produc3882902684156697774_state] :
            ? [Omega3: produc3882902684156697774_state] :
              ( ( Uu3 = Omega3 )
              & ( member6715010751053357271_state @ Omega3 @ A6 )
              & ( sep_gr6114829331755084611_state @ Plus @ Omega2 @ Omega3 ) ) ) ) ) ).

% sep_algebra.under_def
thf(fact_1240_sep__algebra_Ounder__def,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A6: set_Pr4231240917283394591_state,Omega2: produc7272280185086996969_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( sep_un1299216510214111186_state @ Plus @ A6 @ Omega2 )
        = ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [Omega3: produc7272280185086996969_state] :
              ( ( Uu3 = Omega3 )
              & ( member7461423308196221312_state @ Omega3 @ A6 )
              & ( sep_gr1233117237951779860_state @ Plus @ Omega2 @ Omega3 ) ) ) ) ) ).

% sep_algebra.under_def
thf(fact_1241_sep__algebra_Ounder__def,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A6: set_Pr7649655576376376530on_val,Omega2: produc9003781588162623004on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( sep_un3765025543224000005on_val @ Plus @ A6 @ Omega2 )
        = ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Omega3: produc9003781588162623004on_val] :
              ( ( Uu3 = Omega3 )
              & ( member2879030624002546611on_val @ Omega3 @ A6 )
              & ( sep_gr8124549141218502215on_val @ Plus @ Omega2 @ Omega3 ) ) ) ) ) ).

% sep_algebra.under_def
thf(fact_1242_sep__algebra_Ounder__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A6: set_state,Omega2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_under_state @ Plus @ A6 @ Omega2 )
        = ( collect_state
          @ ^ [Uu3: state] :
            ? [Omega3: state] :
              ( ( Uu3 = Omega3 )
              & ( member_state @ Omega3 @ A6 )
              & ( sep_greater_state @ Plus @ Omega2 @ Omega3 ) ) ) ) ) ).

% sep_algebra.under_def
thf(fact_1243_sep__algebra_Obigger__singleton,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Phi2: state,Phi: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Phi2 @ Phi )
       => ( sep_gr7105985528888466643_state @ Plus @ ( insert_state @ Phi2 @ bot_bot_set_state ) @ ( insert_state @ Phi @ bot_bot_set_state ) ) ) ) ).

% sep_algebra.bigger_singleton
thf(fact_1244_sep__algebra_Ominus__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B2: val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_minus_val @ Plus @ Core @ B2 @ A3 )
        = ( fun_THE_default_val @ B2
          @ ^ [X5: val] :
              ( ( ( some_val @ B2 )
                = ( Plus @ A3 @ X5 ) )
              & ( sep_greater_val @ Plus @ X5 @ ( Core @ B2 ) ) ) ) ) ) ).

% sep_algebra.minus_def
thf(fact_1245_sep__algebra_Ominus__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B2: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_minus_state @ Plus @ Core @ B2 @ A3 )
        = ( fun_TH8221542053827138557_state @ B2
          @ ^ [X5: state] :
              ( ( ( some_state @ B2 )
                = ( Plus @ A3 @ X5 ) )
              & ( sep_greater_state @ Plus @ X5 @ ( Core @ B2 ) ) ) ) ) ) ).

% sep_algebra.minus_def
thf(fact_1246_package__logic_Osat__star__exists__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A6: aassertion_val,B4: aassertion_val,Phi: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ ( aStar_val @ A6 @ B4 ) @ Phi )
       => ( ( packag5732365195153136185on_val @ Plus @ Core @ A6 )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
           => ? [A7: val,B6: val] :
                ( ( sep_greater_val @ Plus @ ( Core @ A7 ) @ ( Core @ Phi ) )
                & ( sep_greater_val @ Plus @ ( Core @ B6 ) @ ( Core @ Phi ) )
                & ( ( some_val @ Phi )
                  = ( Plus @ A7 @ B6 ) )
                & ( package_sat_val @ Plus @ A6 @ A7 )
                & ( package_sat_val @ Plus @ B4 @ B6 ) ) ) ) ) ) ).

% package_logic.sat_star_exists_bigger
thf(fact_1247_package__logic_Osat__star__exists__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A6: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aStar_state @ A6 @ B4 ) @ Phi )
       => ( ( packag7298478212905792770_state @ Plus @ Core @ A6 )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
           => ? [A7: state,B6: state] :
                ( ( sep_greater_state @ Plus @ ( Core @ A7 ) @ ( Core @ Phi ) )
                & ( sep_greater_state @ Plus @ ( Core @ B6 ) @ ( Core @ Phi ) )
                & ( ( some_state @ Phi )
                  = ( Plus @ A7 @ B6 ) )
                & ( package_sat_state @ Plus @ A6 @ A7 )
                & ( package_sat_state @ Plus @ B4 @ B6 ) ) ) ) ) ) ).

% package_logic.sat_star_exists_bigger
thf(fact_1248_package__logic_Ovalid__package__setI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A7: state,U: state,T3: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A7 @ ( produc8632743443909064678_state @ U @ T3 ) ) @ S2 )
           => ( ( sep_defined_state @ Plus @ A7 @ U )
              & ( sep_greater_state @ Plus @ ( Core @ A7 ) @ ( Core @ U ) )
              & ( packag4817583915586052229_state @ Plus @ Unit @ T3 )
              & ( sep_greater_state @ Plus @ A7 @ ( Core @ ( T3 @ F ) ) ) ) )
       => ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F ) ) ) ).

% package_logic.valid_package_setI
thf(fact_1249_package__logic_Ovalid__package__set__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F )
        = ( ! [X5: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X5 @ S2 )
             => ( produc1745419677418529872tate_o
                @ ^ [A2: state] :
                    ( produc3645877548210629341tate_o
                    @ ^ [U6: state,T4: state > state] :
                        ( ( sep_defined_state @ Plus @ A2 @ U6 )
                        & ( sep_greater_state @ Plus @ ( Core @ A2 ) @ ( Core @ U6 ) )
                        & ( packag4817583915586052229_state @ Plus @ Unit @ T4 )
                        & ( sep_greater_state @ Plus @ A2 @ ( Core @ ( T4 @ F ) ) ) ) )
                @ X5 ) ) ) ) ) ).

% package_logic.valid_package_set_def
thf(fact_1250_sup_OcoboundedI2,axiom,
    ! [C: set_Pr4231240917283394591_state,B2: set_Pr4231240917283394591_state,A3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ B2 )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A3 @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1251_sup_OcoboundedI2,axiom,
    ! [C: set_state,B2: set_state,A3: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ B2 )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A3 @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1252_sup_OcoboundedI1,axiom,
    ! [C: set_Pr4231240917283394591_state,A3: set_Pr4231240917283394591_state,B2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ A3 )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A3 @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1253_sup_OcoboundedI1,axiom,
    ! [C: set_state,A3: set_state,B2: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ A3 )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A3 @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1254_sup_Oabsorb__iff2,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A2: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A2 @ B )
          = B ) ) ) ).

% sup.absorb_iff2
thf(fact_1255_sup_Oabsorb__iff2,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A2: set_state,B: set_state] :
          ( ( sup_sup_set_state @ A2 @ B )
          = B ) ) ) ).

% sup.absorb_iff2
thf(fact_1256_PartialSA_Owf__assertion_Opelims_I1_J,axiom,
    ! [X2: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X2 )
        = Y )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( Y
                  = ( ( packag7298478212905792770_state @ plus @ core @ A11 )
                    & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) )
               => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A11 @ B7 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( Y
                    = ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) )
                 => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A11 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( Y
                      = ( packag2456304381420842418_state @ plus @ A11 ) )
                   => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A11 ) ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(1)
thf(fact_1257_PartialSA_Owf__assertion_Opelims_I2_J,axiom,
    ! [X2: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X2 )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A11 @ B7 ) )
               => ~ ( ( packag7298478212905792770_state @ plus @ core @ A11 )
                    & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A11 ) )
                 => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A11 ) )
                   => ~ ( packag2456304381420842418_state @ plus @ A11 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(2)
thf(fact_1258_PartialSA_Owf__assertion_Opelims_I3_J,axiom,
    ! [X2: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X2 )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X2 )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A11 @ B7 ) )
               => ( ( packag7298478212905792770_state @ plus @ core @ A11 )
                  & ( packag7298478212905792770_state @ plus @ core @ B7 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A11 ) )
                 => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                    & ( packag7298478212905792770_state @ plus @ core @ A11 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A11 ) )
                   => ( packag2456304381420842418_state @ plus @ A11 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(3)
thf(fact_1259_PartialSA_Osat_Opelims_I3_J,axiom,
    ! [X2: aassertion_state,Xa2: state] :
      ( ~ ( package_sat_state @ plus @ X2 @ Xa2 )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X2 @ Xa2 ) )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A11 @ B7 ) @ Xa2 ) )
               => ? [A5: state,B9: state] :
                    ( ( ( some_state @ Xa2 )
                      = ( plus @ A5 @ B9 ) )
                    & ( package_sat_state @ plus @ A11 @ A5 )
                    & ( package_sat_state @ plus @ B7 @ B9 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A11 ) @ Xa2 ) )
                 => ( ( B6 @ Xa2 )
                   => ( package_sat_state @ plus @ A11 @ Xa2 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A11 ) @ Xa2 ) )
                   => ( A11 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(3)
thf(fact_1260_PartialSA_Osat_Opelims_I2_J,axiom,
    ! [X2: aassertion_state,Xa2: state] :
      ( ( package_sat_state @ plus @ X2 @ Xa2 )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X2 @ Xa2 ) )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A11 @ B7 ) @ Xa2 ) )
               => ~ ? [A7: state,B6: state] :
                      ( ( ( some_state @ Xa2 )
                        = ( plus @ A7 @ B6 ) )
                      & ( package_sat_state @ plus @ A11 @ A7 )
                      & ( package_sat_state @ plus @ B7 @ B6 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A11 ) @ Xa2 ) )
                 => ~ ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A11 @ Xa2 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A11 ) @ Xa2 ) )
                   => ~ ( A11 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(2)
thf(fact_1261_PartialSA_Osat_Opelims_I1_J,axiom,
    ! [X2: aassertion_state,Xa2: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X2 @ Xa2 )
        = Y )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X2 @ Xa2 ) )
       => ( ! [A11: aassertion_state,B7: aassertion_state] :
              ( ( X2
                = ( aStar_state @ A11 @ B7 ) )
             => ( ( Y
                  = ( ? [A2: state,B: state] :
                        ( ( ( some_state @ Xa2 )
                          = ( plus @ A2 @ B ) )
                        & ( package_sat_state @ plus @ A11 @ A2 )
                        & ( package_sat_state @ plus @ B7 @ B ) ) ) )
               => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A11 @ B7 ) @ Xa2 ) ) ) )
         => ( ! [B6: state > $o,A11: aassertion_state] :
                ( ( X2
                  = ( aImp_state @ B6 @ A11 ) )
               => ( ( Y
                    = ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A11 @ Xa2 ) ) )
                 => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A11 ) @ Xa2 ) ) ) )
           => ~ ! [A11: state > $o] :
                  ( ( X2
                    = ( aSem_state @ A11 ) )
                 => ( ( Y
                      = ( A11 @ Xa2 ) )
                   => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A11 ) @ Xa2 ) ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(1)
thf(fact_1262_cwand__def,axiom,
    ( cwand
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A2: state,X5: state] :
                  ( ( ( member_state @ A2 @ A )
                    & ( ( some_state @ X5 )
                      = ( plus @ ( r @ A2 @ W2 ) @ A2 ) ) )
                 => ( member_state @ X5 @ B5 ) ) ) ) ) ) ).

% cwand_def
thf(fact_1263_wand__def,axiom,
    ( wand
    = ( ^ [A: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A2: state,X5: state] :
                  ( ( ( member_state @ A2 @ A )
                    & ( ( some_state @ X5 )
                      = ( plus @ W2 @ A2 ) ) )
                 => ( member_state @ X5 @ B5 ) ) ) ) ) ) ).

% wand_def
thf(fact_1264_type__definition__state,axiom,
    ( type_d7385716227342696708on_val @ rep_state @ abs_state
    @ ( collec7475294502966882545on_val
      @ ^ [Uu3: produc9003781588162623004on_val] :
        ? [Phi4: produc9003781588162623004on_val] :
          ( ( Uu3 = Phi4 )
          & ( valid_state @ Phi4 ) ) ) ) ).

% type_definition_state
thf(fact_1265_get__m_Osimps,axiom,
    ( get_m
    = ( ^ [A2: state] : ( produc5239619271231976746on_val @ ( rep_state @ A2 ) ) ) ) ).

% get_m.simps
thf(fact_1266_get__m_Oelims,axiom,
    ! [X2: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X2 )
        = Y )
     => ( Y
        = ( produc5239619271231976746on_val @ ( rep_state @ X2 ) ) ) ) ).

% get_m.elims
thf(fact_1267_get__pre_I2_J,axiom,
    ( get_m
    = ( ^ [X5: state] : ( produc5239619271231976746on_val @ ( rep_state @ X5 ) ) ) ) ).

% get_pre(2)
thf(fact_1268_get__m_Opelims,axiom,
    ! [X2: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X2 )
        = Y )
     => ( ( accp_state @ get_m_rel @ X2 )
       => ~ ( ( Y
              = ( produc5239619271231976746on_val @ ( rep_state @ X2 ) ) )
           => ~ ( accp_state @ get_m_rel @ X2 ) ) ) ) ).

% get_m.pelims
thf(fact_1269_compatibleI__old,axiom,
    ! [Phi: produc9003781588162623004on_val,Phi2: produc9003781588162623004on_val] :
      ( ! [Hl3: produc1457211279475724562t_char,X4: val,Y3: val] :
          ( ( ( ( produc2319605628138516840on_val @ Phi @ Hl3 )
              = ( some_val @ X4 ) )
            & ( ( produc2319605628138516840on_val @ Phi2 @ Hl3 )
              = ( some_val @ Y3 ) ) )
         => ( X4 = Y3 ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( produc5239619271231976746on_val @ Phi ) @ ( produc5239619271231976746on_val @ Phi2 ) ) )
       => ( compatible @ Phi @ Phi2 ) ) ) ).

% compatibleI_old
thf(fact_1270_get__pre_I1_J,axiom,
    ( get_h
    = ( ^ [X5: state] : ( produc2319605628138516840on_val @ ( rep_state @ X5 ) ) ) ) ).

% get_pre(1)
thf(fact_1271_get__h_Oelims,axiom,
    ! [X2: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X2 )
        = Y )
     => ( Y
        = ( produc2319605628138516840on_val @ ( rep_state @ X2 ) ) ) ) ).

% get_h.elims
thf(fact_1272_get__h_Osimps,axiom,
    ( get_h
    = ( ^ [A2: state] : ( produc2319605628138516840on_val @ ( rep_state @ A2 ) ) ) ) ).

% get_h.simps
thf(fact_1273_compatible__def,axiom,
    ( compatible
    = ( ^ [Phi4: produc9003781588162623004on_val,Phi3: produc9003781588162623004on_val] :
          ( ( compatible_heaps @ ( produc2319605628138516840on_val @ Phi4 ) @ ( produc2319605628138516840on_val @ Phi3 ) )
          & ( valid_mask @ ( add_ma6586698345353345811t_char @ ( produc5239619271231976746on_val @ Phi4 ) @ ( produc5239619271231976746on_val @ Phi3 ) ) ) ) ) ) ).

% compatible_def
thf(fact_1274_get__h_Opelims,axiom,
    ! [X2: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X2 )
        = Y )
     => ( ( accp_state @ get_h_rel @ X2 )
       => ~ ( ( Y
              = ( produc2319605628138516840on_val @ ( rep_state @ X2 ) ) )
           => ~ ( accp_state @ get_h_rel @ X2 ) ) ) ) ).

% get_h.pelims

% Helper facts (7)
thf(help_If_2_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X2: prat,Y: prat] :
      ( ( if_prat @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X2: prat,Y: prat] :
      ( ( if_prat @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_2_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X2: state,Y: state] :
      ( ( if_state @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X2: state,Y: state] :
      ( ( if_state @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_3_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [P2: $o] :
      ( ( P2 = $true )
      | ( P2 = $false ) ) ).

thf(help_If_2_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X2: option_state,Y: option_state] :
      ( ( if_option_state @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X2: option_state,Y: option_state] :
      ( ( if_option_state @ $true @ X2 @ Y )
      = X2 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    greater @ w @ xb ).

%------------------------------------------------------------------------------