TPTP Problem File: SLH0529^1.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_00756_038795__8725336_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1932 ( 493 unt; 646 typ;   0 def)
%            Number of atoms       : 4891 (1894 equ;   0 cnn)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives : 17110 ( 459   ~;  35   |; 714   &;13793   @)
%                                         (   0 <=>;2109  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   8 avg)
%            Number of types       :   77 (  76 usr)
%            Number of type conns  : 3355 (3355   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  573 ( 570 usr;  41 con; 0-11 aty)
%            Number of variables   : 5254 ( 504   ^;4287   !; 463   ?;5254   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 09:09:32.309
%------------------------------------------------------------------------------
% Could-be-implicit typings (76)
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    set_Pr1785066336555260981_state: $tType ).

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

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

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

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

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

thf(ty_n_t__Option__Ooption_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    option_state_state: $tType ).

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

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

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

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

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

thf(ty_n_t__Option__Ooption_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    option_set_state: $tType ).

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

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

thf(ty_n_t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J,type,
    option_list_char: $tType ).

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

thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
    set_list_char: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

% Explicit typings (570)
thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    bNF_Ca2815325664443363616_state: set_Pr1688445902015331925_state > ( option_state > set_state ) > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_Fun_Ofun__upd_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    fun_up1601731230164360576on_val: ( ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ) > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val > ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val ).

thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J,type,
    fun_up4009399622604172288t_char: ( nat > option_list_char ) > nat > option_list_char > nat > option_list_char ).

thf(sy_c_Fun_Ofun__upd_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_001t__Option__Ooption_It__Option__Ooption_It__PartialHeapSA__Ostate_J_J,type,
    fun_up8433615654909047651_state: ( option_state > option_option_state ) > option_state > option_option_state > option_state > option_option_state ).

thf(sy_c_Fun_Ofun__upd_001t__PartialHeapSA__Ostate_001t__Option__Ooption_I_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    fun_up4553069608533601692_state: ( state > option_state_state ) > state > option_state_state > state > option_state_state ).

thf(sy_c_Fun_Ofun__upd_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up5073147608505813454on_val: ( state > option_val ) > state > option_val > state > option_val ).

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

thf(sy_c_Fun_Ofun__upd_001t__PartialHeapSA__Ostate_001t__Option__Ooption_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    fun_up2912618647338797435_state: ( state > option886743748074664436_state ) > state > option886743748074664436_state > state > option886743748074664436_state ).

thf(sy_c_Fun_Ofun__upd_001t__PosRat__Oprat_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up1472322128373081433_state: ( prat > option_state ) > prat > option_state > prat > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__PosRat__Oprat_001t__Option__Ooption_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
    fun_up5484256749267628047_state: ( prat > option_set_state ) > prat > option_set_state > prat > option_set_state ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up8559965269643824108on_val: ( produc9003781588162623004on_val > option_val ) > produc9003781588162623004on_val > option_val > produc9003781588162623004on_val > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up6681822530636708645_state: ( produc9003781588162623004on_val > option_state ) > produc9003781588162623004on_val > option_state > produc9003781588162623004on_val > option_state ).

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

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up3736070447144131606on_val: ( produc3882902684156697774_state > option_val ) > produc3882902684156697774_state > option_val > produc3882902684156697774_state > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up3435231866794294907_state: ( produc3882902684156697774_state > option_state ) > produc3882902684156697774_state > option_state > produc3882902684156697774_state > option_state ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Option__Ooption_It__Mask__Oval_J,type,
    fun_up3509650811975514847on_val: ( produc7272280185086996969_state > option_val ) > produc7272280185086996969_state > option_val > produc7272280185086996969_state > option_val ).

thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
    fun_up3650151817091186_state: ( produc7272280185086996969_state > option_state ) > produc7272280185086996969_state > option_state > produc7272280185086996969_state > option_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_Oinj__on_001t__Mask__Oval_001t__Option__Ooption_It__Mask__Oval_J,type,
    inj_on4074814566786472055on_val: ( val > option_val ) > set_val > $o ).

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

thf(sy_c_Fun_Oinj__on_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
    inj_on_state_state: ( state > state ) > set_state > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J,type,
    inj_on3812695684120442372r_prat: ( produc9003781588162623004on_val > produc1457211279475724562t_char > prat ) > set_Pr7649655576376376530on_val > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_001t__Nat__Onat,type,
    inj_on2499120878504899377ar_nat: ( produc1457211279475724562t_char > nat ) > set_Pr2507339680178222706t_char > $o ).

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

thf(sy_c_Fun__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_Fun__Def_Oin__rel_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    fun_in3588502033776859947on_val: set_Pr7649655576376376530on_val > ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o ).

thf(sy_c_Fun__Def_Oin__rel_001t__PartialHeapSA__Ostate_001_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J,type,
    fun_in7949406044791577617_state: set_Pr2391701600042252046_state > state > ( state > state ) > $o ).

thf(sy_c_Fun__Def_Oin__rel_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J,type,
    fun_in233003973860168752_state: set_Pr4231240917283394591_state > state > produc3882902684156697774_state > $o ).

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

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    minus_9160195963678339755on_val: set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    minus_5498279039490143093_state: set_Pr2391701600042252046_state > set_Pr2391701600042252046_state > set_Pr2391701600042252046_state ).

thf(sy_c_Groups_Ominus__class_Ominus_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,
    minus_2078076265878351864_state: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
    uminus472742206872269241_state: set_state > set_state ).

thf(sy_c_Groups_Ouminus__class_Ouminus_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,
    uminus2423024474186858011on_val: set_Pr7649655576376376530on_val > set_Pr7649655576376376530on_val ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    uminus8176724999004996613_state: set_Pr2391701600042252046_state > set_Pr2391701600042252046_state ).

thf(sy_c_Groups_Ouminus__class_Ouminus_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,
    uminus1327639380719934312_state: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state ).

thf(sy_c_HOL_OUniq_001t__PartialHeapSA__Ostate,type,
    uniq_state: ( state > $o ) > $o ).

thf(sy_c_HOL_OUniq_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,
    uniq_P8322667716730457431on_val: ( produc9003781588162623004on_val > $o ) > $o ).

thf(sy_c_HOL_OUniq_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_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__PartialHeapSA__Ostate_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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    ord_le801108382804549175_state: set_Pr6040071838687925911_state > set_Pr6040071838687925911_state > $o ).

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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,
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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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    packag9124413901382861105_state: ( produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state ) > ( produc3882902684156697774_state > produc3882902684156697774_state ) > produc3882902684156697774_state > ( produc3882902684156697774_state > $o ) > $o ).

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    packag2204431621656667814_state: ( produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state ) > ( produc7272280185086996969_state > produc7272280185086996969_state ) > produc7272280185086996969_state > ( produc7272280185086996969_state > $o ) > $o ).

thf(sy_c_PackageLogic_Opackage__logic_Obool__conj_001t__Mask__Oval,type,
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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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    packag5541956234368469604on_val: ( produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val ) > ( produc9003781588162623004on_val > produc9003781588162623004on_val ) > aasser1163550960519286933on_val > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_PartialHeapSA_Ounit,type,
    unit: state ).

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

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

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

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

thf(sy_c_PosRat_Ohalf,type,
    half: prat ).

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

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

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

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

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

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

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

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

thf(sy_c_PosRat_Opnone,type,
    pnone: prat ).

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

thf(sy_c_PosRat_Opwrite,type,
    pwrite: prat ).

thf(sy_c_Product__Type_OPair_001_062_It__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__Mask__Oval_J_001t__Mask__Oval,type,
    produc1969469836606013754al_val: aassertion_val > val > produc1707155752992360906al_val ).

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

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

thf(sy_c_Product__Type_OPair_001t__PartialHeapSA__Ostate_001t__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,
    produc3987245858496418492_state: produc3882902684156697774_state > ( produc3882902684156697774_state > produc3882902684156697774_state ) > produc2023215532613486146_state ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_001t__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_OSigma_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J,type,
    produc1366239611153933861on_val: set_Pr3433046674199179443r_prat > ( ( produc1457211279475724562t_char > prat ) > set_Pr1004501353197068112on_val ) > set_Pr7649655576376376530on_val ).

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

thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_Product__Type_OSigma_001t__PartialHeapSA__Ostate_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J,type,
    produc4123186969287248032on_val: set_state > ( state > set_Pr7649655576376376530on_val ) > set_Pr7332355692443745687on_val ).

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

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

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

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

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thf(sy_c_SepAlgebra_Osep__algebra_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Oadd__set_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_Ogreater__set_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Ominus_001t__Mask__Oval,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Ominus_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Omono__prop_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Opure_001t__Mask__Oval,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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thf(sy_c_SepAlgebra_Osep__algebra_Osplus_001t__Mask__Oval,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Osplus_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_SepAlgebra_Osep__algebra_Oup__closed_001t__PartialHeapSA__Ostate,type,
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thf(sy_c_Set_OCollect_001t__Option__Ooption_It__PartialHeapSA__Ostate_J,type,
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    insert2241947522006009073_state: produc6251377953716854561_state > set_Pr6847263425858009217_state > set_Pr6847263425858009217_state ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__PosRat__Oprat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Mask__Oval_J_J_J_J,type,
    member4602090469187516291on_val: option8887860577033306220on_val > set_op6240181410663953058on_val > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J,type,
    member5919342556599141533_state: option886743748074664436_state > set_op3387789762728285652_state > $o ).

thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__PartialHeapSA__Ostate_Mt__Product____Type__Oprod_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_Mt__PartialHeapSA__Ostate_J_J_J_J,type,
    member3894984953261475024_state: option2747342629145793465_state > set_op8023886964038656367_state > $o ).

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

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

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

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

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

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

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

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

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

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

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

thf(sy_c_member_001t__Product____Type__Oprod_It__PosRat__Oprat_Mt__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_bb____,type,
    bb: state ).

thf(sy_v_hl____,type,
    hl: produc1457211279475724562t_char ).

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 ).

thf(sy_v_y____,type,
    y: state ).

thf(sy_v_ya____,type,
    ya: state ).

thf(sy_v_yb____,type,
    yb: state ).

% Relevant facts (1275)
thf(fact_0_padd__asso,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( padd @ ( padd @ A @ B ) @ C )
      = ( padd @ A @ ( padd @ B @ C ) ) ) ).

% padd_asso
thf(fact_1_padd__comm,axiom,
    ( padd
    = ( ^ [A2: prat,B2: prat] : ( padd @ B2 @ A2 ) ) ) ).

% padd_comm
thf(fact_2_pmult__distr,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( pmult @ A @ ( padd @ B @ C ) )
      = ( padd @ ( pmult @ A @ B ) @ ( pmult @ A @ C ) ) ) ).

% pmult_distr
thf(fact_3__092_060open_062_092_060not_062_Ascalable_Awa_Aa_092_060close_062,axiom,
    ~ ( scalable @ wa @ a2 ) ).

% \<open>\<not> scalable wa a\<close>
thf(fact_4__092_060open_062_092_060not_062_Ascalable_Awb_Aa_092_060close_062,axiom,
    ~ ( scalable @ wb @ a2 ) ).

% \<open>\<not> scalable wb a\<close>
thf(fact_5_calculation_I2_J,axiom,
    ( ( get_m @ y @ hl )
    = ( padd @ ( pmult @ alpha @ ( padd @ ( get_m @ ( r @ a2 @ wa ) @ hl ) @ ( get_m @ a2 @ hl ) ) ) @ ( pmult @ beta @ ( padd @ ( get_m @ ( r @ a2 @ wb ) @ hl ) @ ( get_m @ a2 @ hl ) ) ) ) ) ).

% calculation(2)
thf(fact_6__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_7__092_060open_062R_Aa_Awb_A_124_D_124_Aa_092_060close_062,axiom,
    defined @ ( r @ a2 @ wb ) @ a2 ).

% \<open>R a wb |#| a\<close>
thf(fact_8_asm0,axiom,
    ( ( ppos @ alpha )
    & ( ppos @ beta )
    & ( ( padd @ alpha @ beta )
      = pwrite ) ) ).

% asm0
thf(fact_9_pmult__padd,axiom,
    ! [A: prat,B: prat,X: prat,C: prat,Y: prat] :
      ( ( pmult @ A @ ( padd @ ( pmult @ B @ X ) @ ( pmult @ C @ Y ) ) )
      = ( padd @ ( pmult @ ( pmult @ A @ B ) @ X ) @ ( pmult @ ( pmult @ A @ C ) @ Y ) ) ) ).

% pmult_padd
thf(fact_10_calculation_I1_J,axiom,
    ( ( get_m @ x @ hl )
    = ( padd @ ( get_m @ ( r @ a2 @ w ) @ hl ) @ ( get_m @ a2 @ hl ) ) ) ).

% calculation(1)
thf(fact_11_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_12_r2,axiom,
    ( ( ( get_h @ ( r @ a2 @ wb ) )
      = ( get_h @ wb ) )
    & ( ( get_m @ ( r @ a2 @ wb ) )
      = ( comp_min_mask @ ( get_m @ a2 ) @ ( get_m @ wb ) ) ) ) ).

% r2
thf(fact_13__092_060open_062Some_Aba_A_061_AR_Aa_Awa_A_092_060oplus_062_Aa_092_060close_062,axiom,
    ( ( some_state @ ba )
    = ( plus @ ( r @ a2 @ wa ) @ a2 ) ) ).

% \<open>Some ba = R a wa \<oplus> a\<close>
thf(fact_14__092_060open_062Some_Abb_A_061_AR_Aa_Awb_A_092_060oplus_062_Aa_092_060close_062,axiom,
    ( ( some_state @ bb )
    = ( plus @ ( r @ a2 @ wb ) @ a2 ) ) ).

% \<open>Some bb = R a wb \<oplus> a\<close>
thf(fact_15_pmult__comm,axiom,
    ( pmult
    = ( ^ [A2: prat,B2: prat] : ( pmult @ B2 @ A2 ) ) ) ).

% pmult_comm
thf(fact_16_padd__cancellative,axiom,
    ! [A: prat,X: prat,B: prat,Y: prat] :
      ( ( A
        = ( padd @ X @ B ) )
     => ( ( A
          = ( padd @ Y @ B ) )
       => ( X = Y ) ) ) ).

% padd_cancellative
thf(fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ya_O_ASome_Aya_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,
    ~ ! [Ya: state] :
        ( ( some_state @ Ya )
       != ( plus @ ( r @ a2 @ wa ) @ a2 ) ) ).

% \<open>\<And>thesis. (\<And>ya. Some ya = R a wa \<oplus> a \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_18__092_060open_062_092_060not_062_Ascalable_Aw_Aa_092_060close_062,axiom,
    ~ ( scalable @ w @ a2 ) ).

% \<open>\<not> scalable w a\<close>
thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062yb_O_ASome_Ayb_A_061_AR_Aa_Awb_A_092_060oplus_062_Aa_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Yb: state] :
        ( ( some_state @ Yb )
       != ( plus @ ( r @ a2 @ wb ) @ a2 ) ) ).

% \<open>\<And>thesis. (\<And>yb. Some yb = R a wb \<oplus> a \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_20_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_21__092_060open_062Some_Ayb_A_061_AR_Aa_Awb_A_092_060oplus_062_Aa_092_060close_062,axiom,
    ( ( some_state @ yb )
    = ( plus @ ( r @ a2 @ wb ) @ a2 ) ) ).

% \<open>Some yb = R a wb \<oplus> a\<close>
thf(fact_22__092_060open_062Some_Aya_A_061_AR_Aa_Awa_A_092_060oplus_062_Aa_092_060close_062,axiom,
    ( ( some_state @ ya )
    = ( plus @ ( r @ a2 @ wa ) @ a2 ) ) ).

% \<open>Some ya = R a wa \<oplus> a\<close>
thf(fact_23_asm1,axiom,
    ( ( member_state @ a2 @ a )
    & ( ( some_state @ x )
      = ( plus @ ( r @ a2 @ w ) @ a2 ) ) ) ).

% asm1
thf(fact_24__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_25_ppos__add,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ppos @ ( padd @ A @ B ) ) ) ).

% ppos_add
thf(fact_26_pmult__special_I1_J,axiom,
    ! [X: prat] :
      ( ( pmult @ pwrite @ X )
      = X ) ).

% pmult_special(1)
thf(fact_27_pmult__ppos,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ( ppos @ B )
       => ( ppos @ ( pmult @ A @ B ) ) ) ) ).

% pmult_ppos
thf(fact_28_non__scalable__R__charact,axiom,
    ! [W: state,A: state] :
      ( ~ ( scalable @ W @ A )
     => ( ( ( get_m @ ( r @ A @ W ) )
          = ( comp_min_mask @ ( get_m @ A ) @ ( get_m @ W ) ) )
        & ( ( get_h @ ( r @ A @ W ) )
          = ( get_h @ W ) ) ) ) ).

% non_scalable_R_charact
thf(fact_29_R__compatible__same,axiom,
    ! [A: state,W: state] :
      ( ( defined @ A @ W )
     => ( ( r @ A @ W )
        = W ) ) ).

% R_compatible_same
thf(fact_30__092_060open_062a_A_124_D_124_Amultiply_Ap_Aw_092_060close_062,axiom,
    defined @ a2 @ ( multiply @ p @ w ) ).

% \<open>a |#| multiply p w\<close>
thf(fact_31__092_060open_062larger__heap_A_Iget__h_Ax_J_A_Iget__h_Ay_J_092_060close_062,axiom,
    larger1532547405891354081ar_val @ ( get_h @ x ) @ ( get_h @ y ) ).

% \<open>larger_heap (get_h x) (get_h y)\<close>
thf(fact_32__092_060open_062larger__heap_A_Iget__h_Ax_J_A_Iget__h_Awb_J_092_060close_062,axiom,
    larger1532547405891354081ar_val @ ( get_h @ x ) @ ( get_h @ wb ) ).

% \<open>larger_heap (get_h x) (get_h wb)\<close>
thf(fact_33__092_060open_062larger__heap_A_Iget__h_Ax_J_A_Iget__h_Awa_J_092_060close_062,axiom,
    larger1532547405891354081ar_val @ ( get_h @ x ) @ ( get_h @ wa ) ).

% \<open>larger_heap (get_h x) (get_h wa)\<close>
thf(fact_34__092_060open_062larger__heap_A_Iget__h_Ax_J_A_Iget__h_Aa_J_092_060close_062,axiom,
    larger1532547405891354081ar_val @ ( get_h @ x ) @ ( get_h @ a2 ) ).

% \<open>larger_heap (get_h x) (get_h a)\<close>
thf(fact_35__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_36_PartialSA_Odefined__sum__move,axiom,
    ! [A: state,B: state,X: state,Y: state,A3: state] :
      ( ( defined @ A @ B )
     => ( ( ( some_state @ B )
          = ( plus @ X @ Y ) )
       => ( ( ( some_state @ A3 )
            = ( plus @ A @ X ) )
         => ( defined @ A3 @ Y ) ) ) ) ).

% PartialSA.defined_sum_move
thf(fact_37_scalable__def,axiom,
    ( scalable
    = ( ^ [W2: state,A2: state] :
        ! [X2: state] :
          ( ( member_state @ X2 @ ( scaled @ W2 ) )
         => ~ ( defined @ A2 @ X2 ) ) ) ) ).

% scalable_def
thf(fact_38_option_Oinject,axiom,
    ! [X22: state,Y2: state] :
      ( ( ( some_state @ X22 )
        = ( some_state @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% option.inject
thf(fact_39_option_Oinject,axiom,
    ! [X22: val,Y2: val] :
      ( ( ( some_val @ X22 )
        = ( some_val @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% option.inject
thf(fact_40_state__ext,axiom,
    ! [A: state,B: state] :
      ( ( ( get_h @ A )
        = ( get_h @ B ) )
     => ( ( ( get_m @ A )
          = ( get_m @ B ) )
       => ( A = B ) ) ) ).

% state_ext
thf(fact_41__092_060open_062ppos_Ap_A_092_060and_062_Apgte_Apwrite_Ap_092_060close_062,axiom,
    ( ( ppos @ p )
    & ( pgte @ pwrite @ p ) ) ).

% \<open>ppos p \<and> pgte pwrite p\<close>
thf(fact_42__092_060open_062Some_Ay_A_061_Amultiply_A_092_060alpha_062_Aya_A_092_060oplus_062_Amultiply_A_092_060beta_062_Ayb_092_060close_062,axiom,
    ( ( some_state @ y )
    = ( plus @ ( multiply @ alpha @ ya ) @ ( multiply @ beta @ yb ) ) ) ).

% \<open>Some y = multiply \<alpha> ya \<oplus> multiply \<beta> yb\<close>
thf(fact_43__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,
    ~ ! [P: prat] :
        ( ( defined @ a2 @ ( multiply @ P @ w ) )
       => ~ ( ( ppos @ P )
            & ( pgte @ pwrite @ P ) ) ) ).

% \<open>\<And>thesis. (\<And>p. \<lbrakk>a |#| multiply p w; ppos p \<and> pgte pwrite p\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_44__092_060open_062multiply_A_092_060alpha_062_Aya_A_124_D_124_Amultiply_A_092_060beta_062_Ayb_092_060close_062,axiom,
    defined @ ( multiply @ alpha @ ya ) @ ( multiply @ beta @ yb ) ).

% \<open>multiply \<alpha> ya |#| multiply \<beta> yb\<close>
thf(fact_45__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062y_O_ASome_Ay_A_061_Amultiply_A_092_060alpha_062_Aya_A_092_060oplus_062_Amultiply_A_092_060beta_062_Ayb_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Y3: state] :
        ( ( some_state @ Y3 )
       != ( plus @ ( multiply @ alpha @ ya ) @ ( multiply @ beta @ yb ) ) ) ).

% \<open>\<And>thesis. (\<And>y. Some y = multiply \<alpha> ya \<oplus> multiply \<beta> yb \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_46_mem__Collect__eq,axiom,
    ! [A: produc3882902684156697774_state,P2: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ A @ ( collec394671971739345689_state @ P2 ) )
      = ( P2 @ A ) ) ).

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

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

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

% mem_Collect_eq
thf(fact_50_Collect__mem__eq,axiom,
    ! [A4: set_Pr2391701600042252046_state] :
      ( ( collec394671971739345689_state
        @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_51_Collect__mem__eq,axiom,
    ! [A4: set_Pr4231240917283394591_state] :
      ( ( collec906845016635587262_state
        @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_52_Collect__mem__eq,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( collec7475294502966882545on_val
        @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_53_Collect__mem__eq,axiom,
    ! [A4: set_state] :
      ( ( collect_state
        @ ^ [X2: state] : ( member_state @ X2 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_54_Collect__cong,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
          = ( Q @ X3 ) )
     => ( ( collec906845016635587262_state @ P2 )
        = ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_cong
thf(fact_55_Collect__cong,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( P2 @ X3 )
          = ( Q @ X3 ) )
     => ( ( collec7475294502966882545on_val @ P2 )
        = ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_cong
thf(fact_56_Collect__cong,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
          = ( Q @ X3 ) )
     => ( ( collect_state @ P2 )
        = ( collect_state @ Q ) ) ) ).

% Collect_cong
thf(fact_57__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_58__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_59_pgte__antisym,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pgte @ B @ A )
       => ( A = B ) ) ) ).

% pgte_antisym
thf(fact_60_larger__heap__trans,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ B @ C )
       => ( larger1532547405891354081ar_val @ A @ C ) ) ) ).

% larger_heap_trans
thf(fact_61_larger__heap__refl,axiom,
    ! [H: produc1457211279475724562t_char > option_val] : ( larger1532547405891354081ar_val @ H @ H ) ).

% larger_heap_refl
thf(fact_62_larger__heap__anti,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ B @ A )
       => ( A = B ) ) ) ).

% larger_heap_anti
thf(fact_63_larger__heap__def,axiom,
    ( larger1532547405891354081ar_val
    = ( ^ [H2: produc1457211279475724562t_char > option_val,H3: produc1457211279475724562t_char > option_val] :
        ! [Hl: produc1457211279475724562t_char,X2: val] :
          ( ( ( H3 @ Hl )
            = ( some_val @ X2 ) )
         => ( ( H2 @ Hl )
            = ( some_val @ X2 ) ) ) ) ) ).

% larger_heap_def
thf(fact_64_larger__heapI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H4: produc1457211279475724562t_char > option_val] :
      ( ! [Hl2: produc1457211279475724562t_char,X3: val] :
          ( ( ( H @ Hl2 )
            = ( some_val @ X3 ) )
         => ( ( H4 @ Hl2 )
            = ( some_val @ X3 ) ) )
     => ( larger1532547405891354081ar_val @ H4 @ H ) ) ).

% larger_heapI
thf(fact_65_w__in__scaled,axiom,
    ! [W: state] : ( member_state @ W @ ( scaled @ W ) ) ).

% w_in_scaled
thf(fact_66_get__h__multiply,axiom,
    ! [P3: prat,X: state] :
      ( ( pgte @ pwrite @ P3 )
     => ( ( get_h @ ( multiply @ P3 @ X ) )
        = ( get_h @ X ) ) ) ).

% get_h_multiply
thf(fact_67_multiply__twice,axiom,
    ! [A: prat,B: prat,X: state] :
      ( ( ( pgte @ pwrite @ A )
        & ( pgte @ pwrite @ B ) )
     => ( ( multiply @ A @ ( multiply @ B @ X ) )
        = ( multiply @ ( pmult @ A @ B ) @ X ) ) ) ).

% multiply_twice
thf(fact_68_greater__sum__both,axiom,
    ! [A: prat,B: prat,C: prat] :
      ( ( pgte @ A @ ( padd @ B @ C ) )
     => ? [A1: prat,A22: prat] :
          ( ( A
            = ( padd @ A1 @ A22 ) )
          & ( pgte @ A1 @ B )
          & ( pgte @ A22 @ C ) ) ) ).

% greater_sum_both
thf(fact_69_p__greater__exists,axiom,
    ( pgte
    = ( ^ [A2: prat,B2: prat] :
        ? [R: prat] :
          ( A2
          = ( padd @ B2 @ R ) ) ) ) ).

% p_greater_exists
thf(fact_70_pmult__order,axiom,
    ! [A: prat,B: prat,P3: prat] :
      ( ( pgte @ A @ B )
     => ( pgte @ ( pmult @ P3 @ A ) @ ( pmult @ B @ P3 ) ) ) ).

% pmult_order
thf(fact_71_get__m__smaller,axiom,
    ! [P3: prat,A: state,Hl3: produc1457211279475724562t_char] :
      ( ( pgte @ pwrite @ P3 )
     => ( ( get_m @ ( multiply @ P3 @ A ) @ Hl3 )
        = ( pmult @ P3 @ ( get_m @ A @ Hl3 ) ) ) ) ).

% get_m_smaller
thf(fact_72_multiply__smaller__pwrite,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ pwrite @ A )
     => ( ( pgte @ pwrite @ B )
       => ( pgte @ pwrite @ ( pmult @ A @ B ) ) ) ) ).

% multiply_smaller_pwrite
thf(fact_73_non__scalable__instantiate,axiom,
    ! [W: state,A: state] :
      ( ~ ( scalable @ W @ A )
     => ? [P: prat] :
          ( ( ppos @ P )
          & ( pgte @ pwrite @ P )
          & ( defined @ A @ ( multiply @ P @ W ) ) ) ) ).

% non_scalable_instantiate
thf(fact_74_commutative,axiom,
    ( plus
    = ( ^ [A2: state,B2: state] : ( plus @ B2 @ A2 ) ) ) ).

% commutative
thf(fact_75_padd__one__ineq__sum,axiom,
    ! [A: prat,B: prat,X: prat,Aa: prat,Bb: prat] :
      ( ( ( padd @ A @ B )
        = pwrite )
     => ( ( pgte @ X @ Aa )
       => ( ( pgte @ X @ Bb )
         => ( pgte @ X @ ( padd @ ( pmult @ A @ Aa ) @ ( pmult @ B @ Bb ) ) ) ) ) ) ).

% padd_one_ineq_sum
thf(fact_76_positivity,axiom,
    ! [A: state,B: state,C: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ C ) )
     => ( ( ( some_state @ C )
          = ( plus @ C @ C ) )
       => ( ( some_state @ A )
          = ( plus @ A @ A ) ) ) ) ).

% positivity
thf(fact_77_asso1,axiom,
    ! [A: state,B: state,Ab: state,C: state,Bc: state] :
      ( ( ( ( plus @ A @ B )
          = ( some_state @ Ab ) )
        & ( ( plus @ B @ C )
          = ( some_state @ Bc ) ) )
     => ( ( plus @ Ab @ C )
        = ( plus @ A @ Bc ) ) ) ).

% asso1
thf(fact_78__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,X4: state] :
          ( ( ( member_state @ A5 @ a )
            & ( ( some_state @ X4 )
              = ( plus @ ( r @ A5 @ wa ) @ A5 ) ) )
         => ( member_state @ X4 @ b ) )
     => ~ ! [A5: state,X4: state] :
            ( ( ( member_state @ A5 @ a )
              & ( ( some_state @ X4 )
                = ( plus @ ( r @ A5 @ wb ) @ A5 ) ) )
           => ( member_state @ X4 @ 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_79__092_060open_062get__h_Ay_A_061_Aget__h_Aya_A_L_L_Aget__h_Ayb_092_060close_062,axiom,
    ( ( get_h @ y )
    = ( map_ad2908576761495157028ar_val @ ( get_h @ ya ) @ ( get_h @ yb ) ) ) ).

% \<open>get_h y = get_h ya ++ get_h yb\<close>
thf(fact_80__092_060open_062get__h_Aya_A_061_Aget__h_Awa_A_L_L_Aget__h_Aa_092_060close_062,axiom,
    ( ( get_h @ ya )
    = ( map_ad2908576761495157028ar_val @ ( get_h @ wa ) @ ( get_h @ a2 ) ) ) ).

% \<open>get_h ya = get_h wa ++ get_h a\<close>
thf(fact_81__092_060open_062get__h_Ayb_A_061_Aget__h_Awb_A_L_L_Aget__h_Aa_092_060close_062,axiom,
    ( ( get_h @ yb )
    = ( map_ad2908576761495157028ar_val @ ( get_h @ wb ) @ ( get_h @ a2 ) ) ) ).

% \<open>get_h yb = get_h wb ++ get_h a\<close>
thf(fact_82_r_I2_J,axiom,
    ! [A: state,X: state] :
      ( ( ( member_state @ A @ a )
        & ( ( some_state @ X )
          = ( plus @ ( r @ A @ wb ) @ A ) ) )
     => ( member_state @ X @ b ) ) ).

% r(2)
thf(fact_83_r_I1_J,axiom,
    ! [A: state,X: state] :
      ( ( ( member_state @ A @ a )
        & ( ( some_state @ X )
          = ( plus @ ( r @ A @ wa ) @ A ) ) )
     => ( member_state @ X @ b ) ) ).

% r(1)
thf(fact_84_padd__comp__one,axiom,
    ! [X: prat] :
      ( ( pgte @ pwrite @ X )
     => ( ( padd @ X @ ( comp_one @ X ) )
        = pwrite ) ) ).

% padd_comp_one
thf(fact_85_pinv__pmult__ok,axiom,
    ! [P3: prat] :
      ( ( ppos @ P3 )
     => ( ( pmult @ P3 @ ( pinv @ P3 ) )
        = pwrite ) ) ).

% pinv_pmult_ok
thf(fact_86__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_87__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_88_sum__coeff,axiom,
    ! [A: prat,B: prat] :
      ( ( ppos @ A )
     => ( ( ppos @ B )
       => ( ( padd @ ( pdiv @ A @ ( padd @ A @ B ) ) @ ( pdiv @ B @ ( padd @ A @ B ) ) )
          = pwrite ) ) ) ).

% sum_coeff
thf(fact_89_assms_I1_J,axiom,
    combinable @ b ).

% assms(1)
thf(fact_90_assms_I2_J,axiom,
    intuitionistic @ b ).

% assms(2)
thf(fact_91__092_060open_062ya_A_092_060in_062_AB_092_060close_062,axiom,
    member_state @ ya @ b ).

% \<open>ya \<in> B\<close>
thf(fact_92__092_060open_062yb_A_092_060in_062_AB_092_060close_062,axiom,
    member_state @ yb @ b ).

% \<open>yb \<in> B\<close>
thf(fact_93__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_94__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_95__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_96_PartialSA_Osucc__antisym,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( ( greater @ B @ A )
       => ( A = B ) ) ) ).

% PartialSA.succ_antisym
thf(fact_97_PartialSA_Osucc__trans,axiom,
    ! [A: state,B: state,C: state] :
      ( ( greater @ A @ B )
     => ( ( greater @ B @ C )
       => ( greater @ A @ C ) ) ) ).

% PartialSA.succ_trans
thf(fact_98_PartialSA_Osucc__refl,axiom,
    ! [A: state] : ( greater @ A @ A ) ).

% PartialSA.succ_refl
thf(fact_99_pinv__def,axiom,
    ( pinv
    = ( pdiv @ pwrite ) ) ).

% pinv_def
thf(fact_100_PartialSA_Osmaller__compatible,axiom,
    ! [A3: state,B: state,A: state] :
      ( ( defined @ A3 @ B )
     => ( ( greater @ A3 @ A )
       => ( defined @ A @ B ) ) ) ).

% PartialSA.smaller_compatible
thf(fact_101_R__smaller,axiom,
    ! [W: state,A: state] : ( greater @ W @ ( r @ A @ W ) ) ).

% R_smaller
thf(fact_102_larger__heap__plus,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( larger1532547405891354081ar_val @ A @ C )
       => ( larger1532547405891354081ar_val @ A @ ( map_ad2908576761495157028ar_val @ B @ C ) ) ) ) ).

% larger_heap_plus
thf(fact_103_PartialSA_Obigger__sum,axiom,
    ! [Phi: state,A: state,B: state,Phi2: state] :
      ( ( ( some_state @ Phi )
        = ( plus @ A @ B ) )
     => ( ( greater @ Phi2 @ Phi )
       => ? [B3: state] :
            ( ( greater @ B3 @ B )
            & ( ( some_state @ Phi2 )
              = ( plus @ A @ B3 ) ) ) ) ) ).

% PartialSA.bigger_sum
thf(fact_104_PartialSA_Ogreater__def,axiom,
    ( greater
    = ( ^ [A2: state,B2: state] :
        ? [C2: state] :
          ( ( some_state @ A2 )
          = ( plus @ B2 @ C2 ) ) ) ) ).

% PartialSA.greater_def
thf(fact_105_PartialSA_Ogreater__equiv,axiom,
    ( greater
    = ( ^ [A2: state,B2: state] :
        ? [C2: state] :
          ( ( some_state @ A2 )
          = ( plus @ C2 @ B2 ) ) ) ) ).

% PartialSA.greater_equiv
thf(fact_106_PartialSA_Oaddition__bigger,axiom,
    ! [A3: state,A: state,X5: state,B: state,X: state] :
      ( ( greater @ A3 @ A )
     => ( ( ( some_state @ X5 )
          = ( plus @ A3 @ B ) )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( greater @ X5 @ X ) ) ) ) ).

% PartialSA.addition_bigger
thf(fact_107_PartialSA_Obigger__sum__smaller,axiom,
    ! [C: state,A: state,B: state,A3: state] :
      ( ( ( some_state @ C )
        = ( plus @ A @ B ) )
     => ( ( greater @ A @ A3 )
       => ? [B3: state] :
            ( ( greater @ B3 @ B )
            & ( ( some_state @ C )
              = ( plus @ A3 @ B3 ) ) ) ) ) ).

% PartialSA.bigger_sum_smaller
thf(fact_108_larger__implies__greater__mask__hl,axiom,
    ! [A: state,B: state,Hl3: produc1457211279475724562t_char] :
      ( ( greater @ A @ B )
     => ( pgte @ ( get_m @ A @ Hl3 ) @ ( get_m @ B @ Hl3 ) ) ) ).

% larger_implies_greater_mask_hl
thf(fact_109_larger__implies__larger__heap,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( larger1532547405891354081ar_val @ ( get_h @ A ) @ ( get_h @ B ) ) ) ).

% larger_implies_larger_heap
thf(fact_110_pinv__pwrite,axiom,
    ( ( pinv @ pwrite )
    = pwrite ) ).

% pinv_pwrite
thf(fact_111_ppos__inv,axiom,
    ! [P3: prat] :
      ( ( ppos @ P3 )
     => ( ppos @ ( pinv @ P3 ) ) ) ).

% ppos_inv
thf(fact_112_multiply__order,axiom,
    ! [P3: prat,A: state,B: state] :
      ( ( pgte @ pwrite @ P3 )
     => ( ( greater @ A @ B )
       => ( greater @ ( multiply @ P3 @ A ) @ ( multiply @ P3 @ B ) ) ) ) ).

% multiply_order
thf(fact_113_plus__charact_I2_J,axiom,
    ! [A: state,B: state,X: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ X ) )
     => ( ( get_h @ X )
        = ( map_ad2908576761495157028ar_val @ ( get_h @ A ) @ ( get_h @ B ) ) ) ) ).

% plus_charact(2)
thf(fact_114_pmult__pdiv__cancel,axiom,
    ! [A: prat,X: prat] :
      ( ( ppos @ A )
     => ( ( pmult @ A @ ( pdiv @ X @ A ) )
        = X ) ) ).

% pmult_pdiv_cancel
thf(fact_115_pinv__inverts,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( ppos @ B )
       => ( pgte @ ( pinv @ B ) @ ( pinv @ A ) ) ) ) ).

% pinv_inverts
thf(fact_116_in__cwand,axiom,
    ! [A4: set_state,W: state,B4: set_state] :
      ( ! [A6: state,X3: state] :
          ( ( ( member_state @ A6 @ A4 )
            & ( ( some_state @ X3 )
              = ( plus @ ( r @ A6 @ W ) @ A6 ) ) )
         => ( member_state @ X3 @ B4 ) )
     => ( member_state @ W @ ( cwand @ A4 @ B4 ) ) ) ).

% in_cwand
thf(fact_117_pdiv__smaller,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( ppos @ A )
       => ( pgte @ pwrite @ ( pdiv @ B @ A ) ) ) ) ).

% pdiv_smaller
thf(fact_118__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_119__092_060open_062multiply_A_092_060beta_062_Ayb_A_092_060in_062_Amultiply__sem__assertion_A_092_060beta_062_AB_092_060close_062,axiom,
    member_state @ ( multiply @ beta @ yb ) @ ( multip8064567061438756306ertion @ beta @ b ) ).

% \<open>multiply \<beta> yb \<in> multiply_sem_assertion \<beta> B\<close>
thf(fact_120__092_060open_062multiply_A_092_060alpha_062_Aya_A_092_060in_062_Amultiply__sem__assertion_A_092_060alpha_062_AB_092_060close_062,axiom,
    member_state @ ( multiply @ alpha @ ya ) @ ( multip8064567061438756306ertion @ alpha @ b ) ).

% \<open>multiply \<alpha> ya \<in> multiply_sem_assertion \<alpha> B\<close>
thf(fact_121_asm,axiom,
    member_state @ w @ ( add_set @ ( multip8064567061438756306ertion @ alpha @ ( cwand @ a @ b ) ) @ ( multip8064567061438756306ertion @ beta @ ( cwand @ a @ b ) ) ) ).

% asm
thf(fact_122_map__add__find__right,axiom,
    ! [N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,Xx: val,M: produc1457211279475724562t_char > option_val] :
      ( ( ( N @ K )
        = ( some_val @ Xx ) )
     => ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ Xx ) ) ) ).

% map_add_find_right
thf(fact_123_pinv__double__half,axiom,
    ! [P3: prat] :
      ( ( ppos @ P3 )
     => ( ( pmult @ half @ ( pinv @ P3 ) )
        = ( pinv @ ( padd @ P3 @ P3 ) ) ) ) ).

% pinv_double_half
thf(fact_124_map__add__assoc,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val,M3: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ M1 @ ( map_ad2908576761495157028ar_val @ M2 @ M3 ) )
      = ( map_ad2908576761495157028ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) @ M3 ) ) ).

% map_add_assoc
thf(fact_125_get__m__smaller__mask,axiom,
    ! [P3: prat,A: state] :
      ( ( pgte @ pwrite @ P3 )
     => ( ( get_m @ ( multiply @ P3 @ A ) )
        = ( multiply_mask @ P3 @ ( get_m @ A ) ) ) ) ).

% get_m_smaller_mask
thf(fact_126_greaterI,axiom,
    ! [A: state,B: state] :
      ( ( larger1532547405891354081ar_val @ ( get_h @ A ) @ ( get_h @ B ) )
     => ( ( greate7680731506090375811t_char @ ( get_m @ A ) @ ( get_m @ B ) )
       => ( greater @ A @ B ) ) ) ).

% greaterI
thf(fact_127_comp__min__mask__def,axiom,
    ( comp_min_mask
    = ( ^ [B2: produc1457211279475724562t_char > prat,A2: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char] : ( pmin @ ( A2 @ Hl ) @ ( comp_one @ ( B2 @ Hl ) ) ) ) ) ).

% comp_min_mask_def
thf(fact_128_pmin__comm,axiom,
    ( pmin
    = ( ^ [A2: prat,B2: prat] : ( pmin @ B2 @ A2 ) ) ) ).

% pmin_comm
thf(fact_129_PartialSA_Oadd__set__asso,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( add_set @ ( add_set @ A4 @ B4 ) @ C3 )
      = ( add_set @ A4 @ ( add_set @ B4 @ C3 ) ) ) ).

% PartialSA.add_set_asso
thf(fact_130_PartialSA_Oadd__set__commm,axiom,
    ( add_set
    = ( ^ [A7: set_state,B5: set_state] : ( add_set @ B5 @ A7 ) ) ) ).

% PartialSA.add_set_commm
thf(fact_131_in__multiply__refl,axiom,
    ! [X: state,A4: set_state,P3: prat] :
      ( ( member_state @ X @ A4 )
     => ( member_state @ ( multiply @ P3 @ X ) @ ( multip8064567061438756306ertion @ P3 @ A4 ) ) ) ).

% in_multiply_refl
thf(fact_132_pmin__is,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pmin @ A @ B )
        = B ) ) ).

% pmin_is
thf(fact_133_pmin__greater,axiom,
    ! [A: prat,B: prat] : ( pgte @ A @ ( pmin @ A @ B ) ) ).

% pmin_greater
thf(fact_134_PartialSA_Ox__elem__set__product,axiom,
    ! [X: state,A4: set_state,B4: set_state] :
      ( ( member_state @ X @ ( add_set @ A4 @ B4 ) )
      = ( ? [A2: state,B2: state] :
            ( ( member_state @ A2 @ A4 )
            & ( member_state @ B2 @ B4 )
            & ( ( some_state @ X )
              = ( plus @ A2 @ B2 ) ) ) ) ) ).

% PartialSA.x_elem_set_product
thf(fact_135_PartialSA_Oadd__set__elem,axiom,
    ! [Phi: state,A4: set_state,B4: set_state] :
      ( ( member_state @ Phi @ ( add_set @ A4 @ B4 ) )
      = ( ? [A2: state,B2: state] :
            ( ( ( some_state @ Phi )
              = ( plus @ A2 @ B2 ) )
            & ( member_state @ A2 @ A4 )
            & ( member_state @ B2 @ B4 ) ) ) ) ).

% PartialSA.add_set_elem
thf(fact_136_in__multiply__sem,axiom,
    ! [X: state,P3: prat,A4: set_state] :
      ( ( member_state @ X @ ( multip8064567061438756306ertion @ P3 @ A4 ) )
     => ? [X3: state] :
          ( ( member_state @ X3 @ A4 )
          & ( greater @ X @ ( multiply @ P3 @ X3 ) ) ) ) ).

% in_multiply_sem
thf(fact_137_intuitionistic__def,axiom,
    ( intuitionistic
    = ( ^ [A7: set_state] :
        ! [A2: state,B2: state] :
          ( ( ( greater @ A2 @ B2 )
            & ( member_state @ B2 @ A7 ) )
         => ( member_state @ A2 @ A7 ) ) ) ) ).

% intuitionistic_def
thf(fact_138_half__plus__half,axiom,
    ( ( padd @ half @ half )
    = pwrite ) ).

% half_plus_half
thf(fact_139_mult__greater,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,P3: prat] :
      ( ( greate7680731506090375811t_char @ A @ B )
     => ( greate7680731506090375811t_char @ ( multiply_mask @ P3 @ A ) @ ( multiply_mask @ P3 @ B ) ) ) ).

% mult_greater
thf(fact_140_combinableI,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ! [A6: prat,B6: prat] :
          ( ( ( ppos @ A6 )
            & ( ppos @ B6 )
            & ( ( padd @ A6 @ B6 )
              = pwrite ) )
         => ( ord_le2494988322063910608_state @ ( add_set @ ( multip8064567061438756306ertion @ A6 @ ( cwand @ A4 @ B4 ) ) @ ( multip8064567061438756306ertion @ B6 @ ( cwand @ A4 @ B4 ) ) ) @ ( cwand @ A4 @ B4 ) ) )
     => ( combinable @ ( cwand @ A4 @ B4 ) ) ) ).

% combinableI
thf(fact_141_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_142_multiply__mask__def,axiom,
    ( multiply_mask
    = ( ^ [P5: prat,Pi: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char] : ( pmult @ P5 @ ( Pi @ Hl ) ) ) ) ).

% multiply_mask_def
thf(fact_143_mult__write__mask,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ pwrite @ Pi2 )
      = Pi2 ) ).

% mult_write_mask
thf(fact_144_greater__mask__equiv__def,axiom,
    ( greate7680731506090375811t_char
    = ( ^ [Pi3: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat] :
        ! [Hl: produc1457211279475724562t_char] : ( pgte @ ( Pi3 @ Hl ) @ ( Pi @ Hl ) ) ) ) ).

% greater_mask_equiv_def
thf(fact_145_greater__maskI,axiom,
    ! [Pi4: produc1457211279475724562t_char > prat,Pi2: produc1457211279475724562t_char > prat] :
      ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ ( Pi4 @ Hl2 ) @ ( Pi2 @ Hl2 ) )
     => ( greate7680731506090375811t_char @ Pi4 @ Pi2 ) ) ).

% greater_maskI
thf(fact_146_half__between__0__1,axiom,
    ( ( ppos @ half )
    & ( pgt @ pwrite @ half ) ) ).

% half_between_0_1
thf(fact_147_empty__heap__neutral,axiom,
    ! [A: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ A @ empty_7512026568161686585ar_val )
      = A ) ).

% empty_heap_neutral
thf(fact_148_double__inclusion,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ A4 )
       => ( A4 = B4 ) ) ) ).

% double_inclusion
thf(fact_149_pgt__implies__pgte,axiom,
    ! [A: prat,B: prat] :
      ( ( pgt @ A @ B )
     => ( pgte @ A @ B ) ) ).

% pgt_implies_pgte
thf(fact_150_not__pgte__charact,axiom,
    ! [A: prat,B: prat] :
      ( ( ~ ( pgte @ A @ B ) )
      = ( pgt @ B @ A ) ) ).

% not_pgte_charact
thf(fact_151_greater__mask__properties_I3_J,axiom,
    ! [Pi4: produc1457211279475724562t_char > prat,Pi2: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ Pi4 @ Pi2 )
        & ( greate7680731506090375811t_char @ Pi2 @ Pi4 ) )
     => ( Pi2 = Pi4 ) ) ).

% greater_mask_properties(3)
thf(fact_152_greater__mask__properties_I2_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( ( greate7680731506090375811t_char @ A @ B )
        & ( greate7680731506090375811t_char @ B @ C ) )
     => ( greate7680731506090375811t_char @ A @ C ) ) ).

% greater_mask_properties(2)
thf(fact_153_greater__mask__properties_I1_J,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat] : ( greate7680731506090375811t_char @ Pi2 @ Pi2 ) ).

% greater_mask_properties(1)
thf(fact_154_pgte__pgt,axiom,
    ! [A: prat,B: prat,C: prat,D: prat] :
      ( ( pgt @ A @ B )
     => ( ( pgte @ C @ D )
       => ( pgt @ ( padd @ A @ C ) @ ( padd @ B @ D ) ) ) ) ).

% pgte_pgt
thf(fact_155_subsetI,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( member7461423308196221312_state @ X3 @ B4 ) )
     => ( ord_le4032880777312351359_state @ A4 @ B4 ) ) ).

% subsetI
thf(fact_156_subsetI,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X3 @ A4 )
         => ( member2879030624002546611on_val @ X3 @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A4 @ B4 ) ) ).

% subsetI
thf(fact_157_subsetI,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( member6715010751053357271_state @ X3 @ B4 ) )
     => ( ord_le6483787752022044334_state @ A4 @ B4 ) ) ).

% subsetI
thf(fact_158_subsetI,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member_state @ X3 @ B4 ) )
     => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ).

% subsetI
thf(fact_159_order__refl,axiom,
    ! [X: set_state] : ( ord_le2494988322063910608_state @ X @ X ) ).

% order_refl
thf(fact_160_dual__order_Orefl,axiom,
    ! [A: set_state] : ( ord_le2494988322063910608_state @ A @ A ) ).

% dual_order.refl
thf(fact_161_cwand__stronger,axiom,
    ! [A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( cwand @ A4 @ B4 ) @ ( wand @ A4 @ B4 ) ) ).

% cwand_stronger
thf(fact_162_binary__same,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( binary @ A4 )
     => ( ( intuitionistic @ B4 )
       => ( ord_le2494988322063910608_state @ ( wand @ A4 @ B4 ) @ ( cwand @ A4 @ B4 ) ) ) ) ).

% binary_same
thf(fact_163_greater__mask__uniI,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,Hl3: produc1457211279475724562t_char,R2: prat] :
      ( ( pgte @ ( Pi2 @ Hl3 ) @ R2 )
     => ( greate7680731506090375811t_char @ Pi2 @ ( uni_ma6578582744724537101t_char @ Hl3 @ R2 ) ) ) ).

% greater_mask_uniI
thf(fact_164_greater__mask__uni__equiv,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,Hl3: produc1457211279475724562t_char,R2: prat] :
      ( ( greate7680731506090375811t_char @ Pi2 @ ( uni_ma6578582744724537101t_char @ Hl3 @ R2 ) )
      = ( pgte @ ( Pi2 @ Hl3 ) @ R2 ) ) ).

% greater_mask_uni_equiv
thf(fact_165_wandI,axiom,
    ! [A4: set_state,W: state,B4: set_state] :
      ( ! [A6: state,X3: state] :
          ( ( ( member_state @ A6 @ A4 )
            & ( ( some_state @ X3 )
              = ( plus @ A6 @ W ) ) )
         => ( member_state @ X3 @ B4 ) )
     => ( member_state @ W @ ( wand @ A4 @ B4 ) ) ) ).

% wandI
thf(fact_166_pmin__pmax,axiom,
    ! [X: prat,A: prat,B: prat] :
      ( ( pgte @ X @ ( pmin @ A @ B ) )
     => ( X
        = ( pmin @ ( pmax @ X @ A ) @ ( pmax @ X @ B ) ) ) ) ).

% pmin_pmax
thf(fact_167_pmax__comm,axiom,
    ( pmax
    = ( ^ [A2: prat,B2: prat] : ( pmax @ B2 @ A2 ) ) ) ).

% pmax_comm
thf(fact_168_pmax__is,axiom,
    ! [A: prat,B: prat] :
      ( ( pgte @ A @ B )
     => ( ( pmax @ A @ B )
        = A ) ) ).

% pmax_is
thf(fact_169_pmax__smaller,axiom,
    ! [A: prat,B: prat] : ( pgte @ ( pmax @ A @ B ) @ A ) ).

% pmax_smaller
thf(fact_170_pmax__is__smaller,axiom,
    ! [X: prat,A: prat,B: prat] :
      ( ( pgte @ X @ A )
     => ( ( pgte @ X @ B )
       => ( pgte @ X @ ( pmax @ A @ B ) ) ) ) ).

% pmax_is_smaller
thf(fact_171_order__antisym__conv,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( ord_le2494988322063910608_state @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_172_ord__le__eq__subst,axiom,
    ! [A: set_state,B: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X3: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X3 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X3 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_173_ord__eq__le__subst,axiom,
    ! [A: set_state,F: set_state > set_state,B: set_state,C: set_state] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ! [X3: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X3 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X3 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_174_order__eq__refl,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( X = Y )
     => ( ord_le2494988322063910608_state @ X @ Y ) ) ).

% order_eq_refl
thf(fact_175_order__subst2,axiom,
    ! [A: set_state,B: set_state,F: set_state > set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ ( F @ B ) @ C )
       => ( ! [X3: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X3 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X3 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_176_order__subst1,axiom,
    ! [A: set_state,F: set_state > set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ ( F @ B ) )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ! [X3: set_state,Y3: set_state] :
              ( ( ord_le2494988322063910608_state @ X3 @ Y3 )
             => ( ord_le2494988322063910608_state @ ( F @ X3 ) @ ( F @ Y3 ) ) )
         => ( ord_le2494988322063910608_state @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_177_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A2: set_state,B2: set_state] :
          ( ( ord_le2494988322063910608_state @ A2 @ B2 )
          & ( ord_le2494988322063910608_state @ B2 @ A2 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_178_antisym,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_179_dual__order_Otrans,axiom,
    ! [B: set_state,A: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ C @ B )
       => ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_180_dual__order_Oantisym,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_181_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A2: set_state,B2: set_state] :
          ( ( ord_le2494988322063910608_state @ B2 @ A2 )
          & ( ord_le2494988322063910608_state @ A2 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_182_order__trans,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ Z2 )
       => ( ord_le2494988322063910608_state @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_183_order_Otrans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% order.trans
thf(fact_184_order__antisym,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( ord_le2494988322063910608_state @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_185_ord__le__eq__trans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( B = C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_186_ord__eq__le__trans,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( A = B )
     => ( ( ord_le2494988322063910608_state @ B @ C )
       => ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_187_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [X2: set_state,Y5: set_state] :
          ( ( ord_le2494988322063910608_state @ X2 @ Y5 )
          & ( ord_le2494988322063910608_state @ Y5 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_188_Collect__mono__iff,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P2 ) @ ( collec906845016635587262_state @ Q ) )
      = ( ! [X2: produc7272280185086996969_state] :
            ( ( P2 @ X2 )
           => ( Q @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_189_Collect__mono__iff,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P2 ) @ ( collec7475294502966882545on_val @ Q ) )
      = ( ! [X2: produc9003781588162623004on_val] :
            ( ( P2 @ X2 )
           => ( Q @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_190_Collect__mono__iff,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ ( collect_state @ P2 ) @ ( collect_state @ Q ) )
      = ( ! [X2: state] :
            ( ( P2 @ X2 )
           => ( Q @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_191_set__eq__subset,axiom,
    ( ( ^ [Y4: set_state,Z: set_state] : ( Y4 = Z ) )
    = ( ^ [A7: set_state,B5: set_state] :
          ( ( ord_le2494988322063910608_state @ A7 @ B5 )
          & ( ord_le2494988322063910608_state @ B5 @ A7 ) ) ) ) ).

% set_eq_subset
thf(fact_192_subset__trans,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
       => ( ord_le2494988322063910608_state @ A4 @ C3 ) ) ) ).

% subset_trans
thf(fact_193_Collect__mono,axiom,
    ! [P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
         => ( Q @ X3 ) )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ P2 ) @ ( collec906845016635587262_state @ Q ) ) ) ).

% Collect_mono
thf(fact_194_Collect__mono,axiom,
    ! [P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( P2 @ X3 )
         => ( Q @ X3 ) )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ P2 ) @ ( collec7475294502966882545on_val @ Q ) ) ) ).

% Collect_mono
thf(fact_195_Collect__mono,axiom,
    ! [P2: state > $o,Q: state > $o] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
         => ( Q @ X3 ) )
     => ( ord_le2494988322063910608_state @ ( collect_state @ P2 ) @ ( collect_state @ Q ) ) ) ).

% Collect_mono
thf(fact_196_subset__refl,axiom,
    ! [A4: set_state] : ( ord_le2494988322063910608_state @ A4 @ A4 ) ).

% subset_refl
thf(fact_197_subset__iff,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A7: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
        ! [T: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ T @ A7 )
         => ( member7461423308196221312_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_198_subset__iff,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A7: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
        ! [T: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ T @ A7 )
         => ( member2879030624002546611on_val @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_199_subset__iff,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A7: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
        ! [T: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ T @ A7 )
         => ( member6715010751053357271_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_200_subset__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A7: set_state,B5: set_state] :
        ! [T: state] :
          ( ( member_state @ T @ A7 )
         => ( member_state @ T @ B5 ) ) ) ) ).

% subset_iff
thf(fact_201_equalityD2,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( A4 = B4 )
     => ( ord_le2494988322063910608_state @ B4 @ A4 ) ) ).

% equalityD2
thf(fact_202_equalityD1,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( A4 = B4 )
     => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ).

% equalityD1
thf(fact_203_subset__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A7: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
        ! [X2: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X2 @ A7 )
         => ( member7461423308196221312_state @ X2 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_204_subset__eq,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A7: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
        ! [X2: produc9003781588162623004on_val] :
          ( ( member2879030624002546611on_val @ X2 @ A7 )
         => ( member2879030624002546611on_val @ X2 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_205_subset__eq,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A7: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
        ! [X2: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X2 @ A7 )
         => ( member6715010751053357271_state @ X2 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_206_subset__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A7: set_state,B5: set_state] :
        ! [X2: state] :
          ( ( member_state @ X2 @ A7 )
         => ( member_state @ X2 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_207_equalityE,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( A4 = B4 )
     => ~ ( ( ord_le2494988322063910608_state @ A4 @ B4 )
         => ~ ( ord_le2494988322063910608_state @ B4 @ A4 ) ) ) ).

% equalityE
thf(fact_208_subsetD,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ B4 )
     => ( ( member7461423308196221312_state @ C @ A4 )
       => ( member7461423308196221312_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_209_subsetD,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,C: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A4 @ B4 )
     => ( ( member2879030624002546611on_val @ C @ A4 )
       => ( member2879030624002546611on_val @ C @ B4 ) ) ) ).

% subsetD
thf(fact_210_subsetD,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,C: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ B4 )
     => ( ( member6715010751053357271_state @ C @ A4 )
       => ( member6715010751053357271_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_211_subsetD,axiom,
    ! [A4: set_state,B4: set_state,C: state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( member_state @ C @ A4 )
       => ( member_state @ C @ B4 ) ) ) ).

% subsetD
thf(fact_212_in__mono,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,X: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ B4 )
     => ( ( member7461423308196221312_state @ X @ A4 )
       => ( member7461423308196221312_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_213_in__mono,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A4 @ B4 )
     => ( ( member2879030624002546611on_val @ X @ A4 )
       => ( member2879030624002546611on_val @ X @ B4 ) ) ) ).

% in_mono
thf(fact_214_in__mono,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,X: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ B4 )
     => ( ( member6715010751053357271_state @ X @ A4 )
       => ( member6715010751053357271_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_215_in__mono,axiom,
    ! [A4: set_state,B4: set_state,X: state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( member_state @ X @ A4 )
       => ( member_state @ X @ B4 ) ) ) ).

% in_mono
thf(fact_216_larger__heaps__sum__ineq,axiom,
    ! [A3: produc1457211279475724562t_char > option_val,A: produc1457211279475724562t_char > option_val,B7: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A3 @ A )
     => ( ( larger1532547405891354081ar_val @ B7 @ B )
       => ( ( compatible_heaps @ A3 @ B7 )
         => ( larger1532547405891354081ar_val @ ( map_ad2908576761495157028ar_val @ A3 @ B7 ) @ ( map_ad2908576761495157028ar_val @ A @ B ) ) ) ) ) ).

% larger_heaps_sum_ineq
thf(fact_217_upper__bounded__smaller,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,A: prat,P3: prat] :
      ( ( upper_bounded @ Pi2 @ A )
     => ( upper_bounded @ ( multiply_mask @ P3 @ Pi2 ) @ ( pmult @ P3 @ A ) ) ) ).

% upper_bounded_smaller
thf(fact_218_PartialSA_Ox__elem__set__product__splus,axiom,
    ! [X: state,A4: set_state,B4: set_state] :
      ( ( member_state @ X @ ( add_set @ A4 @ B4 ) )
      = ( ? [A2: state,B2: state] :
            ( ( member_state @ A2 @ A4 )
            & ( member_state @ B2 @ B4 )
            & ( ( some_state @ X )
              = ( sep_splus_state @ plus @ ( some_state @ A2 ) @ ( some_state @ B2 ) ) ) ) ) ) ).

% PartialSA.x_elem_set_product_splus
thf(fact_219_PartialSA_Osmaller__pure__sum__smaller,axiom,
    ! [Y: state,A: state,B: state,X: state] :
      ( ( greater @ Y @ A )
     => ( ( greater @ Y @ B )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( ( sep_pure_state @ plus @ B )
           => ( greater @ Y @ X ) ) ) ) ) ).

% PartialSA.smaller_pure_sum_smaller
thf(fact_220_valid__mult,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,P3: prat] :
      ( ( valid_mask @ Pi2 )
     => ( ( pgte @ pwrite @ P3 )
       => ( valid_mask @ ( multiply_mask @ P3 @ Pi2 ) ) ) ) ).

% valid_mult
thf(fact_221_PartialSA_Omono__propI,axiom,
    ! [P2: state > $o] :
      ( ! [X3: state,Y3: state] :
          ( ( ( greater @ Y3 @ X3 )
            & ( P2 @ X3 ) )
         => ( P2 @ Y3 ) )
     => ( sep_mono_prop_state @ plus @ P2 ) ) ).

% PartialSA.mono_propI
thf(fact_222_PartialSA_Omono__prop__def,axiom,
    ! [P2: state > $o] :
      ( ( sep_mono_prop_state @ plus @ P2 )
      = ( ! [X2: state,Y5: state] :
            ( ( ( greater @ Y5 @ X2 )
              & ( P2 @ X2 ) )
           => ( P2 @ Y5 ) ) ) ) ).

% PartialSA.mono_prop_def
thf(fact_223_PartialSA_Ointuitionistic__def,axiom,
    ! [A4: state > $o] :
      ( ( packag8361946002163212404_state @ plus @ A4 )
      = ( ! [Phi3: state,Phi4: state] :
            ( ( ( greater @ Phi3 @ Phi4 )
              & ( A4 @ Phi4 ) )
           => ( A4 @ Phi3 ) ) ) ) ).

% PartialSA.intuitionistic_def
thf(fact_224_compatible__heapsI,axiom,
    ! [H: produc1457211279475724562t_char > option_val,H4: produc1457211279475724562t_char > option_val] :
      ( ! [Hl2: produc1457211279475724562t_char,A6: val,B6: val] :
          ( ( ( H @ Hl2 )
            = ( some_val @ A6 ) )
         => ( ( ( H4 @ Hl2 )
              = ( some_val @ B6 ) )
           => ( A6 = B6 ) ) )
     => ( compatible_heaps @ H @ H4 ) ) ).

% compatible_heapsI
thf(fact_225_PartialSA_Osplus__asso,axiom,
    ! [A: option_state,B: option_state,C: option_state] :
      ( ( sep_splus_state @ plus @ ( sep_splus_state @ plus @ A @ B ) @ C )
      = ( sep_splus_state @ plus @ A @ ( sep_splus_state @ plus @ B @ C ) ) ) ).

% PartialSA.splus_asso
thf(fact_226_PartialSA_Osplus__comm,axiom,
    ! [A: option_state,B: option_state] :
      ( ( sep_splus_state @ plus @ A @ B )
      = ( sep_splus_state @ plus @ B @ A ) ) ).

% PartialSA.splus_comm
thf(fact_227_upper__boundedI,axiom,
    ! [P3: prat,Pi2: produc1457211279475724562t_char > prat] :
      ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ P3 @ ( Pi2 @ Hl2 ) )
     => ( upper_bounded @ Pi2 @ P3 ) ) ).

% upper_boundedI
thf(fact_228_upper__bounded__def,axiom,
    ( upper_bounded
    = ( ^ [Pi: produc1457211279475724562t_char > prat,P5: prat] :
        ! [Hl: produc1457211279475724562t_char] : ( pgte @ P5 @ ( Pi @ Hl ) ) ) ) ).

% upper_bounded_def
thf(fact_229_upper__bounded__bigger,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,A: prat,B: prat] :
      ( ( upper_bounded @ Pi2 @ A )
     => ( ( pgte @ B @ A )
       => ( upper_bounded @ Pi2 @ B ) ) ) ).

% upper_bounded_bigger
thf(fact_230_compatible__heaps__comm,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A @ B )
     => ( ( map_ad2908576761495157028ar_val @ A @ B )
        = ( map_ad2908576761495157028ar_val @ B @ A ) ) ) ).

% compatible_heaps_comm
thf(fact_231_compatible__heaps__sum,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( compatible_heaps @ A @ B )
     => ( ( compatible_heaps @ A @ C )
       => ( compatible_heaps @ A @ ( map_ad2908576761495157028ar_val @ B @ C ) ) ) ) ).

% compatible_heaps_sum
thf(fact_232_larger__heap__comp,axiom,
    ! [A: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,C: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ B )
     => ( ( compatible_heaps @ A @ C )
       => ( compatible_heaps @ B @ C ) ) ) ).

% larger_heap_comp
thf(fact_233_larger__compatible__sum__heaps,axiom,
    ! [A: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char > option_val,B: produc1457211279475724562t_char > option_val,Y: produc1457211279475724562t_char > option_val] :
      ( ( larger1532547405891354081ar_val @ A @ X )
     => ( ( larger1532547405891354081ar_val @ B @ Y )
       => ( ( compatible_heaps @ A @ B )
         => ( compatible_heaps @ X @ Y ) ) ) ) ).

% larger_compatible_sum_heaps
thf(fact_234_PartialSA_Osplus_Osimps_I3_J,axiom,
    ! [A: state,B: state] :
      ( ( sep_splus_state @ plus @ ( some_state @ A ) @ ( some_state @ B ) )
      = ( plus @ A @ B ) ) ).

% PartialSA.splus.simps(3)
thf(fact_235_PartialSA_Osplus__develop,axiom,
    ! [A: state,B: state,C: state,D: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ C ) )
     => ( ( plus @ A @ D )
        = ( sep_splus_state @ plus @ ( sep_splus_state @ plus @ ( some_state @ B ) @ ( some_state @ C ) ) @ ( some_state @ D ) ) ) ) ).

% PartialSA.splus_develop
thf(fact_236_PartialSA_Opure__def,axiom,
    ! [A: state] :
      ( ( sep_pure_state @ plus @ A )
      = ( ( some_state @ A )
        = ( plus @ A @ A ) ) ) ).

% PartialSA.pure_def
thf(fact_237_PartialSA_Opure__stable,axiom,
    ! [A: state,B: state,C: state] :
      ( ( sep_pure_state @ plus @ A )
     => ( ( sep_pure_state @ plus @ B )
       => ( ( ( some_state @ C )
            = ( plus @ A @ B ) )
         => ( sep_pure_state @ plus @ C ) ) ) ) ).

% PartialSA.pure_stable
thf(fact_238_PartialSA_Opure__smaller,axiom,
    ! [A: state,B: state] :
      ( ( sep_pure_state @ plus @ A )
     => ( ( greater @ A @ B )
       => ( sep_pure_state @ plus @ B ) ) ) ).

% PartialSA.pure_smaller
thf(fact_239_valid__multiply,axiom,
    ! [A: produc1457211279475724562t_char > prat,Ma: prat,P3: prat] :
      ( ( valid_mask @ A )
     => ( ( upper_bounded @ A @ Ma )
       => ( ( pgte @ pwrite @ ( pmult @ Ma @ P3 ) )
         => ( valid_mask @ ( multiply_mask @ P3 @ A ) ) ) ) ) ).

% valid_multiply
thf(fact_240_valid__larger__mask,axiom,
    ( valid_mask
    = ( greate7680731506090375811t_char @ full_mask ) ) ).

% valid_larger_mask
thf(fact_241_compatibleI,axiom,
    ! [A: state,B: state] :
      ( ( compatible_heaps @ ( get_h @ A ) @ ( get_h @ B ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( get_m @ A ) @ ( get_m @ B ) ) )
       => ( defined @ A @ B ) ) ) ).

% compatibleI
thf(fact_242_valid__sum_I2_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( ( upper_bounded @ A @ Ma )
         => ( ( upper_bounded @ B @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( upper_bounded @ ( add_ma6586698345353345811t_char @ A @ B ) @ ( padd @ Ma @ Mb ) ) ) ) ) ) ) ).

% valid_sum(2)
thf(fact_243_valid__sum_I1_J,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,Ma: prat,Mb: prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( ( upper_bounded @ A @ Ma )
         => ( ( upper_bounded @ B @ Mb )
           => ( ( pgte @ pwrite @ ( padd @ Ma @ Mb ) )
             => ( valid_mask @ ( add_ma6586698345353345811t_char @ A @ B ) ) ) ) ) ) ) ).

% valid_sum(1)
thf(fact_244_PartialSA_Omono__pruner__def,axiom,
    ! [P3: state > $o] :
      ( ( packag2456304381420842418_state @ plus @ P3 )
      = ( ! [Phi3: state,Phi4: state,R: state] :
            ( ( ( sep_pure_state @ plus @ R )
              & ( P3 @ Phi4 )
              & ( ( some_state @ Phi3 )
                = ( plus @ Phi4 @ R ) ) )
           => ( P3 @ Phi3 ) ) ) ) ).

% PartialSA.mono_pruner_def
thf(fact_245_valid__mask__full__mask,axiom,
    valid_mask @ full_mask ).

% valid_mask_full_mask
thf(fact_246_PartialSA_Ominus__sum,axiom,
    ! [A: state,B: state,C: state,X: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ C ) )
     => ( ( greater @ X @ A )
       => ( ( minus @ X @ A )
          = ( minus @ ( minus @ X @ B ) @ C ) ) ) ) ).

% PartialSA.minus_sum
thf(fact_247_PartialSA_Ominus__some,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( ( some_state @ A )
        = ( plus @ B @ ( minus @ A @ B ) ) ) ) ).

% PartialSA.minus_some
thf(fact_248_add__masks__asso,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( add_ma6586698345353345811t_char @ ( add_ma6586698345353345811t_char @ A @ B ) @ C )
      = ( add_ma6586698345353345811t_char @ A @ ( add_ma6586698345353345811t_char @ B @ C ) ) ) ).

% add_masks_asso
thf(fact_249_add__masks__comm,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > prat] : ( add_ma6586698345353345811t_char @ B2 @ A2 ) ) ) ).

% add_masks_comm
thf(fact_250_add__masks__cancellative,axiom,
    ! [B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ B @ C )
        = ( add_ma6586698345353345811t_char @ B @ D ) )
     => ( C = D ) ) ).

% add_masks_cancellative
thf(fact_251_upper__valid,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( A
          = ( add_ma6586698345353345811t_char @ B @ C ) )
       => ( ( valid_mask @ B )
          & ( valid_mask @ C ) ) ) ) ).

% upper_valid
thf(fact_252_upper__valid__aux,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( A
          = ( add_ma6586698345353345811t_char @ B @ C ) )
       => ( valid_mask @ B ) ) ) ).

% upper_valid_aux
thf(fact_253_PartialSA_Ominus__default,axiom,
    ! [B: state,A: state] :
      ( ~ ( greater @ B @ A )
     => ( ( minus @ B @ A )
        = B ) ) ).

% PartialSA.minus_default
thf(fact_254_PartialSA_Ominus__smaller,axiom,
    ! [X: state,A: state] :
      ( ( greater @ X @ A )
     => ( greater @ X @ ( minus @ X @ A ) ) ) ).

% PartialSA.minus_smaller
thf(fact_255_PartialSA_Ogreater__minus__trans,axiom,
    ! [Y: state,X: state,A: state] :
      ( ( greater @ Y @ X )
     => ( ( greater @ X @ A )
       => ( greater @ ( minus @ Y @ A ) @ ( minus @ X @ A ) ) ) ) ).

% PartialSA.greater_minus_trans
thf(fact_256_mult__distr__masks,axiom,
    ! [A: prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ A @ ( add_ma6586698345353345811t_char @ B @ C ) )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A @ B ) @ ( multiply_mask @ A @ C ) ) ) ).

% mult_distr_masks
thf(fact_257_add__masks_Oelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa2: produc1457211279475724562t_char > prat,Xb2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa2 @ Xb2 )
        = Y )
     => ( Y
        = ( padd @ ( X @ Xb2 ) @ ( Xa2 @ Xb2 ) ) ) ) ).

% add_masks.elims
thf(fact_258_add__masks_Osimps,axiom,
    ( add_ma6586698345353345811t_char
    = ( ^ [Pi3: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char] : ( padd @ ( Pi3 @ Hl ) @ ( Pi @ Hl ) ) ) ) ).

% add_masks.simps
thf(fact_259_const__sum__mask__greater,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat,D: produc1457211279475724562t_char > prat] :
      ( ( ( add_ma6586698345353345811t_char @ A @ B )
        = ( add_ma6586698345353345811t_char @ C @ D ) )
     => ( ( greate7680731506090375811t_char @ A @ C )
       => ( greate7680731506090375811t_char @ D @ B ) ) ) ).

% const_sum_mask_greater
thf(fact_260_greater__mask__decomp,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,C: produc1457211279475724562t_char > prat] :
      ( ( greate7680731506090375811t_char @ A @ ( add_ma6586698345353345811t_char @ B @ C ) )
     => ? [A1: produc1457211279475724562t_char > prat,A22: produc1457211279475724562t_char > prat] :
          ( ( A
            = ( add_ma6586698345353345811t_char @ A1 @ A22 ) )
          & ( greate7680731506090375811t_char @ A1 @ B )
          & ( greate7680731506090375811t_char @ A22 @ C ) ) ) ).

% greater_mask_decomp
thf(fact_261_greater__mask__def,axiom,
    ( greate7680731506090375811t_char
    = ( ^ [Pi3: produc1457211279475724562t_char > prat,Pi: produc1457211279475724562t_char > prat] :
        ? [R: produc1457211279475724562t_char > prat] :
          ( Pi3
          = ( add_ma6586698345353345811t_char @ Pi @ R ) ) ) ) ).

% greater_mask_def
thf(fact_262_mult__add__states,axiom,
    ! [A: prat,B: prat,Pi2: produc1457211279475724562t_char > prat] :
      ( ( multiply_mask @ ( padd @ A @ B ) @ Pi2 )
      = ( add_ma6586698345353345811t_char @ ( multiply_mask @ A @ Pi2 ) @ ( multiply_mask @ B @ Pi2 ) ) ) ).

% mult_add_states
thf(fact_263_valid__mask__add__comp__min,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ A )
     => ( ( valid_mask @ B )
       => ( valid_mask @ ( add_ma6586698345353345811t_char @ ( comp_min_mask @ B @ A ) @ B ) ) ) ) ).

% valid_mask_add_comp_min
thf(fact_264_compatible__same__mask,axiom,
    ! [A: produc1457211279475724562t_char > prat,W: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ ( add_ma6586698345353345811t_char @ A @ W ) )
     => ( W
        = ( comp_min_mask @ A @ W ) ) ) ).

% compatible_same_mask
thf(fact_265_plus__charact_I1_J,axiom,
    ! [A: state,B: state,X: state] :
      ( ( ( plus @ A @ B )
        = ( some_state @ X ) )
     => ( ( get_m @ X )
        = ( add_ma6586698345353345811t_char @ ( get_m @ A ) @ ( get_m @ B ) ) ) ) ).

% plus_charact(1)
thf(fact_266_PartialSA_Oprove__last__completeness,axiom,
    ! [A3: state,A: state,Nf1: state,F2: state] :
      ( ( greater @ A3 @ A )
     => ( ( ( some_state @ A )
          = ( plus @ Nf1 @ F2 ) )
       => ( greater @ ( minus @ A3 @ Nf1 ) @ F2 ) ) ) ).

% PartialSA.prove_last_completeness
thf(fact_267_PartialSA_Ominus__and__plus,axiom,
    ! [Omega: state,Omega2: state,R2: state,A: state] :
      ( ( ( some_state @ Omega )
        = ( plus @ Omega2 @ R2 ) )
     => ( ( greater @ Omega2 @ A )
       => ( ( some_state @ ( minus @ Omega @ A ) )
          = ( plus @ ( minus @ Omega2 @ A ) @ R2 ) ) ) ) ).

% PartialSA.minus_and_plus
thf(fact_268_PartialSA_Ominus__bigger,axiom,
    ! [X: state,A: state,B: state] :
      ( ( ( some_state @ X )
        = ( plus @ A @ B ) )
     => ( greater @ ( minus @ X @ A ) @ B ) ) ).

% PartialSA.minus_bigger
thf(fact_269_add__acc__uni__mask,axiom,
    ( add_ac6043276672051819257t_char
    = ( ^ [Pi: produc1457211279475724562t_char > prat,Hl: produc1457211279475724562t_char,P5: prat] : ( add_ma6586698345353345811t_char @ Pi @ ( uni_ma6578582744724537101t_char @ Hl @ P5 ) ) ) ) ).

% add_acc_uni_mask
thf(fact_270_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_271_PartialSA_Ominus__equiv__def,axiom,
    ! [B: state,A: state] :
      ( ( greater @ B @ A )
     => ( ( ( some_state @ B )
          = ( plus @ A @ ( minus @ B @ A ) ) )
        & ( greater @ ( minus @ B @ A ) @ ( core @ B ) ) ) ) ).

% PartialSA.minus_equiv_def
thf(fact_272_PartialSA_OminusI,axiom,
    ! [B: state,A: state,X: state] :
      ( ( ( some_state @ B )
        = ( plus @ A @ X ) )
     => ( ( greater @ X @ ( core @ B ) )
       => ( X
          = ( minus @ B @ A ) ) ) ) ).

% PartialSA.minusI
thf(fact_273_add__masks__equiv__valid__null,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat] :
      ( ( valid_null @ ( add_ma6586698345353345811t_char @ A @ B ) )
      = ( ( valid_null @ A )
        & ( valid_null @ B ) ) ) ).

% add_masks_equiv_valid_null
thf(fact_274_not__None__eq,axiom,
    ! [X: option_state] :
      ( ( X != none_state )
      = ( ? [Y5: state] :
            ( X
            = ( some_state @ Y5 ) ) ) ) ).

% not_None_eq
thf(fact_275_not__None__eq,axiom,
    ! [X: option_val] :
      ( ( X != none_val )
      = ( ? [Y5: val] :
            ( X
            = ( some_val @ Y5 ) ) ) ) ).

% not_None_eq
thf(fact_276_not__Some__eq,axiom,
    ! [X: option_state] :
      ( ( ! [Y5: state] :
            ( X
           != ( some_state @ Y5 ) ) )
      = ( X = none_state ) ) ).

% not_Some_eq
thf(fact_277_not__Some__eq,axiom,
    ! [X: option_val] :
      ( ( ! [Y5: val] :
            ( X
           != ( some_val @ Y5 ) ) )
      = ( X = none_val ) ) ).

% not_Some_eq
thf(fact_278_map__add__None,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = none_val )
      = ( ( ( N @ K )
          = none_val )
        & ( ( M @ K )
          = none_val ) ) ) ).

% map_add_None
thf(fact_279_map__add__eq__empty__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( ( map_ad2908576761495157028ar_val @ F @ G )
        = ( ^ [X2: produc1457211279475724562t_char] : none_val ) )
      = ( ( F
          = ( ^ [X2: produc1457211279475724562t_char] : none_val ) )
        & ( G
          = ( ^ [X2: produc1457211279475724562t_char] : none_val ) ) ) ) ).

% map_add_eq_empty_iff
thf(fact_280_PartialSA_Ocore__mono,axiom,
    ! [A: state,B: state] :
      ( ( greater @ A @ B )
     => ( greater @ ( core @ A ) @ ( core @ B ) ) ) ).

% PartialSA.core_mono
thf(fact_281_option_Odistinct_I1_J,axiom,
    ! [X22: state] :
      ( none_state
     != ( some_state @ X22 ) ) ).

% option.distinct(1)
thf(fact_282_option_Odistinct_I1_J,axiom,
    ! [X22: val] :
      ( none_val
     != ( some_val @ X22 ) ) ).

% option.distinct(1)
thf(fact_283_option_OdiscI,axiom,
    ! [Option: option_state,X22: state] :
      ( ( Option
        = ( some_state @ X22 ) )
     => ( Option != none_state ) ) ).

% option.discI
thf(fact_284_option_OdiscI,axiom,
    ! [Option: option_val,X22: val] :
      ( ( Option
        = ( some_val @ X22 ) )
     => ( Option != none_val ) ) ).

% option.discI
thf(fact_285_option_Oexhaust,axiom,
    ! [Y: option_state] :
      ( ( Y != none_state )
     => ~ ! [X23: state] :
            ( Y
           != ( some_state @ X23 ) ) ) ).

% option.exhaust
thf(fact_286_option_Oexhaust,axiom,
    ! [Y: option_val] :
      ( ( Y != none_val )
     => ~ ! [X23: val] :
            ( Y
           != ( some_val @ X23 ) ) ) ).

% option.exhaust
thf(fact_287_split__option__ex,axiom,
    ( ( ^ [P6: option_state > $o] :
        ? [X6: option_state] : ( P6 @ X6 ) )
    = ( ^ [P4: option_state > $o] :
          ( ( P4 @ none_state )
          | ? [X2: state] : ( P4 @ ( some_state @ X2 ) ) ) ) ) ).

% split_option_ex
thf(fact_288_split__option__ex,axiom,
    ( ( ^ [P6: option_val > $o] :
        ? [X6: option_val] : ( P6 @ X6 ) )
    = ( ^ [P4: option_val > $o] :
          ( ( P4 @ none_val )
          | ? [X2: val] : ( P4 @ ( some_val @ X2 ) ) ) ) ) ).

% split_option_ex
thf(fact_289_split__option__all,axiom,
    ( ( ^ [P6: option_state > $o] :
        ! [X6: option_state] : ( P6 @ X6 ) )
    = ( ^ [P4: option_state > $o] :
          ( ( P4 @ none_state )
          & ! [X2: state] : ( P4 @ ( some_state @ X2 ) ) ) ) ) ).

% split_option_all
thf(fact_290_split__option__all,axiom,
    ( ( ^ [P6: option_val > $o] :
        ! [X6: option_val] : ( P6 @ X6 ) )
    = ( ^ [P4: option_val > $o] :
          ( ( P4 @ none_val )
          & ! [X2: val] : ( P4 @ ( some_val @ X2 ) ) ) ) ) ).

% split_option_all
thf(fact_291_combine__options__cases,axiom,
    ! [X: option_state,P2: option_state > option_state > $o,Y: option_state] :
      ( ( ( X = none_state )
       => ( P2 @ X @ Y ) )
     => ( ( ( Y = none_state )
         => ( P2 @ X @ Y ) )
       => ( ! [A6: state,B6: state] :
              ( ( X
                = ( some_state @ A6 ) )
             => ( ( Y
                  = ( some_state @ B6 ) )
               => ( P2 @ X @ Y ) ) )
         => ( P2 @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_292_combine__options__cases,axiom,
    ! [X: option_state,P2: option_state > option_val > $o,Y: option_val] :
      ( ( ( X = none_state )
       => ( P2 @ X @ Y ) )
     => ( ( ( Y = none_val )
         => ( P2 @ X @ Y ) )
       => ( ! [A6: state,B6: val] :
              ( ( X
                = ( some_state @ A6 ) )
             => ( ( Y
                  = ( some_val @ B6 ) )
               => ( P2 @ X @ Y ) ) )
         => ( P2 @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_293_combine__options__cases,axiom,
    ! [X: option_val,P2: option_val > option_state > $o,Y: option_state] :
      ( ( ( X = none_val )
       => ( P2 @ X @ Y ) )
     => ( ( ( Y = none_state )
         => ( P2 @ X @ Y ) )
       => ( ! [A6: val,B6: state] :
              ( ( X
                = ( some_val @ A6 ) )
             => ( ( Y
                  = ( some_state @ B6 ) )
               => ( P2 @ X @ Y ) ) )
         => ( P2 @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_294_combine__options__cases,axiom,
    ! [X: option_val,P2: option_val > option_val > $o,Y: option_val] :
      ( ( ( X = none_val )
       => ( P2 @ X @ Y ) )
     => ( ( ( Y = none_val )
         => ( P2 @ X @ Y ) )
       => ( ! [A6: val,B6: val] :
              ( ( X
                = ( some_val @ A6 ) )
             => ( ( Y
                  = ( some_val @ B6 ) )
               => ( P2 @ X @ Y ) ) )
         => ( P2 @ X @ Y ) ) ) ) ).

% combine_options_cases
thf(fact_295_core__defined_I1_J,axiom,
    ! [Phi: state] :
      ( ( get_h @ ( core @ Phi ) )
      = ( get_h @ Phi ) ) ).

% core_defined(1)
thf(fact_296_PartialSA_Ominus__core__weaker,axiom,
    ! [A: state,B: state] :
      ( ( core @ ( minus @ A @ B ) )
      = ( minus @ ( core @ A ) @ ( core @ B ) ) ) ).

% PartialSA.minus_core_weaker
thf(fact_297_PartialSA_Ominus__core,axiom,
    ! [A: state,B: state] :
      ( ( core @ ( minus @ A @ B ) )
      = ( core @ A ) ) ).

% PartialSA.minus_core
thf(fact_298_empty__heap__def,axiom,
    ( empty_7512026568161686585ar_val
    = ( ^ [Hl: produc1457211279475724562t_char] : none_val ) ) ).

% empty_heap_def
thf(fact_299_core__max,axiom,
    ! [X: state,C: state] :
      ( ( ( some_state @ X )
        = ( plus @ X @ C ) )
     => ? [R3: state] :
          ( ( some_state @ ( core @ X ) )
          = ( plus @ C @ R3 ) ) ) ).

% core_max
thf(fact_300_core__sum,axiom,
    ! [C: state,A: state,B: state] :
      ( ( ( some_state @ C )
        = ( plus @ A @ B ) )
     => ( ( some_state @ ( core @ C ) )
        = ( plus @ ( core @ A ) @ ( core @ B ) ) ) ) ).

% core_sum
thf(fact_301_cancellative,axiom,
    ! [A: state,B: state,X: state,Y: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ X ) )
     => ( ( ( some_state @ A )
          = ( plus @ B @ Y ) )
       => ( ( ( core @ X )
            = ( core @ Y ) )
         => ( X = Y ) ) ) ) ).

% cancellative
thf(fact_302_core__is__pure,axiom,
    ! [X: state] :
      ( ( some_state @ ( core @ X ) )
      = ( plus @ ( core @ X ) @ ( core @ X ) ) ) ).

% core_is_pure
thf(fact_303_core__is__smaller,axiom,
    ( some_state
    = ( ^ [X2: state] : ( plus @ X2 @ ( core @ X2 ) ) ) ) ).

% core_is_smaller
thf(fact_304_PartialSA_Oasso3,axiom,
    ! [A: state,B: state,C: state,Bc: state] :
      ( ( ( plus @ A @ B )
        = none_state )
     => ( ( ( plus @ B @ C )
          = ( some_state @ Bc ) )
       => ( ( plus @ A @ Bc )
          = none_state ) ) ) ).

% PartialSA.asso3
thf(fact_305_asso2,axiom,
    ! [A: state,B: state,Ab: state,C: state] :
      ( ( ( ( plus @ A @ B )
          = ( some_state @ Ab ) )
        & ( ( plus @ B @ C )
          = none_state ) )
     => ( ( plus @ Ab @ C )
        = none_state ) ) ).

% asso2
thf(fact_306_PartialSA_Osmaller__compatible__core,axiom,
    ! [Y: state,X: state] :
      ( ( greater @ Y @ X )
     => ( defined @ X @ ( core @ Y ) ) ) ).

% PartialSA.smaller_compatible_core
thf(fact_307_map__add__SomeD,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ X ) )
     => ( ( ( N @ K )
          = ( some_val @ X ) )
        | ( ( ( N @ K )
            = none_val )
          & ( ( M @ K )
            = ( some_val @ X ) ) ) ) ) ).

% map_add_SomeD
thf(fact_308_map__add__Some__iff,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val,K: produc1457211279475724562t_char,X: val] :
      ( ( ( map_ad2908576761495157028ar_val @ M @ N @ K )
        = ( some_val @ X ) )
      = ( ( ( N @ K )
          = ( some_val @ X ) )
        | ( ( ( N @ K )
            = none_val )
          & ( ( M @ K )
            = ( some_val @ X ) ) ) ) ) ).

% map_add_Some_iff
thf(fact_309_PartialSA_Odefined__def,axiom,
    ( defined
    = ( ^ [A2: state,B2: state] :
          ( ( plus @ A2 @ B2 )
         != none_state ) ) ) ).

% PartialSA.defined_def
thf(fact_310_PartialSA_Osplus_Osimps_I1_J,axiom,
    ! [Uu: option_state] :
      ( ( sep_splus_state @ plus @ none_state @ Uu )
      = none_state ) ).

% PartialSA.splus.simps(1)
thf(fact_311_PartialSA_Oextract__core,axiom,
    ! [B: state,A: state,X: state] :
      ( ( ( ( some_state @ B )
          = ( plus @ A @ X ) )
        & ( greater @ X @ ( core @ B ) ) )
     => ( ( core @ X )
        = ( core @ B ) ) ) ).

% PartialSA.extract_core
thf(fact_312_PartialSA_Ominus__exists,axiom,
    ! [B: state,A: state] :
      ( ( greater @ B @ A )
     => ? [X3: state] :
          ( ( ( some_state @ B )
            = ( plus @ A @ X3 ) )
          & ( greater @ X3 @ ( core @ B ) ) ) ) ).

% PartialSA.minus_exists
thf(fact_313_PartialSA_Ominus__unique,axiom,
    ! [B: state,A: state,X: state,Y: state] :
      ( ( ( ( some_state @ B )
          = ( plus @ A @ X ) )
        & ( greater @ X @ ( core @ B ) ) )
     => ( ( ( ( some_state @ B )
            = ( plus @ A @ Y ) )
          & ( greater @ Y @ ( core @ B ) ) )
       => ( X = Y ) ) ) ).

% PartialSA.minus_unique
thf(fact_314_PartialSA_Osmaller__than__core,axiom,
    ! [Y: state,X: state,Z2: state] :
      ( ( greater @ Y @ X )
     => ( ( ( some_state @ Z2 )
          = ( plus @ X @ ( core @ Y ) ) )
       => ( ( core @ Z2 )
          = ( core @ Y ) ) ) ) ).

% PartialSA.smaller_than_core
thf(fact_315_PartialSA_Obigger__core__sum__defined,axiom,
    ! [A: state,B: state] :
      ( ( greater @ ( core @ A ) @ B )
     => ( ( some_state @ A )
        = ( plus @ A @ B ) ) ) ).

% PartialSA.bigger_core_sum_defined
thf(fact_316_PartialSA_Ogreater__than__sum__exists,axiom,
    ! [A: state,B: state,B1: state,B22: state] :
      ( ( greater @ A @ B )
     => ( ( ( some_state @ B )
          = ( plus @ B1 @ B22 ) )
       => ? [R3: state] :
            ( ( ( some_state @ A )
              = ( plus @ R3 @ B22 ) )
            & ( greater @ ( core @ R3 ) @ ( core @ A ) )
            & ( greater @ R3 @ B1 ) ) ) ) ).

% PartialSA.greater_than_sum_exists
thf(fact_317_PartialSA_Ominus__equiv__def__any__elem,axiom,
    ! [X: state,A: state,B: state] :
      ( ( ( some_state @ X )
        = ( plus @ A @ B ) )
     => ( ( some_state @ ( minus @ X @ A ) )
        = ( plus @ B @ ( core @ X ) ) ) ) ).

% PartialSA.minus_equiv_def_any_elem
thf(fact_318_PartialSA_Osplus_Osimps_I2_J,axiom,
    ! [V: state] :
      ( ( sep_splus_state @ plus @ ( some_state @ V ) @ none_state )
      = none_state ) ).

% PartialSA.splus.simps(2)
thf(fact_319_PartialSA_Osplus_Oelims,axiom,
    ! [X: option_state,Xa2: option_state,Y: option_state] :
      ( ( ( sep_splus_state @ plus @ X @ Xa2 )
        = Y )
     => ( ( ( X = none_state )
         => ( Y != none_state ) )
       => ( ( ? [V2: state] :
                ( X
                = ( some_state @ V2 ) )
           => ( ( Xa2 = none_state )
             => ( Y != none_state ) ) )
         => ~ ! [A6: state] :
                ( ( X
                  = ( some_state @ A6 ) )
               => ! [B6: state] :
                    ( ( Xa2
                      = ( some_state @ B6 ) )
                   => ( Y
                     != ( plus @ A6 @ B6 ) ) ) ) ) ) ) ).

% PartialSA.splus.elims
thf(fact_320_PartialSA_Omono__pure__condI,axiom,
    ! [B: state > $o] :
      ( ! [Phi5: state] :
          ( ( B @ Phi5 )
          = ( B @ ( core @ Phi5 ) ) )
     => ( ! [Phi5: state,Phi6: state,R3: state] :
            ( ( ( sep_pure_state @ plus @ R3 )
              & ( ( some_state @ Phi6 )
                = ( plus @ Phi5 @ R3 ) )
              & ~ ( B @ Phi5 ) )
           => ~ ( B @ Phi6 ) )
       => ( packag6595153354952283300_state @ plus @ core @ B ) ) ) ).

% PartialSA.mono_pure_condI
thf(fact_321_PartialSA_Omono__pure__cond__def,axiom,
    ! [B: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ B )
      = ( ! [Phi4: state] :
            ( ( B @ Phi4 )
            = ( B @ ( core @ Phi4 ) ) )
        & ! [Phi3: state,Phi4: state,R: state] :
            ( ( ( sep_pure_state @ plus @ R )
              & ( ( some_state @ Phi3 )
                = ( plus @ Phi4 @ R ) )
              & ~ ( B @ Phi4 ) )
           => ~ ( B @ Phi3 ) ) ) ) ).

% PartialSA.mono_pure_cond_def
thf(fact_322_PartialSA_Omax__projection__prop__pure__core,axiom,
    sep_ma8214210560313151521_state @ plus @ ( sep_pure_state @ plus ) @ core ).

% PartialSA.max_projection_prop_pure_core
thf(fact_323_PartialSA_Obigger__the,axiom,
    ! [A: state,X5: state,Y: state,X: state] :
      ( ( ( some_state @ A )
        = ( plus @ X5 @ Y ) )
     => ( ( greater @ X5 @ X )
       => ( greater @ ( the_state @ ( plus @ ( core @ A ) @ X5 ) ) @ ( the_state @ ( plus @ ( core @ A ) @ X ) ) ) ) ) ).

% PartialSA.bigger_the
thf(fact_324_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_state,Xa2: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X @ Xa2 )
        = Y )
     => ( ! [A6: state] :
            ( ( X
              = ( some_state @ A6 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( Y
                  = ( A6 != B6 ) ) ) )
       => ( ( ( X = none_state )
           => ~ Y )
         => ~ ( ( Xa2 = none_state )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_325_compatible__options_Oelims_I1_J,axiom,
    ! [X: option_val,Xa2: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X @ Xa2 )
        = Y )
     => ( ! [A6: val] :
            ( ( X
              = ( some_val @ A6 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( Y
                  = ( A6 != B6 ) ) ) )
       => ( ( ( X = none_val )
           => ~ Y )
         => ~ ( ( Xa2 = none_val )
             => ~ Y ) ) ) ) ).

% compatible_options.elims(1)
thf(fact_326_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_state,Xa2: option_state] :
      ( ( compat2278460363914054422_state @ X @ Xa2 )
     => ( ! [A6: state] :
            ( ( X
              = ( some_state @ A6 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( A6 != B6 ) ) )
       => ( ( X != none_state )
         => ( Xa2 = none_state ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_327_compatible__options_Oelims_I2_J,axiom,
    ! [X: option_val,Xa2: option_val] :
      ( ( compat7209469420100717861ns_val @ X @ Xa2 )
     => ( ! [A6: val] :
            ( ( X
              = ( some_val @ A6 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( A6 != B6 ) ) )
       => ( ( X != none_val )
         => ( Xa2 = none_val ) ) ) ) ).

% compatible_options.elims(2)
thf(fact_328_option_Ocollapse,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( ( some_state @ ( the_state @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_329_option_Ocollapse,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( ( some_val @ ( the_val @ Option ) )
        = Option ) ) ).

% option.collapse
thf(fact_330_option_Osel,axiom,
    ! [X22: state] :
      ( ( the_state @ ( some_state @ X22 ) )
      = X22 ) ).

% option.sel
thf(fact_331_option_Osel,axiom,
    ! [X22: val] :
      ( ( the_val @ ( some_val @ X22 ) )
      = X22 ) ).

% option.sel
thf(fact_332_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_333_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_334_PartialSA_Ompp__prop,axiom,
    ! [P2: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( P2 @ ( F @ X ) ) ) ).

% PartialSA.mpp_prop
thf(fact_335_PartialSA_Ompp__invo,axiom,
    ! [P2: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( F @ ( F @ X ) )
        = ( F @ X ) ) ) ).

% PartialSA.mpp_invo
thf(fact_336_compatible__options_Osimps_I1_J,axiom,
    ! [A: state,B: state] :
      ( ( compat2278460363914054422_state @ ( some_state @ A ) @ ( some_state @ B ) )
      = ( A = B ) ) ).

% compatible_options.simps(1)
thf(fact_337_compatible__options_Osimps_I1_J,axiom,
    ! [A: val,B: val] :
      ( ( compat7209469420100717861ns_val @ ( some_val @ A ) @ ( some_val @ B ) )
      = ( A = B ) ) ).

% compatible_options.simps(1)
thf(fact_338_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_state,Xa2: option_state] :
      ( ~ ( compat2278460363914054422_state @ X @ Xa2 )
     => ~ ! [A6: state] :
            ( ( X
              = ( some_state @ A6 ) )
           => ! [B6: state] :
                ( ( Xa2
                  = ( some_state @ B6 ) )
               => ( A6 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_339_compatible__options_Oelims_I3_J,axiom,
    ! [X: option_val,Xa2: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X @ Xa2 )
     => ~ ! [A6: val] :
            ( ( X
              = ( some_val @ A6 ) )
           => ! [B6: val] :
                ( ( Xa2
                  = ( some_val @ B6 ) )
               => ( A6 = B6 ) ) ) ) ).

% compatible_options.elims(3)
thf(fact_340_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_state] : ( compat2278460363914054422_state @ Uu @ none_state ) ).

% compatible_options.simps(3)
thf(fact_341_compatible__options_Osimps_I3_J,axiom,
    ! [Uu: option_val] : ( compat7209469420100717861ns_val @ Uu @ none_val ) ).

% compatible_options.simps(3)
thf(fact_342_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_state] : ( compat2278460363914054422_state @ none_state @ Uv ) ).

% compatible_options.simps(2)
thf(fact_343_compatible__options_Osimps_I2_J,axiom,
    ! [Uv: option_val] : ( compat7209469420100717861ns_val @ none_val @ Uv ) ).

% compatible_options.simps(2)
thf(fact_344_option_Oexhaust__sel,axiom,
    ! [Option: option_state] :
      ( ( Option != none_state )
     => ( Option
        = ( some_state @ ( the_state @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_345_option_Oexhaust__sel,axiom,
    ! [Option: option_val] :
      ( ( Option != none_val )
     => ( Option
        = ( some_val @ ( the_val @ Option ) ) ) ) ).

% option.exhaust_sel
thf(fact_346_compatible__heaps__def,axiom,
    ( compatible_heaps
    = ( ^ [H3: produc1457211279475724562t_char > option_val,H2: produc1457211279475724562t_char > option_val] :
        ! [Hl: produc1457211279475724562t_char] : ( compat7209469420100717861ns_val @ ( H3 @ Hl ) @ ( H2 @ Hl ) ) ) ) ).

% compatible_heaps_def
thf(fact_347_PartialSA_Omax__projection__propE_I3_J,axiom,
    ! [P2: state > $o,F: state > state,P3: state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( ( P2 @ P3 )
          & ( greater @ X @ P3 ) )
       => ( greater @ ( F @ X ) @ P3 ) ) ) ).

% PartialSA.max_projection_propE(3)
thf(fact_348_PartialSA_OmppI,axiom,
    ! [P2: state > $o,F: state > state,A: state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( greater @ A @ X )
       => ( ( P2 @ X )
         => ( ( greater @ X @ ( F @ A ) )
           => ( X
              = ( F @ A ) ) ) ) ) ) ).

% PartialSA.mppI
thf(fact_349_PartialSA_Ompp__mono,axiom,
    ! [P2: state > $o,F: state > state,A: state,B: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( greater @ A @ B )
       => ( greater @ ( F @ A ) @ ( F @ B ) ) ) ) ).

% PartialSA.mpp_mono
thf(fact_350_PartialSA_Ompp__smaller,axiom,
    ! [P2: state > $o,F: state > state,X: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( greater @ X @ ( F @ X ) ) ) ).

% PartialSA.mpp_smaller
thf(fact_351_PartialSA_Omax__projection__propI,axiom,
    ! [F: state > state,P2: state > $o] :
      ( ! [X3: state] : ( greater @ X3 @ ( F @ X3 ) )
     => ( ! [X3: state] : ( P2 @ ( F @ X3 ) )
       => ( ! [X3: state,P: state] :
              ( ( ( P2 @ P )
                & ( greater @ X3 @ P ) )
             => ( greater @ ( F @ X3 ) @ P ) )
         => ( sep_ma8214210560313151521_state @ plus @ P2 @ F ) ) ) ) ).

% PartialSA.max_projection_propI
thf(fact_352_PartialSA_Omax__projection__prop__def,axiom,
    ! [P2: state > $o,F: state > state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
      = ( ! [X2: state] :
            ( ( greater @ X2 @ ( F @ X2 ) )
            & ( P2 @ ( F @ X2 ) )
            & ! [P5: state] :
                ( ( ( P2 @ P5 )
                  & ( greater @ X2 @ P5 ) )
               => ( greater @ ( F @ X2 ) @ P5 ) ) ) ) ) ).

% PartialSA.max_projection_prop_def
thf(fact_353_PartialSA_Ompp__compatible,axiom,
    ! [P2: state > $o,F: state > state,A: state,B: state] :
      ( ( sep_ma8214210560313151521_state @ plus @ P2 @ F )
     => ( ( defined @ A @ B )
       => ( defined @ ( F @ A ) @ ( F @ B ) ) ) ) ).

% PartialSA.mpp_compatible
thf(fact_354_PartialSA_Omono__pure__cond__conj,axiom,
    ! [Pc: state > $o,B: state > $o] :
      ( ( packag6595153354952283300_state @ plus @ core @ Pc )
     => ( ( packag6595153354952283300_state @ plus @ core @ B )
       => ( packag6595153354952283300_state @ plus @ core @ ( packag1330488657391168505_state @ Pc @ B ) ) ) ) ).

% PartialSA.mono_pure_cond_conj
thf(fact_355_core__defined_I2_J,axiom,
    ! [Phi: state] :
      ( ( get_m @ ( core @ Phi ) )
      = empty_3446695950879338768t_char ) ).

% core_defined(2)
thf(fact_356_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_357_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_358_core__def,axiom,
    ( core
    = ( ^ [Phi4: state] : ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ ( get_h @ Phi4 ) ) ) ) ) ).

% core_def
thf(fact_359_valid__state_Ocases,axiom,
    ! [X: produc9003781588162623004on_val] :
      ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc74620467203698198on_val @ Pi5 @ H5 ) ) ).

% valid_state.cases
thf(fact_360_PartialSA_Obool__conj__def,axiom,
    ( packag1330488657391168505_state
    = ( ^ [A2: state > $o,B2: state > $o,X2: state] :
          ( ( A2 @ X2 )
          & ( B2 @ X2 ) ) ) ) ).

% PartialSA.bool_conj_def
thf(fact_361_ssubsetI,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ! [Pi5: state,H5: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi5 @ H5 ) @ A4 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_362_ssubsetI,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ! [Pi5: state,H5: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi5 @ H5 ) @ A4 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_363_ssubsetI,axiom,
    ! [A4: set_Pr1688445902015331925_state,B4: set_Pr1688445902015331925_state] :
      ( ! [Pi5: option_state,H5: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi5 @ H5 ) @ A4 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le6423325748750870005_state @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_364_ssubsetI,axiom,
    ! [A4: set_Pr6039890582625207499_state,B4: set_Pr6039890582625207499_state] :
      ( ! [Pi5: prat,H5: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi5 @ H5 ) @ A4 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le262197048489888875_state @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_365_ssubsetI,axiom,
    ! [A4: set_Pr6847263425858009217_state,B4: set_Pr6847263425858009217_state] :
      ( ! [Pi5: prat,H5: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi5 @ H5 ) @ A4 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le5761494056910127137_state @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_366_ssubsetI,axiom,
    ! [A4: set_Pr2507339680178222706t_char,B4: set_Pr2507339680178222706t_char] :
      ( ! [Pi5: nat,H5: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi5 @ H5 ) @ A4 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le6315511645215477266t_char @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_367_ssubsetI,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ A4 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ A4 @ B4 ) ) ).

% ssubsetI
thf(fact_368_valid__empty,axiom,
    valid_mask @ empty_3446695950879338768t_char ).

% valid_empty
thf(fact_369_stable__sum,axiom,
    ! [A: state,B: state,X: state] :
      ( ( stable @ A )
     => ( ( stable @ B )
       => ( ( ( some_state @ X )
            = ( plus @ A @ B ) )
         => ( stable @ X ) ) ) ) ).

% stable_sum
thf(fact_370_minus__empty,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat] :
      ( Pi2
      = ( add_ma6586698345353345811t_char @ Pi2 @ empty_3446695950879338768t_char ) ) ).

% minus_empty
thf(fact_371_multiply_Oelims,axiom,
    ! [X: prat,Xa2: state,Y: state] :
      ( ( ( multiply @ X @ Xa2 )
        = Y )
     => ( Y
        = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X @ ( get_m @ Xa2 ) ) @ ( get_h @ Xa2 ) ) ) ) ) ).

% multiply.elims
thf(fact_372_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_373_stableI,axiom,
    ! [Phi: state] :
      ( ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( get_m @ Phi @ Hl2 ) )
          = ( ( get_h @ Phi @ Hl2 )
           != none_val ) )
     => ( stable @ Phi ) ) ).

% stableI
thf(fact_374_binary__def,axiom,
    ( binary
    = ( ^ [A7: set_state] :
        ! [X2: state] :
          ( ( member_state @ X2 @ A7 )
         => ( member_state @ ( abs_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ X2 ) ) @ ( get_h @ X2 ) ) ) @ A7 ) ) ) ) ).

% binary_def
thf(fact_375_add__states_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa2: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa2 )
        = Y )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ! [Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
                ( ( Xa2
                  = ( produc74620467203698198on_val @ Pi6 @ H6 ) )
               => ( Y
                 != ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi5 @ Pi6 ) @ ( map_ad2908576761495157028ar_val @ H5 @ H6 ) ) ) ) ) ) ).

% add_states.elims
thf(fact_376_add__states_Osimps,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val,Pi4: produc1457211279475724562t_char > prat,H4: produc1457211279475724562t_char > option_val] :
      ( ( add_states @ ( produc74620467203698198on_val @ Pi2 @ H ) @ ( produc74620467203698198on_val @ Pi4 @ H4 ) )
      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi2 @ Pi4 ) @ ( map_ad2908576761495157028ar_val @ H @ H4 ) ) ) ).

% add_states.simps
thf(fact_377_multiply__valid,axiom,
    ! [P3: prat,Phi: state] :
      ( ( pgte @ pwrite @ P3 )
     => ( valid_state @ ( produc74620467203698198on_val @ ( multiply_mask @ P3 @ ( get_m @ Phi ) ) @ ( get_h @ Phi ) ) ) ) ).

% multiply_valid
thf(fact_378_valid__stateI,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_mask @ Pi2 )
     => ( ! [Hl2: produc1457211279475724562t_char] :
            ( ( ppos @ ( Pi2 @ Hl2 ) )
           => ( ( H @ Hl2 )
             != none_val ) )
       => ( valid_state @ ( produc74620467203698198on_val @ Pi2 @ H ) ) ) ) ).

% valid_stateI
thf(fact_379_valid__heap__def,axiom,
    ( valid_heap
    = ( ^ [Pi: produc1457211279475724562t_char > prat,H3: produc1457211279475724562t_char > option_val] :
        ! [Hl: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi @ Hl ) )
         => ( ( H3 @ Hl )
           != none_val ) ) ) ) ).

% valid_heap_def
thf(fact_380_add__states_Ocases,axiom,
    ! [X: produc1317171644805857433on_val] :
      ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val,Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
          ( X
         != ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ ( produc74620467203698198on_val @ Pi6 @ H6 ) ) ) ).

% add_states.cases
thf(fact_381_valid__state_Osimps,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ Pi2 @ H ) )
      = ( ( valid_mask @ Pi2 )
        & ( valid_heap @ Pi2 @ H ) ) ) ).

% valid_state.simps
thf(fact_382_valid__state_Oelims_I1_J,axiom,
    ! [X: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X )
        = Y )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ( Y
              = ( ~ ( ( valid_mask @ Pi5 )
                    & ( valid_heap @ Pi5 @ H5 ) ) ) ) ) ) ).

% valid_state.elims(1)
thf(fact_383_valid__state_Oelims_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( valid_state @ X )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ~ ( ( valid_mask @ Pi5 )
                & ( valid_heap @ Pi5 @ H5 ) ) ) ) ).

% valid_state.elims(2)
thf(fact_384_valid__state_Oelims_I3_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X )
     => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
            ( ( X
              = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
           => ( ( valid_mask @ Pi5 )
              & ( valid_heap @ Pi5 @ H5 ) ) ) ) ).

% valid_state.elims(3)
thf(fact_385_compatible__options_Ocases,axiom,
    ! [X: produc3142500478612311029_state] :
      ( ! [A6: state,B6: state] :
          ( X
         != ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) )
     => ( ! [Uv2: option_state] :
            ( X
           != ( produc9160152616361873709_state @ none_state @ Uv2 ) )
       => ~ ! [Uu2: option_state] :
              ( X
             != ( produc9160152616361873709_state @ Uu2 @ none_state ) ) ) ) ).

% compatible_options.cases
thf(fact_386_compatible__options_Ocases,axiom,
    ! [X: produc5122021904355189735on_val] :
      ( ! [A6: val,B6: val] :
          ( X
         != ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) )
     => ( ! [Uv2: option_val] :
            ( X
           != ( produc904852209897547607on_val @ none_val @ Uv2 ) )
       => ~ ! [Uu2: option_val] :
              ( X
             != ( produc904852209897547607on_val @ Uu2 @ none_val ) ) ) ) ).

% compatible_options.cases
thf(fact_387_PartialSA_Osplus_Ocases,axiom,
    ! [X: produc3142500478612311029_state] :
      ( ! [Uu2: option_state] :
          ( X
         != ( produc9160152616361873709_state @ none_state @ Uu2 ) )
     => ( ! [V2: state] :
            ( X
           != ( produc9160152616361873709_state @ ( some_state @ V2 ) @ none_state ) )
       => ~ ! [A6: state,B6: state] :
              ( X
             != ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) ) ) ) ).

% PartialSA.splus.cases
thf(fact_388_valid__bin,axiom,
    ! [A: state] : ( valid_state @ ( produc74620467203698198on_val @ ( binary_mask @ ( get_m @ A ) ) @ ( get_h @ A ) ) ) ).

% valid_bin
thf(fact_389_valid__state__decompose,axiom,
    ! [A: produc1457211279475724562t_char > prat,B: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ( valid_state @ ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ A @ B ) @ H ) )
     => ( valid_state @ ( produc74620467203698198on_val @ A @ H ) ) ) ).

% valid_state_decompose
thf(fact_390_valid__pre__unit,axiom,
    valid_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ).

% valid_pre_unit
thf(fact_391_valid__heapI,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat,H: produc1457211279475724562t_char > option_val] :
      ( ! [Hl2: produc1457211279475724562t_char] :
          ( ( ppos @ ( Pi2 @ Hl2 ) )
         => ( ( H @ Hl2 )
           != none_val ) )
     => ( valid_heap @ Pi2 @ H ) ) ).

% valid_heapI
thf(fact_392_subrelI,axiom,
    ! [R2: set_Pr4231240917283394591_state,S: set_Pr4231240917283394591_state] :
      ( ! [X3: state,Y3: produc3882902684156697774_state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y3 ) @ R2 )
         => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X3 @ Y3 ) @ S ) )
     => ( ord_le4032880777312351359_state @ R2 @ S ) ) ).

% subrelI
thf(fact_393_subrelI,axiom,
    ! [R2: set_Pr2391701600042252046_state,S: set_Pr2391701600042252046_state] :
      ( ! [X3: state,Y3: state > state] :
          ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y3 ) @ R2 )
         => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X3 @ Y3 ) @ S ) )
     => ( ord_le6483787752022044334_state @ R2 @ S ) ) ).

% subrelI
thf(fact_394_subrelI,axiom,
    ! [R2: set_Pr1688445902015331925_state,S: set_Pr1688445902015331925_state] :
      ( ! [X3: option_state,Y3: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y3 ) @ R2 )
         => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X3 @ Y3 ) @ S ) )
     => ( ord_le6423325748750870005_state @ R2 @ S ) ) ).

% subrelI
thf(fact_395_subrelI,axiom,
    ! [R2: set_Pr6039890582625207499_state,S: set_Pr6039890582625207499_state] :
      ( ! [X3: prat,Y3: state] :
          ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y3 ) @ R2 )
         => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X3 @ Y3 ) @ S ) )
     => ( ord_le262197048489888875_state @ R2 @ S ) ) ).

% subrelI
thf(fact_396_subrelI,axiom,
    ! [R2: set_Pr6847263425858009217_state,S: set_Pr6847263425858009217_state] :
      ( ! [X3: prat,Y3: set_state] :
          ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y3 ) @ R2 )
         => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X3 @ Y3 ) @ S ) )
     => ( ord_le5761494056910127137_state @ R2 @ S ) ) ).

% subrelI
thf(fact_397_subrelI,axiom,
    ! [R2: set_Pr2507339680178222706t_char,S: set_Pr2507339680178222706t_char] :
      ( ! [X3: nat,Y3: list_char] :
          ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y3 ) @ R2 )
         => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X3 @ Y3 ) @ S ) )
     => ( ord_le6315511645215477266t_char @ R2 @ S ) ) ).

% subrelI
thf(fact_398_subrelI,axiom,
    ! [R2: set_Pr7649655576376376530on_val,S: set_Pr7649655576376376530on_val] :
      ( ! [X3: produc1457211279475724562t_char > prat,Y3: produc1457211279475724562t_char > option_val] :
          ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y3 ) @ R2 )
         => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X3 @ Y3 ) @ S ) )
     => ( ord_le6900622908513426738on_val @ R2 @ S ) ) ).

% subrelI
thf(fact_399_PartialSA_Opackage__rhs__connectionI,axiom,
    ! [Phi: state,F: state,Phi2: state,F3: state,S2: set_Pr4231240917283394591_state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state] :
      ( ( ( plus @ Phi @ F )
        = ( plus @ Phi2 @ F3 ) )
     => ( ( stable @ F3 )
       => ( ( defined @ Phi @ F )
         => ( ( greater @ F3 @ F )
           => ( ! [A6: state,U: state,T2: state > state] :
                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
                 => ? [Au: state] :
                      ( ( ( some_state @ Au )
                        = ( plus @ A6 @ U ) )
                      & ( ( defined @ Au @ ( minus @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                       => ? [A8: state,U2: state] :
                            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A8 @ ( produc8632743443909064678_state @ U2 @ T2 ) ) @ S3 )
                            & ( greater @ ( core @ A8 ) @ ( core @ A6 ) )
                            & ( ( plus @ Au @ ( minus @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                              = ( plus @ A8 @ U2 ) )
                            & ( greater @ U2 @ U )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A4 @ A8 @ U2 @ U ) ) ) ) )
             => ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connectionI
thf(fact_400_PartialSA_Opackage__rhs__connection__instantiate,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state,A: state,U3: state,T3: state > state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
     => ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ ( produc8632743443909064678_state @ U3 @ T3 ) ) @ S2 )
       => ~ ! [Au2: state] :
              ( ( ( some_state @ Au2 )
                = ( plus @ A @ U3 ) )
             => ~ ( ( defined @ Au2 @ ( minus @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                 => ? [A9: state,U4: state] :
                      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A9 @ ( produc8632743443909064678_state @ U4 @ T3 ) ) @ S3 )
                      & ( greater @ ( core @ A9 ) @ ( core @ A ) )
                      & ( ( plus @ Au2 @ ( minus @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                        = ( plus @ A9 @ U4 ) )
                      & ( greater @ U4 @ U3 )
                      & ( packag8070727096299822599_state @ plus @ core @ Pc @ A4 @ A9 @ U4 @ U3 ) ) ) ) ) ) ).

% PartialSA.package_rhs_connection_instantiate
thf(fact_401_multiply_Opelims,axiom,
    ! [X: prat,Xa2: state,Y: state] :
      ( ( ( multiply @ X @ Xa2 )
        = Y )
     => ( ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X @ Xa2 ) )
       => ~ ( ( Y
              = ( abs_state @ ( produc74620467203698198on_val @ ( multiply_mask @ X @ ( get_m @ Xa2 ) ) @ ( get_h @ Xa2 ) ) ) )
           => ~ ( accp_P6233459008282737652_state @ multiply_rel @ ( produc6205719116230455971_state @ X @ Xa2 ) ) ) ) ) ).

% multiply.pelims
thf(fact_402_plus__def,axiom,
    ( plus
    = ( ^ [A2: state,B2: state] : ( if_option_state @ ( compatible @ ( rep_state @ A2 ) @ ( rep_state @ B2 ) ) @ ( some_state @ ( abs_state @ ( add_states @ ( rep_state @ A2 ) @ ( rep_state @ B2 ) ) ) ) @ none_state ) ) ) ).

% plus_def
thf(fact_403_unit__def,axiom,
    ( unit
    = ( abs_state @ ( produc74620467203698198on_val @ empty_3446695950879338768t_char @ empty_7512026568161686585ar_val ) ) ) ).

% unit_def
thf(fact_404_multiply_Ocases,axiom,
    ! [X: produc4844402304972151915_state] :
      ~ ! [P: prat,Phi5: state] :
          ( X
         != ( produc6205719116230455971_state @ P @ Phi5 ) ) ).

% multiply.cases
thf(fact_405_Rep__state__inject,axiom,
    ! [X: state,Y: state] :
      ( ( ( rep_state @ X )
        = ( rep_state @ Y ) )
      = ( X = Y ) ) ).

% Rep_state_inject
thf(fact_406_PartialSA_Ounit__core,axiom,
    ( ( core @ unit )
    = unit ) ).

% PartialSA.unit_core
thf(fact_407_PartialSA_Ounit__smaller,axiom,
    ! [Phi: state] : ( greater @ Phi @ unit ) ).

% PartialSA.unit_smaller
thf(fact_408_stable__unit,axiom,
    stable @ unit ).

% stable_unit
thf(fact_409_unit__charact_I1_J,axiom,
    ( ( get_h @ unit )
    = empty_7512026568161686585ar_val ) ).

% unit_charact(1)
thf(fact_410_Rep__state__inverse,axiom,
    ! [X: state] :
      ( ( abs_state @ ( rep_state @ X ) )
      = X ) ).

% Rep_state_inverse
thf(fact_411_unit__neutral,axiom,
    ( some_state
    = ( ^ [A2: state] : ( plus @ A2 @ unit ) ) ) ).

% unit_neutral
thf(fact_412_unit__charact_I2_J,axiom,
    ( ( get_m @ unit )
    = empty_3446695950879338768t_char ) ).

% unit_charact(2)
thf(fact_413_get__h__m,axiom,
    ( rep_state
    = ( ^ [X2: state] : ( produc74620467203698198on_val @ ( get_m @ X2 ) @ ( get_h @ X2 ) ) ) ) ).

% get_h_m
thf(fact_414_add__states_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Xa2: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( ( add_states @ X @ Xa2 )
        = Y )
     => ( ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ X @ Xa2 ) )
       => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
             => ! [Pi6: produc1457211279475724562t_char > prat,H6: produc1457211279475724562t_char > option_val] :
                  ( ( Xa2
                    = ( produc74620467203698198on_val @ Pi6 @ H6 ) )
                 => ( ( Y
                      = ( produc74620467203698198on_val @ ( add_ma6586698345353345811t_char @ Pi5 @ Pi6 ) @ ( map_ad2908576761495157028ar_val @ H5 @ H6 ) ) )
                   => ~ ( accp_P6797916352740768290on_val @ add_states_rel @ ( produc4958730763592889809on_val @ ( produc74620467203698198on_val @ Pi5 @ H5 ) @ ( produc74620467203698198on_val @ Pi6 @ H6 ) ) ) ) ) ) ) ) ).

% add_states.pelims
thf(fact_415_PartialSA_Ovalid__package__setI,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ! [A6: state,U: state,T2: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
         => ( ( defined @ A6 @ U )
            & ( greater @ ( core @ A6 ) @ ( core @ U ) )
            & ( packag4817583915586052229_state @ plus @ unit @ T2 )
            & ( greater @ A6 @ ( core @ ( T2 @ F ) ) ) ) )
     => ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F ) ) ).

% PartialSA.valid_package_setI
thf(fact_416_PartialSA_Opackage__satI,axiom,
    ! [Pc: state > $o,A3: state,U5: state,U3: state,A4: aassertion_state] :
      ( ( ( Pc @ ( core @ A3 ) )
       => ? [X4: state] :
            ( ( ( some_state @ X4 )
              = ( plus @ ( core @ A3 ) @ ( minus @ U5 @ U3 ) ) )
            & ( package_sat_state @ plus @ A4 @ X4 ) ) )
     => ( packag8070727096299822599_state @ plus @ core @ Pc @ A4 @ A3 @ U5 @ U3 ) ) ).

% PartialSA.package_satI
thf(fact_417_PartialSA_Opackage__sat__def,axiom,
    ! [Pc: state > $o,A4: aassertion_state,A3: state,U5: state,U3: state] :
      ( ( packag8070727096299822599_state @ plus @ core @ Pc @ A4 @ A3 @ U5 @ U3 )
      = ( ( Pc @ ( core @ A3 ) )
       => ? [X2: state] :
            ( ( ( some_state @ X2 )
              = ( plus @ ( core @ A3 ) @ ( minus @ U5 @ U3 ) ) )
            & ( package_sat_state @ plus @ A4 @ X2 ) ) ) ) ).

% PartialSA.package_sat_def
thf(fact_418_PartialSA_Omono__transformer__def,axiom,
    ! [T3: state > state] :
      ( ( packag4817583915586052229_state @ plus @ unit @ T3 )
      = ( ! [Phi4: state,Phi3: state] :
            ( ( greater @ Phi3 @ Phi4 )
           => ( greater @ ( T3 @ Phi3 ) @ ( T3 @ Phi4 ) ) )
        & ( ( T3 @ unit )
          = unit ) ) ) ).

% PartialSA.mono_transformer_def
thf(fact_419_PartialSA_Ois__footprint__standard__def,axiom,
    ! [W: state,A4: aassertion_state,B4: aassertion_state] :
      ( ( packag7096211993527611489_state @ plus @ W @ A4 @ B4 )
      = ( ! [A2: state,B2: state] :
            ( ( ( package_sat_state @ plus @ A4 @ A2 )
              & ( ( some_state @ B2 )
                = ( plus @ A2 @ W ) ) )
           => ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.is_footprint_standard_def
thf(fact_420_PartialSA_Ois__footprint__general__def,axiom,
    ! [W: state,R4: state > state > state,A4: aassertion_state,B4: aassertion_state] :
      ( ( packag6192661653625646554_state @ plus @ W @ R4 @ A4 @ B4 )
      = ( ! [A2: state,B2: state] :
            ( ( ( package_sat_state @ plus @ A4 @ A2 )
              & ( ( some_state @ B2 )
                = ( plus @ A2 @ ( R4 @ A2 @ W ) ) ) )
           => ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.is_footprint_general_def
thf(fact_421_PartialSA_Ois__footprint__standardI,axiom,
    ! [A4: aassertion_state,W: state,B4: aassertion_state] :
      ( ! [A6: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A4 @ A6 )
            & ( ( some_state @ B6 )
              = ( plus @ A6 @ W ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag7096211993527611489_state @ plus @ W @ A4 @ B4 ) ) ).

% PartialSA.is_footprint_standardI
thf(fact_422_PartialSA_Ois__footprint__generalI,axiom,
    ! [A4: aassertion_state,R4: state > state > state,W: state,B4: aassertion_state] :
      ( ! [A6: state,B6: state] :
          ( ( ( package_sat_state @ plus @ A4 @ A6 )
            & ( ( some_state @ B6 )
              = ( plus @ A6 @ ( R4 @ A6 @ W ) ) ) )
         => ( package_sat_state @ plus @ B4 @ B6 ) )
     => ( packag6192661653625646554_state @ plus @ W @ R4 @ A4 @ B4 ) ) ).

% PartialSA.is_footprint_generalI
thf(fact_423_PartialSA_Owf__assertion__and__the,axiom,
    ! [A: state,B: state,A4: aassertion_state] :
      ( ( defined @ ( core @ A ) @ B )
     => ( ( package_sat_state @ plus @ A4 @ B )
       => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
         => ( package_sat_state @ plus @ A4 @ ( the_state @ ( plus @ ( core @ A ) @ B ) ) ) ) ) ) ).

% PartialSA.wf_assertion_and_the
thf(fact_424_PartialSA_Owf__assertion__sat__larger__pure,axiom,
    ! [A4: aassertion_state,Phi: state,Phi2: state,R2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ A4 )
     => ( ( package_sat_state @ plus @ A4 @ Phi )
       => ( ( ( some_state @ Phi2 )
            = ( plus @ Phi @ R2 ) )
         => ( ( sep_pure_state @ plus @ R2 )
           => ( package_sat_state @ plus @ A4 @ Phi2 ) ) ) ) ) ).

% PartialSA.wf_assertion_sat_larger_pure
thf(fact_425_PartialSA_Opackage__rhs__proof,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( stable @ F )
             => ( ( defined @ Phi @ F )
               => ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
                  & ( packag3877571396724326311_state @ plus @ core @ unit @ S3 @ F3 ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs_proof
thf(fact_426_PartialSA_Osat__star__exists__bigger,axiom,
    ! [A4: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ A4 @ B4 ) @ Phi )
     => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
       => ( ( packag7298478212905792770_state @ plus @ core @ B4 )
         => ? [A6: state,B6: state] :
              ( ( greater @ ( core @ A6 ) @ ( core @ Phi ) )
              & ( greater @ ( core @ B6 ) @ ( core @ Phi ) )
              & ( ( some_state @ Phi )
                = ( plus @ A6 @ B6 ) )
              & ( package_sat_state @ plus @ A4 @ A6 )
              & ( package_sat_state @ plus @ B4 @ B6 ) ) ) ) ) ).

% PartialSA.sat_star_exists_bigger
thf(fact_427_PartialSA_Owf__assertion_Osimps_I3_J,axiom,
    ! [A4: state > $o] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aSem_state @ A4 ) )
      = ( packag2456304381420842418_state @ plus @ A4 ) ) ).

% PartialSA.wf_assertion.simps(3)
thf(fact_428_binary__mask__def,axiom,
    ( binary_mask
    = ( ^ [Pi: produc1457211279475724562t_char > prat,L: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( Pi @ L )
            = pwrite )
          @ pwrite
          @ pnone ) ) ) ).

% binary_mask_def
thf(fact_429_PartialSA_Owf__assertion_Osimps_I2_J,axiom,
    ! [B: state > $o,Aa2: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aImp_state @ B @ Aa2 ) )
      = ( ( packag6595153354952283300_state @ plus @ core @ B )
        & ( packag7298478212905792770_state @ plus @ core @ Aa2 ) ) ) ).

% PartialSA.wf_assertion.simps(2)
thf(fact_430_PartialSA_Osat_Ocases,axiom,
    ! [X: produc2756261550280135502_state] :
      ( ! [A10: aassertion_state,B8: aassertion_state,Phi5: state] :
          ( X
         != ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Phi5 ) )
     => ( ! [B6: state > $o,A10: aassertion_state,Phi5: state] :
            ( X
           != ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Phi5 ) )
       => ~ ! [A10: state > $o,Phi5: state] :
              ( X
             != ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Phi5 ) ) ) ) ).

% PartialSA.sat.cases
thf(fact_431_PartialSA_Owf__assertion_Ocases,axiom,
    ! [X: aassertion_state] :
      ( ! [A10: aassertion_state,B8: aassertion_state] :
          ( X
         != ( aStar_state @ A10 @ B8 ) )
     => ( ! [B6: state > $o,A10: aassertion_state] :
            ( X
           != ( aImp_state @ B6 @ A10 ) )
       => ~ ! [A10: state > $o] :
              ( X
             != ( aSem_state @ A10 ) ) ) ) ).

% PartialSA.wf_assertion.cases
thf(fact_432_PartialSA_Osat_Oelims_I1_J,axiom,
    ! [X: aassertion_state,Xa2: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X @ Xa2 )
        = Y )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( Y
              = ( ~ ? [A2: state,B2: state] :
                      ( ( ( some_state @ Xa2 )
                        = ( plus @ A2 @ B2 ) )
                      & ( package_sat_state @ plus @ A10 @ A2 )
                      & ( package_sat_state @ plus @ B8 @ B2 ) ) ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( Y
                = ( ~ ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A10 @ Xa2 ) ) ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( Y
                  = ( ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.elims(1)
thf(fact_433_PartialSA_Osat_Oelims_I2_J,axiom,
    ! [X: aassertion_state,Xa2: state] :
      ( ( package_sat_state @ plus @ X @ Xa2 )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ~ ? [A6: state,B6: state] :
                  ( ( ( some_state @ Xa2 )
                    = ( plus @ A6 @ B6 ) )
                  & ( package_sat_state @ plus @ A10 @ A6 )
                  & ( package_sat_state @ plus @ B8 @ B6 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( ( B6 @ Xa2 )
                 => ( package_sat_state @ plus @ A10 @ Xa2 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ~ ( A10 @ Xa2 ) ) ) ) ) ).

% PartialSA.sat.elims(2)
thf(fact_434_PartialSA_Osat_Oelims_I3_J,axiom,
    ! [X: aassertion_state,Xa2: state] :
      ( ~ ( package_sat_state @ plus @ X @ Xa2 )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ? [A5: state,B9: state] :
                ( ( ( some_state @ Xa2 )
                  = ( plus @ A5 @ B9 ) )
                & ( package_sat_state @ plus @ A10 @ A5 )
                & ( package_sat_state @ plus @ B8 @ B9 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( ( B6 @ Xa2 )
               => ( package_sat_state @ plus @ A10 @ Xa2 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( A10 @ Xa2 ) ) ) ) ) ).

% PartialSA.sat.elims(3)
thf(fact_435_PartialSA_Opackage__rhs_Ointros_I1_J,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state,Ba: aassertion_state,Phi7: state,F4: state,S4: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F3 @ S3 @ Pc @ Ba @ Phi7 @ F4 @ S4 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aStar_state @ A4 @ Ba ) @ Phi7 @ F4 @ S4 ) ) ) ).

% PartialSA.package_rhs.intros(1)
thf(fact_436_PartialSA_OAStar,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state,B4: aassertion_state,Phi7: state,F4: state,S4: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F3 @ S3 @ Pc @ B4 @ Phi7 @ F4 @ S4 )
       => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aStar_state @ A4 @ B4 ) @ Phi7 @ F4 @ S4 ) ) ) ).

% PartialSA.AStar
thf(fact_437_PartialSA_Owf__assertion_Oelims_I3_J,axiom,
    ! [X: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( ( packag7298478212905792770_state @ plus @ core @ A10 )
              & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(3)
thf(fact_438_PartialSA_Owf__assertion_Oelims_I2_J,axiom,
    ! [X: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                  & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(2)
thf(fact_439_PartialSA_Owf__assertion_Oelims_I1_J,axiom,
    ! [X: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X )
        = Y )
     => ( ! [A10: aassertion_state,B8: aassertion_state] :
            ( ( X
              = ( aStar_state @ A10 @ B8 ) )
           => ( Y
              = ( ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( X
                = ( aImp_state @ B6 @ A10 ) )
             => ( Y
                = ( ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) ) )
         => ~ ! [A10: state > $o] :
                ( ( X
                  = ( aSem_state @ A10 ) )
               => ( Y
                  = ( ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.elims(1)
thf(fact_440_padd__zero,axiom,
    ! [A: prat,B: prat] :
      ( ( pnone
        = ( padd @ A @ B ) )
      = ( ( A = pnone )
        & ( B = pnone ) ) ) ).

% padd_zero
thf(fact_441_ppos__eq__pnone,axiom,
    ( ppos
    = ( ^ [P5: prat] : ( P5 != pnone ) ) ) ).

% ppos_eq_pnone
thf(fact_442_pmult__special_I2_J,axiom,
    ! [X: prat] :
      ( ( pmult @ pnone @ X )
      = pnone ) ).

% pmult_special(2)
thf(fact_443_empty__mask_Oelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X )
        = Y )
     => ( Y = pnone ) ) ).

% empty_mask.elims
thf(fact_444_empty__mask_Osimps,axiom,
    ( empty_3446695950879338768t_char
    = ( ^ [Hl: produc1457211279475724562t_char] : pnone ) ) ).

% empty_mask.simps
thf(fact_445_PartialSA_Osat_Osimps_I2_J,axiom,
    ! [B: state > $o,Aa2: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aImp_state @ B @ Aa2 ) @ Phi )
      = ( ( B @ Phi )
       => ( package_sat_state @ plus @ Aa2 @ Phi ) ) ) ).

% PartialSA.sat.simps(2)
thf(fact_446_PartialSA_Osat_Osimps_I3_J,axiom,
    ! [A4: state > $o,Phi: state] :
      ( ( package_sat_state @ plus @ ( aSem_state @ A4 ) @ Phi )
      = ( A4 @ Phi ) ) ).

% PartialSA.sat.simps(3)
thf(fact_447_PartialSA_OAImp,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,B: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ ( packag1330488657391168505_state @ Pc @ B ) @ A4 @ Phi2 @ F3 @ S3 )
     => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ ( aImp_state @ B @ A4 ) @ Phi2 @ F3 @ S3 ) ) ).

% PartialSA.AImp
thf(fact_448_PartialSA_Osat_Osimps_I1_J,axiom,
    ! [Aa2: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_sat_state @ plus @ ( aStar_state @ Aa2 @ B4 ) @ Phi )
      = ( ? [A2: state,B2: state] :
            ( ( ( some_state @ Phi )
              = ( plus @ A2 @ B2 ) )
            & ( package_sat_state @ plus @ Aa2 @ A2 )
            & ( package_sat_state @ plus @ B4 @ B2 ) ) ) ) ).

% PartialSA.sat.simps(1)
thf(fact_449_PartialSA_Owf__assertion_Osimps_I1_J,axiom,
    ! [Aa2: aassertion_state,B4: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ ( aStar_state @ Aa2 @ B4 ) )
      = ( ( packag7298478212905792770_state @ plus @ core @ Aa2 )
        & ( packag7298478212905792770_state @ plus @ core @ B4 ) ) ) ).

% PartialSA.wf_assertion.simps(1)
thf(fact_450_empty__mask_Opelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: prat] :
      ( ( ( empty_3446695950879338768t_char @ X )
        = Y )
     => ( ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P8892882183480857371t_char @ empty_8141283858255108185t_char @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_451_empty__mask_Opelims,axiom,
    ! [X: produc3142500478612311029_state,Y: prat] :
      ( ( ( empty_5858998862663000819_state @ X )
        = Y )
     => ( ( accp_P7183347322223220350_state @ empty_3683758330361983676_state @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P7183347322223220350_state @ empty_3683758330361983676_state @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_452_empty__mask_Opelims,axiom,
    ! [X: produc4844402304972151915_state,Y: prat] :
      ( ( ( empty_3913122416104905065_state @ X )
        = Y )
     => ( ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6233459008282737652_state @ empty_5283331674940636722_state @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_453_empty__mask_Opelims,axiom,
    ! [X: produc6251377953716854561_state,Y: prat] :
      ( ( ( empty_5541330147480151071_state @ X )
        = Y )
     => ( ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P6554740477754186410_state @ empty_7304051301540881640_state @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_454_empty__mask_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: prat] :
      ( ( ( empty_6102255041883331742on_val @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4405556307444930259on_val @ empty_5847456986941130773on_val @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_455_empty__mask_Opelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: prat] :
      ( ( ( empty_6616431780912394577r_prat @ X )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X )
       => ~ ( ( Y = pnone )
           => ~ ( accp_P4765339447491148764r_prat @ empty_3412554051312619034r_prat @ X ) ) ) ) ).

% empty_mask.pelims
thf(fact_456_valid__mask_Oelims_I3_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X )
     => ~ ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl2 ) )
          & ! [F5: list_char] :
              ( ( X @ ( produc120197956887798346t_char @ null_nat @ F5 ) )
              = pnone ) ) ) ).

% valid_mask.elims(3)
thf(fact_457_valid__mask_Oelims_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X )
     => ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl4 ) )
        & ! [F6: list_char] :
            ( ( X @ ( produc120197956887798346t_char @ null_nat @ F6 ) )
            = pnone ) ) ) ).

% valid_mask.elims(2)
thf(fact_458_valid__mask_Oelims_I1_J,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X )
        = Y )
     => ( Y
        = ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl ) )
          & ! [F7: list_char] :
              ( ( X @ ( produc120197956887798346t_char @ null_nat @ F7 ) )
              = pnone ) ) ) ) ).

% valid_mask.elims(1)
thf(fact_459_valid__mask_Osimps,axiom,
    ( valid_mask
    = ( ^ [Pi: produc1457211279475724562t_char > prat] :
          ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi @ Hl ) )
          & ! [F7: list_char] :
              ( ( Pi @ ( produc120197956887798346t_char @ null_nat @ F7 ) )
              = pnone ) ) ) ) ).

% valid_mask.simps
thf(fact_460_valid__null__def,axiom,
    ( valid_null
    = ( ^ [Pi: produc1457211279475724562t_char > prat] :
        ! [F7: list_char] :
          ( ( Pi @ ( produc120197956887798346t_char @ null_nat @ F7 ) )
          = pnone ) ) ) ).

% valid_null_def
thf(fact_461_valid__maskI,axiom,
    ! [Pi2: produc1457211279475724562t_char > prat] :
      ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( Pi2 @ Hl2 ) )
     => ( ! [F5: list_char] :
            ( ( Pi2 @ ( produc120197956887798346t_char @ null_nat @ F5 ) )
            = pnone )
       => ( valid_mask @ Pi2 ) ) ) ).

% valid_maskI
thf(fact_462_add__masks_Opelims,axiom,
    ! [X: produc1457211279475724562t_char > prat,Xa2: produc1457211279475724562t_char > prat,Xb2: produc1457211279475724562t_char,Y: prat] :
      ( ( ( add_ma6586698345353345811t_char @ X @ Xa2 @ Xb2 )
        = Y )
     => ( ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa2 @ Xb2 ) ) )
       => ~ ( ( Y
              = ( padd @ ( X @ Xb2 ) @ ( Xa2 @ Xb2 ) ) )
           => ~ ( accp_P224314924008452035t_char @ add_ma2412268806269088278t_char @ ( produc2957999048406202538t_char @ X @ ( produc2591414526589101846t_char @ Xa2 @ Xb2 ) ) ) ) ) ) ).

% add_masks.pelims
thf(fact_463_valid__mask_Opelims_I1_J,axiom,
    ! [X: produc1457211279475724562t_char > prat,Y: $o] :
      ( ( ( valid_mask @ X )
        = Y )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( Y
              = ( ! [Hl: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl ) )
                & ! [F7: list_char] :
                    ( ( X @ ( produc120197956887798346t_char @ null_nat @ F7 ) )
                    = pnone ) ) )
           => ~ ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X ) ) ) ) ).

% valid_mask.pelims(1)
thf(fact_464_valid__mask_Opelims_I2_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ( valid_mask @ X )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
           => ~ ( ! [Hl4: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl4 ) )
                & ! [F6: list_char] :
                    ( ( X @ ( produc120197956887798346t_char @ null_nat @ F6 ) )
                    = pnone ) ) ) ) ) ).

% valid_mask.pelims(2)
thf(fact_465_valid__mask_Opelims_I3_J,axiom,
    ! [X: produc1457211279475724562t_char > prat] :
      ( ~ ( valid_mask @ X )
     => ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
       => ~ ( ( accp_P4765339447491148764r_prat @ valid_mask_rel @ X )
           => ( ! [Hl2: produc1457211279475724562t_char] : ( pgte @ pwrite @ ( X @ Hl2 ) )
              & ! [F5: list_char] :
                  ( ( X @ ( produc120197956887798346t_char @ null_nat @ F5 ) )
                  = pnone ) ) ) ) ) ).

% valid_mask.pelims(3)
thf(fact_466_PartialSA_Owf__assertion_Opelims_I3_J,axiom,
    ! [X: aassertion_state] :
      ( ~ ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
               => ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                  & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                 => ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                    & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                   => ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(3)
thf(fact_467_PartialSA_Owf__assertion_Opelims_I1_J,axiom,
    ! [X: aassertion_state,Y: $o] :
      ( ( ( packag7298478212905792770_state @ plus @ core @ X )
        = Y )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( Y
                  = ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) )
               => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( Y
                    = ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) )
                 => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( Y
                      = ( packag2456304381420842418_state @ plus @ A10 ) )
                   => ~ ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(1)
thf(fact_468_PartialSA_Owf__assertion_Opelims_I2_J,axiom,
    ! [X: aassertion_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ X )
     => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ X )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aStar_state @ A10 @ B8 ) )
               => ~ ( ( packag7298478212905792770_state @ plus @ core @ A10 )
                    & ( packag7298478212905792770_state @ plus @ core @ B8 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aImp_state @ B6 @ A10 ) )
                 => ~ ( ( packag6595153354952283300_state @ plus @ core @ B6 )
                      & ( packag7298478212905792770_state @ plus @ core @ A10 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_a4361485425079813866_state @ packag4834522500328176237_state @ ( aSem_state @ A10 ) )
                   => ~ ( packag2456304381420842418_state @ plus @ A10 ) ) ) ) ) ) ) ).

% PartialSA.wf_assertion.pelims(2)
thf(fact_469_PartialSA_Osplus_Opelims,axiom,
    ! [X: option_state,Xa2: option_state,Y: option_state] :
      ( ( ( sep_splus_state @ plus @ X @ Xa2 )
        = Y )
     => ( ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ X @ Xa2 ) )
       => ( ( ( X = none_state )
           => ( ( Y = none_state )
             => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
         => ( ! [V2: state] :
                ( ( X
                  = ( some_state @ V2 ) )
               => ( ( Xa2 = none_state )
                 => ( ( Y = none_state )
                   => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ V2 ) @ none_state ) ) ) ) )
           => ~ ! [A6: state] :
                  ( ( X
                    = ( some_state @ A6 ) )
                 => ! [B6: state] :
                      ( ( Xa2
                        = ( some_state @ B6 ) )
                     => ( ( Y
                          = ( plus @ A6 @ B6 ) )
                       => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) ) ) ) ) ) ) ) ) ).

% PartialSA.splus.pelims
thf(fact_470_PartialSA_Osat_Opelims_I3_J,axiom,
    ! [X: aassertion_state,Xa2: state] :
      ( ~ ( package_sat_state @ plus @ X @ Xa2 )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) )
               => ? [A5: state,B9: state] :
                    ( ( ( some_state @ Xa2 )
                      = ( plus @ A5 @ B9 ) )
                    & ( package_sat_state @ plus @ A10 @ A5 )
                    & ( package_sat_state @ plus @ B8 @ B9 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) )
                 => ( ( B6 @ Xa2 )
                   => ( package_sat_state @ plus @ A10 @ Xa2 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) )
                   => ( A10 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(3)
thf(fact_471_PartialSA_Osat_Opelims_I2_J,axiom,
    ! [X: aassertion_state,Xa2: state] :
      ( ( package_sat_state @ plus @ X @ Xa2 )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) )
               => ~ ? [A6: state,B6: state] :
                      ( ( ( some_state @ Xa2 )
                        = ( plus @ A6 @ B6 ) )
                      & ( package_sat_state @ plus @ A10 @ A6 )
                      & ( package_sat_state @ plus @ B8 @ B6 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) )
                 => ~ ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A10 @ Xa2 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) )
                   => ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(2)
thf(fact_472_PartialSA_Osat_Opelims_I1_J,axiom,
    ! [X: aassertion_state,Xa2: state,Y: $o] :
      ( ( ( package_sat_state @ plus @ X @ Xa2 )
        = Y )
     => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( Y
                  = ( ? [A2: state,B2: state] :
                        ( ( ( some_state @ Xa2 )
                          = ( plus @ A2 @ B2 ) )
                        & ( package_sat_state @ plus @ A10 @ A2 )
                        & ( package_sat_state @ plus @ B8 @ B2 ) ) ) )
               => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( Y
                    = ( ( B6 @ Xa2 )
                     => ( package_sat_state @ plus @ A10 @ Xa2 ) ) )
                 => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( ( Y
                      = ( A10 @ Xa2 ) )
                   => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) ) ) ) ) ) ) ) ).

% PartialSA.sat.pelims(1)
thf(fact_473_valid__state_Opelims_I3_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ~ ( valid_state @ X )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi5 @ H5 ) )
               => ( ( valid_mask @ Pi5 )
                  & ( valid_heap @ Pi5 @ H5 ) ) ) ) ) ) ).

% valid_state.pelims(3)
thf(fact_474_valid__state_Opelims_I1_J,axiom,
    ! [X: produc9003781588162623004on_val,Y: $o] :
      ( ( ( valid_state @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
             => ( ( Y
                  = ( ( valid_mask @ Pi5 )
                    & ( valid_heap @ Pi5 @ H5 ) ) )
               => ~ ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi5 @ H5 ) ) ) ) ) ) ).

% valid_state.pelims(1)
thf(fact_475_valid__state_Opelims_I2_J,axiom,
    ! [X: produc9003781588162623004on_val] :
      ( ( valid_state @ X )
     => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ X )
       => ~ ! [Pi5: produc1457211279475724562t_char > prat,H5: produc1457211279475724562t_char > option_val] :
              ( ( X
                = ( produc74620467203698198on_val @ Pi5 @ H5 ) )
             => ( ( accp_P4405556307444930259on_val @ valid_state_rel @ ( produc74620467203698198on_val @ Pi5 @ H5 ) )
               => ~ ( ( valid_mask @ Pi5 )
                    & ( valid_heap @ Pi5 @ H5 ) ) ) ) ) ) ).

% valid_state.pelims(2)
thf(fact_476_compatible__options_Opelims_I2_J,axiom,
    ! [X: option_state,Xa2: option_state] :
      ( ( compat2278460363914054422_state @ X @ Xa2 )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa2 ) )
       => ( ! [A6: state] :
              ( ( X
                = ( some_state @ A6 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) )
                   => ( A6 != B6 ) ) ) )
         => ( ( ( X = none_state )
             => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) )
           => ~ ( ( Xa2 = none_state )
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ none_state ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_477_compatible__options_Opelims_I2_J,axiom,
    ! [X: option_val,Xa2: option_val] :
      ( ( compat7209469420100717861ns_val @ X @ Xa2 )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa2 ) )
       => ( ! [A6: val] :
              ( ( X
                = ( some_val @ A6 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) )
                   => ( A6 != B6 ) ) ) )
         => ( ( ( X = none_val )
             => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) )
           => ~ ( ( Xa2 = none_val )
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ none_val ) ) ) ) ) ) ) ).

% compatible_options.pelims(2)
thf(fact_478_compatible__options_Opelims_I1_J,axiom,
    ! [X: option_state,Xa2: option_state,Y: $o] :
      ( ( ( compat2278460363914054422_state @ X @ Xa2 )
        = Y )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa2 ) )
       => ( ! [A6: state] :
              ( ( X
                = ( some_state @ A6 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( Y
                      = ( A6 = B6 ) )
                   => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) ) ) ) )
         => ( ( ( X = none_state )
             => ( Y
               => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
           => ~ ( ( Xa2 = none_state )
               => ( Y
                 => ~ ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ none_state ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_479_compatible__options_Opelims_I1_J,axiom,
    ! [X: option_val,Xa2: option_val,Y: $o] :
      ( ( ( compat7209469420100717861ns_val @ X @ Xa2 )
        = Y )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa2 ) )
       => ( ! [A6: val] :
              ( ( X
                = ( some_val @ A6 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( Y
                      = ( A6 = B6 ) )
                   => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) ) ) ) )
         => ( ( ( X = none_val )
             => ( Y
               => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) ) )
           => ~ ( ( Xa2 = none_val )
               => ( Y
                 => ~ ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ none_val ) ) ) ) ) ) ) ) ).

% compatible_options.pelims(1)
thf(fact_480_compatible__options_Opelims_I3_J,axiom,
    ! [X: option_state,Xa2: option_state] :
      ( ~ ( compat2278460363914054422_state @ X @ Xa2 )
     => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ X @ Xa2 ) )
       => ~ ! [A6: state] :
              ( ( X
                = ( some_state @ A6 ) )
             => ! [B6: state] :
                  ( ( Xa2
                    = ( some_state @ B6 ) )
                 => ( ( accp_P7183347322223220350_state @ compat1844074344818064729_state @ ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) )
                   => ( A6 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_481_compatible__options_Opelims_I3_J,axiom,
    ! [X: option_val,Xa2: option_val] :
      ( ~ ( compat7209469420100717861ns_val @ X @ Xa2 )
     => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ X @ Xa2 ) )
       => ~ ! [A6: val] :
              ( ( X
                = ( some_val @ A6 ) )
             => ! [B6: val] :
                  ( ( Xa2
                    = ( some_val @ B6 ) )
                 => ( ( accp_P4269981079083053040on_val @ compat8294034345482142370el_val @ ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) )
                   => ( A6 = B6 ) ) ) ) ) ) ).

% compatible_options.pelims(3)
thf(fact_482_package__logic_Osat_Opelims_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val,Y: $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_val @ Plus @ X @ Xa2 )
          = Y )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa2 ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( Y
                    = ( ? [A2: val,B2: val] :
                          ( ( ( some_val @ Xa2 )
                            = ( Plus @ A2 @ B2 ) )
                          & ( package_sat_val @ Plus @ A10 @ A2 )
                          & ( package_sat_val @ Plus @ B8 @ B2 ) ) ) )
                 => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa2 ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( Y
                      = ( ( B6 @ Xa2 )
                       => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) )
                   => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa2 ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( Y
                        = ( A10 @ Xa2 ) )
                     => ~ ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa2 ) ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(1)
thf(fact_483_package__logic_Osat_Opelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_state @ Plus @ X @ Xa2 )
          = Y )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( Y
                    = ( ? [A2: state,B2: state] :
                          ( ( ( some_state @ Xa2 )
                            = ( Plus @ A2 @ B2 ) )
                          & ( package_sat_state @ Plus @ A10 @ A2 )
                          & ( package_sat_state @ Plus @ B8 @ B2 ) ) ) )
                 => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( Y
                      = ( ( B6 @ Xa2 )
                       => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) )
                   => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( Y
                        = ( A10 @ Xa2 ) )
                     => ~ ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(1)
thf(fact_484_package__logic_Osat_Opelims_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ X @ Xa2 )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa2 ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa2 ) )
                 => ~ ? [A6: val,B6: val] :
                        ( ( ( some_val @ Xa2 )
                          = ( Plus @ A6 @ B6 ) )
                        & ( package_sat_val @ Plus @ A10 @ A6 )
                        & ( package_sat_val @ Plus @ B8 @ B6 ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa2 ) )
                   => ~ ( ( B6 @ Xa2 )
                       => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa2 ) )
                     => ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(2)
thf(fact_485_package__logic_Osat_Opelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ X @ Xa2 )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) )
                 => ~ ? [A6: state,B6: state] :
                        ( ( ( some_state @ Xa2 )
                          = ( Plus @ A6 @ B6 ) )
                        & ( package_sat_state @ Plus @ A10 @ A6 )
                        & ( package_sat_state @ Plus @ B8 @ B6 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) )
                   => ~ ( ( B6 @ Xa2 )
                       => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) )
                     => ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(2)
thf(fact_486_package__logic_Ounit__neutral,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( some_val @ A )
        = ( Plus @ A @ Unit ) ) ) ).

% package_logic.unit_neutral
thf(fact_487_package__logic_Ounit__neutral,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( some_state @ A )
        = ( Plus @ A @ Unit ) ) ) ).

% package_logic.unit_neutral
thf(fact_488_package__logic_Ostable__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,B: val,X: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( Stable @ A )
       => ( ( Stable @ B )
         => ( ( ( some_val @ X )
              = ( Plus @ A @ B ) )
           => ( Stable @ X ) ) ) ) ) ).

% package_logic.stable_sum
thf(fact_489_package__logic_Ostable__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,B: state,X: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( Stable @ A )
       => ( ( Stable @ B )
         => ( ( ( some_state @ X )
              = ( Plus @ A @ B ) )
           => ( Stable @ X ) ) ) ) ) ).

% package_logic.stable_sum
thf(fact_490_package__logic_Osat_Osimps_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: aassertion_val,B4: aassertion_val,Phi: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ ( aStar_val @ A4 @ B4 ) @ Phi )
        = ( ? [A2: val,B2: val] :
              ( ( ( some_val @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( package_sat_val @ Plus @ A4 @ A2 )
              & ( package_sat_val @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.sat.simps(1)
thf(fact_491_package__logic_Osat_Osimps_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aStar_state @ A4 @ B4 ) @ Phi )
        = ( ? [A2: state,B2: state] :
              ( ( ( some_state @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( package_sat_state @ Plus @ A4 @ A2 )
              & ( package_sat_state @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.sat.simps(1)
thf(fact_492_package__logic_Omono__pure__cond__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6714868506247462167nd_val @ Plus @ Core @ B )
        = ( ! [Phi4: val] :
              ( ( B @ Phi4 )
              = ( B @ ( Core @ Phi4 ) ) )
          & ! [Phi3: val,Phi4: val,R: val] :
              ( ( ( sep_pure_val @ Plus @ R )
                & ( ( some_val @ Phi3 )
                  = ( Plus @ Phi4 @ R ) )
                & ~ ( B @ Phi4 ) )
             => ~ ( B @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pure_cond_def
thf(fact_493_package__logic_Omono__pure__cond__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6595153354952283300_state @ Plus @ Core @ B )
        = ( ! [Phi4: state] :
              ( ( B @ Phi4 )
              = ( B @ ( Core @ Phi4 ) ) )
          & ! [Phi3: state,Phi4: state,R: state] :
              ( ( ( sep_pure_state @ Plus @ R )
                & ( ( some_state @ Phi3 )
                  = ( Plus @ Phi4 @ R ) )
                & ~ ( B @ Phi4 ) )
             => ~ ( B @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pure_cond_def
thf(fact_494_package__logic_Omono__pure__condI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [Phi5: val] :
            ( ( B @ Phi5 )
            = ( B @ ( Core @ Phi5 ) ) )
       => ( ! [Phi5: val,Phi6: val,R3: val] :
              ( ( ( sep_pure_val @ Plus @ R3 )
                & ( ( some_val @ Phi6 )
                  = ( Plus @ Phi5 @ R3 ) )
                & ~ ( B @ Phi5 ) )
             => ~ ( B @ Phi6 ) )
         => ( packag6714868506247462167nd_val @ Plus @ Core @ B ) ) ) ) ).

% package_logic.mono_pure_condI
thf(fact_495_package__logic_Omono__pure__condI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [Phi5: state] :
            ( ( B @ Phi5 )
            = ( B @ ( Core @ Phi5 ) ) )
       => ( ! [Phi5: state,Phi6: state,R3: state] :
              ( ( ( sep_pure_state @ Plus @ R3 )
                & ( ( some_state @ Phi6 )
                  = ( Plus @ Phi5 @ R3 ) )
                & ~ ( B @ Phi5 ) )
             => ~ ( B @ Phi6 ) )
         => ( packag6595153354952283300_state @ Plus @ Core @ B ) ) ) ) ).

% package_logic.mono_pure_condI
thf(fact_496_package__logic_Ois__footprint__standard__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,W: val,A4: aassertion_val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag685230357167683994rd_val @ Plus @ W @ A4 @ B4 )
        = ( ! [A2: val,B2: val] :
              ( ( ( package_sat_val @ Plus @ A4 @ A2 )
                & ( ( some_val @ B2 )
                  = ( Plus @ A2 @ W ) ) )
             => ( package_sat_val @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.is_footprint_standard_def
thf(fact_497_package__logic_Ois__footprint__standard__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,W: state,A4: aassertion_state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7096211993527611489_state @ Plus @ W @ A4 @ B4 )
        = ( ! [A2: state,B2: state] :
              ( ( ( package_sat_state @ Plus @ A4 @ A2 )
                & ( ( some_state @ B2 )
                  = ( Plus @ A2 @ W ) ) )
             => ( package_sat_state @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.is_footprint_standard_def
thf(fact_498_package__logic_Ois__footprint__general__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,W: val,R4: val > val > val,A4: aassertion_val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag4897621287243763553al_val @ Plus @ W @ R4 @ A4 @ B4 )
        = ( ! [A2: val,B2: val] :
              ( ( ( package_sat_val @ Plus @ A4 @ A2 )
                & ( ( some_val @ B2 )
                  = ( Plus @ A2 @ ( R4 @ A2 @ W ) ) ) )
             => ( package_sat_val @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.is_footprint_general_def
thf(fact_499_package__logic_Ois__footprint__general__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,W: state,R4: state > state > state,A4: aassertion_state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag6192661653625646554_state @ Plus @ W @ R4 @ A4 @ B4 )
        = ( ! [A2: state,B2: state] :
              ( ( ( package_sat_state @ Plus @ A4 @ A2 )
                & ( ( some_state @ B2 )
                  = ( Plus @ A2 @ ( R4 @ A2 @ W ) ) ) )
             => ( package_sat_state @ Plus @ B4 @ B2 ) ) ) ) ) ).

% package_logic.is_footprint_general_def
thf(fact_500_package__logic_Ois__footprint__standardI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: aassertion_val,W: val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: val,B6: val] :
            ( ( ( package_sat_val @ Plus @ A4 @ A6 )
              & ( ( some_val @ B6 )
                = ( Plus @ A6 @ W ) ) )
           => ( package_sat_val @ Plus @ B4 @ B6 ) )
       => ( packag685230357167683994rd_val @ Plus @ W @ A4 @ B4 ) ) ) ).

% package_logic.is_footprint_standardI
thf(fact_501_package__logic_Ois__footprint__standardI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: aassertion_state,W: state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: state,B6: state] :
            ( ( ( package_sat_state @ Plus @ A4 @ A6 )
              & ( ( some_state @ B6 )
                = ( Plus @ A6 @ W ) ) )
           => ( package_sat_state @ Plus @ B4 @ B6 ) )
       => ( packag7096211993527611489_state @ Plus @ W @ A4 @ B4 ) ) ) ).

% package_logic.is_footprint_standardI
thf(fact_502_package__logic_Ois__footprint__generalI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: aassertion_val,R4: val > val > val,W: val,B4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: val,B6: val] :
            ( ( ( package_sat_val @ Plus @ A4 @ A6 )
              & ( ( some_val @ B6 )
                = ( Plus @ A6 @ ( R4 @ A6 @ W ) ) ) )
           => ( package_sat_val @ Plus @ B4 @ B6 ) )
       => ( packag4897621287243763553al_val @ Plus @ W @ R4 @ A4 @ B4 ) ) ) ).

% package_logic.is_footprint_generalI
thf(fact_503_package__logic_Ois__footprint__generalI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: aassertion_state,R4: state > state > state,W: state,B4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: state,B6: state] :
            ( ( ( package_sat_state @ Plus @ A4 @ A6 )
              & ( ( some_state @ B6 )
                = ( Plus @ A6 @ ( R4 @ A6 @ W ) ) ) )
           => ( package_sat_state @ Plus @ B4 @ B6 ) )
       => ( packag6192661653625646554_state @ Plus @ W @ R4 @ A4 @ B4 ) ) ) ).

% package_logic.is_footprint_generalI
thf(fact_504_package__logic_Omono__pruner__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,P3: val > $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8699728003424501129er_val @ Plus @ P3 )
        = ( ! [Phi3: val,Phi4: val,R: val] :
              ( ( ( sep_pure_val @ Plus @ R )
                & ( P3 @ Phi4 )
                & ( ( some_val @ Phi3 )
                  = ( Plus @ Phi4 @ R ) ) )
             => ( P3 @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pruner_def
thf(fact_505_package__logic_Omono__pruner__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,P3: state > $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2456304381420842418_state @ Plus @ P3 )
        = ( ! [Phi3: state,Phi4: state,R: state] :
              ( ( ( sep_pure_state @ Plus @ R )
                & ( P3 @ Phi4 )
                & ( ( some_state @ Phi3 )
                  = ( Plus @ Phi4 @ R ) ) )
             => ( P3 @ Phi3 ) ) ) ) ) ).

% package_logic.mono_pruner_def
thf(fact_506_package__logic_Owf__assertion__sat__larger__pure,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: aassertion_val,Phi: val,Phi2: val,R2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ A4 )
       => ( ( package_sat_val @ Plus @ A4 @ Phi )
         => ( ( ( some_val @ Phi2 )
              = ( Plus @ Phi @ R2 ) )
           => ( ( sep_pure_val @ Plus @ R2 )
             => ( package_sat_val @ Plus @ A4 @ Phi2 ) ) ) ) ) ) ).

% package_logic.wf_assertion_sat_larger_pure
thf(fact_507_package__logic_Owf__assertion__sat__larger__pure,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: aassertion_state,Phi: state,Phi2: state,R2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ A4 )
       => ( ( package_sat_state @ Plus @ A4 @ Phi )
         => ( ( ( some_state @ Phi2 )
              = ( Plus @ Phi @ R2 ) )
           => ( ( sep_pure_state @ Plus @ R2 )
             => ( package_sat_state @ Plus @ A4 @ Phi2 ) ) ) ) ) ) ).

% package_logic.wf_assertion_sat_larger_pure
thf(fact_508_package__logic_Osat_Oelims_I1_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val,Y: $o] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_val @ Plus @ X @ Xa2 )
          = Y )
       => ( ! [A10: aassertion_val,B8: aassertion_val] :
              ( ( X
                = ( aStar_val @ A10 @ B8 ) )
             => ( Y
                = ( ~ ? [A2: val,B2: val] :
                        ( ( ( some_val @ Xa2 )
                          = ( Plus @ A2 @ B2 ) )
                        & ( package_sat_val @ Plus @ A10 @ A2 )
                        & ( package_sat_val @ Plus @ B8 @ B2 ) ) ) ) )
         => ( ! [B6: val > $o,A10: aassertion_val] :
                ( ( X
                  = ( aImp_val @ B6 @ A10 ) )
               => ( Y
                  = ( ~ ( ( B6 @ Xa2 )
                       => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) ) ) )
           => ~ ! [A10: val > $o] :
                  ( ( X
                    = ( aSem_val @ A10 ) )
                 => ( Y
                    = ( ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.elims(1)
thf(fact_509_package__logic_Osat_Oelims_I1_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state,Y: $o] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( package_sat_state @ Plus @ X @ Xa2 )
          = Y )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ( Y
                = ( ~ ? [A2: state,B2: state] :
                        ( ( ( some_state @ Xa2 )
                          = ( Plus @ A2 @ B2 ) )
                        & ( package_sat_state @ Plus @ A10 @ A2 )
                        & ( package_sat_state @ Plus @ B8 @ B2 ) ) ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( Y
                  = ( ~ ( ( B6 @ Xa2 )
                       => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( Y
                    = ( ~ ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.elims(1)
thf(fact_510_package__logic_Osat_Oelims_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ X @ Xa2 )
       => ( ! [A10: aassertion_val,B8: aassertion_val] :
              ( ( X
                = ( aStar_val @ A10 @ B8 ) )
             => ~ ? [A6: val,B6: val] :
                    ( ( ( some_val @ Xa2 )
                      = ( Plus @ A6 @ B6 ) )
                    & ( package_sat_val @ Plus @ A10 @ A6 )
                    & ( package_sat_val @ Plus @ B8 @ B6 ) ) )
         => ( ! [B6: val > $o,A10: aassertion_val] :
                ( ( X
                  = ( aImp_val @ B6 @ A10 ) )
               => ~ ( ( B6 @ Xa2 )
                   => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) )
           => ~ ! [A10: val > $o] :
                  ( ( X
                    = ( aSem_val @ A10 ) )
                 => ~ ( A10 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(2)
thf(fact_511_package__logic_Osat_Oelims_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ X @ Xa2 )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ~ ? [A6: state,B6: state] :
                    ( ( ( some_state @ Xa2 )
                      = ( Plus @ A6 @ B6 ) )
                    & ( package_sat_state @ Plus @ A10 @ A6 )
                    & ( package_sat_state @ Plus @ B8 @ B6 ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ~ ( ( B6 @ Xa2 )
                   => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ~ ( A10 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(2)
thf(fact_512_package__logic_Osat_Oelims_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_val @ Plus @ X @ Xa2 )
       => ( ! [A10: aassertion_val,B8: aassertion_val] :
              ( ( X
                = ( aStar_val @ A10 @ B8 ) )
             => ? [A5: val,B9: val] :
                  ( ( ( some_val @ Xa2 )
                    = ( Plus @ A5 @ B9 ) )
                  & ( package_sat_val @ Plus @ A10 @ A5 )
                  & ( package_sat_val @ Plus @ B8 @ B9 ) ) )
         => ( ! [B6: val > $o,A10: aassertion_val] :
                ( ( X
                  = ( aImp_val @ B6 @ A10 ) )
               => ( ( B6 @ Xa2 )
                 => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) )
           => ~ ! [A10: val > $o] :
                  ( ( X
                    = ( aSem_val @ A10 ) )
                 => ( A10 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(3)
thf(fact_513_package__logic_Osat_Oelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_state @ Plus @ X @ Xa2 )
       => ( ! [A10: aassertion_state,B8: aassertion_state] :
              ( ( X
                = ( aStar_state @ A10 @ B8 ) )
             => ? [A5: state,B9: state] :
                  ( ( ( some_state @ Xa2 )
                    = ( Plus @ A5 @ B9 ) )
                  & ( package_sat_state @ Plus @ A10 @ A5 )
                  & ( package_sat_state @ Plus @ B8 @ B9 ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( X
                  = ( aImp_state @ B6 @ A10 ) )
               => ( ( B6 @ Xa2 )
                 => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) )
           => ~ ! [A10: state > $o] :
                  ( ( X
                    = ( aSem_state @ A10 ) )
                 => ( A10 @ Xa2 ) ) ) ) ) ) ).

% package_logic.sat.elims(3)
thf(fact_514_PartialSA_Opackage__logic__axioms,axiom,
    package_logic_state @ plus @ core @ unit @ stable ).

% PartialSA.package_logic_axioms
thf(fact_515_package__logic_Osat_Opelims_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,X: aassertion_val,Xa2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_val @ Plus @ X @ Xa2 )
       => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ X @ Xa2 ) )
         => ( ! [A10: aassertion_val,B8: aassertion_val] :
                ( ( X
                  = ( aStar_val @ A10 @ B8 ) )
               => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aStar_val @ A10 @ B8 ) @ Xa2 ) )
                 => ? [A5: val,B9: val] :
                      ( ( ( some_val @ Xa2 )
                        = ( Plus @ A5 @ B9 ) )
                      & ( package_sat_val @ Plus @ A10 @ A5 )
                      & ( package_sat_val @ Plus @ B8 @ B9 ) ) ) )
           => ( ! [B6: val > $o,A10: aassertion_val] :
                  ( ( X
                    = ( aImp_val @ B6 @ A10 ) )
                 => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aImp_val @ B6 @ A10 ) @ Xa2 ) )
                   => ( ( B6 @ Xa2 )
                     => ( package_sat_val @ Plus @ A10 @ Xa2 ) ) ) )
             => ~ ! [A10: val > $o] :
                    ( ( X
                      = ( aSem_val @ A10 ) )
                   => ( ( accp_P7007234769827254483al_val @ package_sat_rel_val @ ( produc1969469836606013754al_val @ ( aSem_val @ A10 ) @ Xa2 ) )
                     => ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(3)
thf(fact_516_package__logic_Osat_Opelims_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,X: aassertion_state,Xa2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ~ ( package_sat_state @ Plus @ X @ Xa2 )
       => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ X @ Xa2 ) )
         => ( ! [A10: aassertion_state,B8: aassertion_state] :
                ( ( X
                  = ( aStar_state @ A10 @ B8 ) )
               => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aStar_state @ A10 @ B8 ) @ Xa2 ) )
                 => ? [A5: state,B9: state] :
                      ( ( ( some_state @ Xa2 )
                        = ( Plus @ A5 @ B9 ) )
                      & ( package_sat_state @ Plus @ A10 @ A5 )
                      & ( package_sat_state @ Plus @ B8 @ B9 ) ) ) )
           => ( ! [B6: state > $o,A10: aassertion_state] :
                  ( ( X
                    = ( aImp_state @ B6 @ A10 ) )
                 => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aImp_state @ B6 @ A10 ) @ Xa2 ) )
                   => ( ( B6 @ Xa2 )
                     => ( package_sat_state @ Plus @ A10 @ Xa2 ) ) ) )
             => ~ ! [A10: state > $o] :
                    ( ( X
                      = ( aSem_state @ A10 ) )
                   => ( ( accp_P1644577663358802135_state @ packag1918864394588125018_state @ ( produc6654088501289988998_state @ ( aSem_state @ A10 ) @ Xa2 ) )
                     => ( A10 @ Xa2 ) ) ) ) ) ) ) ) ).

% package_logic.sat.pelims(3)
thf(fact_517_PartialSA_Ogeneral__completeness,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state,A4: aassertion_state,Phi: state,Phi2: state] :
      ( ! [A6: state,U: state,T2: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
         => ! [X3: state] :
              ( ( ( some_state @ X3 )
                = ( plus @ A6 @ ( T2 @ F ) ) )
             => ( package_sat_state @ plus @ A4 @ X3 ) ) )
     => ( ( ( some_state @ Phi )
          = ( plus @ Phi2 @ F ) )
       => ( ( stable @ F )
         => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ unit )
           => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
             => ? [X_1: set_Pr4231240917283394591_state] :
                  ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ unit @ S2
                  @ ^ [Uu3: state] : $true
                  @ A4
                  @ Phi2
                  @ F
                  @ X_1 ) ) ) ) ) ) ).

% PartialSA.general_completeness
thf(fact_518_full__mask__def,axiom,
    ( full_mask
    = ( ^ [Hl: produc1457211279475724562t_char] :
          ( if_prat
          @ ( ( produc6204653154488278070t_char @ Hl )
            = null_nat )
          @ pnone
          @ pwrite ) ) ) ).

% full_mask_def
thf(fact_519_package__logic_Opackage__sat__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Pc: val > $o,A4: aassertion_val,A3: val,U5: val,U3: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A4 @ A3 @ U5 @ U3 )
        = ( ( Pc @ ( Core @ A3 ) )
         => ? [X2: val] :
              ( ( ( some_val @ X2 )
                = ( Plus @ ( Core @ A3 ) @ ( sep_minus_val @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_val @ Plus @ A4 @ X2 ) ) ) ) ) ).

% package_logic.package_sat_def
thf(fact_520_package__logic_Opackage__sat__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Pc: state > $o,A4: aassertion_state,A3: state,U5: state,U3: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A4 @ A3 @ U5 @ U3 )
        = ( ( Pc @ ( Core @ A3 ) )
         => ? [X2: state] :
              ( ( ( some_state @ X2 )
                = ( Plus @ ( Core @ A3 ) @ ( sep_minus_state @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_state @ Plus @ A4 @ X2 ) ) ) ) ) ).

% package_logic.package_sat_def
thf(fact_521_package__logic_Opackage__satI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Pc: val > $o,A3: val,U5: val,U3: val,A4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Pc @ ( Core @ A3 ) )
         => ? [X4: val] :
              ( ( ( some_val @ X4 )
                = ( Plus @ ( Core @ A3 ) @ ( sep_minus_val @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_val @ Plus @ A4 @ X4 ) ) )
       => ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A4 @ A3 @ U5 @ U3 ) ) ) ).

% package_logic.package_satI
thf(fact_522_package__logic_Opackage__satI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Pc: state > $o,A3: state,U5: state,U3: state,A4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Pc @ ( Core @ A3 ) )
         => ? [X4: state] :
              ( ( ( some_state @ X4 )
                = ( Plus @ ( Core @ A3 ) @ ( sep_minus_state @ Plus @ Core @ U5 @ U3 ) ) )
              & ( package_sat_state @ Plus @ A4 @ X4 ) ) )
       => ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A4 @ A3 @ U5 @ U3 ) ) ) ).

% package_logic.package_satI
thf(fact_523_sep__algebra_Osplus_Opelims,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: option_val,Xa2: option_val,Y: option_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( sep_splus_val @ Plus @ X @ Xa2 )
          = Y )
       => ( ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ X @ Xa2 ) )
         => ( ( ( X = none_val )
             => ( ( Y = none_val )
               => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ none_val @ Xa2 ) ) ) )
           => ( ! [V2: val] :
                  ( ( X
                    = ( some_val @ V2 ) )
                 => ( ( Xa2 = none_val )
                   => ( ( Y = none_val )
                     => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ ( some_val @ V2 ) @ none_val ) ) ) ) )
             => ~ ! [A6: val] :
                    ( ( X
                      = ( some_val @ A6 ) )
                   => ! [B6: val] :
                        ( ( Xa2
                          = ( some_val @ B6 ) )
                       => ( ( Y
                            = ( Plus @ A6 @ B6 ) )
                         => ~ ( accp_P4269981079083053040on_val @ sep_splus_rel_val @ ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.pelims
thf(fact_524_sep__algebra_Osplus_Opelims,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: option_state,Xa2: option_state,Y: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( sep_splus_state @ Plus @ X @ Xa2 )
          = Y )
       => ( ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ X @ Xa2 ) )
         => ( ( ( X = none_state )
             => ( ( Y = none_state )
               => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ none_state @ Xa2 ) ) ) )
           => ( ! [V2: state] :
                  ( ( X
                    = ( some_state @ V2 ) )
                 => ( ( Xa2 = none_state )
                   => ( ( Y = none_state )
                     => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ V2 ) @ none_state ) ) ) ) )
             => ~ ! [A6: state] :
                    ( ( X
                      = ( some_state @ A6 ) )
                   => ! [B6: state] :
                        ( ( Xa2
                          = ( some_state @ B6 ) )
                       => ( ( Y
                            = ( Plus @ A6 @ B6 ) )
                         => ~ ( accp_P7183347322223220350_state @ sep_splus_rel_state @ ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.pelims
thf(fact_525_empty__eq__map__add__iff,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val] :
      ( ( ( ^ [X2: produc1457211279475724562t_char] : none_val )
        = ( map_ad2908576761495157028ar_val @ F @ G ) )
      = ( ( F
          = ( ^ [X2: produc1457211279475724562t_char] : none_val ) )
        & ( G
          = ( ^ [X2: produc1457211279475724562t_char] : none_val ) ) ) ) ).

% empty_eq_map_add_iff
thf(fact_526_map__add__empty,axiom,
    ! [M: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val @ M
        @ ^ [X2: produc1457211279475724562t_char] : none_val )
      = M ) ).

% map_add_empty
thf(fact_527_empty__map__add,axiom,
    ! [M: produc1457211279475724562t_char > option_val] :
      ( ( map_ad2908576761495157028ar_val
        @ ^ [X2: produc1457211279475724562t_char] : none_val
        @ M )
      = M ) ).

% empty_map_add
thf(fact_528_pred__subset__eq2,axiom,
    ! [R4: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le6704609105599929480tate_o
        @ ^ [X2: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: state,Y5: produc3882902684156697774_state] : ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le4032880777312351359_state @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_529_pred__subset__eq2,axiom,
    ! [R4: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le1106678366802930969tate_o
        @ ^ [X2: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: state,Y5: state > state] : ( member6715010751053357271_state @ ( produc8632743443909064678_state @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le6483787752022044334_state @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_530_pred__subset__eq2,axiom,
    ! [R4: set_Pr1688445902015331925_state,S2: set_Pr1688445902015331925_state] :
      ( ( ord_le2052508915978315794tate_o
        @ ^ [X2: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: option_state,Y5: option_state] : ( member3029510603097127326_state @ ( produc9160152616361873709_state @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le6423325748750870005_state @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_531_pred__subset__eq2,axiom,
    ! [R4: set_Pr6039890582625207499_state,S2: set_Pr6039890582625207499_state] :
      ( ( ord_le9040380983013460636tate_o
        @ ^ [X2: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: prat,Y5: state] : ( member6226390569306242836_state @ ( produc6205719116230455971_state @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le262197048489888875_state @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_532_pred__subset__eq2,axiom,
    ! [R4: set_Pr6847263425858009217_state,S2: set_Pr6847263425858009217_state] :
      ( ( ord_le8830457724327557734tate_o
        @ ^ [X2: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: prat,Y5: set_state] : ( member6708919011922255306_state @ ( produc9080284787853255769_state @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le5761494056910127137_state @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_533_pred__subset__eq2,axiom,
    ! [R4: set_Pr2507339680178222706t_char,S2: set_Pr2507339680178222706t_char] :
      ( ( ord_le2712619360209801397char_o
        @ ^ [X2: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: nat,Y5: list_char] : ( member484235747325421115t_char @ ( produc120197956887798346t_char @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le6315511645215477266t_char @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_534_pred__subset__eq2,axiom,
    ! [R4: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le3852884270828607079_val_o
        @ ^ [X2: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X2 @ Y5 ) @ R4 )
        @ ^ [X2: produc1457211279475724562t_char > prat,Y5: produc1457211279475724562t_char > option_val] : ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ X2 @ Y5 ) @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R4 @ S2 ) ) ).

% pred_subset_eq2
thf(fact_535_Collect__subset,axiom,
    ! [A4: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X2: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X2 @ A4 )
            & ( P2 @ X2 ) ) )
      @ A4 ) ).

% Collect_subset
thf(fact_536_Collect__subset,axiom,
    ! [A4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ A4 )
            & ( P2 @ X2 ) ) )
      @ A4 ) ).

% Collect_subset
thf(fact_537_Collect__subset,axiom,
    ! [A4: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X2: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X2 @ A4 )
            & ( P2 @ X2 ) ) )
      @ A4 ) ).

% Collect_subset
thf(fact_538_Collect__subset,axiom,
    ! [A4: set_state,P2: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X2: state] :
            ( ( member_state @ X2 @ A4 )
            & ( P2 @ X2 ) ) )
      @ A4 ) ).

% Collect_subset
thf(fact_539_less__eq__set__def,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A7: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( ord_le7281427340513060550tate_o
          @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ A7 )
          @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_540_less__eq__set__def,axiom,
    ( ord_le6900622908513426738on_val
    = ( ^ [A7: set_Pr7649655576376376530on_val,B5: set_Pr7649655576376376530on_val] :
          ( ord_le6140313152057869779_val_o
          @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ A7 )
          @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_541_less__eq__set__def,axiom,
    ( ord_le6483787752022044334_state
    = ( ^ [A7: set_Pr2391701600042252046_state,B5: set_Pr2391701600042252046_state] :
          ( ord_le8077393285996101039tate_o
          @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ A7 )
          @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_542_less__eq__set__def,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A7: set_state,B5: set_state] :
          ( ord_less_eq_state_o
          @ ^ [X2: state] : ( member_state @ X2 @ A7 )
          @ ^ [X2: state] : ( member_state @ X2 @ B5 ) ) ) ) ).

% less_eq_set_def
thf(fact_543_sep__algebra_Ominus__equiv__def__any__elem,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X )
          = ( Plus @ A @ B ) )
       => ( ( some_val @ ( sep_minus_val @ Plus @ Core @ X @ A ) )
          = ( Plus @ B @ ( Core @ X ) ) ) ) ) ).

% sep_algebra.minus_equiv_def_any_elem
thf(fact_544_sep__algebra_Ominus__equiv__def__any__elem,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X )
          = ( Plus @ A @ B ) )
       => ( ( some_state @ ( sep_minus_state @ Plus @ Core @ X @ A ) )
          = ( Plus @ B @ ( Core @ X ) ) ) ) ) ).

% sep_algebra.minus_equiv_def_any_elem
thf(fact_545_sep__algebra_Oasso1,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,Ab: val,C: val,Bc: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( Plus @ A @ B )
            = ( some_val @ Ab ) )
          & ( ( Plus @ B @ C )
            = ( some_val @ Bc ) ) )
       => ( ( Plus @ Ab @ C )
          = ( Plus @ A @ Bc ) ) ) ) ).

% sep_algebra.asso1
thf(fact_546_sep__algebra_Oasso1,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,Ab: state,C: state,Bc: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( Plus @ A @ B )
            = ( some_state @ Ab ) )
          & ( ( Plus @ B @ C )
            = ( some_state @ Bc ) ) )
       => ( ( Plus @ Ab @ C )
          = ( Plus @ A @ Bc ) ) ) ) ).

% sep_algebra.asso1
thf(fact_547_sep__algebra_Ocore__max,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X )
          = ( Plus @ X @ C ) )
       => ? [R3: val] :
            ( ( some_val @ ( Core @ X ) )
            = ( Plus @ C @ R3 ) ) ) ) ).

% sep_algebra.core_max
thf(fact_548_sep__algebra_Ocore__max,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X )
          = ( Plus @ X @ C ) )
       => ? [R3: state] :
            ( ( some_state @ ( Core @ X ) )
            = ( Plus @ C @ R3 ) ) ) ) ).

% sep_algebra.core_max
thf(fact_549_sep__algebra_Ocore__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,C: val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ C )
          = ( Plus @ A @ B ) )
       => ( ( some_val @ ( Core @ C ) )
          = ( Plus @ ( Core @ A ) @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.core_sum
thf(fact_550_sep__algebra_Ocore__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,C: state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ C )
          = ( Plus @ A @ B ) )
       => ( ( some_state @ ( Core @ C ) )
          = ( Plus @ ( Core @ A ) @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.core_sum
thf(fact_551_sep__algebra_Opositivity,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( Plus @ A @ B )
          = ( some_val @ C ) )
       => ( ( ( some_val @ C )
            = ( Plus @ C @ C ) )
         => ( ( some_val @ A )
            = ( Plus @ A @ A ) ) ) ) ) ).

% sep_algebra.positivity
thf(fact_552_sep__algebra_Opositivity,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( Plus @ A @ B )
          = ( some_state @ C ) )
       => ( ( ( some_state @ C )
            = ( Plus @ C @ C ) )
         => ( ( some_state @ A )
            = ( Plus @ A @ A ) ) ) ) ) ).

% sep_algebra.positivity
thf(fact_553_sep__algebra_Ocancellative,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,X: val,Y: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A )
          = ( Plus @ B @ X ) )
       => ( ( ( some_val @ A )
            = ( Plus @ B @ Y ) )
         => ( ( ( Core @ X )
              = ( Core @ Y ) )
           => ( X = Y ) ) ) ) ) ).

% sep_algebra.cancellative
thf(fact_554_sep__algebra_Ocancellative,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,X: state,Y: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A )
          = ( Plus @ B @ X ) )
       => ( ( ( some_state @ A )
            = ( Plus @ B @ Y ) )
         => ( ( ( Core @ X )
              = ( Core @ Y ) )
           => ( X = Y ) ) ) ) ) ).

% sep_algebra.cancellative
thf(fact_555_sep__algebra_Ocore__is__pure,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( some_val @ ( Core @ X ) )
        = ( Plus @ ( Core @ X ) @ ( Core @ X ) ) ) ) ).

% sep_algebra.core_is_pure
thf(fact_556_sep__algebra_Ocore__is__pure,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( some_state @ ( Core @ X ) )
        = ( Plus @ ( Core @ X ) @ ( Core @ X ) ) ) ) ).

% sep_algebra.core_is_pure
thf(fact_557_sep__algebra_Ocore__is__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( some_val @ X )
        = ( Plus @ X @ ( Core @ X ) ) ) ) ).

% sep_algebra.core_is_smaller
thf(fact_558_sep__algebra_Ocore__is__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( some_state @ X )
        = ( Plus @ X @ ( Core @ X ) ) ) ) ).

% sep_algebra.core_is_smaller
thf(fact_559_map__add__def,axiom,
    ( map_ad2908576761495157028ar_val
    = ( ^ [M12: produc1457211279475724562t_char > option_val,M22: produc1457211279475724562t_char > option_val,X2: produc1457211279475724562t_char] : ( case_o7794706883426356101al_val @ ( M12 @ X2 ) @ some_val @ ( M22 @ X2 ) ) ) ) ).

% map_add_def
thf(fact_560_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_561_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_562_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_563_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_564_case__optionE,axiom,
    ! [P2: $o,Q: state > $o,X: option_state] :
      ( ( case_option_o_state @ P2 @ Q @ X )
     => ( ( ( X = none_state )
         => ~ P2 )
       => ~ ! [Y3: state] :
              ( ( X
                = ( some_state @ Y3 ) )
             => ~ ( Q @ Y3 ) ) ) ) ).

% case_optionE
thf(fact_565_case__optionE,axiom,
    ! [P2: $o,Q: val > $o,X: option_val] :
      ( ( case_option_o_val @ P2 @ Q @ X )
     => ( ( ( X = none_val )
         => ~ P2 )
       => ~ ! [Y3: val] :
              ( ( X
                = ( some_val @ Y3 ) )
             => ~ ( Q @ Y3 ) ) ) ) ).

% case_optionE
thf(fact_566_pred__subset__eq,axiom,
    ! [R4: set_Pr4231240917283394591_state,S2: set_Pr4231240917283394591_state] :
      ( ( ord_le7281427340513060550tate_o
        @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ R4 )
        @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ S2 ) )
      = ( ord_le4032880777312351359_state @ R4 @ S2 ) ) ).

% pred_subset_eq
thf(fact_567_pred__subset__eq,axiom,
    ! [R4: set_Pr7649655576376376530on_val,S2: set_Pr7649655576376376530on_val] :
      ( ( ord_le6140313152057869779_val_o
        @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ R4 )
        @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ S2 ) )
      = ( ord_le6900622908513426738on_val @ R4 @ S2 ) ) ).

% pred_subset_eq
thf(fact_568_pred__subset__eq,axiom,
    ! [R4: set_Pr2391701600042252046_state,S2: set_Pr2391701600042252046_state] :
      ( ( ord_le8077393285996101039tate_o
        @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ R4 )
        @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ S2 ) )
      = ( ord_le6483787752022044334_state @ R4 @ S2 ) ) ).

% pred_subset_eq
thf(fact_569_pred__subset__eq,axiom,
    ! [R4: set_state,S2: set_state] :
      ( ( ord_less_eq_state_o
        @ ^ [X2: state] : ( member_state @ X2 @ R4 )
        @ ^ [X2: state] : ( member_state @ X2 @ S2 ) )
      = ( ord_le2494988322063910608_state @ R4 @ S2 ) ) ).

% pred_subset_eq
thf(fact_570_sep__algebra_Oasso2,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,Ab: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( Plus @ A @ B )
            = ( some_val @ Ab ) )
          & ( ( Plus @ B @ C )
            = none_val ) )
       => ( ( Plus @ Ab @ C )
          = none_val ) ) ) ).

% sep_algebra.asso2
thf(fact_571_sep__algebra_Oasso2,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,Ab: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( Plus @ A @ B )
            = ( some_state @ Ab ) )
          & ( ( Plus @ B @ C )
            = none_state ) )
       => ( ( Plus @ Ab @ C )
          = none_state ) ) ) ).

% sep_algebra.asso2
thf(fact_572_sep__algebra_Oasso3,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val,Bc: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( Plus @ A @ B )
          = none_val )
       => ( ( ( Plus @ B @ C )
            = ( some_val @ Bc ) )
         => ( ( Plus @ A @ Bc )
            = none_val ) ) ) ) ).

% sep_algebra.asso3
thf(fact_573_sep__algebra_Oasso3,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state,Bc: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( Plus @ A @ B )
          = none_state )
       => ( ( ( Plus @ B @ C )
            = ( some_state @ Bc ) )
         => ( ( Plus @ A @ Bc )
            = none_state ) ) ) ) ).

% sep_algebra.asso3
thf(fact_574_sep__algebra_Ointro,axiom,
    ! [Plus: val > val > option_val,Core: val > val] :
      ( ! [A6: val,B6: val] :
          ( ( Plus @ A6 @ B6 )
          = ( Plus @ B6 @ A6 ) )
     => ( ! [A6: val,B6: val,Ab2: val,C4: val,Bc2: val] :
            ( ( ( ( Plus @ A6 @ B6 )
                = ( some_val @ Ab2 ) )
              & ( ( Plus @ B6 @ C4 )
                = ( some_val @ Bc2 ) ) )
           => ( ( Plus @ Ab2 @ C4 )
              = ( Plus @ A6 @ Bc2 ) ) )
       => ( ! [A6: val,B6: val,Ab2: val,C4: val] :
              ( ( ( ( Plus @ A6 @ B6 )
                  = ( some_val @ Ab2 ) )
                & ( ( Plus @ B6 @ C4 )
                  = none_val ) )
             => ( ( Plus @ Ab2 @ C4 )
                = none_val ) )
         => ( ! [X3: val] :
                ( ( some_val @ X3 )
                = ( Plus @ X3 @ ( Core @ X3 ) ) )
           => ( ! [X3: val] :
                  ( ( some_val @ ( Core @ X3 ) )
                  = ( Plus @ ( Core @ X3 ) @ ( Core @ X3 ) ) )
             => ( ! [X3: val,C4: val] :
                    ( ( ( some_val @ X3 )
                      = ( Plus @ X3 @ C4 ) )
                   => ? [R5: val] :
                        ( ( some_val @ ( Core @ X3 ) )
                        = ( Plus @ C4 @ R5 ) ) )
               => ( ! [C4: val,A6: val,B6: val] :
                      ( ( ( some_val @ C4 )
                        = ( Plus @ A6 @ B6 ) )
                     => ( ( some_val @ ( Core @ C4 ) )
                        = ( Plus @ ( Core @ A6 ) @ ( Core @ B6 ) ) ) )
                 => ( ! [A6: val,B6: val,C4: val] :
                        ( ( ( Plus @ A6 @ B6 )
                          = ( some_val @ C4 ) )
                       => ( ( ( some_val @ C4 )
                            = ( Plus @ C4 @ C4 ) )
                         => ( ( some_val @ A6 )
                            = ( Plus @ A6 @ A6 ) ) ) )
                   => ( ! [A6: val,B6: val,X3: val,Y3: val] :
                          ( ( ( some_val @ A6 )
                            = ( Plus @ B6 @ X3 ) )
                         => ( ( ( some_val @ A6 )
                              = ( Plus @ B6 @ Y3 ) )
                           => ( ( ( Core @ X3 )
                                = ( Core @ Y3 ) )
                             => ( X3 = Y3 ) ) ) )
                     => ( sep_algebra_val @ Plus @ Core ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.intro
thf(fact_575_sep__algebra_Ointro,axiom,
    ! [Plus: state > state > option_state,Core: state > state] :
      ( ! [A6: state,B6: state] :
          ( ( Plus @ A6 @ B6 )
          = ( Plus @ B6 @ A6 ) )
     => ( ! [A6: state,B6: state,Ab2: state,C4: state,Bc2: state] :
            ( ( ( ( Plus @ A6 @ B6 )
                = ( some_state @ Ab2 ) )
              & ( ( Plus @ B6 @ C4 )
                = ( some_state @ Bc2 ) ) )
           => ( ( Plus @ Ab2 @ C4 )
              = ( Plus @ A6 @ Bc2 ) ) )
       => ( ! [A6: state,B6: state,Ab2: state,C4: state] :
              ( ( ( ( Plus @ A6 @ B6 )
                  = ( some_state @ Ab2 ) )
                & ( ( Plus @ B6 @ C4 )
                  = none_state ) )
             => ( ( Plus @ Ab2 @ C4 )
                = none_state ) )
         => ( ! [X3: state] :
                ( ( some_state @ X3 )
                = ( Plus @ X3 @ ( Core @ X3 ) ) )
           => ( ! [X3: state] :
                  ( ( some_state @ ( Core @ X3 ) )
                  = ( Plus @ ( Core @ X3 ) @ ( Core @ X3 ) ) )
             => ( ! [X3: state,C4: state] :
                    ( ( ( some_state @ X3 )
                      = ( Plus @ X3 @ C4 ) )
                   => ? [R5: state] :
                        ( ( some_state @ ( Core @ X3 ) )
                        = ( Plus @ C4 @ R5 ) ) )
               => ( ! [C4: state,A6: state,B6: state] :
                      ( ( ( some_state @ C4 )
                        = ( Plus @ A6 @ B6 ) )
                     => ( ( some_state @ ( Core @ C4 ) )
                        = ( Plus @ ( Core @ A6 ) @ ( Core @ B6 ) ) ) )
                 => ( ! [A6: state,B6: state,C4: state] :
                        ( ( ( Plus @ A6 @ B6 )
                          = ( some_state @ C4 ) )
                       => ( ( ( some_state @ C4 )
                            = ( Plus @ C4 @ C4 ) )
                         => ( ( some_state @ A6 )
                            = ( Plus @ A6 @ A6 ) ) ) )
                   => ( ! [A6: state,B6: state,X3: state,Y3: state] :
                          ( ( ( some_state @ A6 )
                            = ( Plus @ B6 @ X3 ) )
                         => ( ( ( some_state @ A6 )
                              = ( Plus @ B6 @ Y3 ) )
                           => ( ( ( Core @ X3 )
                                = ( Core @ Y3 ) )
                             => ( X3 = Y3 ) ) ) )
                     => ( sep_algebra_state @ Plus @ Core ) ) ) ) ) ) ) ) ) ) ).

% sep_algebra.intro
thf(fact_576_sep__algebra__def,axiom,
    ( sep_algebra_val
    = ( ^ [Plus2: val > val > option_val,Core2: val > val] :
          ( ! [A2: val,B2: val] :
              ( ( Plus2 @ A2 @ B2 )
              = ( Plus2 @ B2 @ A2 ) )
          & ! [A2: val,B2: val,Ab3: val,C2: val,Bc3: val] :
              ( ( ( ( Plus2 @ A2 @ B2 )
                  = ( some_val @ Ab3 ) )
                & ( ( Plus2 @ B2 @ C2 )
                  = ( some_val @ Bc3 ) ) )
             => ( ( Plus2 @ Ab3 @ C2 )
                = ( Plus2 @ A2 @ Bc3 ) ) )
          & ! [A2: val,B2: val,Ab3: val,C2: val] :
              ( ( ( ( Plus2 @ A2 @ B2 )
                  = ( some_val @ Ab3 ) )
                & ( ( Plus2 @ B2 @ C2 )
                  = none_val ) )
             => ( ( Plus2 @ Ab3 @ C2 )
                = none_val ) )
          & ! [X2: val] :
              ( ( some_val @ X2 )
              = ( Plus2 @ X2 @ ( Core2 @ X2 ) ) )
          & ! [X2: val] :
              ( ( some_val @ ( Core2 @ X2 ) )
              = ( Plus2 @ ( Core2 @ X2 ) @ ( Core2 @ X2 ) ) )
          & ! [X2: val,C2: val] :
              ( ( ( some_val @ X2 )
                = ( Plus2 @ X2 @ C2 ) )
             => ? [R: val] :
                  ( ( some_val @ ( Core2 @ X2 ) )
                  = ( Plus2 @ C2 @ R ) ) )
          & ! [C2: val,A2: val,B2: val] :
              ( ( ( some_val @ C2 )
                = ( Plus2 @ A2 @ B2 ) )
             => ( ( some_val @ ( Core2 @ C2 ) )
                = ( Plus2 @ ( Core2 @ A2 ) @ ( Core2 @ B2 ) ) ) )
          & ! [A2: val,B2: val,C2: val] :
              ( ( ( Plus2 @ A2 @ B2 )
                = ( some_val @ C2 ) )
             => ( ( ( some_val @ C2 )
                  = ( Plus2 @ C2 @ C2 ) )
               => ( ( some_val @ A2 )
                  = ( Plus2 @ A2 @ A2 ) ) ) )
          & ! [A2: val,B2: val,X2: val,Y5: val] :
              ( ( ( some_val @ A2 )
                = ( Plus2 @ B2 @ X2 ) )
             => ( ( ( some_val @ A2 )
                  = ( Plus2 @ B2 @ Y5 ) )
               => ( ( ( Core2 @ X2 )
                    = ( Core2 @ Y5 ) )
                 => ( X2 = Y5 ) ) ) ) ) ) ) ).

% sep_algebra_def
thf(fact_577_sep__algebra__def,axiom,
    ( sep_algebra_state
    = ( ^ [Plus2: state > state > option_state,Core2: state > state] :
          ( ! [A2: state,B2: state] :
              ( ( Plus2 @ A2 @ B2 )
              = ( Plus2 @ B2 @ A2 ) )
          & ! [A2: state,B2: state,Ab3: state,C2: state,Bc3: state] :
              ( ( ( ( Plus2 @ A2 @ B2 )
                  = ( some_state @ Ab3 ) )
                & ( ( Plus2 @ B2 @ C2 )
                  = ( some_state @ Bc3 ) ) )
             => ( ( Plus2 @ Ab3 @ C2 )
                = ( Plus2 @ A2 @ Bc3 ) ) )
          & ! [A2: state,B2: state,Ab3: state,C2: state] :
              ( ( ( ( Plus2 @ A2 @ B2 )
                  = ( some_state @ Ab3 ) )
                & ( ( Plus2 @ B2 @ C2 )
                  = none_state ) )
             => ( ( Plus2 @ Ab3 @ C2 )
                = none_state ) )
          & ! [X2: state] :
              ( ( some_state @ X2 )
              = ( Plus2 @ X2 @ ( Core2 @ X2 ) ) )
          & ! [X2: state] :
              ( ( some_state @ ( Core2 @ X2 ) )
              = ( Plus2 @ ( Core2 @ X2 ) @ ( Core2 @ X2 ) ) )
          & ! [X2: state,C2: state] :
              ( ( ( some_state @ X2 )
                = ( Plus2 @ X2 @ C2 ) )
             => ? [R: state] :
                  ( ( some_state @ ( Core2 @ X2 ) )
                  = ( Plus2 @ C2 @ R ) ) )
          & ! [C2: state,A2: state,B2: state] :
              ( ( ( some_state @ C2 )
                = ( Plus2 @ A2 @ B2 ) )
             => ( ( some_state @ ( Core2 @ C2 ) )
                = ( Plus2 @ ( Core2 @ A2 ) @ ( Core2 @ B2 ) ) ) )
          & ! [A2: state,B2: state,C2: state] :
              ( ( ( Plus2 @ A2 @ B2 )
                = ( some_state @ C2 ) )
             => ( ( ( some_state @ C2 )
                  = ( Plus2 @ C2 @ C2 ) )
               => ( ( some_state @ A2 )
                  = ( Plus2 @ A2 @ A2 ) ) ) )
          & ! [A2: state,B2: state,X2: state,Y5: state] :
              ( ( ( some_state @ A2 )
                = ( Plus2 @ B2 @ X2 ) )
             => ( ( ( some_state @ A2 )
                  = ( Plus2 @ B2 @ Y5 ) )
               => ( ( ( Core2 @ X2 )
                    = ( Core2 @ Y5 ) )
                 => ( X2 = Y5 ) ) ) ) ) ) ) ).

% sep_algebra_def
thf(fact_578_sep__algebra_Osplus_Osimps_I3_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_splus_val @ Plus @ ( some_val @ A ) @ ( some_val @ B ) )
        = ( Plus @ A @ B ) ) ) ).

% sep_algebra.splus.simps(3)
thf(fact_579_sep__algebra_Osplus_Osimps_I3_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ ( some_state @ A ) @ ( some_state @ B ) )
        = ( Plus @ A @ B ) ) ) ).

% sep_algebra.splus.simps(3)
thf(fact_580_sep__algebra_Osplus__develop,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val,D: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A )
          = ( Plus @ B @ C ) )
       => ( ( Plus @ A @ D )
          = ( sep_splus_val @ Plus @ ( sep_splus_val @ Plus @ ( some_val @ B ) @ ( some_val @ C ) ) @ ( some_val @ D ) ) ) ) ) ).

% sep_algebra.splus_develop
thf(fact_581_sep__algebra_Osplus__develop,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state,D: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A )
          = ( Plus @ B @ C ) )
       => ( ( Plus @ A @ D )
          = ( sep_splus_state @ Plus @ ( sep_splus_state @ Plus @ ( some_state @ B ) @ ( some_state @ C ) ) @ ( some_state @ D ) ) ) ) ) ).

% sep_algebra.splus_develop
thf(fact_582_sep__algebra_Opure__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_pure_val @ Plus @ A )
        = ( ( some_val @ A )
          = ( Plus @ A @ A ) ) ) ) ).

% sep_algebra.pure_def
thf(fact_583_sep__algebra_Opure__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_pure_state @ Plus @ A )
        = ( ( some_state @ A )
          = ( Plus @ A @ A ) ) ) ) ).

% sep_algebra.pure_def
thf(fact_584_sep__algebra_Opure__stable,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_pure_val @ Plus @ A )
       => ( ( sep_pure_val @ Plus @ B )
         => ( ( ( some_val @ C )
              = ( Plus @ A @ B ) )
           => ( sep_pure_val @ Plus @ C ) ) ) ) ) ).

% sep_algebra.pure_stable
thf(fact_585_sep__algebra_Opure__stable,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_pure_state @ Plus @ A )
       => ( ( sep_pure_state @ Plus @ B )
         => ( ( ( some_state @ C )
              = ( Plus @ A @ B ) )
           => ( sep_pure_state @ Plus @ C ) ) ) ) ) ).

% sep_algebra.pure_stable
thf(fact_586_PartialSA_Osep__algebra__axioms,axiom,
    sep_algebra_state @ plus @ core ).

% PartialSA.sep_algebra_axioms
thf(fact_587_sep__algebra_Osplus_Osimps_I2_J,axiom,
    ! [Plus: val > val > option_val,Core: val > val,V: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_splus_val @ Plus @ ( some_val @ V ) @ none_val )
        = none_val ) ) ).

% sep_algebra.splus.simps(2)
thf(fact_588_sep__algebra_Osplus_Osimps_I2_J,axiom,
    ! [Plus: state > state > option_state,Core: state > state,V: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_splus_state @ Plus @ ( some_state @ V ) @ none_state )
        = none_state ) ) ).

% sep_algebra.splus.simps(2)
thf(fact_589_sep__algebra_Osplus_Oelims,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: option_val,Xa2: option_val,Y: option_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( sep_splus_val @ Plus @ X @ Xa2 )
          = Y )
       => ( ( ( X = none_val )
           => ( Y != none_val ) )
         => ( ( ? [V2: val] :
                  ( X
                  = ( some_val @ V2 ) )
             => ( ( Xa2 = none_val )
               => ( Y != none_val ) ) )
           => ~ ! [A6: val] :
                  ( ( X
                    = ( some_val @ A6 ) )
                 => ! [B6: val] :
                      ( ( Xa2
                        = ( some_val @ B6 ) )
                     => ( Y
                       != ( Plus @ A6 @ B6 ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.elims
thf(fact_590_sep__algebra_Osplus_Oelims,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: option_state,Xa2: option_state,Y: option_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( sep_splus_state @ Plus @ X @ Xa2 )
          = Y )
       => ( ( ( X = none_state )
           => ( Y != none_state ) )
         => ( ( ? [V2: state] :
                  ( X
                  = ( some_state @ V2 ) )
             => ( ( Xa2 = none_state )
               => ( Y != none_state ) ) )
           => ~ ! [A6: state] :
                  ( ( X
                    = ( some_state @ A6 ) )
                 => ! [B6: state] :
                      ( ( Xa2
                        = ( some_state @ B6 ) )
                     => ( Y
                       != ( Plus @ A6 @ B6 ) ) ) ) ) ) ) ) ).

% sep_algebra.splus.elims
thf(fact_591_sep__algebra_Osplus_Ocases,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: produc5122021904355189735on_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ! [Uu2: option_val] :
            ( X
           != ( produc904852209897547607on_val @ none_val @ Uu2 ) )
       => ( ! [V2: val] :
              ( X
             != ( produc904852209897547607on_val @ ( some_val @ V2 ) @ none_val ) )
         => ~ ! [A6: val,B6: val] :
                ( X
               != ( produc904852209897547607on_val @ ( some_val @ A6 ) @ ( some_val @ B6 ) ) ) ) ) ) ).

% sep_algebra.splus.cases
thf(fact_592_sep__algebra_Osplus_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: produc3142500478612311029_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ! [Uu2: option_state] :
            ( X
           != ( produc9160152616361873709_state @ none_state @ Uu2 ) )
       => ( ! [V2: state] :
              ( X
             != ( produc9160152616361873709_state @ ( some_state @ V2 ) @ none_state ) )
         => ~ ! [A6: state,B6: state] :
                ( X
               != ( produc9160152616361873709_state @ ( some_state @ A6 ) @ ( some_state @ B6 ) ) ) ) ) ) ).

% sep_algebra.splus.cases
thf(fact_593_minus__def,axiom,
    ( minus
    = ( sep_minus_state @ plus @ core ) ) ).

% minus_def
thf(fact_594_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,S2: set_Pr4723104092121316667al_val,F: val,A4: aassertion_val,Phi: val,Phi2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: val,U: val,T2: val > val] :
            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A6 @ ( produc303288909735261391al_val @ U @ T2 ) ) @ S2 )
           => ! [X3: val] :
                ( ( ( some_val @ X3 )
                  = ( Plus @ A6 @ ( T2 @ F ) ) )
               => ( package_sat_val @ Plus @ A4 @ X3 ) ) )
       => ( ( ( some_val @ Phi )
            = ( Plus @ Phi2 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag7517340229427718612et_val @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag5732365195153136185on_val @ Plus @ Core @ A4 )
               => ? [X_1: set_Pr4723104092121316667al_val] :
                    ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ Unit @ S2
                    @ ^ [Uu3: val] : $true
                    @ A4
                    @ Phi2
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_595_package__logic_Ogeneral__completeness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F: state,A4: aassertion_state,Phi: state,Phi2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: state,U: state,T2: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
           => ! [X3: state] :
                ( ( ( some_state @ X3 )
                  = ( Plus @ A6 @ ( T2 @ F ) ) )
               => ( package_sat_state @ Plus @ A4 @ X3 ) ) )
       => ( ( ( some_state @ Phi )
            = ( Plus @ Phi2 @ F ) )
         => ( ( Stable @ F )
           => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ Unit )
             => ( ( packag7298478212905792770_state @ Plus @ Core @ A4 )
               => ? [X_1: set_Pr4231240917283394591_state] :
                    ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ Unit @ S2
                    @ ^ [Uu3: state] : $true
                    @ A4
                    @ Phi2
                    @ F
                    @ X_1 ) ) ) ) ) ) ) ).

% package_logic.general_completeness
thf(fact_596_PartialSA_Ocompleteness,axiom,
    ! [B4: aassertion_state,W: state,R4: state > state > state,A4: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag6192661653625646554_state @ plus @ W @ R4 @ A4 @ B4 ) )
       => ( ( ( some_state @ Sigma )
            = ( plus @ Sigma2 @ W ) )
         => ( ! [A6: state] :
                ( ( package_sat_state @ plus @ A4 @ A6 )
               => ( packag4817583915586052229_state @ plus @ unit @ ( R4 @ A6 ) ) )
           => ? [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 @ ( R4 @ A2 ) ) ) )
                      & ( package_sat_state @ plus @ A4 @ A2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% PartialSA.completeness
thf(fact_597_package__logic_Ocompleteness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,R4: val > val > val,A4: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag4897621287243763553al_val @ Plus @ W @ R4 @ A4 @ B4 ) )
         => ( ( ( some_val @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A6: val] :
                  ( ( package_sat_val @ Plus @ A4 @ A6 )
                 => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R4 @ A6 ) ) )
             => ? [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 @ ( R4 @ A2 ) ) ) )
                        & ( package_sat_val @ Plus @ A4 @ A2 ) ) )
                  @ ^ [Uu3: val] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_598_package__logic_Ocompleteness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,R4: state > state > state,A4: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag6192661653625646554_state @ Plus @ W @ R4 @ A4 @ B4 ) )
         => ( ( ( some_state @ Sigma )
              = ( Plus @ Sigma2 @ W ) )
           => ( ! [A6: state] :
                  ( ( package_sat_state @ Plus @ A4 @ A6 )
                 => ( packag4817583915586052229_state @ Plus @ Unit @ ( R4 @ A6 ) ) )
             => ? [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 @ ( R4 @ A2 ) ) ) )
                        & ( package_sat_state @ Plus @ A4 @ A2 ) ) )
                  @ ^ [Uu3: state] : $true
                  @ B4
                  @ Sigma2
                  @ W
                  @ X_1 ) ) ) ) ) ) ).

% package_logic.completeness
thf(fact_599_PartialSA_Osoundness,axiom,
    ! [B4: aassertion_state,A4: aassertion_state,S2: set_state,R4: state > state > state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A6: state] :
            ( ( package_sat_state @ plus @ A4 @ A6 )
           => ( member_state @ A6 @ S2 ) )
       => ( ! [A6: state] :
              ( ( member_state @ A6 @ S2 )
             => ( packag4817583915586052229_state @ plus @ unit @ ( R4 @ A6 ) ) )
         => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Sigma @ unit
              @ ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ).

% PartialSA.soundness
thf(fact_600_PartialSA_Ominus__def,axiom,
    ( minus
    = ( ^ [B2: state,A2: state] :
          ( fun_TH8221542053827138557_state @ B2
          @ ^ [X2: state] :
              ( ( ( some_state @ B2 )
                = ( plus @ A2 @ X2 ) )
              & ( greater @ X2 @ ( core @ B2 ) ) ) ) ) ) ).

% PartialSA.minus_def
thf(fact_601_Rep__state,axiom,
    ! [X: state] :
      ( member2879030624002546611on_val @ ( rep_state @ X )
      @ ( collec7475294502966882545on_val
        @ ^ [Uu3: produc9003781588162623004on_val] :
          ? [Phi4: produc9003781588162623004on_val] :
            ( ( Uu3 = Phi4 )
            & ( valid_state @ Phi4 ) ) ) ) ).

% Rep_state
thf(fact_602_Rep__state__cases,axiom,
    ! [Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ Y @ ( collec7475294502966882545on_val @ valid_state ) )
     => ~ ! [X3: state] :
            ( Y
           != ( rep_state @ X3 ) ) ) ).

% Rep_state_cases
thf(fact_603_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 ) ) ) )
     => ( ! [X3: state] : ( P2 @ ( rep_state @ X3 ) )
       => ( P2 @ Y ) ) ) ).

% Rep_state_induct
thf(fact_604_Abs__state__cases,axiom,
    ! [X: state] :
      ~ ! [Y3: produc9003781588162623004on_val] :
          ( ( X
            = ( abs_state @ Y3 ) )
         => ~ ( member2879030624002546611on_val @ Y3 @ ( collec7475294502966882545on_val @ valid_state ) ) ) ).

% Abs_state_cases
thf(fact_605_Abs__state__induct,axiom,
    ! [P2: state > $o,X: 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 @ X ) ) ).

% Abs_state_induct
thf(fact_606_Abs__state__inject,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc9003781588162623004on_val] :
      ( ( member2879030624002546611on_val @ X
        @ ( 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 @ X )
            = ( abs_state @ Y ) )
          = ( X = Y ) ) ) ) ).

% Abs_state_inject
thf(fact_607_PartialSA_Oadd__set__def,axiom,
    ( add_set
    = ( ^ [A7: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state,A2: state,B2: state] :
              ( ( Uu3 = Phi4 )
              & ( member_state @ A2 @ A7 )
              & ( member_state @ B2 @ B5 )
              & ( ( some_state @ Phi4 )
                = ( plus @ A2 @ B2 ) ) ) ) ) ) ).

% PartialSA.add_set_def
thf(fact_608_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_609_PartialSA_OAddFromOutside,axiom,
    ! [Phi: state,Phi2: state,M: state,F3: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi7: state,F4: state,S4: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( ( some_state @ Phi )
        = ( plus @ Phi2 @ M ) )
     => ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi2 @ F3 @ S3 @ Pc @ A4 @ Phi7 @ F4 @ S4 )
       => ( ( stable @ M )
         => ( ( ( some_state @ F3 )
              = ( plus @ F @ M ) )
           => ( ( S3
                = ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state,R: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                      & ( ( some_state @ R )
                        = ( plus @ A2 @ ( minus @ ( T4 @ F3 ) @ ( T4 @ F ) ) ) )
                      & ( defined @ R @ U6 ) ) ) )
             => ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi7 @ F4 @ S4 ) ) ) ) ) ) ).

% PartialSA.AddFromOutside
thf(fact_610_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_611_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,A4: aasser7019605857572776418_state,S2: set_Pr4231240917283394591_state,R4: 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 )
       => ( ! [A6: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A4 @ A6 )
             => ( member7461423308196221312_state @ A6 @ S2 ) )
         => ( ! [A6: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ A6 @ S2 )
               => ( packag3884151059541177780_state @ Plus @ Unit @ ( R4 @ A6 ) ) )
           => ( ( packag3630742828623380589_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec7677102015826254172_state
                  @ ^ [Uu3: produc3057782296003698823_state] :
                    ? [A2: produc7272280185086996969_state] :
                      ( ( Uu3
                        = ( produc1904032489304825401_state @ A2 @ ( produc7648782313880683123_state @ Unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_612_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,A4: aasser1163550960519286933on_val,S2: set_Pr7649655576376376530on_val,R4: 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 )
       => ( ! [A6: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A4 @ A6 )
             => ( member2879030624002546611on_val @ A6 @ S2 ) )
         => ( ! [A6: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ A6 @ S2 )
               => ( packag5955012701910386663on_val @ Plus @ Unit @ ( R4 @ A6 ) ) )
           => ( ( packag6843733491101478048on_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec3787697688312515330on_val
                  @ ^ [Uu3: produc217507841372899885on_val] :
                    ? [A2: produc9003781588162623004on_val] :
                      ( ( Uu3
                        = ( produc6985948203474072671on_val @ A2 @ ( produc6949276712527400972on_val @ Unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_613_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,A4: aasser3179708585289803787_state,S2: set_Pr2391701600042252046_state,R4: 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 )
       => ( ! [A6: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A4 @ A6 )
             => ( member6715010751053357271_state @ A6 @ S2 ) )
         => ( ! [A6: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ A6 @ S2 )
               => ( packag5827594511758291363_state @ Plus @ Unit @ ( R4 @ A6 ) ) )
           => ( ( packag4061699384143886122_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec6806307004801468532_state
                  @ ^ [Uu3: produc6455357576889117855_state] :
                    ? [A2: produc3882902684156697774_state] :
                      ( ( Uu3
                        = ( produc5427679348311974809_state @ A2 @ ( produc3987245858496418492_state @ Unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_614_package__logic_Osoundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A4: aassertion_val,S2: set_val,R4: 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 )
       => ( ! [A6: val] :
              ( ( package_sat_val @ Plus @ A4 @ A6 )
             => ( member_val @ A6 @ S2 ) )
         => ( ! [A6: val] :
                ( ( member_val @ A6 @ S2 )
               => ( packag4175576287423129206er_val @ Plus @ Unit @ ( R4 @ A6 ) ) )
           => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A2: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ Unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_615_package__logic_Osoundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A4: aassertion_state,S2: set_state,R4: 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 )
       => ( ! [A6: state] :
              ( ( package_sat_state @ Plus @ A4 @ A6 )
             => ( member_state @ A6 @ S2 ) )
         => ( ! [A6: state] :
                ( ( member_state @ A6 @ S2 )
               => ( packag4817583915586052229_state @ Plus @ Unit @ ( R4 @ A6 ) ) )
           => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Sigma @ Unit
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ Unit @ ( R4 @ 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 @ R4 @ A4 @ B4 ) ) ) ) ) ) ) ) ).

% package_logic.soundness
thf(fact_616_PartialSA_Opackage__rhs_Ocases,axiom,
    ! [A12: state,A23: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
     => ( ! [A10: aassertion_state,Phi6: state,F8: state,S5: set_Pr4231240917283394591_state,B8: aassertion_state] :
            ( ( A52
              = ( aStar_state @ A10 @ B8 ) )
           => ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A23 @ A32 @ A42 @ A10 @ Phi6 @ F8 @ S5 )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ Phi6 @ F8 @ S5 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
       => ( ! [B6: state > $o,A10: aassertion_state] :
              ( ( A52
                = ( aImp_state @ B6 @ A10 ) )
             => ~ ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A23 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
         => ( ! [Witness: produc7272280185086996969_state > state,B8: state > $o] :
                ( ( A52
                  = ( aSem_state @ B8 ) )
               => ( ( A62 = A12 )
                 => ( ( A72 = A23 )
                   => ( ! [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 ) ) ) )
                              & ( B8 @ ( 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,M4: state] :
                  ( ( ( some_state @ A12 )
                    = ( plus @ Phi6 @ M4 ) )
                 => ! [F8: state,S5: set_Pr4231240917283394591_state] :
                      ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi6 @ F8 @ S5 @ A42 @ A52 @ A62 @ A72 @ A82 )
                     => ( ( stable @ M4 )
                       => ( ( ( some_state @ F8 )
                            = ( plus @ A23 @ M4 ) )
                         => ( S5
                           != ( collec906845016635587262_state
                              @ ^ [Uu3: produc7272280185086996969_state] :
                                ? [A2: state,U6: state,T4: state > state,R: state] :
                                  ( ( Uu3
                                    = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                  & ( ( some_state @ R )
                                    = ( plus @ A2 @ ( minus @ ( T4 @ F8 ) @ ( T4 @ A23 ) ) ) )
                                  & ( defined @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.cases
thf(fact_617_PartialSA_Opackage__rhs_Osimps,axiom,
    ! [A12: state,A23: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( packag3171892606229212990_state @ plus @ core @ stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
      = ( ? [Phi4: state,F7: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,A7: aassertion_state,Phi3: state,F9: state,S7: set_Pr4231240917283394591_state,B5: aassertion_state,Phi8: state,F10: state,S8: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi4 )
            & ( A23 = F7 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aStar_state @ A7 @ B5 ) )
            & ( A62 = Phi8 )
            & ( A72 = F10 )
            & ( A82 = S8 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F7 @ S6 @ Pc2 @ A7 @ Phi3 @ F9 @ S7 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi3 @ F9 @ S7 @ Pc2 @ B5 @ Phi8 @ F10 @ S8 ) )
        | ? [Phi4: state,F7: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,B2: state > $o,A7: aassertion_state,Phi3: state,F9: state,S7: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi4 )
            & ( A23 = F7 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aImp_state @ B2 @ A7 ) )
            & ( A62 = Phi3 )
            & ( A72 = F9 )
            & ( A82 = S7 )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi4 @ F7 @ S6 @ ( packag1330488657391168505_state @ Pc2 @ B2 ) @ A7 @ Phi3 @ F9 @ S7 ) )
        | ? [S6: set_Pr4231240917283394591_state,Pc2: state > $o,Witness2: produc7272280185086996969_state > state,B5: state > $o,S7: set_Pr4231240917283394591_state,Phi4: state,F7: state] :
            ( ( A12 = Phi4 )
            & ( A23 = F7 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52
              = ( aSem_state @ B5 ) )
            & ( A62 = Phi4 )
            & ( A72 = F7 )
            & ( A82 = S7 )
            & ! [X2: state,Y5: state,Z3: state > state,Aa3: state] :
                ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ ( produc8632743443909064678_state @ Y5 @ Z3 ) ) @ S6 )
               => ( ( Pc2 @ X2 )
                 => ( ( Aa3
                      = ( Witness2 @ ( produc5886875603596089627_state @ X2 @ ( produc8632743443909064678_state @ Y5 @ Z3 ) ) ) )
                   => ( ( greater @ X2 @ Aa3 )
                      & ( B5 @ Aa3 ) ) ) ) )
            & ( S7
              = ( 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 ) ) @ S6 )
                      & ~ ( Pc2 @ A2 ) ) )
                @ ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state,B2: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ ( minus @ A2 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B2 ) ) @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S6 )
                      & ( Pc2 @ A2 )
                      & ( B2
                        = ( Witness2 @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) ) ) ) )
        | ? [Phi4: state,Phi3: state,M5: state,F9: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,A7: aassertion_state,Phi8: state,F10: state,S8: set_Pr4231240917283394591_state,F7: state,S6: set_Pr4231240917283394591_state] :
            ( ( A12 = Phi4 )
            & ( A23 = F7 )
            & ( A32 = S6 )
            & ( A42 = Pc2 )
            & ( A52 = A7 )
            & ( A62 = Phi8 )
            & ( A72 = F10 )
            & ( A82 = S8 )
            & ( ( some_state @ Phi4 )
              = ( plus @ Phi3 @ M5 ) )
            & ( packag3171892606229212990_state @ plus @ core @ stable @ Phi3 @ F9 @ S7 @ Pc2 @ A7 @ Phi8 @ F10 @ S8 )
            & ( stable @ M5 )
            & ( ( some_state @ F9 )
              = ( plus @ F7 @ M5 ) )
            & ( S7
              = ( collec906845016635587262_state
                @ ^ [Uu3: produc7272280185086996969_state] :
                  ? [A2: state,U6: state,T4: state > state,R: state] :
                    ( ( Uu3
                      = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S6 )
                    & ( ( some_state @ R )
                      = ( plus @ A2 @ ( minus @ ( T4 @ F9 ) @ ( T4 @ F7 ) ) ) )
                    & ( defined @ R @ U6 ) ) ) ) ) ) ) ).

% PartialSA.package_rhs.simps
thf(fact_618_PartialSA_Osoundness__paper,axiom,
    ! [B4: aassertion_state,A4: aassertion_state,S2: set_state,Sigma: state,Sigma2: state,W: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ! [A6: state] :
            ( ( package_sat_state @ plus @ A4 @ A6 )
           => ( member_state @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ).

% PartialSA.soundness_paper
thf(fact_619_Un__subset__iff,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A4 @ B4 ) @ C3 )
      = ( ( ord_le4032880777312351359_state @ A4 @ C3 )
        & ( ord_le4032880777312351359_state @ B4 @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_620_Un__subset__iff,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A4 @ B4 ) @ C3 )
      = ( ( ord_le2494988322063910608_state @ A4 @ C3 )
        & ( ord_le2494988322063910608_state @ B4 @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_621_subset__Un__eq,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A7: set_Pr4231240917283394591_state,B5: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A7 @ B5 )
          = B5 ) ) ) ).

% subset_Un_eq
thf(fact_622_subset__Un__eq,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A7: set_state,B5: set_state] :
          ( ( sup_sup_set_state @ A7 @ B5 )
          = B5 ) ) ) ).

% subset_Un_eq
thf(fact_623_subset__UnE,axiom,
    ! [C3: set_Pr4231240917283394591_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C3 @ ( sup_su3837536599209510219_state @ A4 @ B4 ) )
     => ~ ! [A11: set_Pr4231240917283394591_state] :
            ( ( ord_le4032880777312351359_state @ A11 @ A4 )
           => ! [B10: set_Pr4231240917283394591_state] :
                ( ( ord_le4032880777312351359_state @ B10 @ B4 )
               => ( C3
                 != ( sup_su3837536599209510219_state @ A11 @ B10 ) ) ) ) ) ).

% subset_UnE
thf(fact_624_subset__UnE,axiom,
    ! [C3: set_state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ C3 @ ( sup_sup_set_state @ A4 @ B4 ) )
     => ~ ! [A11: set_state] :
            ( ( ord_le2494988322063910608_state @ A11 @ A4 )
           => ! [B10: set_state] :
                ( ( ord_le2494988322063910608_state @ B10 @ B4 )
               => ( C3
                 != ( sup_sup_set_state @ A11 @ B10 ) ) ) ) ) ).

% subset_UnE
thf(fact_625_Un__absorb2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B4 @ A4 )
     => ( ( sup_su3837536599209510219_state @ A4 @ B4 )
        = A4 ) ) ).

% Un_absorb2
thf(fact_626_Un__absorb2,axiom,
    ! [B4: set_state,A4: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ A4 )
     => ( ( sup_sup_set_state @ A4 @ B4 )
        = A4 ) ) ).

% Un_absorb2
thf(fact_627_Un__absorb1,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ B4 )
     => ( ( sup_su3837536599209510219_state @ A4 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_628_Un__absorb1,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( sup_sup_set_state @ A4 @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_629_Un__upper2,axiom,
    ! [B4: set_Pr4231240917283394591_state,A4: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ B4 @ ( sup_su3837536599209510219_state @ A4 @ B4 ) ) ).

% Un_upper2
thf(fact_630_Un__upper2,axiom,
    ! [B4: set_state,A4: set_state] : ( ord_le2494988322063910608_state @ B4 @ ( sup_sup_set_state @ A4 @ B4 ) ) ).

% Un_upper2
thf(fact_631_Un__upper1,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ A4 @ ( sup_su3837536599209510219_state @ A4 @ B4 ) ) ).

% Un_upper1
thf(fact_632_Un__upper1,axiom,
    ! [A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ A4 @ ( sup_sup_set_state @ A4 @ B4 ) ) ).

% Un_upper1
thf(fact_633_Un__least,axiom,
    ! [A4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ C3 )
     => ( ( ord_le4032880777312351359_state @ B4 @ C3 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A4 @ B4 ) @ C3 ) ) ) ).

% Un_least
thf(fact_634_Un__least,axiom,
    ! [A4: set_state,C3: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ C3 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A4 @ B4 ) @ C3 ) ) ) ).

% Un_least
thf(fact_635_Un__mono,axiom,
    ! [A4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,D2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ C3 )
     => ( ( ord_le4032880777312351359_state @ B4 @ D2 )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A4 @ B4 ) @ ( sup_su3837536599209510219_state @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_636_Un__mono,axiom,
    ! [A4: set_state,C3: set_state,B4: set_state,D2: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ C3 )
     => ( ( ord_le2494988322063910608_state @ B4 @ D2 )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A4 @ B4 ) @ ( sup_sup_set_state @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_637_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,W: val,A4: aassertion_val,Sigma: val,Sigma2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag685230357167683994rd_val @ Plus @ W @ A4 @ 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 @ A4 @ A2 ) ) )
                @ ^ [Uu3: val] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_638_package__logic_Ocompleteness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,W: state,A4: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
       => ( ( ( Stable @ W )
            & ( packag7096211993527611489_state @ Plus @ W @ A4 @ 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 @ A4 @ A2 ) ) )
                @ ^ [Uu3: state] : $true
                @ B4
                @ Sigma2
                @ W
                @ X_1 ) ) ) ) ) ).

% package_logic.completeness_paper
thf(fact_639_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,A4: 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 )
       => ( ! [A6: produc7272280185086996969_state] :
              ( ( packag4865960244449834244_state @ Plus @ A4 @ A6 )
             => ( member7461423308196221312_state @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_640_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,A4: 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 )
       => ( ! [A6: produc9003781588162623004on_val] :
              ( ( packag3677137384183703351on_val @ Plus @ A4 @ A6 )
             => ( member2879030624002546611on_val @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_641_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,A4: 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 )
       => ( ! [A6: produc3882902684156697774_state] :
              ( ( packag2518615827549365843_state @ Plus @ A4 @ A6 )
             => ( member6715010751053357271_state @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_642_package__logic_Osoundness__paper,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,B4: aassertion_val,A4: 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 )
       => ( ! [A6: val] :
              ( ( package_sat_val @ Plus @ A4 @ A6 )
             => ( member_val @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_643_package__logic_Osoundness__paper,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,B4: aassertion_state,A4: 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 )
       => ( ! [A6: state] :
              ( ( package_sat_state @ Plus @ A4 @ A6 )
             => ( member_state @ A6 @ 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 @ A4 @ B4 ) ) ) ) ) ) ) ).

% package_logic.soundness_paper
thf(fact_644_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] :
      ( ! [A6: state,U: state,T2: state > state,B6: state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
         => ( ( Pc @ A6 )
           => ( ( B6
                = ( Witness3 @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) ) )
             => ( ( greater @ A6 @ 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,B2: state] :
                  ( ( Uu3
                    = ( produc5886875603596089627_state @ ( minus @ A2 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( plus @ U6 @ B2 ) ) @ T4 ) ) )
                  & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                  & ( Pc @ A2 )
                  & ( B2
                    = ( 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_645_PartialSA_Ocompleteness__paper,axiom,
    ! [B4: aassertion_state,W: state,A4: aassertion_state,Sigma: state,Sigma2: state] :
      ( ( packag7298478212905792770_state @ plus @ core @ B4 )
     => ( ( ( stable @ W )
          & ( packag7096211993527611489_state @ plus @ W @ A4 @ 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 @ A4 @ A2 ) ) )
              @ ^ [Uu3: state] : $true
              @ B4
              @ Sigma2
              @ W
              @ X_1 ) ) ) ) ).

% PartialSA.completeness_paper
thf(fact_646_le__sup__iff,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ X @ Y ) @ Z2 )
      = ( ( ord_le4032880777312351359_state @ X @ Z2 )
        & ( ord_le4032880777312351359_state @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_647_le__sup__iff,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X @ Y ) @ Z2 )
      = ( ( ord_le2494988322063910608_state @ X @ Z2 )
        & ( ord_le2494988322063910608_state @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_648_sup_Obounded__iff,axiom,
    ! [B: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A )
      = ( ( ord_le4032880777312351359_state @ B @ A )
        & ( ord_le4032880777312351359_state @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_649_sup_Obounded__iff,axiom,
    ! [B: set_state,C: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A )
      = ( ( ord_le2494988322063910608_state @ B @ A )
        & ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_650_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_651_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_652_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_653_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_654_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_655_package__logic_OAddFromOutside,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,Phi2: val,M: val,F3: val,S3: set_Pr4723104092121316667al_val,Pc: val > $o,A4: aassertion_val,Phi7: val,F4: val,S4: set_Pr4723104092121316667al_val,F: val,S2: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ Phi )
          = ( Plus @ Phi2 @ M ) )
       => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi2 @ F3 @ S3 @ Pc @ A4 @ Phi7 @ F4 @ S4 )
         => ( ( Stable @ M )
           => ( ( ( some_val @ F3 )
                = ( Plus @ F @ M ) )
             => ( ( S3
                  = ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A2: val,U6: val,T4: val > val,R: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ S2 )
                        & ( ( some_val @ R )
                          = ( Plus @ A2 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) ) )
                        & ( sep_defined_val @ Plus @ R @ U6 ) ) ) )
               => ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi7 @ F4 @ S4 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_656_package__logic_OAddFromOutside,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,Phi2: state,M: state,F3: state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi7: state,F4: state,S4: set_Pr4231240917283394591_state,F: state,S2: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ Phi )
          = ( Plus @ Phi2 @ M ) )
       => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi2 @ F3 @ S3 @ Pc @ A4 @ Phi7 @ F4 @ S4 )
         => ( ( Stable @ M )
           => ( ( ( some_state @ F3 )
                = ( Plus @ F @ M ) )
             => ( ( S3
                  = ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A2: state,U6: state,T4: state > state,R: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S2 )
                        & ( ( some_state @ R )
                          = ( Plus @ A2 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) ) )
                        & ( sep_defined_state @ Plus @ R @ U6 ) ) ) )
               => ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi7 @ F4 @ S4 ) ) ) ) ) ) ) ).

% package_logic.AddFromOutside
thf(fact_657_package__logic_Odefined__sum__move,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,B: val,X: val,Y: val,A3: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_defined_val @ Plus @ A @ B )
       => ( ( ( some_val @ B )
            = ( Plus @ X @ Y ) )
         => ( ( ( some_val @ A3 )
              = ( Plus @ A @ X ) )
           => ( sep_defined_val @ Plus @ A3 @ Y ) ) ) ) ) ).

% package_logic.defined_sum_move
thf(fact_658_package__logic_Odefined__sum__move,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,B: state,X: state,Y: state,A3: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_defined_state @ Plus @ A @ B )
       => ( ( ( some_state @ B )
            = ( Plus @ X @ Y ) )
         => ( ( ( some_state @ A3 )
              = ( Plus @ A @ X ) )
           => ( sep_defined_state @ Plus @ A3 @ Y ) ) ) ) ) ).

% package_logic.defined_sum_move
thf(fact_659_defined__def,axiom,
    ( defined
    = ( sep_defined_state @ plus ) ) ).

% defined_def
thf(fact_660_inf__sup__ord_I4_J,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_661_inf__sup__ord_I4_J,axiom,
    ! [Y: set_state,X: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_662_inf__sup__ord_I3_J,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_663_inf__sup__ord_I3_J,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ X @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_664_le__supE,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ X )
     => ~ ( ( ord_le4032880777312351359_state @ A @ X )
         => ~ ( ord_le4032880777312351359_state @ B @ X ) ) ) ).

% le_supE
thf(fact_665_le__supE,axiom,
    ! [A: set_state,B: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ X )
     => ~ ( ( ord_le2494988322063910608_state @ A @ X )
         => ~ ( ord_le2494988322063910608_state @ B @ X ) ) ) ).

% le_supE
thf(fact_666_le__supI,axiom,
    ! [A: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ X )
     => ( ( ord_le4032880777312351359_state @ B @ X )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_667_le__supI,axiom,
    ! [A: set_state,X: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ X )
     => ( ( ord_le2494988322063910608_state @ B @ X )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ X ) ) ) ).

% le_supI
thf(fact_668_sup__ge1,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% sup_ge1
thf(fact_669_sup__ge1,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ X @ Y ) ) ).

% sup_ge1
thf(fact_670_sup__ge2,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y @ ( sup_su3837536599209510219_state @ X @ Y ) ) ).

% sup_ge2
thf(fact_671_sup__ge2,axiom,
    ! [Y: set_state,X: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X @ Y ) ) ).

% sup_ge2
thf(fact_672_le__supI1,axiom,
    ! [X: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ A )
     => ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% le_supI1
thf(fact_673_le__supI1,axiom,
    ! [X: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ A )
     => ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ A @ B ) ) ) ).

% le_supI1
thf(fact_674_le__supI2,axiom,
    ! [X: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ B )
     => ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% le_supI2
thf(fact_675_le__supI2,axiom,
    ! [X: set_state,B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ B )
     => ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ A @ B ) ) ) ).

% le_supI2
thf(fact_676_sup_Omono,axiom,
    ! [C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,D: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ A )
     => ( ( ord_le4032880777312351359_state @ D @ B )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ C @ D ) @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_677_sup_Omono,axiom,
    ! [C: set_state,A: set_state,D: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ A )
     => ( ( ord_le2494988322063910608_state @ D @ B )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ C @ D ) @ ( sup_sup_set_state @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_678_sup__mono,axiom,
    ! [A: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,D: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ C )
     => ( ( ord_le4032880777312351359_state @ B @ D )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ A @ B ) @ ( sup_su3837536599209510219_state @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_679_sup__mono,axiom,
    ! [A: set_state,C: set_state,B: set_state,D: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ C )
     => ( ( ord_le2494988322063910608_state @ B @ D )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ ( sup_sup_set_state @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_680_sup__least,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ Y @ X )
     => ( ( ord_le4032880777312351359_state @ Z2 @ X )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_681_sup__least,axiom,
    ! [Y: set_state,X: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( ord_le2494988322063910608_state @ Z2 @ X )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ Y @ Z2 ) @ X ) ) ) ).

% sup_least
thf(fact_682_le__iff__sup,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [X2: set_Pr4231240917283394591_state,Y5: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ X2 @ Y5 )
          = Y5 ) ) ) ).

% le_iff_sup
thf(fact_683_le__iff__sup,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [X2: set_state,Y5: set_state] :
          ( ( sup_sup_set_state @ X2 @ Y5 )
          = Y5 ) ) ) ).

% le_iff_sup
thf(fact_684_sup_OorderE,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( A
        = ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.orderE
thf(fact_685_sup_OorderE,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( A
        = ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.orderE
thf(fact_686_sup_OorderI,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( A
        = ( sup_su3837536599209510219_state @ A @ B ) )
     => ( ord_le4032880777312351359_state @ B @ A ) ) ).

% sup.orderI
thf(fact_687_sup_OorderI,axiom,
    ! [A: set_state,B: set_state] :
      ( ( A
        = ( sup_sup_set_state @ A @ B ) )
     => ( ord_le2494988322063910608_state @ B @ A ) ) ).

% sup.orderI
thf(fact_688_sup__unique,axiom,
    ! [F: set_Pr4231240917283394591_state > set_Pr4231240917283394591_state > set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] :
      ( ! [X3: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ X3 @ ( F @ X3 @ Y3 ) )
     => ( ! [X3: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ Y3 @ ( F @ X3 @ Y3 ) )
       => ( ! [X3: set_Pr4231240917283394591_state,Y3: set_Pr4231240917283394591_state,Z4: set_Pr4231240917283394591_state] :
              ( ( ord_le4032880777312351359_state @ Y3 @ X3 )
             => ( ( ord_le4032880777312351359_state @ Z4 @ X3 )
               => ( ord_le4032880777312351359_state @ ( F @ Y3 @ Z4 ) @ X3 ) ) )
         => ( ( sup_su3837536599209510219_state @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_689_sup__unique,axiom,
    ! [F: set_state > set_state > set_state,X: set_state,Y: set_state] :
      ( ! [X3: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ X3 @ ( F @ X3 @ Y3 ) )
     => ( ! [X3: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ Y3 @ ( F @ X3 @ Y3 ) )
       => ( ! [X3: set_state,Y3: set_state,Z4: set_state] :
              ( ( ord_le2494988322063910608_state @ Y3 @ X3 )
             => ( ( ord_le2494988322063910608_state @ Z4 @ X3 )
               => ( ord_le2494988322063910608_state @ ( F @ Y3 @ Z4 ) @ X3 ) ) )
         => ( ( sup_sup_set_state @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_690_sup_Oabsorb1,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( ( sup_su3837536599209510219_state @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_691_sup_Oabsorb1,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( sup_sup_set_state @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_692_sup_Oabsorb2,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A @ B )
     => ( ( sup_su3837536599209510219_state @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_693_sup_Oabsorb2,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( sup_sup_set_state @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_694_sup__absorb1,axiom,
    ! [Y: set_Pr4231240917283394591_state,X: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ Y @ X )
     => ( ( sup_su3837536599209510219_state @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_695_sup__absorb1,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( sup_sup_set_state @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_696_sup__absorb2,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X @ Y )
     => ( ( sup_su3837536599209510219_state @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_697_sup__absorb2,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( sup_sup_set_state @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_698_sup_OboundedE,axiom,
    ! [B: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A )
     => ~ ( ( ord_le4032880777312351359_state @ B @ A )
         => ~ ( ord_le4032880777312351359_state @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_699_sup_OboundedE,axiom,
    ! [B: set_state,C: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A )
     => ~ ( ( ord_le2494988322063910608_state @ B @ A )
         => ~ ( ord_le2494988322063910608_state @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_700_sup_OboundedI,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,C: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ B @ A )
     => ( ( ord_le4032880777312351359_state @ C @ A )
       => ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_701_sup_OboundedI,axiom,
    ! [B: set_state,A: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( ord_le2494988322063910608_state @ C @ A )
       => ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_702_sup_Oorder__iff,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [B2: set_Pr4231240917283394591_state,A2: set_Pr4231240917283394591_state] :
          ( A2
          = ( sup_su3837536599209510219_state @ A2 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_703_sup_Oorder__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [B2: set_state,A2: set_state] :
          ( A2
          = ( sup_sup_set_state @ A2 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_704_sup_Ocobounded1,axiom,
    ! [A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ A @ ( sup_su3837536599209510219_state @ A @ B ) ) ).

% sup.cobounded1
thf(fact_705_sup_Ocobounded1,axiom,
    ! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ A @ ( sup_sup_set_state @ A @ B ) ) ).

% sup.cobounded1
thf(fact_706_sup_Ocobounded2,axiom,
    ! [B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ B @ ( sup_su3837536599209510219_state @ A @ B ) ) ).

% sup.cobounded2
thf(fact_707_sup_Ocobounded2,axiom,
    ! [B: set_state,A: set_state] : ( ord_le2494988322063910608_state @ B @ ( sup_sup_set_state @ A @ B ) ) ).

% sup.cobounded2
thf(fact_708_sup_Oabsorb__iff1,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [B2: set_Pr4231240917283394591_state,A2: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A2 @ B2 )
          = A2 ) ) ) ).

% sup.absorb_iff1
thf(fact_709_sup_Oabsorb__iff1,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [B2: set_state,A2: set_state] :
          ( ( sup_sup_set_state @ A2 @ B2 )
          = A2 ) ) ) ).

% sup.absorb_iff1
thf(fact_710_sup_Oabsorb__iff2,axiom,
    ( ord_le4032880777312351359_state
    = ( ^ [A2: set_Pr4231240917283394591_state,B2: set_Pr4231240917283394591_state] :
          ( ( sup_su3837536599209510219_state @ A2 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_711_sup_Oabsorb__iff2,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A2: set_state,B2: set_state] :
          ( ( sup_sup_set_state @ A2 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_712_sup_OcoboundedI1,axiom,
    ! [C: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ A )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_713_sup_OcoboundedI1,axiom,
    ! [C: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ A )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_714_sup_OcoboundedI2,axiom,
    ! [C: set_Pr4231240917283394591_state,B: set_Pr4231240917283394591_state,A: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ C @ B )
     => ( ord_le4032880777312351359_state @ C @ ( sup_su3837536599209510219_state @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_715_sup_OcoboundedI2,axiom,
    ! [C: set_state,B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ C @ B )
     => ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_716_accp__subset__induct,axiom,
    ! [D2: produc3142500478612311029_state > $o,R4: produc3142500478612311029_state > produc3142500478612311029_state > $o,X: produc3142500478612311029_state,P2: produc3142500478612311029_state > $o] :
      ( ( ord_le5366583112655343912tate_o @ D2 @ ( accp_P7183347322223220350_state @ R4 ) )
     => ( ! [X3: produc3142500478612311029_state,Z4: produc3142500478612311029_state] :
            ( ( D2 @ X3 )
           => ( ( R4 @ Z4 @ X3 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X )
         => ( ! [X3: produc3142500478612311029_state] :
                ( ( D2 @ X3 )
               => ( ! [Z5: produc3142500478612311029_state] :
                      ( ( R4 @ Z5 @ X3 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X3 ) ) )
           => ( P2 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_717_accp__subset__induct,axiom,
    ! [D2: produc4844402304972151915_state > $o,R4: produc4844402304972151915_state > produc4844402304972151915_state > $o,X: produc4844402304972151915_state,P2: produc4844402304972151915_state > $o] :
      ( ( ord_le5681876185599785522tate_o @ D2 @ ( accp_P6233459008282737652_state @ R4 ) )
     => ( ! [X3: produc4844402304972151915_state,Z4: produc4844402304972151915_state] :
            ( ( D2 @ X3 )
           => ( ( R4 @ Z4 @ X3 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X )
         => ( ! [X3: produc4844402304972151915_state] :
                ( ( D2 @ X3 )
               => ( ! [Z5: produc4844402304972151915_state] :
                      ( ( R4 @ Z5 @ X3 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X3 ) ) )
           => ( P2 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_718_accp__subset__induct,axiom,
    ! [D2: produc6251377953716854561_state > $o,R4: produc6251377953716854561_state > produc6251377953716854561_state > $o,X: produc6251377953716854561_state,P2: produc6251377953716854561_state > $o] :
      ( ( ord_le8699832056682887676tate_o @ D2 @ ( accp_P6554740477754186410_state @ R4 ) )
     => ( ! [X3: produc6251377953716854561_state,Z4: produc6251377953716854561_state] :
            ( ( D2 @ X3 )
           => ( ( R4 @ Z4 @ X3 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X )
         => ( ! [X3: produc6251377953716854561_state] :
                ( ( D2 @ X3 )
               => ( ! [Z5: produc6251377953716854561_state] :
                      ( ( R4 @ Z5 @ X3 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X3 ) ) )
           => ( P2 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_719_accp__subset__induct,axiom,
    ! [D2: produc9003781588162623004on_val > $o,R4: produc9003781588162623004on_val > produc9003781588162623004on_val > $o,X: produc9003781588162623004on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( ord_le6140313152057869779_val_o @ D2 @ ( accp_P4405556307444930259on_val @ R4 ) )
     => ( ! [X3: produc9003781588162623004on_val,Z4: produc9003781588162623004on_val] :
            ( ( D2 @ X3 )
           => ( ( R4 @ Z4 @ X3 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X )
         => ( ! [X3: produc9003781588162623004on_val] :
                ( ( D2 @ X3 )
               => ( ! [Z5: produc9003781588162623004on_val] :
                      ( ( R4 @ Z5 @ X3 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X3 ) ) )
           => ( P2 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_720_accp__subset__induct,axiom,
    ! [D2: ( produc1457211279475724562t_char > prat ) > $o,R4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > prat ) > $o,X: produc1457211279475724562t_char > prat,P2: ( produc1457211279475724562t_char > prat ) > $o] :
      ( ( ord_le2830794348966088778prat_o @ D2 @ ( accp_P4765339447491148764r_prat @ R4 ) )
     => ( ! [X3: produc1457211279475724562t_char > prat,Z4: produc1457211279475724562t_char > prat] :
            ( ( D2 @ X3 )
           => ( ( R4 @ Z4 @ X3 )
             => ( D2 @ Z4 ) ) )
       => ( ( D2 @ X )
         => ( ! [X3: produc1457211279475724562t_char > prat] :
                ( ( D2 @ X3 )
               => ( ! [Z5: produc1457211279475724562t_char > prat] :
                      ( ( R4 @ Z5 @ X3 )
                     => ( P2 @ Z5 ) )
                 => ( P2 @ X3 ) ) )
           => ( P2 @ X ) ) ) ) ) ).

% accp_subset_induct
thf(fact_721_package__logic_Opackage__rhs_Osimps,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A12: val,A23: val,A32: set_Pr4723104092121316667al_val,A42: val > $o,A52: aassertion_val,A62: val,A72: val,A82: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
        = ( ? [Phi4: val,F7: val,S6: set_Pr4723104092121316667al_val,Pc2: val > $o,A7: aassertion_val,Phi3: val,F9: val,S7: set_Pr4723104092121316667al_val,B5: aassertion_val,Phi8: val,F10: val,S8: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aStar_val @ A7 @ B5 ) )
              & ( A62 = Phi8 )
              & ( A72 = F10 )
              & ( A82 = S8 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi4 @ F7 @ S6 @ Pc2 @ A7 @ Phi3 @ F9 @ S7 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi3 @ F9 @ S7 @ Pc2 @ B5 @ Phi8 @ F10 @ S8 ) )
          | ? [Phi4: val,F7: val,S6: set_Pr4723104092121316667al_val,Pc2: val > $o,B2: val > $o,A7: aassertion_val,Phi3: val,F9: val,S7: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aImp_val @ B2 @ A7 ) )
              & ( A62 = Phi3 )
              & ( A72 = F9 )
              & ( A82 = S7 )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi4 @ F7 @ S6 @ ( packag6750194596558674946nj_val @ Pc2 @ B2 ) @ A7 @ Phi3 @ F9 @ S7 ) )
          | ? [S6: set_Pr4723104092121316667al_val,Pc2: val > $o,Witness2: produc2072440392815185925al_val > val,B5: val > $o,S7: set_Pr4723104092121316667al_val,Phi4: val,F7: val] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aSem_val @ B5 ) )
              & ( A62 = Phi4 )
              & ( A72 = F7 )
              & ( A82 = S7 )
              & ! [X2: val,Y5: val,Z3: val > val,Aa3: val] :
                  ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ X2 @ ( produc303288909735261391al_val @ Y5 @ Z3 ) ) @ S6 )
                 => ( ( Pc2 @ X2 )
                   => ( ( Aa3
                        = ( Witness2 @ ( produc7187740677493149823al_val @ X2 @ ( produc303288909735261391al_val @ Y5 @ Z3 ) ) ) )
                     => ( ( sep_greater_val @ Plus @ X2 @ Aa3 )
                        & ( B5 @ Aa3 ) ) ) ) )
              & ( S7
                = ( 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 ) ) @ S6 )
                        & ~ ( Pc2 @ A2 ) ) )
                  @ ( collec8300311316619386842al_val
                    @ ^ [Uu3: produc2072440392815185925al_val] :
                      ? [A2: val,U6: val,T4: val > val,B2: val] :
                        ( ( Uu3
                          = ( produc7187740677493149823al_val @ ( sep_minus_val @ Plus @ Core @ A2 @ B2 ) @ ( produc303288909735261391al_val @ ( the_val @ ( Plus @ U6 @ B2 ) ) @ T4 ) ) )
                        & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ S6 )
                        & ( Pc2 @ A2 )
                        & ( B2
                          = ( Witness2 @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) ) ) ) ) ) ) )
          | ? [Phi4: val,Phi3: val,M5: val,F9: val,S7: set_Pr4723104092121316667al_val,Pc2: val > $o,A7: aassertion_val,Phi8: val,F10: val,S8: set_Pr4723104092121316667al_val,F7: val,S6: set_Pr4723104092121316667al_val] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52 = A7 )
              & ( A62 = Phi8 )
              & ( A72 = F10 )
              & ( A82 = S8 )
              & ( ( some_val @ Phi4 )
                = ( Plus @ Phi3 @ M5 ) )
              & ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi3 @ F9 @ S7 @ Pc2 @ A7 @ Phi8 @ F10 @ S8 )
              & ( Stable @ M5 )
              & ( ( some_val @ F9 )
                = ( Plus @ F7 @ M5 ) )
              & ( S7
                = ( collec8300311316619386842al_val
                  @ ^ [Uu3: produc2072440392815185925al_val] :
                    ? [A2: val,U6: val,T4: val > val,R: val] :
                      ( ( Uu3
                        = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                      & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ S6 )
                      & ( ( some_val @ R )
                        = ( Plus @ A2 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F9 ) @ ( T4 @ F7 ) ) ) )
                      & ( sep_defined_val @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.simps
thf(fact_722_package__logic_Opackage__rhs_Osimps,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A12: state,A23: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
        = ( ? [Phi4: state,F7: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,A7: aassertion_state,Phi3: state,F9: state,S7: set_Pr4231240917283394591_state,B5: aassertion_state,Phi8: state,F10: state,S8: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aStar_state @ A7 @ B5 ) )
              & ( A62 = Phi8 )
              & ( A72 = F10 )
              & ( A82 = S8 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi4 @ F7 @ S6 @ Pc2 @ A7 @ Phi3 @ F9 @ S7 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi3 @ F9 @ S7 @ Pc2 @ B5 @ Phi8 @ F10 @ S8 ) )
          | ? [Phi4: state,F7: state,S6: set_Pr4231240917283394591_state,Pc2: state > $o,B2: state > $o,A7: aassertion_state,Phi3: state,F9: state,S7: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aImp_state @ B2 @ A7 ) )
              & ( A62 = Phi3 )
              & ( A72 = F9 )
              & ( A82 = S7 )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi4 @ F7 @ S6 @ ( packag1330488657391168505_state @ Pc2 @ B2 ) @ A7 @ Phi3 @ F9 @ S7 ) )
          | ? [S6: set_Pr4231240917283394591_state,Pc2: state > $o,Witness2: produc7272280185086996969_state > state,B5: state > $o,S7: set_Pr4231240917283394591_state,Phi4: state,F7: state] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52
                = ( aSem_state @ B5 ) )
              & ( A62 = Phi4 )
              & ( A72 = F7 )
              & ( A82 = S7 )
              & ! [X2: state,Y5: state,Z3: state > state,Aa3: state] :
                  ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ X2 @ ( produc8632743443909064678_state @ Y5 @ Z3 ) ) @ S6 )
                 => ( ( Pc2 @ X2 )
                   => ( ( Aa3
                        = ( Witness2 @ ( produc5886875603596089627_state @ X2 @ ( produc8632743443909064678_state @ Y5 @ Z3 ) ) ) )
                     => ( ( sep_greater_state @ Plus @ X2 @ Aa3 )
                        & ( B5 @ Aa3 ) ) ) ) )
              & ( S7
                = ( 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 ) ) @ S6 )
                        & ~ ( Pc2 @ A2 ) ) )
                  @ ( collec906845016635587262_state
                    @ ^ [Uu3: produc7272280185086996969_state] :
                      ? [A2: state,U6: state,T4: state > state,B2: state] :
                        ( ( Uu3
                          = ( produc5886875603596089627_state @ ( sep_minus_state @ Plus @ Core @ A2 @ B2 ) @ ( produc8632743443909064678_state @ ( the_state @ ( Plus @ U6 @ B2 ) ) @ T4 ) ) )
                        & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S6 )
                        & ( Pc2 @ A2 )
                        & ( B2
                          = ( Witness2 @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) ) ) ) ) ) ) )
          | ? [Phi4: state,Phi3: state,M5: state,F9: state,S7: set_Pr4231240917283394591_state,Pc2: state > $o,A7: aassertion_state,Phi8: state,F10: state,S8: set_Pr4231240917283394591_state,F7: state,S6: set_Pr4231240917283394591_state] :
              ( ( A12 = Phi4 )
              & ( A23 = F7 )
              & ( A32 = S6 )
              & ( A42 = Pc2 )
              & ( A52 = A7 )
              & ( A62 = Phi8 )
              & ( A72 = F10 )
              & ( A82 = S8 )
              & ( ( some_state @ Phi4 )
                = ( Plus @ Phi3 @ M5 ) )
              & ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi3 @ F9 @ S7 @ Pc2 @ A7 @ Phi8 @ F10 @ S8 )
              & ( Stable @ M5 )
              & ( ( some_state @ F9 )
                = ( Plus @ F7 @ M5 ) )
              & ( S7
                = ( collec906845016635587262_state
                  @ ^ [Uu3: produc7272280185086996969_state] :
                    ? [A2: state,U6: state,T4: state > state,R: state] :
                      ( ( Uu3
                        = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                      & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ S6 )
                      & ( ( some_state @ R )
                        = ( Plus @ A2 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F9 ) @ ( T4 @ F7 ) ) ) )
                      & ( sep_defined_state @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.simps
thf(fact_723_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A12: val,A23: val,A32: set_Pr4723104092121316667al_val,A42: val > $o,A52: aassertion_val,A62: val,A72: val,A82: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A10: aassertion_val,Phi6: val,F8: val,S5: set_Pr4723104092121316667al_val,B8: aassertion_val] :
              ( ( A52
                = ( aStar_val @ A10 @ B8 ) )
             => ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A10 @ Phi6 @ F8 @ S5 )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi6 @ F8 @ S5 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: val > $o,A10: aassertion_val] :
                ( ( A52
                  = ( aImp_val @ B6 @ A10 ) )
               => ~ ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ ( packag6750194596558674946nj_val @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness: produc2072440392815185925al_val > val,B8: val > $o] :
                  ( ( A52
                    = ( aSem_val @ B8 ) )
                 => ( ( A62 = A12 )
                   => ( ( A72 = A23 )
                     => ( ! [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 ) ) ) )
                                & ( B8 @ ( 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,M4: val] :
                    ( ( ( some_val @ A12 )
                      = ( Plus @ Phi6 @ M4 ) )
                   => ! [F8: val,S5: set_Pr4723104092121316667al_val] :
                        ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi6 @ F8 @ S5 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M4 )
                         => ( ( ( some_val @ F8 )
                              = ( Plus @ A23 @ M4 ) )
                           => ( S5
                             != ( collec8300311316619386842al_val
                                @ ^ [Uu3: produc2072440392815185925al_val] :
                                  ? [A2: val,U6: val,T4: val > val,R: val] :
                                    ( ( Uu3
                                      = ( produc7187740677493149823al_val @ R @ ( produc303288909735261391al_val @ U6 @ T4 ) ) )
                                    & ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ A32 )
                                    & ( ( some_val @ R )
                                      = ( Plus @ A2 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F8 ) @ ( T4 @ A23 ) ) ) )
                                    & ( sep_defined_val @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_724_package__logic_Opackage__rhs_Ocases,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A12: state,A23: state,A32: set_Pr4231240917283394591_state,A42: state > $o,A52: aassertion_state,A62: state,A72: state,A82: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A52 @ A62 @ A72 @ A82 )
       => ( ! [A10: aassertion_state,Phi6: state,F8: state,S5: set_Pr4231240917283394591_state,B8: aassertion_state] :
              ( ( A52
                = ( aStar_state @ A10 @ B8 ) )
             => ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ A42 @ A10 @ Phi6 @ F8 @ S5 )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi6 @ F8 @ S5 @ A42 @ B8 @ A62 @ A72 @ A82 ) ) )
         => ( ! [B6: state > $o,A10: aassertion_state] :
                ( ( A52
                  = ( aImp_state @ B6 @ A10 ) )
               => ~ ( packag3171892606229212990_state @ Plus @ Core @ Stable @ A12 @ A23 @ A32 @ ( packag1330488657391168505_state @ A42 @ B6 ) @ A10 @ A62 @ A72 @ A82 ) )
           => ( ! [Witness: produc7272280185086996969_state > state,B8: state > $o] :
                  ( ( A52
                    = ( aSem_state @ B8 ) )
                 => ( ( A62 = A12 )
                   => ( ( A72 = A23 )
                     => ( ! [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 ) ) ) )
                                & ( B8 @ ( 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,M4: state] :
                    ( ( ( some_state @ A12 )
                      = ( Plus @ Phi6 @ M4 ) )
                   => ! [F8: state,S5: set_Pr4231240917283394591_state] :
                        ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi6 @ F8 @ S5 @ A42 @ A52 @ A62 @ A72 @ A82 )
                       => ( ( Stable @ M4 )
                         => ( ( ( some_state @ F8 )
                              = ( Plus @ A23 @ M4 ) )
                           => ( S5
                             != ( collec906845016635587262_state
                                @ ^ [Uu3: produc7272280185086996969_state] :
                                  ? [A2: state,U6: state,T4: state > state,R: state] :
                                    ( ( Uu3
                                      = ( produc5886875603596089627_state @ R @ ( produc8632743443909064678_state @ U6 @ T4 ) ) )
                                    & ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A2 @ ( produc8632743443909064678_state @ U6 @ T4 ) ) @ A32 )
                                    & ( ( some_state @ R )
                                      = ( Plus @ A2 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F8 ) @ ( T4 @ A23 ) ) ) )
                                    & ( sep_defined_state @ Plus @ R @ U6 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% package_logic.package_rhs.cases
thf(fact_725_PartialSA_Ogeneral__soundness,axiom,
    ! [Phi: state,S2: set_Pr2391701600042252046_state,A4: 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
        @ A4
        @ Phi2
        @ F
        @ S3 )
     => ( ! [A6: state,T2: state > state] :
            ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A6 @ T2 ) @ S2 )
           => ( packag4817583915586052229_state @ plus @ unit @ T2 ) )
       => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
         => ( ( ( packag8361946002163212404_state @ plus @ ( package_sat_state @ plus @ A4 ) )
              | ( packag4152378406607043437_state @ plus @ S3 ) )
           => ( ( ( some_state @ Phi )
                = ( plus @ Phi2 @ F ) )
              & ( stable @ F )
              & ! [X4: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ X4 @ S2 )
                 => ( produc3645877548210629341tate_o
                    @ ^ [A2: state,T4: state > state] :
                        ( ( defined @ A2 @ ( T4 @ F ) )
                       => ( package_sat_state @ plus @ A4 @ ( the_state @ ( plus @ A2 @ ( T4 @ F ) ) ) ) )
                    @ X4 ) ) ) ) ) ) ) ).

% PartialSA.general_soundness
thf(fact_726_sep__algebra_Obigger__sum__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,C: val,A: val,B: val,A3: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ C )
          = ( Plus @ A @ B ) )
       => ( ( sep_greater_val @ Plus @ A @ A3 )
         => ? [B3: val] :
              ( ( sep_greater_val @ Plus @ B3 @ B )
              & ( ( some_val @ C )
                = ( Plus @ A3 @ B3 ) ) ) ) ) ) ).

% sep_algebra.bigger_sum_smaller
thf(fact_727_sep__algebra_Obigger__sum__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,C: state,A: state,B: state,A3: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ C )
          = ( Plus @ A @ B ) )
       => ( ( sep_greater_state @ Plus @ A @ A3 )
         => ? [B3: state] :
              ( ( sep_greater_state @ Plus @ B3 @ B )
              & ( ( some_state @ C )
                = ( Plus @ A3 @ B3 ) ) ) ) ) ) ).

% sep_algebra.bigger_sum_smaller
thf(fact_728_sep__algebra_Osmaller__than__core,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Y: val,X: val,Z2: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ Y @ X )
       => ( ( ( some_val @ Z2 )
            = ( Plus @ X @ ( Core @ Y ) ) )
         => ( ( Core @ Z2 )
            = ( Core @ Y ) ) ) ) ) ).

% sep_algebra.smaller_than_core
thf(fact_729_sep__algebra_Osmaller__than__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,X: state,Z2: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ X )
       => ( ( ( some_state @ Z2 )
            = ( Plus @ X @ ( Core @ Y ) ) )
         => ( ( Core @ Z2 )
            = ( Core @ Y ) ) ) ) ) ).

% sep_algebra.smaller_than_core
thf(fact_730_sep__algebra_Oaddition__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A3: val,A: val,X5: val,B: val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A3 @ A )
       => ( ( ( some_val @ X5 )
            = ( Plus @ A3 @ B ) )
         => ( ( ( some_val @ X )
              = ( Plus @ A @ B ) )
           => ( sep_greater_val @ Plus @ X5 @ X ) ) ) ) ) ).

% sep_algebra.addition_bigger
thf(fact_731_sep__algebra_Oaddition__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A3: state,A: state,X5: state,B: state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A3 @ A )
       => ( ( ( some_state @ X5 )
            = ( Plus @ A3 @ B ) )
         => ( ( ( some_state @ X )
              = ( Plus @ A @ B ) )
           => ( sep_greater_state @ Plus @ X5 @ X ) ) ) ) ) ).

% sep_algebra.addition_bigger
thf(fact_732_sep__algebra_Ogreater__equiv,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A @ B )
        = ( ? [C2: val] :
              ( ( some_val @ A )
              = ( Plus @ C2 @ B ) ) ) ) ) ).

% sep_algebra.greater_equiv
thf(fact_733_sep__algebra_Ogreater__equiv,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A @ B )
        = ( ? [C2: state] :
              ( ( some_state @ A )
              = ( Plus @ C2 @ B ) ) ) ) ) ).

% sep_algebra.greater_equiv
thf(fact_734_sep__algebra_Ominus__unique,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val,X: val,Y: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( some_val @ B )
            = ( Plus @ A @ X ) )
          & ( sep_greater_val @ Plus @ X @ ( Core @ B ) ) )
       => ( ( ( ( some_val @ B )
              = ( Plus @ A @ Y ) )
            & ( sep_greater_val @ Plus @ Y @ ( Core @ B ) ) )
         => ( X = Y ) ) ) ) ).

% sep_algebra.minus_unique
thf(fact_735_sep__algebra_Ominus__unique,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state,X: state,Y: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( some_state @ B )
            = ( Plus @ A @ X ) )
          & ( sep_greater_state @ Plus @ X @ ( Core @ B ) ) )
       => ( ( ( ( some_state @ B )
              = ( Plus @ A @ Y ) )
            & ( sep_greater_state @ Plus @ Y @ ( Core @ B ) ) )
         => ( X = Y ) ) ) ) ).

% sep_algebra.minus_unique
thf(fact_736_sep__algebra_Ominus__exists,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ B @ A )
       => ? [X3: val] :
            ( ( ( some_val @ B )
              = ( Plus @ A @ X3 ) )
            & ( sep_greater_val @ Plus @ X3 @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.minus_exists
thf(fact_737_sep__algebra_Ominus__exists,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ B @ A )
       => ? [X3: state] :
            ( ( ( some_state @ B )
              = ( Plus @ A @ X3 ) )
            & ( sep_greater_state @ Plus @ X3 @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.minus_exists
thf(fact_738_sep__algebra_Oextract__core,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( ( some_val @ B )
            = ( Plus @ A @ X ) )
          & ( sep_greater_val @ Plus @ X @ ( Core @ B ) ) )
       => ( ( Core @ X )
          = ( Core @ B ) ) ) ) ).

% sep_algebra.extract_core
thf(fact_739_sep__algebra_Oextract__core,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( ( some_state @ B )
            = ( Plus @ A @ X ) )
          & ( sep_greater_state @ Plus @ X @ ( Core @ B ) ) )
       => ( ( Core @ X )
          = ( Core @ B ) ) ) ) ).

% sep_algebra.extract_core
thf(fact_740_sep__algebra_Ogreater__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ A @ B )
        = ( ? [C2: val] :
              ( ( some_val @ A )
              = ( Plus @ B @ C2 ) ) ) ) ) ).

% sep_algebra.greater_def
thf(fact_741_sep__algebra_Ogreater__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ A @ B )
        = ( ? [C2: state] :
              ( ( some_state @ A )
              = ( Plus @ B @ C2 ) ) ) ) ) ).

% sep_algebra.greater_def
thf(fact_742_greater__def,axiom,
    ( greater
    = ( sep_greater_state @ plus ) ) ).

% greater_def
thf(fact_743_package__logic_Ogreater__than__sum__exists,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,B: val,B1: val,B22: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A @ B )
       => ( ( ( some_val @ B )
            = ( Plus @ B1 @ B22 ) )
         => ? [R3: val] :
              ( ( ( some_val @ A )
                = ( Plus @ R3 @ B22 ) )
              & ( sep_greater_val @ Plus @ ( Core @ R3 ) @ ( Core @ A ) )
              & ( sep_greater_val @ Plus @ R3 @ B1 ) ) ) ) ) ).

% package_logic.greater_than_sum_exists
thf(fact_744_package__logic_Ogreater__than__sum__exists,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,B: state,B1: state,B22: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A @ B )
       => ( ( ( some_state @ B )
            = ( Plus @ B1 @ B22 ) )
         => ? [R3: state] :
              ( ( ( some_state @ A )
                = ( Plus @ R3 @ B22 ) )
              & ( sep_greater_state @ Plus @ ( Core @ R3 ) @ ( Core @ A ) )
              & ( sep_greater_state @ Plus @ R3 @ B1 ) ) ) ) ) ).

% package_logic.greater_than_sum_exists
thf(fact_745_package__logic_Obigger__core__sum__defined,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,B: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ ( Core @ A ) @ B )
       => ( ( some_val @ A )
          = ( Plus @ A @ B ) ) ) ) ).

% package_logic.bigger_core_sum_defined
thf(fact_746_package__logic_Obigger__core__sum__defined,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,B: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ ( Core @ A ) @ B )
       => ( ( some_state @ A )
          = ( Plus @ A @ B ) ) ) ) ).

% package_logic.bigger_core_sum_defined
thf(fact_747_package__logic_Obigger__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,A: val,B: val,Phi2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ Phi )
          = ( Plus @ A @ B ) )
       => ( ( sep_greater_val @ Plus @ Phi2 @ Phi )
         => ? [B3: val] :
              ( ( sep_greater_val @ Plus @ B3 @ B )
              & ( ( some_val @ Phi2 )
                = ( Plus @ A @ B3 ) ) ) ) ) ) ).

% package_logic.bigger_sum
thf(fact_748_package__logic_Obigger__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,A: state,B: state,Phi2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ Phi )
          = ( Plus @ A @ B ) )
       => ( ( sep_greater_state @ Plus @ Phi2 @ Phi )
         => ? [B3: state] :
              ( ( sep_greater_state @ Plus @ B3 @ B )
              & ( ( some_state @ Phi2 )
                = ( Plus @ A @ B3 ) ) ) ) ) ) ).

% package_logic.bigger_sum
thf(fact_749_package__logic_Obigger__the,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,X5: val,Y: val,X: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_val @ A )
          = ( Plus @ X5 @ Y ) )
       => ( ( sep_greater_val @ Plus @ X5 @ X )
         => ( sep_greater_val @ Plus @ ( the_val @ ( Plus @ ( Core @ A ) @ X5 ) ) @ ( the_val @ ( Plus @ ( Core @ A ) @ X ) ) ) ) ) ) ).

% package_logic.bigger_the
thf(fact_750_package__logic_Obigger__the,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,X5: state,Y: state,X: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( some_state @ A )
          = ( Plus @ X5 @ Y ) )
       => ( ( sep_greater_state @ Plus @ X5 @ X )
         => ( sep_greater_state @ Plus @ ( the_state @ ( Plus @ ( Core @ A ) @ X5 ) ) @ ( the_state @ ( Plus @ ( Core @ A ) @ X ) ) ) ) ) ) ).

% package_logic.bigger_the
thf(fact_751_sep__algebra_Ominus__equiv__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ B @ A )
       => ( ( ( some_val @ B )
            = ( Plus @ A @ ( sep_minus_val @ Plus @ Core @ B @ A ) ) )
          & ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ B @ A ) @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.minus_equiv_def
thf(fact_752_sep__algebra_Ominus__equiv__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ B @ A )
       => ( ( ( some_state @ B )
            = ( Plus @ A @ ( sep_minus_state @ Plus @ Core @ B @ A ) ) )
          & ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ B @ A ) @ ( Core @ B ) ) ) ) ) ).

% sep_algebra.minus_equiv_def
thf(fact_753_sep__algebra_Ominus__and__plus,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Omega: val,Omega2: val,R2: val,A: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ Omega )
          = ( Plus @ Omega2 @ R2 ) )
       => ( ( sep_greater_val @ Plus @ Omega2 @ A )
         => ( ( some_val @ ( sep_minus_val @ Plus @ Core @ Omega @ A ) )
            = ( Plus @ ( sep_minus_val @ Plus @ Core @ Omega2 @ A ) @ R2 ) ) ) ) ) ).

% sep_algebra.minus_and_plus
thf(fact_754_sep__algebra_Ominus__and__plus,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Omega: state,Omega2: state,R2: state,A: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ Omega )
          = ( Plus @ Omega2 @ R2 ) )
       => ( ( sep_greater_state @ Plus @ Omega2 @ A )
         => ( ( some_state @ ( sep_minus_state @ Plus @ Core @ Omega @ A ) )
            = ( Plus @ ( sep_minus_state @ Plus @ Core @ Omega2 @ A ) @ R2 ) ) ) ) ) ).

% sep_algebra.minus_and_plus
thf(fact_755_sep__algebra_Ominus__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val,A: val,B: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ X )
          = ( Plus @ A @ B ) )
       => ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ X @ A ) @ B ) ) ) ).

% sep_algebra.minus_bigger
thf(fact_756_sep__algebra_Ominus__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state,A: state,B: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ X )
          = ( Plus @ A @ B ) )
       => ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ X @ A ) @ B ) ) ) ).

% sep_algebra.minus_bigger
thf(fact_757_sep__algebra_Ominus__sum,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A )
          = ( Plus @ B @ C ) )
       => ( ( sep_greater_val @ Plus @ X @ A )
         => ( ( sep_minus_val @ Plus @ Core @ X @ A )
            = ( sep_minus_val @ Plus @ Core @ ( sep_minus_val @ Plus @ Core @ X @ B ) @ C ) ) ) ) ) ).

% sep_algebra.minus_sum
thf(fact_758_sep__algebra_Ominus__sum,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A )
          = ( Plus @ B @ C ) )
       => ( ( sep_greater_state @ Plus @ X @ A )
         => ( ( sep_minus_state @ Plus @ Core @ X @ A )
            = ( sep_minus_state @ Plus @ Core @ ( sep_minus_state @ Plus @ Core @ X @ B ) @ C ) ) ) ) ) ).

% sep_algebra.minus_sum
thf(fact_759_sep__algebra_OminusI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ B )
          = ( Plus @ A @ X ) )
       => ( ( sep_greater_val @ Plus @ X @ ( Core @ B ) )
         => ( X
            = ( sep_minus_val @ Plus @ Core @ B @ A ) ) ) ) ) ).

% sep_algebra.minusI
thf(fact_760_sep__algebra_OminusI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ B )
          = ( Plus @ A @ X ) )
       => ( ( sep_greater_state @ Plus @ X @ ( Core @ B ) )
         => ( X
            = ( sep_minus_state @ Plus @ Core @ B @ A ) ) ) ) ) ).

% sep_algebra.minusI
thf(fact_761_package__logic_Ominus__some,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A: val,B: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A @ B )
       => ( ( some_val @ A )
          = ( Plus @ B @ ( sep_minus_val @ Plus @ Core @ A @ B ) ) ) ) ) ).

% package_logic.minus_some
thf(fact_762_package__logic_Ominus__some,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A: state,B: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A @ B )
       => ( ( some_state @ A )
          = ( Plus @ B @ ( sep_minus_state @ Plus @ Core @ A @ B ) ) ) ) ) ).

% package_logic.minus_some
thf(fact_763_package__logic_Oprove__last__completeness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A3: val,A: val,Nf1: val,F2: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_val @ Plus @ A3 @ A )
       => ( ( ( some_val @ A )
            = ( Plus @ Nf1 @ F2 ) )
         => ( sep_greater_val @ Plus @ ( sep_minus_val @ Plus @ Core @ A3 @ Nf1 ) @ F2 ) ) ) ) ).

% package_logic.prove_last_completeness
thf(fact_764_package__logic_Oprove__last__completeness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A3: state,A: state,Nf1: state,F2: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( sep_greater_state @ Plus @ A3 @ A )
       => ( ( ( some_state @ A )
            = ( Plus @ Nf1 @ F2 ) )
         => ( sep_greater_state @ Plus @ ( sep_minus_state @ Plus @ Core @ A3 @ Nf1 ) @ F2 ) ) ) ) ).

% package_logic.prove_last_completeness
thf(fact_765_sep__algebra_Osmaller__pure__sum__smaller,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Y: val,A: val,B: val,X: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_greater_val @ Plus @ Y @ A )
       => ( ( sep_greater_val @ Plus @ Y @ B )
         => ( ( ( some_val @ X )
              = ( Plus @ A @ B ) )
           => ( ( sep_pure_val @ Plus @ B )
             => ( sep_greater_val @ Plus @ Y @ X ) ) ) ) ) ) ).

% sep_algebra.smaller_pure_sum_smaller
thf(fact_766_sep__algebra_Osmaller__pure__sum__smaller,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Y: state,A: state,B: state,X: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_greater_state @ Plus @ Y @ A )
       => ( ( sep_greater_state @ Plus @ Y @ B )
         => ( ( ( some_state @ X )
              = ( Plus @ A @ B ) )
           => ( ( sep_pure_state @ Plus @ B )
             => ( sep_greater_state @ Plus @ Y @ X ) ) ) ) ) ) ).

% sep_algebra.smaller_pure_sum_smaller
thf(fact_767_sep__algebra_Ominus__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,B: val,A: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_minus_val @ Plus @ Core @ B @ A )
        = ( fun_THE_default_val @ B
          @ ^ [X2: val] :
              ( ( ( some_val @ B )
                = ( Plus @ A @ X2 ) )
              & ( sep_greater_val @ Plus @ X2 @ ( Core @ B ) ) ) ) ) ) ).

% sep_algebra.minus_def
thf(fact_768_sep__algebra_Ominus__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B: state,A: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_minus_state @ Plus @ Core @ B @ A )
        = ( fun_TH8221542053827138557_state @ B
          @ ^ [X2: state] :
              ( ( ( some_state @ B )
                = ( Plus @ A @ X2 ) )
              & ( sep_greater_state @ Plus @ X2 @ ( Core @ B ) ) ) ) ) ) ).

% sep_algebra.minus_def
thf(fact_769_package__logic_Osat__star__exists__bigger,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,A4: aassertion_val,B4: aassertion_val,Phi: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_val @ Plus @ ( aStar_val @ A4 @ B4 ) @ Phi )
       => ( ( packag5732365195153136185on_val @ Plus @ Core @ A4 )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ B4 )
           => ? [A6: val,B6: val] :
                ( ( sep_greater_val @ Plus @ ( Core @ A6 ) @ ( Core @ Phi ) )
                & ( sep_greater_val @ Plus @ ( Core @ B6 ) @ ( Core @ Phi ) )
                & ( ( some_val @ Phi )
                  = ( Plus @ A6 @ B6 ) )
                & ( package_sat_val @ Plus @ A4 @ A6 )
                & ( package_sat_val @ Plus @ B4 @ B6 ) ) ) ) ) ) ).

% package_logic.sat_star_exists_bigger
thf(fact_770_package__logic_Osat__star__exists__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,A4: aassertion_state,B4: aassertion_state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( package_sat_state @ Plus @ ( aStar_state @ A4 @ B4 ) @ Phi )
       => ( ( packag7298478212905792770_state @ Plus @ Core @ A4 )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ B4 )
           => ? [A6: state,B6: state] :
                ( ( sep_greater_state @ Plus @ ( Core @ A6 ) @ ( Core @ Phi ) )
                & ( sep_greater_state @ Plus @ ( Core @ B6 ) @ ( Core @ Phi ) )
                & ( ( some_state @ Phi )
                  = ( Plus @ A6 @ B6 ) )
                & ( package_sat_state @ Plus @ A4 @ A6 )
                & ( package_sat_state @ Plus @ B4 @ B6 ) ) ) ) ) ) ).

% package_logic.sat_star_exists_bigger
thf(fact_771_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,S2: set_Pr6546617632949187467al_val,A4: 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
          @ A4
          @ Phi2
          @ F
          @ S3 )
       => ( ! [A6: val,T2: val > val] :
              ( ( member331055627401653996al_val @ ( produc303288909735261391al_val @ A6 @ T2 ) @ S2 )
             => ( packag4175576287423129206er_val @ Plus @ Unit @ T2 ) )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ A4 )
           => ( ( ( packag2085742556458808647ic_val @ Plus @ ( package_sat_val @ Plus @ A4 ) )
                | ( packag3202507263771882441al_val @ Plus @ S3 ) )
             => ( ( ( some_val @ Phi )
                  = ( Plus @ Phi2 @ F ) )
                & ( Stable @ F )
                & ! [X4: produc5503543764249810261al_val] :
                    ( ( member331055627401653996al_val @ X4 @ S2 )
                   => ( produc7666680587469814684_val_o
                      @ ^ [A2: val,T4: val > val] :
                          ( ( sep_defined_val @ Plus @ A2 @ ( T4 @ F ) )
                         => ( package_sat_val @ Plus @ A4 @ ( the_val @ ( Plus @ A2 @ ( T4 @ F ) ) ) ) )
                      @ X4 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_772_package__logic_Ogeneral__soundness,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,S2: set_Pr2391701600042252046_state,A4: 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
          @ A4
          @ Phi2
          @ F
          @ S3 )
       => ( ! [A6: state,T2: state > state] :
              ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ A6 @ T2 ) @ S2 )
             => ( packag4817583915586052229_state @ Plus @ Unit @ T2 ) )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A4 )
           => ( ( ( packag8361946002163212404_state @ Plus @ ( package_sat_state @ Plus @ A4 ) )
                | ( packag4152378406607043437_state @ Plus @ S3 ) )
             => ( ( ( some_state @ Phi )
                  = ( Plus @ Phi2 @ F ) )
                & ( Stable @ F )
                & ! [X4: produc3882902684156697774_state] :
                    ( ( member6715010751053357271_state @ X4 @ S2 )
                   => ( produc3645877548210629341tate_o
                      @ ^ [A2: state,T4: state > state] :
                          ( ( sep_defined_state @ Plus @ A2 @ ( T4 @ F ) )
                         => ( package_sat_state @ Plus @ A4 @ ( the_state @ ( Plus @ A2 @ ( T4 @ F ) ) ) ) )
                      @ X4 ) ) ) ) ) ) ) ) ).

% package_logic.general_soundness
thf(fact_773_package__logic_Opackage__rhs__connectionI,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,F: val,Phi2: val,F3: val,S2: set_Pr4723104092121316667al_val,S3: set_Pr4723104092121316667al_val,Pc: val > $o,A4: aassertion_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Plus @ Phi @ F )
          = ( Plus @ Phi2 @ F3 ) )
       => ( ( Stable @ F3 )
         => ( ( sep_defined_val @ Plus @ Phi @ F )
           => ( ( sep_greater_val @ Plus @ F3 @ F )
             => ( ! [A6: val,U: val,T2: val > val] :
                    ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A6 @ ( produc303288909735261391al_val @ U @ T2 ) ) @ S2 )
                   => ? [Au: val] :
                        ( ( ( some_val @ Au )
                          = ( Plus @ A6 @ U ) )
                        & ( ( sep_defined_val @ Plus @ Au @ ( sep_minus_val @ Plus @ Core @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                         => ? [A8: val,U2: val] :
                              ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A8 @ ( produc303288909735261391al_val @ U2 @ T2 ) ) @ S3 )
                              & ( sep_greater_val @ Plus @ ( Core @ A8 ) @ ( Core @ A6 ) )
                              & ( ( Plus @ Au @ ( sep_minus_val @ Plus @ Core @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                                = ( Plus @ A8 @ U2 ) )
                              & ( sep_greater_val @ Plus @ U2 @ U )
                              & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A4 @ A8 @ U2 @ U ) ) ) ) )
               => ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connectionI
thf(fact_774_package__logic_Opackage__rhs__connectionI,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,Phi: state,F: state,Phi2: state,F3: state,S2: set_Pr4231240917283394591_state,S3: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( ( Plus @ Phi @ F )
          = ( Plus @ Phi2 @ F3 ) )
       => ( ( Stable @ F3 )
         => ( ( sep_defined_state @ Plus @ Phi @ F )
           => ( ( sep_greater_state @ Plus @ F3 @ F )
             => ( ! [A6: state,U: state,T2: state > state] :
                    ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
                   => ? [Au: state] :
                        ( ( ( some_state @ Au )
                          = ( Plus @ A6 @ U ) )
                        & ( ( sep_defined_state @ Plus @ Au @ ( sep_minus_state @ Plus @ Core @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                         => ? [A8: state,U2: state] :
                              ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A8 @ ( produc8632743443909064678_state @ U2 @ T2 ) ) @ S3 )
                              & ( sep_greater_state @ Plus @ ( Core @ A8 ) @ ( Core @ A6 ) )
                              & ( ( Plus @ Au @ ( sep_minus_state @ Plus @ Core @ ( T2 @ F3 ) @ ( T2 @ F ) ) )
                                = ( Plus @ A8 @ U2 ) )
                              & ( sep_greater_state @ Plus @ U2 @ U )
                              & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A4 @ A8 @ U2 @ U ) ) ) ) )
               => ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connectionI
thf(fact_775_package__logic_Opackage__rhs__connection__instantiate,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,F: val,S2: set_Pr4723104092121316667al_val,Pc: val > $o,A4: aassertion_val,Phi2: val,F3: val,S3: set_Pr4723104092121316667al_val,A: val,U3: val,T3: val > val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
       => ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A @ ( produc303288909735261391al_val @ U3 @ T3 ) ) @ S2 )
         => ~ ! [Au2: val] :
                ( ( ( some_val @ Au2 )
                  = ( Plus @ A @ U3 ) )
               => ~ ( ( sep_defined_val @ Plus @ Au2 @ ( sep_minus_val @ Plus @ Core @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                   => ? [A9: val,U4: val] :
                        ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A9 @ ( produc303288909735261391al_val @ U4 @ T3 ) ) @ S3 )
                        & ( sep_greater_val @ Plus @ ( Core @ A9 ) @ ( Core @ A ) )
                        & ( ( Plus @ Au2 @ ( sep_minus_val @ Plus @ Core @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                          = ( Plus @ A9 @ U4 ) )
                        & ( sep_greater_val @ Plus @ U4 @ U3 )
                        & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A4 @ A9 @ U4 @ U3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connection_instantiate
thf(fact_776_package__logic_Opackage__rhs__connection__instantiate,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,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state,A: state,U3: state,T3: state > state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
       => ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A @ ( produc8632743443909064678_state @ U3 @ T3 ) ) @ S2 )
         => ~ ! [Au2: state] :
                ( ( ( some_state @ Au2 )
                  = ( Plus @ A @ U3 ) )
               => ~ ( ( sep_defined_state @ Plus @ Au2 @ ( sep_minus_state @ Plus @ Core @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                   => ? [A9: state,U4: state] :
                        ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A9 @ ( produc8632743443909064678_state @ U4 @ T3 ) ) @ S3 )
                        & ( sep_greater_state @ Plus @ ( Core @ A9 ) @ ( Core @ A ) )
                        & ( ( Plus @ Au2 @ ( sep_minus_state @ Plus @ Core @ ( T3 @ F3 ) @ ( T3 @ F ) ) )
                          = ( Plus @ A9 @ U4 ) )
                        & ( sep_greater_state @ Plus @ U4 @ U3 )
                        & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A4 @ A9 @ U4 @ U3 ) ) ) ) ) ) ) ).

% package_logic.package_rhs_connection_instantiate
thf(fact_777_Collect__case__prod__mono,axiom,
    ! [A4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,B4: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( ord_le3852884270828607079_val_o @ A4 @ B4 )
     => ( ord_le6900622908513426738on_val @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ A4 ) ) @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_778_Collect__case__prod__mono,axiom,
    ! [A4: state > ( state > state ) > $o,B4: state > ( state > state ) > $o] :
      ( ( ord_le1106678366802930969tate_o @ A4 @ B4 )
     => ( ord_le6483787752022044334_state @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ A4 ) ) @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_779_Collect__case__prod__mono,axiom,
    ! [A4: state > produc3882902684156697774_state > $o,B4: state > produc3882902684156697774_state > $o] :
      ( ( ord_le6704609105599929480tate_o @ A4 @ B4 )
     => ( ord_le4032880777312351359_state @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ A4 ) ) @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ B4 ) ) ) ) ).

% Collect_case_prod_mono
thf(fact_780_PartialSA_Ounder__def,axiom,
    ! [A4: set_state,Omega2: state] :
      ( ( sep_under_state @ plus @ A4 @ Omega2 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Omega3: state] :
            ( ( Uu3 = Omega3 )
            & ( member_state @ Omega3 @ A4 )
            & ( greater @ Omega2 @ Omega3 ) ) ) ) ).

% PartialSA.under_def
thf(fact_781_PartialSA_Ocompleteness__aux,axiom,
    ! [S2: set_Pr4231240917283394591_state,F1: state > state > ( state > state ) > state,F2: state > state > ( state > state ) > state,Pc: state > $o,A4: aassertion_state,F: state,Phi: state] :
      ( ! [A6: state,U: state,T2: state > state] :
          ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
         => ( ( greater @ ( core @ ( F1 @ A6 @ U @ T2 ) ) @ ( core @ A6 ) )
            & ( ( some_state @ A6 )
              = ( plus @ ( F1 @ A6 @ U @ T2 ) @ ( F2 @ A6 @ U @ T2 ) ) )
            & ( ( Pc @ ( core @ A6 ) )
             => ( package_sat_state @ plus @ A4 @ ( the_state @ ( plus @ ( core @ A6 ) @ ( F1 @ A6 @ U @ T2 ) ) ) ) ) ) )
     => ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
       => ( ( packag7298478212905792770_state @ plus @ core @ A4 )
         => ( ( packag6595153354952283300_state @ plus @ core @ Pc )
           => ( ( ( stable @ F )
                & ( defined @ Phi @ F ) )
             => ? [S5: set_Pr4231240917283394591_state] :
                  ( ( packag3171892606229212990_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi @ F @ S5 )
                  & ! [X4: produc7272280185086996969_state] :
                      ( ( member7461423308196221312_state @ X4 @ S5 )
                     => ( 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 ) ) ) )
                        @ X4 ) ) ) ) ) ) ) ) ).

% PartialSA.completeness_aux
thf(fact_782_PartialSA_Ovalid__package__set__def,axiom,
    ! [S2: set_Pr4231240917283394591_state,F: state] :
      ( ( packag3877571396724326311_state @ plus @ core @ unit @ S2 @ F )
      = ( ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ 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 ) ) ) ) )
              @ X2 ) ) ) ) ).

% PartialSA.valid_package_set_def
thf(fact_783_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr523392378426063460_state] :
      ( ( packag9013619817833129428_state @ plus @ S2 )
      = ( ! [X2: produc4357056439811976324_state] :
            ( ( member5752234768399382829_state @ X2 @ S2 )
           => ( produc8801812494870056711tate_o
              @ ^ [A2: state] :
                  ( produc1745419677418529872tate_o
                  @ ^ [U6: state,P5: produc3882902684156697774_state] : ( sep_pure_state @ plus @ A2 ) )
              @ X2 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_784_PartialSA_Opure__remains__def,axiom,
    ! [S2: set_Pr4231240917283394591_state] :
      ( ( packag4152378406607043437_state @ plus @ S2 )
      = ( ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A2: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,P5: state > state] : ( sep_pure_state @ plus @ A2 ) )
              @ X2 ) ) ) ) ).

% PartialSA.pure_remains_def
thf(fact_785_package__logic_Opackage__rhs__connection__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,Phi: val,F: val,S2: set_Pr4723104092121316667al_val,Pc: val > $o,A4: aassertion_val,Phi2: val,F3: val,S3: set_Pr4723104092121316667al_val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ( packag1944724486178758143on_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
        = ( ( sep_greater_val @ Plus @ F3 @ F )
          & ( sep_defined_val @ Plus @ Phi @ F )
          & ( ( Plus @ Phi @ F )
            = ( Plus @ Phi2 @ F3 ) )
          & ( Stable @ F3 )
          & ! [X2: produc2072440392815185925al_val] :
              ( ( member5640714103519202460al_val @ X2 @ S2 )
             => ( produc6995717860488419308_val_o
                @ ^ [A2: val] :
                    ( produc7666680587469814684_val_o
                    @ ^ [U6: val,T4: val > val] :
                      ? [Au3: val] :
                        ( ( ( some_val @ Au3 )
                          = ( Plus @ A2 @ U6 ) )
                        & ( ( sep_defined_val @ Plus @ Au3 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) )
                         => ? [A13: val,U8: val] :
                              ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A13 @ ( produc303288909735261391al_val @ U8 @ T4 ) ) @ S3 )
                              & ( sep_greater_val @ Plus @ ( Core @ A13 ) @ ( Core @ A2 ) )
                              & ( ( Plus @ Au3 @ ( sep_minus_val @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) )
                                = ( Plus @ A13 @ U8 ) )
                              & ( sep_greater_val @ Plus @ U8 @ U6 )
                              & ( packag5057539306968662900at_val @ Plus @ Core @ Pc @ A4 @ A13 @ U8 @ U6 ) ) ) ) )
                @ X2 ) ) ) ) ) ).

% package_logic.package_rhs_connection_def
thf(fact_786_package__logic_Opackage__rhs__connection__def,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,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ( packag2054414653763826108_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
        = ( ( sep_greater_state @ Plus @ F3 @ F )
          & ( sep_defined_state @ Plus @ Phi @ F )
          & ( ( Plus @ Phi @ F )
            = ( Plus @ Phi2 @ F3 ) )
          & ( Stable @ F3 )
          & ! [X2: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X2 @ S2 )
             => ( produc1745419677418529872tate_o
                @ ^ [A2: state] :
                    ( produc3645877548210629341tate_o
                    @ ^ [U6: state,T4: state > state] :
                      ? [Au3: state] :
                        ( ( ( some_state @ Au3 )
                          = ( Plus @ A2 @ U6 ) )
                        & ( ( sep_defined_state @ Plus @ Au3 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) )
                         => ? [A13: state,U8: state] :
                              ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A13 @ ( produc8632743443909064678_state @ U8 @ T4 ) ) @ S3 )
                              & ( sep_greater_state @ Plus @ ( Core @ A13 ) @ ( Core @ A2 ) )
                              & ( ( Plus @ Au3 @ ( sep_minus_state @ Plus @ Core @ ( T4 @ F3 ) @ ( T4 @ F ) ) )
                                = ( Plus @ A13 @ U8 ) )
                              & ( sep_greater_state @ Plus @ U8 @ U6 )
                              & ( packag8070727096299822599_state @ Plus @ Core @ Pc @ A4 @ A13 @ U8 @ U6 ) ) ) ) )
                @ X2 ) ) ) ) ) ).

% package_logic.package_rhs_connection_def
thf(fact_787_package__logic_Ocompleteness__aux,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Unit: val,Stable: val > $o,S2: set_Pr4723104092121316667al_val,F1: val > val > ( val > val ) > val,F2: val > val > ( val > val ) > val,Pc: val > $o,A4: aassertion_val,F: val,Phi: val] :
      ( ( package_logic_val @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: val,U: val,T2: val > val] :
            ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A6 @ ( produc303288909735261391al_val @ U @ T2 ) ) @ S2 )
           => ( ( sep_greater_val @ Plus @ ( Core @ ( F1 @ A6 @ U @ T2 ) ) @ ( Core @ A6 ) )
              & ( ( some_val @ A6 )
                = ( Plus @ ( F1 @ A6 @ U @ T2 ) @ ( F2 @ A6 @ U @ T2 ) ) )
              & ( ( Pc @ ( Core @ A6 ) )
               => ( package_sat_val @ Plus @ A4 @ ( the_val @ ( Plus @ ( Core @ A6 ) @ ( F1 @ A6 @ U @ T2 ) ) ) ) ) ) )
       => ( ( packag7517340229427718612et_val @ Plus @ Core @ Unit @ S2 @ F )
         => ( ( packag5732365195153136185on_val @ Plus @ Core @ A4 )
           => ( ( packag6714868506247462167nd_val @ Plus @ Core @ Pc )
             => ( ( ( Stable @ F )
                  & ( sep_defined_val @ Plus @ Phi @ F ) )
               => ? [S5: set_Pr4723104092121316667al_val] :
                    ( ( packag2280635229005757181hs_val @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi @ F @ S5 )
                    & ! [X4: produc2072440392815185925al_val] :
                        ( ( member5640714103519202460al_val @ X4 @ S5 )
                       => ( produc6995717860488419308_val_o
                          @ ^ [A13: val] :
                              ( produc7666680587469814684_val_o
                              @ ^ [U8: val,T4: val > val] :
                                ? [A2: val,U6: val] :
                                  ( ( member5640714103519202460al_val @ ( produc7187740677493149823al_val @ A2 @ ( produc303288909735261391al_val @ U6 @ T4 ) ) @ S2 )
                                  & ( sep_greater_val @ Plus @ A13 @ ( F2 @ A2 @ U6 @ T4 ) )
                                  & ( ( Core @ A13 )
                                    = ( Core @ A2 ) ) ) )
                          @ X4 ) ) ) ) ) ) ) ) ) ).

% package_logic.completeness_aux
thf(fact_788_package__logic_Ocompleteness__aux,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Unit: state,Stable: state > $o,S2: set_Pr4231240917283394591_state,F1: state > state > ( state > state ) > state,F2: state > state > ( state > state ) > state,Pc: state > $o,A4: aassertion_state,F: state,Phi: state] :
      ( ( package_logic_state @ Plus @ Core @ Unit @ Stable )
     => ( ! [A6: state,U: state,T2: state > state] :
            ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ A6 @ ( produc8632743443909064678_state @ U @ T2 ) ) @ S2 )
           => ( ( sep_greater_state @ Plus @ ( Core @ ( F1 @ A6 @ U @ T2 ) ) @ ( Core @ A6 ) )
              & ( ( some_state @ A6 )
                = ( Plus @ ( F1 @ A6 @ U @ T2 ) @ ( F2 @ A6 @ U @ T2 ) ) )
              & ( ( Pc @ ( Core @ A6 ) )
               => ( package_sat_state @ Plus @ A4 @ ( the_state @ ( Plus @ ( Core @ A6 ) @ ( F1 @ A6 @ U @ T2 ) ) ) ) ) ) )
       => ( ( packag3877571396724326311_state @ Plus @ Core @ Unit @ S2 @ F )
         => ( ( packag7298478212905792770_state @ Plus @ Core @ A4 )
           => ( ( packag6595153354952283300_state @ Plus @ Core @ Pc )
             => ( ( ( Stable @ F )
                  & ( sep_defined_state @ Plus @ Phi @ F ) )
               => ? [S5: set_Pr4231240917283394591_state] :
                    ( ( packag3171892606229212990_state @ Plus @ Core @ Stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi @ F @ S5 )
                    & ! [X4: produc7272280185086996969_state] :
                        ( ( member7461423308196221312_state @ X4 @ S5 )
                       => ( 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 )
                                  & ( sep_greater_state @ Plus @ A13 @ ( F2 @ A2 @ U6 @ T4 ) )
                                  & ( ( Core @ A13 )
                                    = ( Core @ A2 ) ) ) )
                          @ X4 ) ) ) ) ) ) ) ) ) ).

% package_logic.completeness_aux
thf(fact_789_PartialSA_Opackage__rhs__connection__def,axiom,
    ! [Phi: state,F: state,S2: set_Pr4231240917283394591_state,Pc: state > $o,A4: aassertion_state,Phi2: state,F3: state,S3: set_Pr4231240917283394591_state] :
      ( ( packag2054414653763826108_state @ plus @ core @ stable @ Phi @ F @ S2 @ Pc @ A4 @ Phi2 @ F3 @ S3 )
      = ( ( greater @ F3 @ F )
        & ( defined @ Phi @ F )
        & ( ( plus @ Phi @ F )
          = ( plus @ Phi2 @ F3 ) )
        & ( stable @ F3 )
        & ! [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ S2 )
           => ( produc1745419677418529872tate_o
              @ ^ [A2: state] :
                  ( produc3645877548210629341tate_o
                  @ ^ [U6: state,T4: state > state] :
                    ? [Au3: state] :
                      ( ( ( some_state @ Au3 )
                        = ( plus @ A2 @ U6 ) )
                      & ( ( defined @ Au3 @ ( minus @ ( T4 @ F3 ) @ ( 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 @ F3 ) @ ( T4 @ F ) ) )
                              = ( plus @ A13 @ U8 ) )
                            & ( greater @ U8 @ U6 )
                            & ( packag8070727096299822599_state @ plus @ core @ Pc @ A4 @ A13 @ U8 @ U6 ) ) ) ) )
              @ X2 ) ) ) ) ).

% PartialSA.package_rhs_connection_def
thf(fact_790_Ball__Collect,axiom,
    ( ball_P7403102246598991807_state
    = ( ^ [A7: set_Pr4231240917283394591_state,P4: produc7272280185086996969_state > $o] : ( ord_le4032880777312351359_state @ A7 @ ( collec906845016635587262_state @ P4 ) ) ) ) ).

% Ball_Collect
thf(fact_791_Ball__Collect,axiom,
    ( ball_P2871712132005019634on_val
    = ( ^ [A7: set_Pr7649655576376376530on_val,P4: produc9003781588162623004on_val > $o] : ( ord_le6900622908513426738on_val @ A7 @ ( collec7475294502966882545on_val @ P4 ) ) ) ) ).

% Ball_Collect
thf(fact_792_Ball__Collect,axiom,
    ( ball_state
    = ( ^ [A7: set_state,P4: state > $o] : ( ord_le2494988322063910608_state @ A7 @ ( collect_state @ P4 ) ) ) ) ).

% Ball_Collect
thf(fact_793_PartialSA_Oupper__closure__def,axiom,
    ! [A4: set_state] :
      ( ( sep_up1246176804924251236_state @ plus @ A4 )
      = ( collect_state
        @ ^ [Uu3: state] :
          ? [Phi3: state,Phi4: state] :
            ( ( Uu3 = Phi3 )
            & ( greater @ Phi3 @ Phi4 )
            & ( member_state @ Phi4 @ A4 ) ) ) ) ).

% PartialSA.upper_closure_def
thf(fact_794_cwand__def,axiom,
    ( cwand
    = ( ^ [A7: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A2: state,X2: state] :
                  ( ( ( member_state @ A2 @ A7 )
                    & ( ( some_state @ X2 )
                      = ( plus @ ( r @ A2 @ W2 ) @ A2 ) ) )
                 => ( member_state @ X2 @ B5 ) ) ) ) ) ) ).

% cwand_def
thf(fact_795_wand__def,axiom,
    ( wand
    = ( ^ [A7: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [W2: state] :
              ( ( Uu3 = W2 )
              & ! [A2: state,X2: state] :
                  ( ( ( member_state @ A2 @ A7 )
                    & ( ( some_state @ X2 )
                      = ( plus @ W2 @ A2 ) ) )
                 => ( member_state @ X2 @ B5 ) ) ) ) ) ) ).

% wand_def
thf(fact_796_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_797_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_798_image__mono,axiom,
    ! [A4: set_state,B4: set_state,F: state > state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_mono
thf(fact_799_image__subsetI,axiom,
    ! [A4: set_state,F: state > state,B4: set_state] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_800_image__subsetI,axiom,
    ! [A4: set_state,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_801_image__subsetI,axiom,
    ! [A4: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > state,B4: set_state] :
      ( ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_6759111139246981411_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_802_image__subsetI,axiom,
    ! [A4: set_state,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member7461423308196221312_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_803_image__subsetI,axiom,
    ! [A4: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_804_image__subsetI,axiom,
    ! [A4: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_508898238547643525_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_805_image__subsetI,axiom,
    ! [A4: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_806_image__subsetI,axiom,
    ! [A4: set_Pr2391701600042252046_state,F: produc3882902684156697774_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: produc3882902684156697774_state] :
          ( ( member6715010751053357271_state @ X3 @ A4 )
         => ( member7461423308196221312_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_4364510454419742290_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_807_image__subsetI,axiom,
    ! [A4: set_Pr4231240917283394591_state,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( member7461423308196221312_state @ X3 @ A4 )
         => ( member7461423308196221312_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_808_image__subsetI,axiom,
    ! [A4: set_state,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X3: state] :
          ( ( member_state @ X3 @ A4 )
         => ( member2879030624002546611on_val @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ A4 ) @ B4 ) ) ).

% image_subsetI
thf(fact_809_subset__imageE,axiom,
    ! [B4: set_state,F: state > state,A4: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A4 ) )
     => ~ ! [C5: set_state] :
            ( ( ord_le2494988322063910608_state @ C5 @ A4 )
           => ( B4
             != ( image_state_state @ F @ C5 ) ) ) ) ).

% subset_imageE
thf(fact_810_image__subset__iff,axiom,
    ! [F: state > state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ B4 )
      = ( ! [X2: state] :
            ( ( member_state @ X2 @ A4 )
           => ( member_state @ ( F @ X2 ) @ B4 ) ) ) ) ).

% image_subset_iff
thf(fact_811_subset__image__iff,axiom,
    ! [B4: set_state,F: state > state,A4: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ ( image_state_state @ F @ A4 ) )
      = ( ? [AA: set_state] :
            ( ( ord_le2494988322063910608_state @ AA @ A4 )
            & ( B4
              = ( image_state_state @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_812_multiply__sem__assertion_Oelims,axiom,
    ! [X: prat,Xa2: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X @ Xa2 )
        = Y )
     => ( Y
        = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X ) @ Xa2 ) ) ) ) ).

% multiply_sem_assertion.elims
thf(fact_813_multiply__sem__assertion_Opelims,axiom,
    ! [X: prat,Xa2: set_state,Y: set_state] :
      ( ( ( multip8064567061438756306ertion @ X @ Xa2 )
        = Y )
     => ( ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X @ Xa2 ) )
       => ~ ( ( Y
              = ( sep_up1246176804924251236_state @ plus @ ( image_state_state @ ( multiply @ X ) @ Xa2 ) ) )
           => ~ ( accp_P6554740477754186410_state @ multip8073008153270241703on_rel @ ( produc9080284787853255769_state @ X @ Xa2 ) ) ) ) ) ).

% multiply_sem_assertion.pelims
thf(fact_814_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > state,B4: set_state] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_state_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_815_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_5311902671526399277_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_816_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
         => ( member7461423308196221312_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_632992669292831658_state @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_817_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > state,B4: set_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_2710133271811360426_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_818_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_7466395622266389182_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_819_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
         => ( member7461423308196221312_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le4032880777312351359_state @ ( image_3064086290059306969_state @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_820_image__Collect__subsetI,axiom,
    ! [P2: state > $o,F: state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X3: state] :
          ( ( P2 @ X3 )
         => ( member2879030624002546611on_val @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_4772210114854293981on_val @ F @ ( collect_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_821_image__Collect__subsetI,axiom,
    ! [P2: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > state,B4: set_state] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( P2 @ X3 )
         => ( member_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le2494988322063910608_state @ ( image_1205529093420515805_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_822_image__Collect__subsetI,axiom,
    ! [P2: produc9003781588162623004on_val > $o,F: produc9003781588162623004on_val > produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc9003781588162623004on_val] :
          ( ( P2 @ X3 )
         => ( member6715010751053357271_state @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6483787752022044334_state @ ( image_4494208899119068747_state @ F @ ( collec7475294502966882545on_val @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_823_image__Collect__subsetI,axiom,
    ! [P2: produc7272280185086996969_state > $o,F: produc7272280185086996969_state > produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ! [X3: produc7272280185086996969_state] :
          ( ( P2 @ X3 )
         => ( member2879030624002546611on_val @ ( F @ X3 ) @ B4 ) )
     => ( ord_le6900622908513426738on_val @ ( image_3393013468800240652on_val @ F @ ( collec906845016635587262_state @ P2 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_824_all__subset__image,axiom,
    ! [F: state > state,A4: set_state,P2: set_state > $o] :
      ( ( ! [B5: set_state] :
            ( ( ord_le2494988322063910608_state @ B5 @ ( image_state_state @ F @ A4 ) )
           => ( P2 @ B5 ) ) )
      = ( ! [B5: set_state] :
            ( ( ord_le2494988322063910608_state @ B5 @ A4 )
           => ( P2 @ ( image_state_state @ F @ B5 ) ) ) ) ) ).

% all_subset_image
thf(fact_825_multiply__sem__assertion_Ocases,axiom,
    ! [X: produc6251377953716854561_state] :
      ~ ! [P: prat,P7: set_state] :
          ( X
         != ( produc9080284787853255769_state @ P @ P7 ) ) ).

% multiply_sem_assertion.cases
thf(fact_826_None__notin__image__Some,axiom,
    ! [A4: set_state] :
      ~ ( member_option_state @ none_state @ ( image_6076465424260689483_state @ some_state @ A4 ) ) ).

% None_notin_image_Some
thf(fact_827_None__notin__image__Some,axiom,
    ! [A4: set_val] :
      ~ ( member_option_val @ none_val @ ( image_val_option_val @ some_val @ A4 ) ) ).

% None_notin_image_Some
thf(fact_828_prop__restrict,axiom,
    ! [X: produc3882902684156697774_state,Z6: set_Pr2391701600042252046_state,X7: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ( member6715010751053357271_state @ X @ Z6 )
     => ( ( ord_le6483787752022044334_state @ Z6
          @ ( collec394671971739345689_state
            @ ^ [X2: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X2 @ X7 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_829_prop__restrict,axiom,
    ! [X: produc7272280185086996969_state,Z6: set_Pr4231240917283394591_state,X7: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( member7461423308196221312_state @ X @ Z6 )
     => ( ( ord_le4032880777312351359_state @ Z6
          @ ( collec906845016635587262_state
            @ ^ [X2: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X2 @ X7 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_830_prop__restrict,axiom,
    ! [X: produc9003781588162623004on_val,Z6: set_Pr7649655576376376530on_val,X7: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( member2879030624002546611on_val @ X @ Z6 )
     => ( ( ord_le6900622908513426738on_val @ Z6
          @ ( collec7475294502966882545on_val
            @ ^ [X2: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X2 @ X7 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_831_prop__restrict,axiom,
    ! [X: state,Z6: set_state,X7: set_state,P2: state > $o] :
      ( ( member_state @ X @ Z6 )
     => ( ( ord_le2494988322063910608_state @ Z6
          @ ( collect_state
            @ ^ [X2: state] :
                ( ( member_state @ X2 @ X7 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_832_Collect__restrict,axiom,
    ! [X7: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ord_le6483787752022044334_state
      @ ( collec394671971739345689_state
        @ ^ [X2: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X2 @ X7 )
            & ( P2 @ X2 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_833_Collect__restrict,axiom,
    ! [X7: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ord_le4032880777312351359_state
      @ ( collec906845016635587262_state
        @ ^ [X2: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X2 @ X7 )
            & ( P2 @ X2 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_834_Collect__restrict,axiom,
    ! [X7: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ord_le6900622908513426738on_val
      @ ( collec7475294502966882545on_val
        @ ^ [X2: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X2 @ X7 )
            & ( P2 @ X2 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_835_Collect__restrict,axiom,
    ! [X7: set_state,P2: state > $o] :
      ( ord_le2494988322063910608_state
      @ ( collect_state
        @ ^ [X2: state] :
            ( ( member_state @ X2 @ X7 )
            & ( P2 @ X2 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_836_comp__one__def,axiom,
    ( comp_one
    = ( ^ [P5: prat] :
          ( fChoice_prat
          @ ^ [R: prat] :
              ( ( padd @ P5 @ R )
              = pwrite ) ) ) ) ).

% comp_one_def
thf(fact_837_conj__subset__def,axiom,
    ! [A4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ A4
        @ ( collec906845016635587262_state
          @ ^ [X2: produc7272280185086996969_state] :
              ( ( P2 @ X2 )
              & ( Q @ X2 ) ) ) )
      = ( ( ord_le4032880777312351359_state @ A4 @ ( collec906845016635587262_state @ P2 ) )
        & ( ord_le4032880777312351359_state @ A4 @ ( collec906845016635587262_state @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_838_conj__subset__def,axiom,
    ! [A4: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ A4
        @ ( collec7475294502966882545on_val
          @ ^ [X2: produc9003781588162623004on_val] :
              ( ( P2 @ X2 )
              & ( Q @ X2 ) ) ) )
      = ( ( ord_le6900622908513426738on_val @ A4 @ ( collec7475294502966882545on_val @ P2 ) )
        & ( ord_le6900622908513426738on_val @ A4 @ ( collec7475294502966882545on_val @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_839_conj__subset__def,axiom,
    ! [A4: set_state,P2: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ A4
        @ ( collect_state
          @ ^ [X2: state] :
              ( ( P2 @ X2 )
              & ( Q @ X2 ) ) ) )
      = ( ( ord_le2494988322063910608_state @ A4 @ ( collect_state @ P2 ) )
        & ( ord_le2494988322063910608_state @ A4 @ ( collect_state @ Q ) ) ) ) ).

% conj_subset_def
thf(fact_840_subset__CollectI,axiom,
    ! [B4: set_Pr2391701600042252046_state,A4: set_Pr2391701600042252046_state,Q: produc3882902684156697774_state > $o,P2: produc3882902684156697774_state > $o] :
      ( ( ord_le6483787752022044334_state @ B4 @ A4 )
     => ( ! [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ B4 )
           => ( ( Q @ X3 )
             => ( P2 @ X3 ) ) )
       => ( ord_le6483787752022044334_state
          @ ( collec394671971739345689_state
            @ ^ [X2: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X2 @ B4 )
                & ( Q @ X2 ) ) )
          @ ( collec394671971739345689_state
            @ ^ [X2: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_841_subset__CollectI,axiom,
    ! [B4: set_Pr4231240917283394591_state,A4: set_Pr4231240917283394591_state,Q: produc7272280185086996969_state > $o,P2: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ B4 @ A4 )
     => ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ B4 )
           => ( ( Q @ X3 )
             => ( P2 @ X3 ) ) )
       => ( ord_le4032880777312351359_state
          @ ( collec906845016635587262_state
            @ ^ [X2: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X2 @ B4 )
                & ( Q @ X2 ) ) )
          @ ( collec906845016635587262_state
            @ ^ [X2: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_842_subset__CollectI,axiom,
    ! [B4: set_Pr7649655576376376530on_val,A4: set_Pr7649655576376376530on_val,Q: produc9003781588162623004on_val > $o,P2: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ B4 @ A4 )
     => ( ! [X3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ B4 )
           => ( ( Q @ X3 )
             => ( P2 @ X3 ) ) )
       => ( ord_le6900622908513426738on_val
          @ ( collec7475294502966882545on_val
            @ ^ [X2: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X2 @ B4 )
                & ( Q @ X2 ) ) )
          @ ( collec7475294502966882545on_val
            @ ^ [X2: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_843_subset__CollectI,axiom,
    ! [B4: set_state,A4: set_state,Q: state > $o,P2: state > $o] :
      ( ( ord_le2494988322063910608_state @ B4 @ A4 )
     => ( ! [X3: state] :
            ( ( member_state @ X3 @ B4 )
           => ( ( Q @ X3 )
             => ( P2 @ X3 ) ) )
       => ( ord_le2494988322063910608_state
          @ ( collect_state
            @ ^ [X2: state] :
                ( ( member_state @ X2 @ B4 )
                & ( Q @ X2 ) ) )
          @ ( collect_state
            @ ^ [X2: state] :
                ( ( member_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_844_subset__Collect__iff,axiom,
    ! [B4: set_Pr2391701600042252046_state,A4: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o] :
      ( ( ord_le6483787752022044334_state @ B4 @ A4 )
     => ( ( ord_le6483787752022044334_state @ B4
          @ ( collec394671971739345689_state
            @ ^ [X2: produc3882902684156697774_state] :
                ( ( member6715010751053357271_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) )
        = ( ! [X2: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ X2 @ B4 )
             => ( P2 @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_845_subset__Collect__iff,axiom,
    ! [B4: set_Pr4231240917283394591_state,A4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ B4 @ A4 )
     => ( ( ord_le4032880777312351359_state @ B4
          @ ( collec906845016635587262_state
            @ ^ [X2: produc7272280185086996969_state] :
                ( ( member7461423308196221312_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) )
        = ( ! [X2: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ X2 @ B4 )
             => ( P2 @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_846_subset__Collect__iff,axiom,
    ! [B4: set_Pr7649655576376376530on_val,A4: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ B4 @ A4 )
     => ( ( ord_le6900622908513426738on_val @ B4
          @ ( collec7475294502966882545on_val
            @ ^ [X2: produc9003781588162623004on_val] :
                ( ( member2879030624002546611on_val @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) )
        = ( ! [X2: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ X2 @ B4 )
             => ( P2 @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_847_subset__Collect__iff,axiom,
    ! [B4: set_state,A4: set_state,P2: state > $o] :
      ( ( ord_le2494988322063910608_state @ B4 @ A4 )
     => ( ( ord_le2494988322063910608_state @ B4
          @ ( collect_state
            @ ^ [X2: state] :
                ( ( member_state @ X2 @ A4 )
                & ( P2 @ X2 ) ) ) )
        = ( ! [X2: state] :
              ( ( member_state @ X2 @ B4 )
             => ( P2 @ X2 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_848_Some__image__these__eq,axiom,
    ! [A4: set_option_state] :
      ( ( image_6076465424260689483_state @ some_state @ ( these_state @ A4 ) )
      = ( collect_option_state
        @ ^ [X2: option_state] :
            ( ( member_option_state @ X2 @ A4 )
            & ( X2 != none_state ) ) ) ) ).

% Some_image_these_eq
thf(fact_849_Some__image__these__eq,axiom,
    ! [A4: set_option_val] :
      ( ( image_val_option_val @ some_val @ ( these_val @ A4 ) )
      = ( collect_option_val
        @ ^ [X2: option_val] :
            ( ( member_option_val @ X2 @ A4 )
            & ( X2 != none_val ) ) ) ) ).

% Some_image_these_eq
thf(fact_850_these__image__Some__eq,axiom,
    ! [A4: set_state] :
      ( ( these_state @ ( image_6076465424260689483_state @ some_state @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_851_these__image__Some__eq,axiom,
    ! [A4: set_val] :
      ( ( these_val @ ( image_val_option_val @ some_val @ A4 ) )
      = A4 ) ).

% these_image_Some_eq
thf(fact_852_Option_Othese__def,axiom,
    ( these_state
    = ( ^ [A7: set_option_state] :
          ( image_3532137647693456075_state @ the_state
          @ ( collect_option_state
            @ ^ [X2: option_state] :
                ( ( member_option_state @ X2 @ A7 )
                & ( X2 != none_state ) ) ) ) ) ) ).

% Option.these_def
thf(fact_853_Option_Othese__def,axiom,
    ( these_val
    = ( ^ [A7: set_option_val] :
          ( image_option_val_val @ the_val
          @ ( collect_option_val
            @ ^ [X2: option_val] :
                ( ( member_option_val @ X2 @ A7 )
                & ( X2 != none_val ) ) ) ) ) ) ).

% Option.these_def
thf(fact_854_in__these__eq,axiom,
    ! [X: produc7272280185086996969_state,A4: set_op8023886964038656367_state] :
      ( ( member7461423308196221312_state @ X @ ( these_4347185934205712492_state @ A4 ) )
      = ( member3894984953261475024_state @ ( some_P6297086604321900740_state @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_855_in__these__eq,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_op6240181410663953058on_val] :
      ( ( member2879030624002546611on_val @ X @ ( these_3919539662624406175on_val @ A4 ) )
      = ( member4602090469187516291on_val @ ( some_P2581650809551911671on_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_856_in__these__eq,axiom,
    ! [X: produc3882902684156697774_state,A4: set_op3387789762728285652_state] :
      ( ( member6715010751053357271_state @ X @ ( these_7452845017025203435_state @ A4 ) )
      = ( member5919342556599141533_state @ ( some_P5383513176685068947_state @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_857_in__these__eq,axiom,
    ! [X: state,A4: set_option_state] :
      ( ( member_state @ X @ ( these_state @ A4 ) )
      = ( member_option_state @ ( some_state @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_858_in__these__eq,axiom,
    ! [X: val,A4: set_option_val] :
      ( ( member_val @ X @ ( these_val @ A4 ) )
      = ( member_option_val @ ( some_val @ X ) @ A4 ) ) ).

% in_these_eq
thf(fact_859_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( sep_ad8203089552910907580_state @ Plus @ A4 @ B4 )
        = ( collec394671971739345689_state
          @ ^ [Uu3: produc3882902684156697774_state] :
            ? [Phi4: produc3882902684156697774_state,A2: produc3882902684156697774_state,B2: produc3882902684156697774_state] :
              ( ( Uu3 = Phi4 )
              & ( member6715010751053357271_state @ A2 @ A4 )
              & ( member6715010751053357271_state @ B2 @ B4 )
              & ( ( some_P5383513176685068947_state @ Phi4 )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_860_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( sep_ad3908482799505143387_state @ Plus @ A4 @ B4 )
        = ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [Phi4: produc7272280185086996969_state,A2: produc7272280185086996969_state,B2: produc7272280185086996969_state] :
              ( ( Uu3 = Phi4 )
              & ( member7461423308196221312_state @ A2 @ A4 )
              & ( member7461423308196221312_state @ B2 @ B4 )
              & ( ( some_P6297086604321900740_state @ Phi4 )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_861_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( sep_ad8320153009520438926on_val @ Plus @ A4 @ B4 )
        = ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [Phi4: produc9003781588162623004on_val,A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
              ( ( Uu3 = Phi4 )
              & ( member2879030624002546611on_val @ A2 @ A4 )
              & ( member2879030624002546611on_val @ B2 @ B4 )
              & ( ( some_P2581650809551911671on_val @ Phi4 )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_862_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A4: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( sep_add_set_val @ Plus @ A4 @ B4 )
        = ( collect_val
          @ ^ [Uu3: val] :
            ? [Phi4: val,A2: val,B2: val] :
              ( ( Uu3 = Phi4 )
              & ( member_val @ A2 @ A4 )
              & ( member_val @ B2 @ B4 )
              & ( ( some_val @ Phi4 )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_863_sep__algebra_Oadd__set__def,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A4: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_add_set_state @ Plus @ A4 @ B4 )
        = ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state,A2: state,B2: state] :
              ( ( Uu3 = Phi4 )
              & ( member_state @ A2 @ A4 )
              & ( member_state @ B2 @ B4 )
              & ( ( some_state @ Phi4 )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.add_set_def
thf(fact_864_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ X @ ( sep_ad3908482799505143387_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B2: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ A2 @ A4 )
              & ( member7461423308196221312_state @ B2 @ B4 )
              & ( ( some_P6297086604321900740_state @ X )
                = ( sep_sp9219505543755390023_state @ Plus @ ( some_P6297086604321900740_state @ A2 ) @ ( some_P6297086604321900740_state @ B2 ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_865_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ X @ ( sep_ad8320153009520438926on_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ A2 @ A4 )
              & ( member2879030624002546611on_val @ B2 @ B4 )
              & ( ( some_P2581650809551911671on_val @ X )
                = ( sep_sp4146280900173761658on_val @ Plus @ ( some_P2581650809551911671on_val @ A2 ) @ ( some_P2581650809551911671on_val @ B2 ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_866_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ X @ ( sep_ad8203089552910907580_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B2: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ A2 @ A4 )
              & ( member6715010751053357271_state @ B2 @ B4 )
              & ( ( some_P5383513176685068947_state @ X )
                = ( sep_sp7584349535955199440_state @ Plus @ ( some_P5383513176685068947_state @ A2 ) @ ( some_P5383513176685068947_state @ B2 ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_867_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val,A4: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ X @ ( sep_add_set_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: val,B2: val] :
              ( ( member_val @ A2 @ A4 )
              & ( member_val @ B2 @ B4 )
              & ( ( some_val @ X )
                = ( sep_splus_val @ Plus @ ( some_val @ A2 ) @ ( some_val @ B2 ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_868_sep__algebra_Ox__elem__set__product__splus,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state,A4: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ X @ ( sep_add_set_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: state,B2: state] :
              ( ( member_state @ A2 @ A4 )
              & ( member_state @ B2 @ B4 )
              & ( ( some_state @ X )
                = ( sep_splus_state @ Plus @ ( some_state @ A2 ) @ ( some_state @ B2 ) ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product_splus
thf(fact_869_graph__def,axiom,
    ( graph_7551141711029462004_state
    = ( ^ [M5: state > option886743748074664436_state] :
          ( collec906845016635587262_state
          @ ^ [Uu3: produc7272280185086996969_state] :
            ? [A2: state,B2: produc3882902684156697774_state] :
              ( ( Uu3
                = ( produc5886875603596089627_state @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_P5383513176685068947_state @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_870_graph__def,axiom,
    ( graph_628825510059920660_state
    = ( ^ [M5: option_state > option_option_state] :
          ( collec8144523193623705312_state
          @ ^ [Uu3: produc3142500478612311029_state] :
            ? [A2: option_state,B2: option_state] :
              ( ( Uu3
                = ( produc9160152616361873709_state @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_option_state @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_871_graph__def,axiom,
    ( graph_prat_set_state
    = ( ^ [M5: prat > option_set_state] :
          ( collec5094083866753559820_state
          @ ^ [Uu3: produc6251377953716854561_state] :
            ? [A2: prat,B2: set_state] :
              ( ( Uu3
                = ( produc9080284787853255769_state @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_set_state @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_872_graph__def,axiom,
    ( graph_nat_list_char
    = ( ^ [M5: nat > option_list_char] :
          ( collec2458894688891239037t_char
          @ ^ [Uu3: produc1457211279475724562t_char] :
            ? [A2: nat,B2: list_char] :
              ( ( Uu3
                = ( produc120197956887798346t_char @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_list_char @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_873_graph__def,axiom,
    ( graph_1288227317702120175on_val
    = ( ^ [M5: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
          ( collec7475294502966882545on_val
          @ ^ [Uu3: produc9003781588162623004on_val] :
            ? [A2: produc1457211279475724562t_char > prat,B2: produc1457211279475724562t_char > option_val] :
              ( ( Uu3
                = ( produc74620467203698198on_val @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_P7669353234731512949on_val @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_874_graph__def,axiom,
    ( graph_prat_state
    = ( ^ [M5: prat > option_state] :
          ( collec9096564466166568534_state
          @ ^ [Uu3: produc4844402304972151915_state] :
            ? [A2: prat,B2: state] :
              ( ( Uu3
                = ( produc6205719116230455971_state @ A2 @ B2 ) )
              & ( ( M5 @ A2 )
                = ( some_state @ B2 ) ) ) ) ) ) ).

% graph_def
thf(fact_875_in__graphI,axiom,
    ! [M: state > option886743748074664436_state,K: state,V: produc3882902684156697774_state] :
      ( ( ( M @ K )
        = ( some_P5383513176685068947_state @ V ) )
     => ( member7461423308196221312_state @ ( produc5886875603596089627_state @ K @ V ) @ ( graph_7551141711029462004_state @ M ) ) ) ).

% in_graphI
thf(fact_876_in__graphI,axiom,
    ! [M: state > option_state_state,K: state,V: state > state] :
      ( ( ( M @ K )
        = ( some_state_state @ V ) )
     => ( member6715010751053357271_state @ ( produc8632743443909064678_state @ K @ V ) @ ( graph_5871261288037090637_state @ M ) ) ) ).

% in_graphI
thf(fact_877_in__graphI,axiom,
    ! [M: option_state > option_option_state,K: option_state,V: option_state] :
      ( ( ( M @ K )
        = ( some_option_state @ V ) )
     => ( member3029510603097127326_state @ ( produc9160152616361873709_state @ K @ V ) @ ( graph_628825510059920660_state @ M ) ) ) ).

% in_graphI
thf(fact_878_in__graphI,axiom,
    ! [M: prat > option_set_state,K: prat,V: set_state] :
      ( ( ( M @ K )
        = ( some_set_state @ V ) )
     => ( member6708919011922255306_state @ ( produc9080284787853255769_state @ K @ V ) @ ( graph_prat_set_state @ M ) ) ) ).

% in_graphI
thf(fact_879_in__graphI,axiom,
    ! [M: nat > option_list_char,K: nat,V: list_char] :
      ( ( ( M @ K )
        = ( some_list_char @ V ) )
     => ( member484235747325421115t_char @ ( produc120197956887798346t_char @ K @ V ) @ ( graph_nat_list_char @ M ) ) ) ).

% in_graphI
thf(fact_880_in__graphI,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,V: produc1457211279475724562t_char > option_val] :
      ( ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V ) )
     => ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V ) @ ( graph_1288227317702120175on_val @ M ) ) ) ).

% in_graphI
thf(fact_881_in__graphI,axiom,
    ! [M: prat > option_state,K: prat,V: state] :
      ( ( ( M @ K )
        = ( some_state @ V ) )
     => ( member6226390569306242836_state @ ( produc6205719116230455971_state @ K @ V ) @ ( graph_prat_state @ M ) ) ) ).

% in_graphI
thf(fact_882_in__graphD,axiom,
    ! [K: state,V: produc3882902684156697774_state,M: state > option886743748074664436_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ K @ V ) @ ( graph_7551141711029462004_state @ M ) )
     => ( ( M @ K )
        = ( some_P5383513176685068947_state @ V ) ) ) ).

% in_graphD
thf(fact_883_in__graphD,axiom,
    ! [K: state,V: state > state,M: state > option_state_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ K @ V ) @ ( graph_5871261288037090637_state @ M ) )
     => ( ( M @ K )
        = ( some_state_state @ V ) ) ) ).

% in_graphD
thf(fact_884_in__graphD,axiom,
    ! [K: option_state,V: option_state,M: option_state > option_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ K @ V ) @ ( graph_628825510059920660_state @ M ) )
     => ( ( M @ K )
        = ( some_option_state @ V ) ) ) ).

% in_graphD
thf(fact_885_in__graphD,axiom,
    ! [K: prat,V: set_state,M: prat > option_set_state] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ K @ V ) @ ( graph_prat_set_state @ M ) )
     => ( ( M @ K )
        = ( some_set_state @ V ) ) ) ).

% in_graphD
thf(fact_886_in__graphD,axiom,
    ! [K: nat,V: list_char,M: nat > option_list_char] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ K @ V ) @ ( graph_nat_list_char @ M ) )
     => ( ( M @ K )
        = ( some_list_char @ V ) ) ) ).

% in_graphD
thf(fact_887_in__graphD,axiom,
    ! [K: produc1457211279475724562t_char > prat,V: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V ) @ ( graph_1288227317702120175on_val @ M ) )
     => ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V ) ) ) ).

% in_graphD
thf(fact_888_in__graphD,axiom,
    ! [K: prat,V: state,M: prat > option_state] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ K @ V ) @ ( graph_prat_state @ M ) )
     => ( ( M @ K )
        = ( some_state @ V ) ) ) ).

% in_graphD
thf(fact_889_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,Phi: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ Phi @ ( sep_ad3908482799505143387_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B2: produc7272280185086996969_state] :
              ( ( ( some_P6297086604321900740_state @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( member7461423308196221312_state @ A2 @ A4 )
              & ( member7461423308196221312_state @ B2 @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_890_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,Phi: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ Phi @ ( sep_ad8320153009520438926on_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
              ( ( ( some_P2581650809551911671on_val @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( member2879030624002546611on_val @ A2 @ A4 )
              & ( member2879030624002546611on_val @ B2 @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_891_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,Phi: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ Phi @ ( sep_ad8203089552910907580_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B2: produc3882902684156697774_state] :
              ( ( ( some_P5383513176685068947_state @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( member6715010751053357271_state @ A2 @ A4 )
              & ( member6715010751053357271_state @ B2 @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_892_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: val > val > option_val,Core: val > val,Phi: val,A4: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ Phi @ ( sep_add_set_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: val,B2: val] :
              ( ( ( some_val @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( member_val @ A2 @ A4 )
              & ( member_val @ B2 @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_893_sep__algebra_Oadd__set__elem,axiom,
    ! [Plus: state > state > option_state,Core: state > state,Phi: state,A4: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ Phi @ ( sep_add_set_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: state,B2: state] :
              ( ( ( some_state @ Phi )
                = ( Plus @ A2 @ B2 ) )
              & ( member_state @ A2 @ A4 )
              & ( member_state @ B2 @ B4 ) ) ) ) ) ).

% sep_algebra.add_set_elem
thf(fact_894_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc7272280185086996969_state > produc7272280185086996969_state > option2747342629145793465_state,Core: produc7272280185086996969_state > produc7272280185086996969_state,X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( sep_al4323785819428540618_state @ Plus @ Core )
     => ( ( member7461423308196221312_state @ X @ ( sep_ad3908482799505143387_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc7272280185086996969_state,B2: produc7272280185086996969_state] :
              ( ( member7461423308196221312_state @ A2 @ A4 )
              & ( member7461423308196221312_state @ B2 @ B4 )
              & ( ( some_P6297086604321900740_state @ X )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_895_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc9003781588162623004on_val > produc9003781588162623004on_val > option8887860577033306220on_val,Core: produc9003781588162623004on_val > produc9003781588162623004on_val,X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( sep_al5697130883215687421on_val @ Plus @ Core )
     => ( ( member2879030624002546611on_val @ X @ ( sep_ad8320153009520438926on_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc9003781588162623004on_val,B2: produc9003781588162623004on_val] :
              ( ( member2879030624002546611on_val @ A2 @ A4 )
              & ( member2879030624002546611on_val @ B2 @ B4 )
              & ( ( some_P2581650809551911671on_val @ X )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_896_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: produc3882902684156697774_state > produc3882902684156697774_state > option886743748074664436_state,Core: produc3882902684156697774_state > produc3882902684156697774_state,X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( sep_al8268612531242297357_state @ Plus @ Core )
     => ( ( member6715010751053357271_state @ X @ ( sep_ad8203089552910907580_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: produc3882902684156697774_state,B2: produc3882902684156697774_state] :
              ( ( member6715010751053357271_state @ A2 @ A4 )
              & ( member6715010751053357271_state @ B2 @ B4 )
              & ( ( some_P5383513176685068947_state @ X )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_897_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: val > val > option_val,Core: val > val,X: val,A4: set_val,B4: set_val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( member_val @ X @ ( sep_add_set_val @ Plus @ A4 @ B4 ) )
        = ( ? [A2: val,B2: val] :
              ( ( member_val @ A2 @ A4 )
              & ( member_val @ B2 @ B4 )
              & ( ( some_val @ X )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_898_sep__algebra_Ox__elem__set__product,axiom,
    ! [Plus: state > state > option_state,Core: state > state,X: state,A4: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( member_state @ X @ ( sep_add_set_state @ Plus @ A4 @ B4 ) )
        = ( ? [A2: state,B2: state] :
              ( ( member_state @ A2 @ A4 )
              & ( member_state @ B2 @ B4 )
              & ( ( some_state @ X )
                = ( Plus @ A2 @ B2 ) ) ) ) ) ) ).

% sep_algebra.x_elem_set_product
thf(fact_899_add__set__def,axiom,
    ( add_set
    = ( sep_add_set_state @ plus ) ) ).

% add_set_def
thf(fact_900_combine__options__def,axiom,
    ( combin3633514924185701883_state
    = ( ^ [F7: state > state > state,X2: option_state,Y5: option_state] :
          ( case_o8916064052540797265_state @ Y5
          @ ^ [Z3: state] :
              ( case_o8916064052540797265_state @ ( some_state @ Z3 )
              @ ^ [Aa3: state] : ( some_state @ ( F7 @ Z3 @ Aa3 ) )
              @ Y5 )
          @ X2 ) ) ) ).

% combine_options_def
thf(fact_901_combine__options__def,axiom,
    ( combine_options_val
    = ( ^ [F7: val > val > val,X2: option_val,Y5: option_val] :
          ( case_o7794706883426356101al_val @ Y5
          @ ^ [Z3: val] :
              ( case_o7794706883426356101al_val @ ( some_val @ Z3 )
              @ ^ [Aa3: val] : ( some_val @ ( F7 @ Z3 @ Aa3 ) )
              @ Y5 )
          @ X2 ) ) ) ).

% combine_options_def
thf(fact_902_pre__get__m_Oelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat] :
      ( ( ( pre_ge2740421702909910421t_char @ X )
        = Y )
     => ( Y
        = ( produc6204653154488278070t_char @ X ) ) ) ).

% pre_get_m.elims
thf(fact_903_pre__get__m_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat] :
      ( ( ( pre_ge8481574585653477131on_val @ X )
        = Y )
     => ( Y
        = ( produc5239619271231976746on_val @ X ) ) ) ).

% pre_get_m.elims
thf(fact_904_pre__get__m_Osimps,axiom,
    pre_ge2740421702909910421t_char = produc6204653154488278070t_char ).

% pre_get_m.simps
thf(fact_905_pre__get__m_Osimps,axiom,
    pre_ge8481574585653477131on_val = produc5239619271231976746on_val ).

% pre_get_m.simps
thf(fact_906_combine__options__simps_I3_J,axiom,
    ! [F: state > state > state,A: state,B: state] :
      ( ( combin3633514924185701883_state @ F @ ( some_state @ A ) @ ( some_state @ B ) )
      = ( some_state @ ( F @ A @ B ) ) ) ).

% combine_options_simps(3)
thf(fact_907_combine__options__simps_I3_J,axiom,
    ! [F: val > val > val,A: val,B: val] :
      ( ( combine_options_val @ F @ ( some_val @ A ) @ ( some_val @ B ) )
      = ( some_val @ ( F @ A @ B ) ) ) ).

% combine_options_simps(3)
thf(fact_908_combine__options__simps_I1_J,axiom,
    ! [F: state > state > state,Y: option_state] :
      ( ( combin3633514924185701883_state @ F @ none_state @ Y )
      = Y ) ).

% combine_options_simps(1)
thf(fact_909_combine__options__simps_I1_J,axiom,
    ! [F: val > val > val,Y: option_val] :
      ( ( combine_options_val @ F @ none_val @ Y )
      = Y ) ).

% combine_options_simps(1)
thf(fact_910_combine__options__simps_I2_J,axiom,
    ! [F: state > state > state,X: option_state] :
      ( ( combin3633514924185701883_state @ F @ X @ none_state )
      = X ) ).

% combine_options_simps(2)
thf(fact_911_combine__options__simps_I2_J,axiom,
    ! [F: val > val > val,X: option_val] :
      ( ( combine_options_val @ F @ X @ none_val )
      = X ) ).

% combine_options_simps(2)
thf(fact_912_get__m_Osimps,axiom,
    ( get_m
    = ( ^ [A2: state] : ( produc5239619271231976746on_val @ ( rep_state @ A2 ) ) ) ) ).

% get_m.simps
thf(fact_913_get__m_Oelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X )
        = Y )
     => ( Y
        = ( produc5239619271231976746on_val @ ( rep_state @ X ) ) ) ) ).

% get_m.elims
thf(fact_914_get__pre_I2_J,axiom,
    ( get_m
    = ( ^ [X2: state] : ( produc5239619271231976746on_val @ ( rep_state @ X2 ) ) ) ) ).

% get_pre(2)
thf(fact_915_pre__get__m_Opelims,axiom,
    ! [X: produc3142500478612311029_state,Y: option_state] :
      ( ( ( pre_ge4435996478124457464_state @ X )
        = Y )
     => ( ( accp_P7183347322223220350_state @ pre_ge9112490230592956973_state @ X )
       => ~ ( ( Y
              = ( produc3900939990612242713_state @ X ) )
           => ~ ( accp_P7183347322223220350_state @ pre_ge9112490230592956973_state @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_916_pre__get__m_Opelims,axiom,
    ! [X: produc4844402304972151915_state,Y: prat] :
      ( ( ( pre_get_m_prat_state @ X )
        = Y )
     => ( ( accp_P6233459008282737652_state @ pre_ge6835382860682234787_state @ X )
       => ~ ( ( Y
              = ( produc6030790797199838863_state @ X ) )
           => ~ ( accp_P6233459008282737652_state @ pre_ge6835382860682234787_state @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_917_pre__get__m_Opelims,axiom,
    ! [X: produc6251377953716854561_state,Y: prat] :
      ( ( ( pre_ge1435879308799382564_state @ X )
        = Y )
     => ( ( accp_P6554740477754186410_state @ pre_ge4013444835548200281_state @ X )
       => ~ ( ( Y
              = ( produc7279835715735703621_state @ X ) )
           => ~ ( accp_P6554740477754186410_state @ pre_ge4013444835548200281_state @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_918_pre__get__m_Opelims,axiom,
    ! [X: produc1457211279475724562t_char,Y: nat] :
      ( ( ( pre_ge2740421702909910421t_char @ X )
        = Y )
     => ( ( accp_P8892882183480857371t_char @ pre_ge8748858970926381898t_char @ X )
       => ~ ( ( Y
              = ( produc6204653154488278070t_char @ X ) )
           => ~ ( accp_P8892882183480857371t_char @ pre_ge8748858970926381898t_char @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_919_pre__get__m_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > prat] :
      ( ( ( pre_ge8481574585653477131on_val @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ pre_ge4462515927930180886on_val @ X )
       => ~ ( ( Y
              = ( produc5239619271231976746on_val @ X ) )
           => ~ ( accp_P4405556307444930259on_val @ pre_ge4462515927930180886on_val @ X ) ) ) ) ).

% pre_get_m.pelims
thf(fact_920_get__m_Opelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > prat] :
      ( ( ( get_m @ X )
        = Y )
     => ( ( accp_state @ get_m_rel @ X )
       => ~ ( ( Y
              = ( produc5239619271231976746on_val @ ( rep_state @ X ) ) )
           => ~ ( accp_state @ get_m_rel @ X ) ) ) ) ).

% get_m.pelims
thf(fact_921_compatibleI__old,axiom,
    ! [Phi: produc9003781588162623004on_val,Phi2: produc9003781588162623004on_val] :
      ( ! [Hl2: produc1457211279475724562t_char,X3: val,Y3: val] :
          ( ( ( ( produc2319605628138516840on_val @ Phi @ Hl2 )
              = ( some_val @ X3 ) )
            & ( ( produc2319605628138516840on_val @ Phi2 @ Hl2 )
              = ( some_val @ Y3 ) ) )
         => ( X3 = Y3 ) )
     => ( ( valid_mask @ ( add_ma6586698345353345811t_char @ ( produc5239619271231976746on_val @ Phi ) @ ( produc5239619271231976746on_val @ Phi2 ) ) )
       => ( compatible @ Phi @ Phi2 ) ) ) ).

% compatibleI_old
thf(fact_922_get__h_Osimps,axiom,
    ( get_h
    = ( ^ [A2: state] : ( produc2319605628138516840on_val @ ( rep_state @ A2 ) ) ) ) ).

% get_h.simps
thf(fact_923_get__h_Oelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X )
        = Y )
     => ( Y
        = ( produc2319605628138516840on_val @ ( rep_state @ X ) ) ) ) ).

% get_h.elims
thf(fact_924_get__pre_I1_J,axiom,
    ( get_h
    = ( ^ [X2: state] : ( produc2319605628138516840on_val @ ( rep_state @ X2 ) ) ) ) ).

% get_pre(1)
thf(fact_925_Collect__split__mono__strong,axiom,
    ! [X7: set_nat,A4: set_Pr2507339680178222706t_char,Y6: set_list_char,P2: nat > list_char > $o,Q: nat > list_char > $o] :
      ( ( X7
        = ( image_3548405822317538717ar_nat @ produc6204653154488278070t_char @ A4 ) )
     => ( ( Y6
          = ( image_3034139768025083822t_char @ produc1900778367047502200t_char @ A4 ) )
       => ( ! [X3: nat] :
              ( ( member_nat @ X3 @ X7 )
             => ! [Xa: list_char] :
                  ( ( member_list_char @ Xa @ Y6 )
                 => ( ( P2 @ X3 @ Xa )
                   => ( Q @ X3 @ Xa ) ) ) )
         => ( ( ord_le6315511645215477266t_char @ A4 @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ P2 ) ) )
           => ( ord_le6315511645215477266t_char @ A4 @ ( collec2458894688891239037t_char @ ( produc8526122873445342073char_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_926_Collect__split__mono__strong,axiom,
    ! [X7: set_Pr3433046674199179443r_prat,A4: set_Pr7649655576376376530on_val,Y6: set_Pr1004501353197068112on_val,P2: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o,Q: ( produc1457211279475724562t_char > prat ) > ( produc1457211279475724562t_char > option_val ) > $o] :
      ( ( X7
        = ( image_3067683418878703216r_prat @ produc5239619271231976746on_val @ A4 ) )
     => ( ( Y6
          = ( image_2330660378567450301on_val @ produc2319605628138516840on_val @ A4 ) )
       => ( ! [X3: produc1457211279475724562t_char > prat] :
              ( ( member2336342582916103932r_prat @ X3 @ X7 )
             => ! [Xa: produc1457211279475724562t_char > option_val] :
                  ( ( member1577473829074448177on_val @ Xa @ Y6 )
                 => ( ( P2 @ X3 @ Xa )
                   => ( Q @ X3 @ Xa ) ) ) )
         => ( ( ord_le6900622908513426738on_val @ A4 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ P2 ) ) )
           => ( ord_le6900622908513426738on_val @ A4 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_927_Collect__split__mono__strong,axiom,
    ! [X7: set_state,A4: set_Pr2391701600042252046_state,Y6: set_state_state,P2: state > ( state > state ) > $o,Q: state > ( state > state ) > $o] :
      ( ( X7
        = ( image_6759111139246981411_state @ produc7095885521192019410_state @ A4 ) )
     => ( ( Y6
          = ( image_6089932313839440636_state @ produc1734700239402139924_state @ A4 ) )
       => ( ! [X3: state] :
              ( ( member_state @ X3 @ X7 )
             => ! [Xa: state > state] :
                  ( ( member_state_state @ Xa @ Y6 )
                 => ( ( P2 @ X3 @ Xa )
                   => ( Q @ X3 @ Xa ) ) ) )
         => ( ( ord_le6483787752022044334_state @ A4 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ P2 ) ) )
           => ( ord_le6483787752022044334_state @ A4 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_928_Collect__split__mono__strong,axiom,
    ! [X7: set_state,A4: set_Pr4231240917283394591_state,Y6: set_Pr2391701600042252046_state,P2: state > produc3882902684156697774_state > $o,Q: state > produc3882902684156697774_state > $o] :
      ( ( X7
        = ( image_2710133271811360426_state @ produc848024588167747631_state @ A4 ) )
     => ( ( Y6
          = ( image_7466395622266389182_state @ produc6310399636379773037_state @ A4 ) )
       => ( ! [X3: state] :
              ( ( member_state @ X3 @ X7 )
             => ! [Xa: produc3882902684156697774_state] :
                  ( ( member6715010751053357271_state @ Xa @ Y6 )
                 => ( ( P2 @ X3 @ Xa )
                   => ( Q @ X3 @ Xa ) ) ) )
         => ( ( ord_le4032880777312351359_state @ A4 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ P2 ) ) )
           => ( ord_le4032880777312351359_state @ A4 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ Q ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_929_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_930_get__h_Opelims,axiom,
    ! [X: state,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( get_h @ X )
        = Y )
     => ( ( accp_state @ get_h_rel @ X )
       => ~ ( ( Y
              = ( produc2319605628138516840on_val @ ( rep_state @ X ) ) )
           => ~ ( accp_state @ get_h_rel @ X ) ) ) ) ).

% get_h.pelims
thf(fact_931_pre__get__h_Oelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( pre_ge1486375753531218896on_val @ X )
        = Y )
     => ( Y
        = ( produc2319605628138516840on_val @ X ) ) ) ).

% pre_get_h.elims
thf(fact_932_pre__get__h_Osimps,axiom,
    pre_ge1486375753531218896on_val = produc2319605628138516840on_val ).

% pre_get_h.simps
thf(fact_933_pre__get__h_Opelims,axiom,
    ! [X: produc3142500478612311029_state,Y: option_state] :
      ( ( ( pre_ge6337690187194669811_state @ X )
        = Y )
     => ( ( accp_P7183347322223220350_state @ pre_ge4642282138912335602_state @ X )
       => ~ ( ( Y
              = ( produc9117690093182453595_state @ X ) )
           => ~ ( accp_P7183347322223220350_state @ pre_ge4642282138912335602_state @ X ) ) ) ) ).

% pre_get_h.pelims
thf(fact_934_pre__get__h_Opelims,axiom,
    ! [X: produc4844402304972151915_state,Y: state] :
      ( ( ( pre_get_h_prat_state @ X )
        = Y )
     => ( ( accp_P6233459008282737652_state @ pre_ge6006653645540518248_state @ X )
       => ~ ( ( Y
              = ( produc8138835347214057169_state @ X ) )
           => ~ ( accp_P6233459008282737652_state @ pre_ge6006653645540518248_state @ X ) ) ) ) ).

% pre_get_h.pelims
thf(fact_935_pre__get__h_Opelims,axiom,
    ! [X: produc6251377953716854561_state,Y: set_state] :
      ( ( ( pre_ge1447473398360597535_state @ X )
        = Y )
     => ( ( accp_P6554740477754186410_state @ pre_ge3291400433338533662_state @ X )
       => ~ ( ( Y
              = ( produc4944973370551335047_state @ X ) )
           => ~ ( accp_P6554740477754186410_state @ pre_ge3291400433338533662_state @ X ) ) ) ) ).

% pre_get_h.pelims
thf(fact_936_pre__get__h_Opelims,axiom,
    ! [X: produc9003781588162623004on_val,Y: produc1457211279475724562t_char > option_val] :
      ( ( ( pre_ge1486375753531218896on_val @ X )
        = Y )
     => ( ( accp_P4405556307444930259on_val @ pre_ge6140436789258014353on_val @ X )
       => ~ ( ( Y
              = ( produc2319605628138516840on_val @ X ) )
           => ~ ( accp_P4405556307444930259on_val @ pre_ge6140436789258014353on_val @ X ) ) ) ) ).

% pre_get_h.pelims
thf(fact_937_snd__graph__ran,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( image_2330660378567450301on_val @ produc2319605628138516840on_val @ ( graph_1288227317702120175on_val @ M ) )
      = ( ran_Pr878516737976613822on_val @ M ) ) ).

% snd_graph_ran
thf(fact_938_subset__fst__snd,axiom,
    ! [A4: set_Pr2507339680178222706t_char] :
      ( ord_le6315511645215477266t_char @ A4
      @ ( produc6030673636645808891t_char @ ( image_3548405822317538717ar_nat @ produc6204653154488278070t_char @ A4 )
        @ ^ [Uu3: nat] : ( image_3034139768025083822t_char @ produc1900778367047502200t_char @ A4 ) ) ) ).

% subset_fst_snd
thf(fact_939_subset__fst__snd,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ord_le6900622908513426738on_val @ A4
      @ ( produc1366239611153933861on_val @ ( image_3067683418878703216r_prat @ produc5239619271231976746on_val @ A4 )
        @ ^ [Uu3: produc1457211279475724562t_char > prat] : ( image_2330660378567450301on_val @ produc2319605628138516840on_val @ A4 ) ) ) ).

% subset_fst_snd
thf(fact_940_Sigma__mono,axiom,
    ! [A4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state,B4: produc7272280185086996969_state > set_state,D2: produc7272280185086996969_state > set_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ C3 )
     => ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ A4 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X3 ) @ ( D2 @ X3 ) ) )
       => ( ord_le9131031735280434308_state @ ( produc1406734553846628205_state @ A4 @ B4 ) @ ( produc1406734553846628205_state @ C3 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_941_Sigma__mono,axiom,
    ! [A4: set_Pr7649655576376376530on_val,C3: set_Pr7649655576376376530on_val,B4: produc9003781588162623004on_val > set_state,D2: produc9003781588162623004on_val > set_state] :
      ( ( ord_le6900622908513426738on_val @ A4 @ C3 )
     => ( ! [X3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ A4 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X3 ) @ ( D2 @ X3 ) ) )
       => ( ord_le801108382804549175_state @ ( produc556505947853469856_state @ A4 @ B4 ) @ ( produc556505947853469856_state @ C3 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_942_Sigma__mono,axiom,
    ! [A4: set_Pr2391701600042252046_state,C3: set_Pr2391701600042252046_state,B4: produc3882902684156697774_state > set_state,D2: produc3882902684156697774_state > set_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ C3 )
     => ( ! [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ A4 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X3 ) @ ( D2 @ X3 ) ) )
       => ( ord_le4167756422255405229_state @ ( produc4278832915810242336_state @ A4 @ B4 ) @ ( produc4278832915810242336_state @ C3 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_943_Sigma__mono,axiom,
    ! [A4: set_state,C3: set_state,B4: state > set_state,D2: state > set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ C3 )
     => ( ! [X3: state] :
            ( ( member_state @ X3 @ A4 )
           => ( ord_le2494988322063910608_state @ ( B4 @ X3 ) @ ( D2 @ X3 ) ) )
       => ( ord_le2777189432094499797_state @ ( produc4572292869282958142_state @ A4 @ B4 ) @ ( produc4572292869282958142_state @ C3 @ D2 ) ) ) ) ).

% Sigma_mono
thf(fact_944_Times__subset__cancel2,axiom,
    ! [X: state,C3: set_state,A4: set_state,B4: set_state] :
      ( ( member_state @ X @ C3 )
     => ( ( ord_le2777189432094499797_state
          @ ( produc4572292869282958142_state @ A4
            @ ^ [Uu3: state] : C3 )
          @ ( produc4572292869282958142_state @ B4
            @ ^ [Uu3: state] : C3 ) )
        = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_945_Times__subset__cancel2,axiom,
    ! [X: produc7272280185086996969_state,C3: set_Pr4231240917283394591_state,A4: set_state,B4: set_state] :
      ( ( member7461423308196221312_state @ X @ C3 )
     => ( ( ord_le6305643028697367044_state
          @ ( produc8552965988182875245_state @ A4
            @ ^ [Uu3: state] : C3 )
          @ ( produc8552965988182875245_state @ B4
            @ ^ [Uu3: state] : C3 ) )
        = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_946_Times__subset__cancel2,axiom,
    ! [X: produc9003781588162623004on_val,C3: set_Pr7649655576376376530on_val,A4: set_state,B4: set_state] :
      ( ( member2879030624002546611on_val @ X @ C3 )
     => ( ( ord_le2093392236560368951on_val
          @ ( produc4123186969287248032on_val @ A4
            @ ^ [Uu3: state] : C3 )
          @ ( produc4123186969287248032on_val @ B4
            @ ^ [Uu3: state] : C3 ) )
        = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_947_Times__subset__cancel2,axiom,
    ! [X: produc3882902684156697774_state,C3: set_Pr2391701600042252046_state,A4: set_state,B4: set_state] :
      ( ( member6715010751053357271_state @ X @ C3 )
     => ( ( ord_le4032880777312351359_state
          @ ( produc2831624448089660202_state @ A4
            @ ^ [Uu3: state] : C3 )
          @ ( produc2831624448089660202_state @ B4
            @ ^ [Uu3: state] : C3 ) )
        = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_948_graph__ranD,axiom,
    ! [X: produc7272280185086996969_state,M: state > option886743748074664436_state] :
      ( ( member7461423308196221312_state @ X @ ( graph_7551141711029462004_state @ M ) )
     => ( member6715010751053357271_state @ ( produc6310399636379773037_state @ X ) @ ( ran_st8815263174283155139_state @ M ) ) ) ).

% graph_ranD
thf(fact_949_graph__ranD,axiom,
    ! [X: produc3882902684156697774_state,M: state > option_state_state] :
      ( ( member6715010751053357271_state @ X @ ( graph_5871261288037090637_state @ M ) )
     => ( member_state_state @ ( produc1734700239402139924_state @ X ) @ ( ran_st4772285088427521086_state @ M ) ) ) ).

% graph_ranD
thf(fact_950_graph__ranD,axiom,
    ! [X: produc9003781588162623004on_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( member2879030624002546611on_val @ X @ ( graph_1288227317702120175on_val @ M ) )
     => ( member1577473829074448177on_val @ ( produc2319605628138516840on_val @ X ) @ ( ran_Pr878516737976613822on_val @ M ) ) ) ).

% graph_ranD
thf(fact_951_Gr__incl,axiom,
    ! [A4: set_state,F: state > state,B4: set_state] :
      ( ( ord_le2777189432094499797_state @ ( bNF_Gr_state_state @ A4 @ F )
        @ ( produc4572292869282958142_state @ A4
          @ ^ [Uu3: state] : B4 ) )
      = ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ B4 ) ) ).

% Gr_incl
thf(fact_952_relChain__def,axiom,
    ( bNF_Ca2815325664443363616_state
    = ( ^ [R: set_Pr1688445902015331925_state,As: option_state > set_state] :
        ! [I: option_state,J: option_state] :
          ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ I @ J ) @ R )
         => ( ord_le2494988322063910608_state @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).

% relChain_def
thf(fact_953_Collect__case__prod__in__rel__leE,axiom,
    ! [X7: set_Pr7649655576376376530on_val,Y6: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ X7 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ ( fun_in3588502033776859947on_val @ Y6 ) ) ) )
     => ( ord_le6900622908513426738on_val @ X7 @ Y6 ) ) ).

% Collect_case_prod_in_rel_leE
thf(fact_954_Collect__case__prod__in__rel__leE,axiom,
    ! [X7: set_Pr2391701600042252046_state,Y6: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ X7 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ ( fun_in7949406044791577617_state @ Y6 ) ) ) )
     => ( ord_le6483787752022044334_state @ X7 @ Y6 ) ) ).

% Collect_case_prod_in_rel_leE
thf(fact_955_Collect__case__prod__in__rel__leE,axiom,
    ! [X7: set_Pr4231240917283394591_state,Y6: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X7 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ ( fun_in233003973860168752_state @ Y6 ) ) ) )
     => ( ord_le4032880777312351359_state @ X7 @ Y6 ) ) ).

% Collect_case_prod_in_rel_leE
thf(fact_956_Collect__case__prod__in__rel__leI,axiom,
    ! [X7: set_Pr7649655576376376530on_val,Y6: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ X7 @ Y6 )
     => ( ord_le6900622908513426738on_val @ X7 @ ( collec7475294502966882545on_val @ ( produc5248837549992124053_val_o @ ( fun_in3588502033776859947on_val @ Y6 ) ) ) ) ) ).

% Collect_case_prod_in_rel_leI
thf(fact_957_Collect__case__prod__in__rel__leI,axiom,
    ! [X7: set_Pr2391701600042252046_state,Y6: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ X7 @ Y6 )
     => ( ord_le6483787752022044334_state @ X7 @ ( collec394671971739345689_state @ ( produc3645877548210629341tate_o @ ( fun_in7949406044791577617_state @ Y6 ) ) ) ) ) ).

% Collect_case_prod_in_rel_leI
thf(fact_958_Collect__case__prod__in__rel__leI,axiom,
    ! [X7: set_Pr4231240917283394591_state,Y6: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ X7 @ Y6 )
     => ( ord_le4032880777312351359_state @ X7 @ ( collec906845016635587262_state @ ( produc1745419677418529872tate_o @ ( fun_in233003973860168752_state @ Y6 ) ) ) ) ) ).

% Collect_case_prod_in_rel_leI
thf(fact_959_graph__restrictD_I2_J,axiom,
    ! [K: state,V: produc3882902684156697774_state,M: state > option886743748074664436_state,A4: set_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ K @ V ) @ ( graph_7551141711029462004_state @ ( restri5259549408567034562_state @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_P5383513176685068947_state @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_960_graph__restrictD_I2_J,axiom,
    ! [K: state,V: state > state,M: state > option_state_state,A4: set_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ K @ V ) @ ( graph_5871261288037090637_state @ ( restri1822066007074788863_state @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_state_state @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_961_graph__restrictD_I2_J,axiom,
    ! [K: option_state,V: option_state,M: option_state > option_option_state,A4: set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ K @ V ) @ ( graph_628825510059920660_state @ ( restri6741197069250724038_state @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_option_state @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_962_graph__restrictD_I2_J,axiom,
    ! [K: prat,V: set_state,M: prat > option_set_state,A4: set_prat] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ K @ V ) @ ( graph_prat_set_state @ ( restri5781717399629468914_state @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_set_state @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_963_graph__restrictD_I2_J,axiom,
    ! [K: nat,V: list_char,M: nat > option_list_char,A4: set_nat] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ K @ V ) @ ( graph_nat_list_char @ ( restri7497266720855523683t_char @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_list_char @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_964_graph__restrictD_I2_J,axiom,
    ! [K: produc1457211279475724562t_char > prat,V: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V ) @ ( graph_1288227317702120175on_val @ ( restri7594233908965391805on_val @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_P7669353234731512949on_val @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_965_graph__restrictD_I2_J,axiom,
    ! [K: prat,V: state,M: prat > option_state,A4: set_prat] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ K @ V ) @ ( graph_prat_state @ ( restri7349097791805130556_state @ M @ A4 ) ) )
     => ( ( M @ K )
        = ( some_state @ V ) ) ) ).

% graph_restrictD(2)
thf(fact_966_times__subset__iff,axiom,
    ! [A4: set_state,C3: set_state,B4: set_state,D2: set_state] :
      ( ( ord_le2777189432094499797_state
        @ ( produc4572292869282958142_state @ A4
          @ ^ [Uu3: state] : C3 )
        @ ( produc4572292869282958142_state @ B4
          @ ^ [Uu3: state] : D2 ) )
      = ( ( A4 = bot_bot_set_state )
        | ( C3 = bot_bot_set_state )
        | ( ( ord_le2494988322063910608_state @ A4 @ B4 )
          & ( ord_le2494988322063910608_state @ C3 @ D2 ) ) ) ) ).

% times_subset_iff
thf(fact_967_image__Fpow__mono,axiom,
    ! [F: state > state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ B4 )
     => ( ord_le5175021213330142598_state @ ( image_2476256681063834599_state @ ( image_state_state @ F ) @ ( finite_Fpow_state @ A4 ) ) @ ( finite_Fpow_state @ B4 ) ) ) ).

% image_Fpow_mono
thf(fact_968_subset__empty,axiom,
    ! [A4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ bot_bot_set_state )
      = ( A4 = bot_bot_set_state ) ) ).

% subset_empty
thf(fact_969_empty__subsetI,axiom,
    ! [A4: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A4 ) ).

% empty_subsetI
thf(fact_970_restrict__out,axiom,
    ! [X: state,A4: set_state,M: state > option_state] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( restri2287918369865870758_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_971_restrict__out,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_state] :
      ( ~ ( member7461423308196221312_state @ X @ A4 )
     => ( ( restri6145314162897174997_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_972_restrict__out,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_state] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( restri5336766904122854152_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_973_restrict__out,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_state] :
      ( ~ ( member6715010751053357271_state @ X @ A4 )
     => ( ( restri6706757876287616696_state @ M @ A4 @ X )
        = none_state ) ) ).

% restrict_out
thf(fact_974_restrict__out,axiom,
    ! [X: state,A4: set_state,M: state > option_val] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( restri6052284935360306837te_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_975_restrict__out,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_val] :
      ( ~ ( member7461423308196221312_state @ X @ A4 )
     => ( ( restri6051517647513894te_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_976_restrict__out,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( restri5251746167140823987al_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_977_restrict__out,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_val] :
      ( ~ ( member6715010751053357271_state @ X @ A4 )
     => ( ( restri214263546473948163te_val @ M @ A4 @ X )
        = none_val ) ) ).

% restrict_out
thf(fact_978_these__empty,axiom,
    ( ( these_state @ bot_bo710180891245420500_state )
    = bot_bot_set_state ) ).

% these_empty
thf(fact_979_restrict__map__to__empty,axiom,
    ! [M: state > option_state] :
      ( ( restri2287918369865870758_state @ M @ bot_bot_set_state )
      = ( ^ [X2: state] : none_state ) ) ).

% restrict_map_to_empty
thf(fact_980_restrict__map__to__empty,axiom,
    ! [M: state > option_val] :
      ( ( restri6052284935360306837te_val @ M @ bot_bot_set_state )
      = ( ^ [X2: state] : none_val ) ) ).

% restrict_map_to_empty
thf(fact_981_subset__emptyI,axiom,
    ! [A4: set_Pr4231240917283394591_state] :
      ( ! [X3: produc7272280185086996969_state] :
          ~ ( member7461423308196221312_state @ X3 @ A4 )
     => ( ord_le4032880777312351359_state @ A4 @ bot_bo6430881413863817907_state ) ) ).

% subset_emptyI
thf(fact_982_subset__emptyI,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ! [X3: produc9003781588162623004on_val] :
          ~ ( member2879030624002546611on_val @ X3 @ A4 )
     => ( ord_le6900622908513426738on_val @ A4 @ bot_bo6722054719108133734on_val ) ) ).

% subset_emptyI
thf(fact_983_subset__emptyI,axiom,
    ! [A4: set_Pr2391701600042252046_state] :
      ( ! [X3: produc3882902684156697774_state] :
          ~ ( member6715010751053357271_state @ X3 @ A4 )
     => ( ord_le6483787752022044334_state @ A4 @ bot_bo3524941057552913786_state ) ) ).

% subset_emptyI
thf(fact_984_subset__emptyI,axiom,
    ! [A4: set_state] :
      ( ! [X3: state] :
          ~ ( member_state @ X3 @ A4 )
     => ( ord_le2494988322063910608_state @ A4 @ bot_bot_set_state ) ) ).

% subset_emptyI
thf(fact_985_PartialSA_Oempty__set__sum,axiom,
    ! [A4: set_state] :
      ( ( add_set @ bot_bot_set_state @ A4 )
      = bot_bot_set_state ) ).

% PartialSA.empty_set_sum
thf(fact_986_restrict__map__def,axiom,
    ( restri2287918369865870758_state
    = ( ^ [M5: state > option_state,A7: set_state,X2: state] : ( if_option_state @ ( member_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_state ) ) ) ).

% restrict_map_def
thf(fact_987_restrict__map__def,axiom,
    ( restri6145314162897174997_state
    = ( ^ [M5: produc7272280185086996969_state > option_state,A7: set_Pr4231240917283394591_state,X2: produc7272280185086996969_state] : ( if_option_state @ ( member7461423308196221312_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_state ) ) ) ).

% restrict_map_def
thf(fact_988_restrict__map__def,axiom,
    ( restri5336766904122854152_state
    = ( ^ [M5: produc9003781588162623004on_val > option_state,A7: set_Pr7649655576376376530on_val,X2: produc9003781588162623004on_val] : ( if_option_state @ ( member2879030624002546611on_val @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_state ) ) ) ).

% restrict_map_def
thf(fact_989_restrict__map__def,axiom,
    ( restri6706757876287616696_state
    = ( ^ [M5: produc3882902684156697774_state > option_state,A7: set_Pr2391701600042252046_state,X2: produc3882902684156697774_state] : ( if_option_state @ ( member6715010751053357271_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_state ) ) ) ).

% restrict_map_def
thf(fact_990_restrict__map__def,axiom,
    ( restri6052284935360306837te_val
    = ( ^ [M5: state > option_val,A7: set_state,X2: state] : ( if_option_val @ ( member_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_val ) ) ) ).

% restrict_map_def
thf(fact_991_restrict__map__def,axiom,
    ( restri6051517647513894te_val
    = ( ^ [M5: produc7272280185086996969_state > option_val,A7: set_Pr4231240917283394591_state,X2: produc7272280185086996969_state] : ( if_option_val @ ( member7461423308196221312_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_val ) ) ) ).

% restrict_map_def
thf(fact_992_restrict__map__def,axiom,
    ( restri5251746167140823987al_val
    = ( ^ [M5: produc9003781588162623004on_val > option_val,A7: set_Pr7649655576376376530on_val,X2: produc9003781588162623004on_val] : ( if_option_val @ ( member2879030624002546611on_val @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_val ) ) ) ).

% restrict_map_def
thf(fact_993_restrict__map__def,axiom,
    ( restri214263546473948163te_val
    = ( ^ [M5: produc3882902684156697774_state > option_val,A7: set_Pr2391701600042252046_state,X2: produc3882902684156697774_state] : ( if_option_val @ ( member6715010751053357271_state @ X2 @ A7 ) @ ( M5 @ X2 ) @ none_val ) ) ) ).

% restrict_map_def
thf(fact_994_bot_Oextremum,axiom,
    ! [A: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A ) ).

% bot.extremum
thf(fact_995_bot_Oextremum__unique,axiom,
    ! [A: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ bot_bot_set_state )
      = ( A = bot_bot_set_state ) ) ).

% bot.extremum_unique
thf(fact_996_bot_Oextremum__uniqueI,axiom,
    ! [A: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ bot_bot_set_state )
     => ( A = bot_bot_set_state ) ) ).

% bot.extremum_uniqueI
thf(fact_997_Fpow__mono,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ord_le5175021213330142598_state @ ( finite_Fpow_state @ A4 ) @ ( finite_Fpow_state @ B4 ) ) ) ).

% Fpow_mono
thf(fact_998_graph__restrictD_I1_J,axiom,
    ! [K: state,V: produc3882902684156697774_state,M: state > option886743748074664436_state,A4: set_state] :
      ( ( member7461423308196221312_state @ ( produc5886875603596089627_state @ K @ V ) @ ( graph_7551141711029462004_state @ ( restri5259549408567034562_state @ M @ A4 ) ) )
     => ( member_state @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_999_graph__restrictD_I1_J,axiom,
    ! [K: state,V: state > state,M: state > option_state_state,A4: set_state] :
      ( ( member6715010751053357271_state @ ( produc8632743443909064678_state @ K @ V ) @ ( graph_5871261288037090637_state @ ( restri1822066007074788863_state @ M @ A4 ) ) )
     => ( member_state @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1000_graph__restrictD_I1_J,axiom,
    ! [K: option_state,V: option_state,M: option_state > option_option_state,A4: set_option_state] :
      ( ( member3029510603097127326_state @ ( produc9160152616361873709_state @ K @ V ) @ ( graph_628825510059920660_state @ ( restri6741197069250724038_state @ M @ A4 ) ) )
     => ( member_option_state @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1001_graph__restrictD_I1_J,axiom,
    ! [K: prat,V: state,M: prat > option_state,A4: set_prat] :
      ( ( member6226390569306242836_state @ ( produc6205719116230455971_state @ K @ V ) @ ( graph_prat_state @ ( restri7349097791805130556_state @ M @ A4 ) ) )
     => ( member_prat @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1002_graph__restrictD_I1_J,axiom,
    ! [K: prat,V: set_state,M: prat > option_set_state,A4: set_prat] :
      ( ( member6708919011922255306_state @ ( produc9080284787853255769_state @ K @ V ) @ ( graph_prat_set_state @ ( restri5781717399629468914_state @ M @ A4 ) ) )
     => ( member_prat @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1003_graph__restrictD_I1_J,axiom,
    ! [K: nat,V: list_char,M: nat > option_list_char,A4: set_nat] :
      ( ( member484235747325421115t_char @ ( produc120197956887798346t_char @ K @ V ) @ ( graph_nat_list_char @ ( restri7497266720855523683t_char @ M @ A4 ) ) )
     => ( member_nat @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1004_graph__restrictD_I1_J,axiom,
    ! [K: produc1457211279475724562t_char > prat,V: produc1457211279475724562t_char > option_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,A4: set_Pr3433046674199179443r_prat] :
      ( ( member2879030624002546611on_val @ ( produc74620467203698198on_val @ K @ V ) @ ( graph_1288227317702120175on_val @ ( restri7594233908965391805on_val @ M @ A4 ) ) )
     => ( member2336342582916103932r_prat @ K @ A4 ) ) ).

% graph_restrictD(1)
thf(fact_1005_wand__equiv__def,axiom,
    ( wand
    = ( ^ [A7: set_state,B5: set_state] :
          ( collect_state
          @ ^ [Uu3: state] :
            ? [Phi4: state] :
              ( ( Uu3 = Phi4 )
              & ( ord_le2494988322063910608_state @ ( add_set @ A7 @ ( insert_state @ Phi4 @ bot_bot_set_state ) ) @ B5 ) ) ) ) ) ).

% wand_equiv_def
thf(fact_1006_image__Pow__mono,axiom,
    ! [F: state > state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A4 ) @ B4 )
     => ( ord_le5175021213330142598_state @ ( image_2476256681063834599_state @ ( image_state_state @ F ) @ ( pow_state @ A4 ) ) @ ( pow_state @ B4 ) ) ) ).

% image_Pow_mono
thf(fact_1007_sep__algebra_Osum__then__singleton,axiom,
    ! [Plus: val > val > option_val,Core: val > val,A: val,B: val,C: val] :
      ( ( sep_algebra_val @ Plus @ Core )
     => ( ( ( some_val @ A )
          = ( Plus @ B @ C ) )
        = ( ( insert_val @ A @ bot_bot_set_val )
          = ( sep_add_set_val @ Plus @ ( insert_val @ B @ bot_bot_set_val ) @ ( insert_val @ C @ bot_bot_set_val ) ) ) ) ) ).

% sep_algebra.sum_then_singleton
thf(fact_1008_sep__algebra_Osum__then__singleton,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A: state,B: state,C: state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ( some_state @ A )
          = ( Plus @ B @ C ) )
        = ( ( insert_state @ A @ bot_bot_set_state )
          = ( sep_add_set_state @ Plus @ ( insert_state @ B @ bot_bot_set_state ) @ ( insert_state @ C @ bot_bot_set_state ) ) ) ) ) ).

% sep_algebra.sum_then_singleton
thf(fact_1009_insert__subset,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( insert175804457004744729_state @ X @ A4 ) @ B4 )
      = ( ( member7461423308196221312_state @ X @ B4 )
        & ( ord_le4032880777312351359_state @ A4 @ B4 ) ) ) ).

% insert_subset
thf(fact_1010_insert__subset,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ ( insert3030518898131756108on_val @ X @ A4 ) @ B4 )
      = ( ( member2879030624002546611on_val @ X @ B4 )
        & ( ord_le6900622908513426738on_val @ A4 @ B4 ) ) ) ).

% insert_subset
thf(fact_1011_insert__subset,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ ( insert94804854012721790_state @ X @ A4 ) @ B4 )
      = ( ( member6715010751053357271_state @ X @ B4 )
        & ( ord_le6483787752022044334_state @ A4 @ B4 ) ) ) ).

% insert_subset
thf(fact_1012_insert__subset,axiom,
    ! [X: state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( insert_state @ X @ A4 ) @ B4 )
      = ( ( member_state @ X @ B4 )
        & ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% insert_subset
thf(fact_1013_PowI,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( member_set_state @ A4 @ ( pow_state @ B4 ) ) ) ).

% PowI
thf(fact_1014_Pow__iff,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( member_set_state @ A4 @ ( pow_state @ B4 ) )
      = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ).

% Pow_iff
thf(fact_1015_these__insert__None,axiom,
    ! [A4: set_option_state] :
      ( ( these_state @ ( insert_option_state @ none_state @ A4 ) )
      = ( these_state @ A4 ) ) ).

% these_insert_None
thf(fact_1016_these__insert__None,axiom,
    ! [A4: set_option_val] :
      ( ( these_val @ ( insert_option_val @ none_val @ A4 ) )
      = ( these_val @ A4 ) ) ).

% these_insert_None
thf(fact_1017_singleton__insert__inj__eq_H,axiom,
    ! [A: state,A4: set_state,B: state] :
      ( ( ( insert_state @ A @ A4 )
        = ( insert_state @ B @ bot_bot_set_state ) )
      = ( ( A = B )
        & ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ B @ bot_bot_set_state ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_1018_singleton__insert__inj__eq,axiom,
    ! [B: state,A: state,A4: set_state] :
      ( ( ( insert_state @ B @ bot_bot_set_state )
        = ( insert_state @ A @ A4 ) )
      = ( ( A = B )
        & ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ B @ bot_bot_set_state ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_1019_these__insert__Some,axiom,
    ! [X: state,A4: set_option_state] :
      ( ( these_state @ ( insert_option_state @ ( some_state @ X ) @ A4 ) )
      = ( insert_state @ X @ ( these_state @ A4 ) ) ) ).

% these_insert_Some
thf(fact_1020_these__insert__Some,axiom,
    ! [X: val,A4: set_option_val] :
      ( ( these_val @ ( insert_option_val @ ( some_val @ X ) @ A4 ) )
      = ( insert_val @ X @ ( these_val @ A4 ) ) ) ).

% these_insert_Some
thf(fact_1021_insert__subsetI,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,X7: set_Pr4231240917283394591_state] :
      ( ( member7461423308196221312_state @ X @ A4 )
     => ( ( ord_le4032880777312351359_state @ X7 @ A4 )
       => ( ord_le4032880777312351359_state @ ( insert175804457004744729_state @ X @ X7 ) @ A4 ) ) ) ).

% insert_subsetI
thf(fact_1022_insert__subsetI,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,X7: set_Pr7649655576376376530on_val] :
      ( ( member2879030624002546611on_val @ X @ A4 )
     => ( ( ord_le6900622908513426738on_val @ X7 @ A4 )
       => ( ord_le6900622908513426738on_val @ ( insert3030518898131756108on_val @ X @ X7 ) @ A4 ) ) ) ).

% insert_subsetI
thf(fact_1023_insert__subsetI,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,X7: set_Pr2391701600042252046_state] :
      ( ( member6715010751053357271_state @ X @ A4 )
     => ( ( ord_le6483787752022044334_state @ X7 @ A4 )
       => ( ord_le6483787752022044334_state @ ( insert94804854012721790_state @ X @ X7 ) @ A4 ) ) ) ).

% insert_subsetI
thf(fact_1024_insert__subsetI,axiom,
    ! [X: state,A4: set_state,X7: set_state] :
      ( ( member_state @ X @ A4 )
     => ( ( ord_le2494988322063910608_state @ X7 @ A4 )
       => ( ord_le2494988322063910608_state @ ( insert_state @ X @ X7 ) @ A4 ) ) ) ).

% insert_subsetI
thf(fact_1025_Pow__def,axiom,
    ( pow_state
    = ( ^ [A7: set_state] :
          ( collect_set_state
          @ ^ [B5: set_state] : ( ord_le2494988322063910608_state @ B5 @ A7 ) ) ) ) ).

% Pow_def
thf(fact_1026_PowD,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( member_set_state @ A4 @ ( pow_state @ B4 ) )
     => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ).

% PowD
thf(fact_1027_insert__mono,axiom,
    ! [C3: set_state,D2: set_state,A: state] :
      ( ( ord_le2494988322063910608_state @ C3 @ D2 )
     => ( ord_le2494988322063910608_state @ ( insert_state @ A @ C3 ) @ ( insert_state @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_1028_subset__insert,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ~ ( member7461423308196221312_state @ X @ A4 )
     => ( ( ord_le4032880777312351359_state @ A4 @ ( insert175804457004744729_state @ X @ B4 ) )
        = ( ord_le4032880777312351359_state @ A4 @ B4 ) ) ) ).

% subset_insert
thf(fact_1029_subset__insert,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( ord_le6900622908513426738on_val @ A4 @ ( insert3030518898131756108on_val @ X @ B4 ) )
        = ( ord_le6900622908513426738on_val @ A4 @ B4 ) ) ) ).

% subset_insert
thf(fact_1030_subset__insert,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state] :
      ( ~ ( member6715010751053357271_state @ X @ A4 )
     => ( ( ord_le6483787752022044334_state @ A4 @ ( insert94804854012721790_state @ X @ B4 ) )
        = ( ord_le6483787752022044334_state @ A4 @ B4 ) ) ) ).

% subset_insert
thf(fact_1031_subset__insert,axiom,
    ! [X: state,A4: set_state,B4: set_state] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ X @ B4 ) )
        = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% subset_insert
thf(fact_1032_subset__insertI,axiom,
    ! [B4: set_state,A: state] : ( ord_le2494988322063910608_state @ B4 @ ( insert_state @ A @ B4 ) ) ).

% subset_insertI
thf(fact_1033_subset__insertI2,axiom,
    ! [A4: set_state,B4: set_state,B: state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ B @ B4 ) ) ) ).

% subset_insertI2
thf(fact_1034_subset__singleton__iff,axiom,
    ! [X7: set_state,A: state] :
      ( ( ord_le2494988322063910608_state @ X7 @ ( insert_state @ A @ bot_bot_set_state ) )
      = ( ( X7 = bot_bot_set_state )
        | ( X7
          = ( insert_state @ A @ bot_bot_set_state ) ) ) ) ).

% subset_singleton_iff
thf(fact_1035_subset__singletonD,axiom,
    ! [A4: set_state,X: state] :
      ( ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ X @ bot_bot_set_state ) )
     => ( ( A4 = bot_bot_set_state )
        | ( A4
          = ( insert_state @ X @ bot_bot_set_state ) ) ) ) ).

% subset_singletonD
thf(fact_1036_Pow__mono,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ord_le5175021213330142598_state @ ( pow_state @ A4 ) @ ( pow_state @ B4 ) ) ) ).

% Pow_mono
thf(fact_1037_Un__Pow__subset,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] : ( ord_le8498320074568675253_state @ ( sup_su6129196281181032577_state @ ( pow_Pr3120271928052550924_state @ A4 ) @ ( pow_Pr3120271928052550924_state @ B4 ) ) @ ( pow_Pr3120271928052550924_state @ ( sup_su3837536599209510219_state @ A4 @ B4 ) ) ) ).

% Un_Pow_subset
thf(fact_1038_PartialSA_Osum__then__singleton,axiom,
    ! [A: state,B: state,C: state] :
      ( ( ( some_state @ A )
        = ( plus @ B @ C ) )
      = ( ( insert_state @ A @ bot_bot_set_state )
        = ( add_set @ ( insert_state @ B @ bot_bot_set_state ) @ ( insert_state @ C @ bot_bot_set_state ) ) ) ) ).

% PartialSA.sum_then_singleton
thf(fact_1039_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_1040_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_1041_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_1042_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_1043_PartialSA_Osetify__sum__image,axiom,
    ! [P2: state > $o,F: state > state,A4: set_state,B4: set_state] :
      ( ( sep_setify_state @ P2 @ ( add_set @ ( image_state_state @ F @ A4 ) @ B4 ) )
      = ( ! [X2: state] :
            ( ( member_state @ X2 @ A4 )
           => ( sep_setify_state @ P2 @ ( add_set @ ( insert_state @ ( F @ X2 ) @ bot_bot_set_state ) @ B4 ) ) ) ) ) ).

% PartialSA.setify_sum_image
thf(fact_1044_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_1045_PartialSA_Obigger__set,axiom,
    ! [A14: set_state,A4: set_state,B4: set_state] :
      ( ( greater_set @ A14 @ A4 )
     => ( greater_set @ ( add_set @ A14 @ B4 ) @ ( add_set @ A4 @ B4 ) ) ) ).

% PartialSA.bigger_set
thf(fact_1046_PartialSA_Osetify__def,axiom,
    ( sep_setify_state
    = ( ^ [P4: state > $o,A7: set_state] :
        ! [X2: state] :
          ( ( member_state @ X2 @ A7 )
         => ( P4 @ X2 ) ) ) ) ).

% PartialSA.setify_def
thf(fact_1047_PartialSA_Osucc__set__trans,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( greater_set @ A4 @ B4 )
     => ( ( greater_set @ B4 @ C3 )
       => ( greater_set @ A4 @ C3 ) ) ) ).

% PartialSA.succ_set_trans
thf(fact_1048_PartialSA_Olarger__set__refl,axiom,
    ! [A4: set_state] : ( greater_set @ A4 @ A4 ) ).

% PartialSA.larger_set_refl
thf(fact_1049_PartialSA_Ogreater__set__def,axiom,
    ( greater_set
    = ( ^ [A7: set_state,B5: set_state] :
        ! [X2: state] :
          ( ( member_state @ X2 @ A7 )
         => ? [Y5: state] :
              ( ( member_state @ Y5 @ B5 )
              & ( greater @ X2 @ Y5 ) ) ) ) ) ).

% PartialSA.greater_set_def
thf(fact_1050_PartialSA_Ogreater__setI,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ! [A6: state] :
          ( ( member_state @ A6 @ A4 )
         => ? [X4: state] :
              ( ( member_state @ X4 @ B4 )
              & ( greater @ A6 @ X4 ) ) )
     => ( greater_set @ A4 @ B4 ) ) ).

% PartialSA.greater_setI
thf(fact_1051_PartialSA_Omono__prop__set,axiom,
    ! [A4: set_state,B4: set_state,P2: state > $o] :
      ( ( greater_set @ A4 @ B4 )
     => ( ( sep_setify_state @ P2 @ B4 )
       => ( ( sep_mono_prop_state @ plus @ P2 )
         => ( sep_setify_state @ P2 @ A4 ) ) ) ) ).

% PartialSA.mono_prop_set
thf(fact_1052_PartialSA_Osub__bigger,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( greater_set @ A4 @ B4 ) ) ).

% PartialSA.sub_bigger
thf(fact_1053_PartialSA_Osetify__sum,axiom,
    ! [P2: state > $o,A4: set_state,B4: set_state] :
      ( ( sep_setify_state @ P2 @ ( add_set @ A4 @ B4 ) )
      = ( ! [X2: state] :
            ( ( member_state @ X2 @ A4 )
           => ( sep_setify_state @ P2 @ ( add_set @ ( insert_state @ X2 @ bot_bot_set_state ) @ B4 ) ) ) ) ) ).

% PartialSA.setify_sum
thf(fact_1054_PartialSA_Omono__prop__set__equiv,axiom,
    ! [P2: state > $o,A4: set_state,B4: set_state] :
      ( ( sep_mono_prop_state @ plus @ P2 )
     => ( ( sep_equiv_state @ plus @ A4 @ B4 )
       => ( ( sep_setify_state @ P2 @ A4 )
          = ( sep_setify_state @ P2 @ B4 ) ) ) ) ).

% PartialSA.mono_prop_set_equiv
thf(fact_1055_subset__singleton__iff__Uniq,axiom,
    ! [A4: set_Pr4231240917283394591_state] :
      ( ( ? [A2: produc7272280185086996969_state] : ( ord_le4032880777312351359_state @ A4 @ ( insert175804457004744729_state @ A2 @ bot_bo6430881413863817907_state ) ) )
      = ( uniq_P5665941292895050532_state
        @ ^ [X2: produc7272280185086996969_state] : ( member7461423308196221312_state @ X2 @ A4 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1056_subset__singleton__iff__Uniq,axiom,
    ! [A4: set_Pr7649655576376376530on_val] :
      ( ( ? [A2: produc9003781588162623004on_val] : ( ord_le6900622908513426738on_val @ A4 @ ( insert3030518898131756108on_val @ A2 @ bot_bo6722054719108133734on_val ) ) )
      = ( uniq_P8322667716730457431on_val
        @ ^ [X2: produc9003781588162623004on_val] : ( member2879030624002546611on_val @ X2 @ A4 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1057_subset__singleton__iff__Uniq,axiom,
    ! [A4: set_Pr2391701600042252046_state] :
      ( ( ? [A2: produc3882902684156697774_state] : ( ord_le6483787752022044334_state @ A4 @ ( insert94804854012721790_state @ A2 @ bot_bo3524941057552913786_state ) ) )
      = ( uniq_P5626546806380709939_state
        @ ^ [X2: produc3882902684156697774_state] : ( member6715010751053357271_state @ X2 @ A4 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1058_subset__singleton__iff__Uniq,axiom,
    ! [A4: set_state] :
      ( ( ? [A2: state] : ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ A2 @ bot_bot_set_state ) ) )
      = ( uniq_state
        @ ^ [X2: state] : ( member_state @ X2 @ A4 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1059_PartialSA_Oup__closed__bigger__subset,axiom,
    ! [B4: set_state,A4: set_state] :
      ( ( sep_up_closed_state @ plus @ B4 )
     => ( ( greater_set @ A4 @ B4 )
       => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ).

% PartialSA.up_closed_bigger_subset
thf(fact_1060_sep__algebra_Oequiv__up__closed__subset,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A4: set_state,B4: set_state,C3: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ A4 )
       => ( ( sep_equiv_state @ Plus @ B4 @ C3 )
         => ( ( ord_le2494988322063910608_state @ B4 @ A4 )
            = ( ord_le2494988322063910608_state @ C3 @ A4 ) ) ) ) ) ).

% sep_algebra.equiv_up_closed_subset
thf(fact_1061_PartialSA_Oequiv__up__closed__subset,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( sep_up_closed_state @ plus @ A4 )
     => ( ( sep_equiv_state @ plus @ B4 @ C3 )
       => ( ( ord_le2494988322063910608_state @ B4 @ A4 )
          = ( ord_le2494988322063910608_state @ C3 @ A4 ) ) ) ) ).

% PartialSA.equiv_up_closed_subset
thf(fact_1062_PartialSA_Oup__close__equiv,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A4 )
     => ( ( sep_up_closed_state @ plus @ B4 )
       => ( ( sep_equiv_state @ plus @ A4 @ B4 )
          = ( A4 = B4 ) ) ) ) ).

% PartialSA.up_close_equiv
thf(fact_1063_PartialSA_Oup__closed__def,axiom,
    ! [A4: set_state] :
      ( ( sep_up_closed_state @ plus @ A4 )
      = ( ! [Phi3: state] :
            ( ? [X2: state] :
                ( ( member_state @ X2 @ A4 )
                & ( greater @ Phi3 @ X2 ) )
           => ( member_state @ Phi3 @ A4 ) ) ) ) ).

% PartialSA.up_closed_def
thf(fact_1064_PartialSA_Oup__closedI,axiom,
    ! [A4: set_state] :
      ( ! [Phi6: state,Phi5: state] :
          ( ( ( greater @ Phi6 @ Phi5 )
            & ( member_state @ Phi5 @ A4 ) )
         => ( member_state @ Phi6 @ A4 ) )
     => ( sep_up_closed_state @ plus @ A4 ) ) ).

% PartialSA.up_closedI
thf(fact_1065_PartialSA_Oup__closed__sum,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( sep_up_closed_state @ plus @ A4 )
     => ( sep_up_closed_state @ plus @ ( add_set @ A4 @ B4 ) ) ) ).

% PartialSA.up_closed_sum
thf(fact_1066_PartialSA_Oequiv__stable__sum,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( sep_equiv_state @ plus @ A4 @ B4 )
     => ( sep_equiv_state @ plus @ ( add_set @ A4 @ C3 ) @ ( add_set @ B4 @ C3 ) ) ) ).

% PartialSA.equiv_stable_sum
thf(fact_1067_PartialSA_Oequiv__def,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( sep_equiv_state @ plus @ A4 @ B4 )
      = ( ( greater_set @ A4 @ B4 )
        & ( greater_set @ B4 @ A4 ) ) ) ).

% PartialSA.equiv_def
thf(fact_1068_PartialSA_OequivI,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( greater_set @ A4 @ B4 )
     => ( ( greater_set @ B4 @ A4 )
       => ( sep_equiv_state @ plus @ A4 @ B4 ) ) ) ).

% PartialSA.equivI
thf(fact_1069_PartialSA_Oupper__closure__up__closed,axiom,
    ! [A4: set_state] : ( sep_up_closed_state @ plus @ ( sep_up1246176804924251236_state @ plus @ A4 ) ) ).

% PartialSA.upper_closure_up_closed
thf(fact_1070_sep__algebra_Oup__closed__bigger__subset,axiom,
    ! [Plus: state > state > option_state,Core: state > state,B4: set_state,A4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( sep_up_closed_state @ Plus @ B4 )
       => ( ( sep_gr7105985528888466643_state @ Plus @ A4 @ B4 )
         => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ) ).

% sep_algebra.up_closed_bigger_subset
thf(fact_1071_map__add__upd,axiom,
    ! [F: produc1457211279475724562t_char > option_val,G: produc1457211279475724562t_char > option_val,X: produc1457211279475724562t_char,Y: val] :
      ( ( map_ad2908576761495157028ar_val @ F @ ( fun_up5735975307950539954on_val @ G @ X @ ( some_val @ Y ) ) )
      = ( fun_up5735975307950539954on_val @ ( map_ad2908576761495157028ar_val @ F @ G ) @ X @ ( some_val @ Y ) ) ) ).

% map_add_upd
thf(fact_1072_image__map__upd,axiom,
    ! [X: state,A4: set_state,M: state > option_state,Y: state] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( image_6076465424260689483_state @ ( fun_up8843634000204221123_state @ M @ X @ ( some_state @ Y ) ) @ A4 )
        = ( image_6076465424260689483_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1073_image__map__upd,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_state,Y: state] :
      ( ~ ( member7461423308196221312_state @ X @ A4 )
     => ( ( image_2999075161041214458_state @ ( fun_up3650151817091186_state @ M @ X @ ( some_state @ Y ) ) @ A4 )
        = ( image_2999075161041214458_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1074_image__map__upd,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_state,Y: state] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( image_2102623794538073773_state @ ( fun_up6681822530636708645_state @ M @ X @ ( some_state @ Y ) ) @ A4 )
        = ( image_2102623794538073773_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1075_image__map__upd,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_state,Y: state] :
      ( ~ ( member6715010751053357271_state @ X @ A4 )
     => ( ( image_514124101551762675_state @ ( fun_up3435231866794294907_state @ M @ X @ ( some_state @ Y ) ) @ A4 )
        = ( image_514124101551762675_state @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1076_image__map__upd,axiom,
    ! [X: state,A4: set_state,M: state > option_val,Y: val] :
      ( ~ ( member_state @ X @ A4 )
     => ( ( image_6342712743741534278on_val @ ( fun_up5073147608505813454on_val @ M @ X @ ( some_val @ Y ) ) @ A4 )
        = ( image_6342712743741534278on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1077_image__map__upd,axiom,
    ! [X: produc7272280185086996969_state,A4: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_val,Y: val] :
      ( ~ ( member7461423308196221312_state @ X @ A4 )
     => ( ( image_6558870149253005655on_val @ ( fun_up3509650811975514847on_val @ M @ X @ ( some_val @ Y ) ) @ A4 )
        = ( image_6558870149253005655on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1078_image__map__upd,axiom,
    ! [X: produc9003781588162623004on_val,A4: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_val,Y: val] :
      ( ~ ( member2879030624002546611on_val @ X @ A4 )
     => ( ( image_453284115904594532on_val @ ( fun_up8559965269643824108on_val @ M @ X @ ( some_val @ Y ) ) @ A4 )
        = ( image_453284115904594532on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1079_image__map__upd,axiom,
    ! [X: produc3882902684156697774_state,A4: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_val,Y: val] :
      ( ~ ( member6715010751053357271_state @ X @ A4 )
     => ( ( image_4156654006938117022on_val @ ( fun_up3736070447144131606on_val @ M @ X @ ( some_val @ Y ) ) @ A4 )
        = ( image_4156654006938117022on_val @ M @ A4 ) ) ) ).

% image_map_upd
thf(fact_1080_graph__map__upd,axiom,
    ! [M: option_state > option_option_state,K: option_state,V: option_state] :
      ( ( graph_628825510059920660_state @ ( fun_up8433615654909047651_state @ M @ K @ ( some_option_state @ V ) ) )
      = ( insert4171857611248116165_state @ ( produc9160152616361873709_state @ K @ V ) @ ( graph_628825510059920660_state @ ( fun_up8433615654909047651_state @ M @ K @ none_option_state ) ) ) ) ).

% graph_map_upd
thf(fact_1081_graph__map__upd,axiom,
    ! [M: prat > option_set_state,K: prat,V: set_state] :
      ( ( graph_prat_set_state @ ( fun_up5484256749267628047_state @ M @ K @ ( some_set_state @ V ) ) )
      = ( insert2241947522006009073_state @ ( produc9080284787853255769_state @ K @ V ) @ ( graph_prat_set_state @ ( fun_up5484256749267628047_state @ M @ K @ none_set_state ) ) ) ) ).

% graph_map_upd
thf(fact_1082_graph__map__upd,axiom,
    ! [M: nat > option_list_char,K: nat,V: list_char] :
      ( ( graph_nat_list_char @ ( fun_up4009399622604172288t_char @ M @ K @ ( some_list_char @ V ) ) )
      = ( insert3372640069787401954t_char @ ( produc120197956887798346t_char @ K @ V ) @ ( graph_nat_list_char @ ( fun_up4009399622604172288t_char @ M @ K @ none_list_char ) ) ) ) ).

% graph_map_upd
thf(fact_1083_graph__map__upd,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat,V: produc1457211279475724562t_char > option_val] :
      ( ( graph_1288227317702120175on_val @ ( fun_up1601731230164360576on_val @ M @ K @ ( some_P7669353234731512949on_val @ V ) ) )
      = ( insert3030518898131756108on_val @ ( produc74620467203698198on_val @ K @ V ) @ ( graph_1288227317702120175on_val @ ( fun_up1601731230164360576on_val @ M @ K @ none_P1334921381875262201on_val ) ) ) ) ).

% graph_map_upd
thf(fact_1084_graph__map__upd,axiom,
    ! [M: prat > option_state,K: prat,V: state] :
      ( ( graph_prat_state @ ( fun_up1472322128373081433_state @ M @ K @ ( some_state @ V ) ) )
      = ( insert3559717418277143099_state @ ( produc6205719116230455971_state @ K @ V ) @ ( graph_prat_state @ ( fun_up1472322128373081433_state @ M @ K @ none_state ) ) ) ) ).

% graph_map_upd
thf(fact_1085_sep__algebra_Osub__bigger,axiom,
    ! [Plus: state > state > option_state,Core: state > state,A4: set_state,B4: set_state] :
      ( ( sep_algebra_state @ Plus @ Core )
     => ( ( ord_le2494988322063910608_state @ A4 @ B4 )
       => ( sep_gr7105985528888466643_state @ Plus @ A4 @ B4 ) ) ) ).

% sep_algebra.sub_bigger
thf(fact_1086_greater__set__def,axiom,
    ( greater_set
    = ( sep_gr7105985528888466643_state @ plus ) ) ).

% greater_set_def
thf(fact_1087_graph__fun__upd__None,axiom,
    ! [M: state > option_state_state,K: state] :
      ( ( graph_5871261288037090637_state @ ( fun_up4553069608533601692_state @ M @ K @ none_state_state ) )
      = ( collec394671971739345689_state
        @ ^ [E: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ E @ ( graph_5871261288037090637_state @ M ) )
            & ( ( produc7095885521192019410_state @ E )
             != K ) ) ) ) ).

% graph_fun_upd_None
thf(fact_1088_graph__fun__upd__None,axiom,
    ! [M: state > option886743748074664436_state,K: state] :
      ( ( graph_7551141711029462004_state @ ( fun_up2912618647338797435_state @ M @ K @ none_P5922852279678757647_state ) )
      = ( collec906845016635587262_state
        @ ^ [E: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ E @ ( graph_7551141711029462004_state @ M ) )
            & ( ( produc848024588167747631_state @ E )
             != K ) ) ) ) ).

% graph_fun_upd_None
thf(fact_1089_graph__fun__upd__None,axiom,
    ! [M: nat > option_list_char,K: nat] :
      ( ( graph_nat_list_char @ ( fun_up4009399622604172288t_char @ M @ K @ none_list_char ) )
      = ( collec2458894688891239037t_char
        @ ^ [E: produc1457211279475724562t_char] :
            ( ( member484235747325421115t_char @ E @ ( graph_nat_list_char @ M ) )
            & ( ( produc6204653154488278070t_char @ E )
             != K ) ) ) ) ).

% graph_fun_upd_None
thf(fact_1090_graph__fun__upd__None,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val,K: produc1457211279475724562t_char > prat] :
      ( ( graph_1288227317702120175on_val @ ( fun_up1601731230164360576on_val @ M @ K @ none_P1334921381875262201on_val ) )
      = ( collec7475294502966882545on_val
        @ ^ [E: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ E @ ( graph_1288227317702120175on_val @ M ) )
            & ( ( produc5239619271231976746on_val @ E )
             != K ) ) ) ) ).

% graph_fun_upd_None
thf(fact_1091_fun__upd__None__restrict,axiom,
    ! [X: produc7272280185086996969_state,D2: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_state] :
      ( ( ( member7461423308196221312_state @ X @ D2 )
       => ( ( fun_up3650151817091186_state @ ( restri6145314162897174997_state @ M @ D2 ) @ X @ none_state )
          = ( restri6145314162897174997_state @ M @ ( minus_2078076265878351864_state @ D2 @ ( insert175804457004744729_state @ X @ bot_bo6430881413863817907_state ) ) ) ) )
      & ( ~ ( member7461423308196221312_state @ X @ D2 )
       => ( ( fun_up3650151817091186_state @ ( restri6145314162897174997_state @ M @ D2 ) @ X @ none_state )
          = ( restri6145314162897174997_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1092_fun__upd__None__restrict,axiom,
    ! [X: produc9003781588162623004on_val,D2: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_state] :
      ( ( ( member2879030624002546611on_val @ X @ D2 )
       => ( ( fun_up6681822530636708645_state @ ( restri5336766904122854152_state @ M @ D2 ) @ X @ none_state )
          = ( restri5336766904122854152_state @ M @ ( minus_9160195963678339755on_val @ D2 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ) ) )
      & ( ~ ( member2879030624002546611on_val @ X @ D2 )
       => ( ( fun_up6681822530636708645_state @ ( restri5336766904122854152_state @ M @ D2 ) @ X @ none_state )
          = ( restri5336766904122854152_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1093_fun__upd__None__restrict,axiom,
    ! [X: produc3882902684156697774_state,D2: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_state] :
      ( ( ( member6715010751053357271_state @ X @ D2 )
       => ( ( fun_up3435231866794294907_state @ ( restri6706757876287616696_state @ M @ D2 ) @ X @ none_state )
          = ( restri6706757876287616696_state @ M @ ( minus_5498279039490143093_state @ D2 @ ( insert94804854012721790_state @ X @ bot_bo3524941057552913786_state ) ) ) ) )
      & ( ~ ( member6715010751053357271_state @ X @ D2 )
       => ( ( fun_up3435231866794294907_state @ ( restri6706757876287616696_state @ M @ D2 ) @ X @ none_state )
          = ( restri6706757876287616696_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1094_fun__upd__None__restrict,axiom,
    ! [X: produc7272280185086996969_state,D2: set_Pr4231240917283394591_state,M: produc7272280185086996969_state > option_val] :
      ( ( ( member7461423308196221312_state @ X @ D2 )
       => ( ( fun_up3509650811975514847on_val @ ( restri6051517647513894te_val @ M @ D2 ) @ X @ none_val )
          = ( restri6051517647513894te_val @ M @ ( minus_2078076265878351864_state @ D2 @ ( insert175804457004744729_state @ X @ bot_bo6430881413863817907_state ) ) ) ) )
      & ( ~ ( member7461423308196221312_state @ X @ D2 )
       => ( ( fun_up3509650811975514847on_val @ ( restri6051517647513894te_val @ M @ D2 ) @ X @ none_val )
          = ( restri6051517647513894te_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1095_fun__upd__None__restrict,axiom,
    ! [X: produc9003781588162623004on_val,D2: set_Pr7649655576376376530on_val,M: produc9003781588162623004on_val > option_val] :
      ( ( ( member2879030624002546611on_val @ X @ D2 )
       => ( ( fun_up8559965269643824108on_val @ ( restri5251746167140823987al_val @ M @ D2 ) @ X @ none_val )
          = ( restri5251746167140823987al_val @ M @ ( minus_9160195963678339755on_val @ D2 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) ) ) )
      & ( ~ ( member2879030624002546611on_val @ X @ D2 )
       => ( ( fun_up8559965269643824108on_val @ ( restri5251746167140823987al_val @ M @ D2 ) @ X @ none_val )
          = ( restri5251746167140823987al_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1096_fun__upd__None__restrict,axiom,
    ! [X: produc3882902684156697774_state,D2: set_Pr2391701600042252046_state,M: produc3882902684156697774_state > option_val] :
      ( ( ( member6715010751053357271_state @ X @ D2 )
       => ( ( fun_up3736070447144131606on_val @ ( restri214263546473948163te_val @ M @ D2 ) @ X @ none_val )
          = ( restri214263546473948163te_val @ M @ ( minus_5498279039490143093_state @ D2 @ ( insert94804854012721790_state @ X @ bot_bo3524941057552913786_state ) ) ) ) )
      & ( ~ ( member6715010751053357271_state @ X @ D2 )
       => ( ( fun_up3736070447144131606on_val @ ( restri214263546473948163te_val @ M @ D2 ) @ X @ none_val )
          = ( restri214263546473948163te_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1097_fun__upd__None__restrict,axiom,
    ! [X: state,D2: set_state,M: state > option_state] :
      ( ( ( member_state @ X @ D2 )
       => ( ( fun_up8843634000204221123_state @ ( restri2287918369865870758_state @ M @ D2 ) @ X @ none_state )
          = ( restri2287918369865870758_state @ M @ ( minus_3933957440811877961_state @ D2 @ ( insert_state @ X @ bot_bot_set_state ) ) ) ) )
      & ( ~ ( member_state @ X @ D2 )
       => ( ( fun_up8843634000204221123_state @ ( restri2287918369865870758_state @ M @ D2 ) @ X @ none_state )
          = ( restri2287918369865870758_state @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1098_fun__upd__None__restrict,axiom,
    ! [X: state,D2: set_state,M: state > option_val] :
      ( ( ( member_state @ X @ D2 )
       => ( ( fun_up5073147608505813454on_val @ ( restri6052284935360306837te_val @ M @ D2 ) @ X @ none_val )
          = ( restri6052284935360306837te_val @ M @ ( minus_3933957440811877961_state @ D2 @ ( insert_state @ X @ bot_bot_set_state ) ) ) ) )
      & ( ~ ( member_state @ X @ D2 )
       => ( ( fun_up5073147608505813454on_val @ ( restri6052284935360306837te_val @ M @ D2 ) @ X @ none_val )
          = ( restri6052284935360306837te_val @ M @ D2 ) ) ) ) ).

% fun_upd_None_restrict
thf(fact_1099_restrict__upd__same,axiom,
    ! [M: state > option_state,X: state,Y: state] :
      ( ( restri2287918369865870758_state @ ( fun_up8843634000204221123_state @ M @ X @ ( some_state @ Y ) ) @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) )
      = ( restri2287918369865870758_state @ M @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) ) ) ).

% restrict_upd_same
thf(fact_1100_restrict__upd__same,axiom,
    ! [M: state > option_val,X: state,Y: val] :
      ( ( restri6052284935360306837te_val @ ( fun_up5073147608505813454on_val @ M @ X @ ( some_val @ Y ) ) @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) )
      = ( restri6052284935360306837te_val @ M @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) ) ) ).

% restrict_upd_same
thf(fact_1101_Compl__anti__mono,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ B4 ) @ ( uminus472742206872269241_state @ A4 ) ) ) ).

% Compl_anti_mono
thf(fact_1102_Compl__subset__Compl__iff,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ A4 ) @ ( uminus472742206872269241_state @ B4 ) )
      = ( ord_le2494988322063910608_state @ B4 @ A4 ) ) ).

% Compl_subset_Compl_iff
thf(fact_1103_Diff__eq__empty__iff,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ( minus_3933957440811877961_state @ A4 @ B4 )
        = bot_bot_set_state )
      = ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ).

% Diff_eq_empty_iff
thf(fact_1104_subset__Compl__singleton,axiom,
    ! [A4: set_Pr4231240917283394591_state,B: produc7272280185086996969_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ ( uminus1327639380719934312_state @ ( insert175804457004744729_state @ B @ bot_bo6430881413863817907_state ) ) )
      = ( ~ ( member7461423308196221312_state @ B @ A4 ) ) ) ).

% subset_Compl_singleton
thf(fact_1105_subset__Compl__singleton,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B: produc9003781588162623004on_val] :
      ( ( ord_le6900622908513426738on_val @ A4 @ ( uminus2423024474186858011on_val @ ( insert3030518898131756108on_val @ B @ bot_bo6722054719108133734on_val ) ) )
      = ( ~ ( member2879030624002546611on_val @ B @ A4 ) ) ) ).

% subset_Compl_singleton
thf(fact_1106_subset__Compl__singleton,axiom,
    ! [A4: set_Pr2391701600042252046_state,B: produc3882902684156697774_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ ( uminus8176724999004996613_state @ ( insert94804854012721790_state @ B @ bot_bo3524941057552913786_state ) ) )
      = ( ~ ( member6715010751053357271_state @ B @ A4 ) ) ) ).

% subset_Compl_singleton
thf(fact_1107_subset__Compl__singleton,axiom,
    ! [A4: set_state,B: state] :
      ( ( ord_le2494988322063910608_state @ A4 @ ( uminus472742206872269241_state @ ( insert_state @ B @ bot_bot_set_state ) ) )
      = ( ~ ( member_state @ B @ A4 ) ) ) ).

% subset_Compl_singleton
thf(fact_1108_subset__Diff__insert,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,X: produc7272280185086996969_state,C3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ ( minus_2078076265878351864_state @ B4 @ ( insert175804457004744729_state @ X @ C3 ) ) )
      = ( ( ord_le4032880777312351359_state @ A4 @ ( minus_2078076265878351864_state @ B4 @ C3 ) )
        & ~ ( member7461423308196221312_state @ X @ A4 ) ) ) ).

% subset_Diff_insert
thf(fact_1109_subset__Diff__insert,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val,C3: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ A4 @ ( minus_9160195963678339755on_val @ B4 @ ( insert3030518898131756108on_val @ X @ C3 ) ) )
      = ( ( ord_le6900622908513426738on_val @ A4 @ ( minus_9160195963678339755on_val @ B4 @ C3 ) )
        & ~ ( member2879030624002546611on_val @ X @ A4 ) ) ) ).

% subset_Diff_insert
thf(fact_1110_subset__Diff__insert,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,X: produc3882902684156697774_state,C3: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ ( minus_5498279039490143093_state @ B4 @ ( insert94804854012721790_state @ X @ C3 ) ) )
      = ( ( ord_le6483787752022044334_state @ A4 @ ( minus_5498279039490143093_state @ B4 @ C3 ) )
        & ~ ( member6715010751053357271_state @ X @ A4 ) ) ) ).

% subset_Diff_insert
thf(fact_1111_subset__Diff__insert,axiom,
    ! [A4: set_state,B4: set_state,X: state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ ( minus_3933957440811877961_state @ B4 @ ( insert_state @ X @ C3 ) ) )
      = ( ( ord_le2494988322063910608_state @ A4 @ ( minus_3933957440811877961_state @ B4 @ C3 ) )
        & ~ ( member_state @ X @ A4 ) ) ) ).

% subset_Diff_insert
thf(fact_1112_image__diff__subset,axiom,
    ! [F: state > state,A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ ( image_state_state @ F @ A4 ) @ ( image_state_state @ F @ B4 ) ) @ ( image_state_state @ F @ ( minus_3933957440811877961_state @ A4 @ B4 ) ) ) ).

% image_diff_subset
thf(fact_1113_Diff__partition,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ B4 )
     => ( ( sup_su3837536599209510219_state @ A4 @ ( minus_2078076265878351864_state @ B4 @ A4 ) )
        = B4 ) ) ).

% Diff_partition
thf(fact_1114_Diff__partition,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( sup_sup_set_state @ A4 @ ( minus_3933957440811877961_state @ B4 @ A4 ) )
        = B4 ) ) ).

% Diff_partition
thf(fact_1115_Diff__subset__conv,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( minus_2078076265878351864_state @ A4 @ B4 ) @ C3 )
      = ( ord_le4032880777312351359_state @ A4 @ ( sup_su3837536599209510219_state @ B4 @ C3 ) ) ) ).

% Diff_subset_conv
thf(fact_1116_Diff__subset__conv,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ B4 ) @ C3 )
      = ( ord_le2494988322063910608_state @ A4 @ ( sup_sup_set_state @ B4 @ C3 ) ) ) ).

% Diff_subset_conv
thf(fact_1117_Diff__mono,axiom,
    ! [A4: set_state,C3: set_state,D2: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ C3 )
     => ( ( ord_le2494988322063910608_state @ D2 @ B4 )
       => ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ B4 ) @ ( minus_3933957440811877961_state @ C3 @ D2 ) ) ) ) ).

% Diff_mono
thf(fact_1118_Diff__subset,axiom,
    ! [A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ B4 ) @ A4 ) ).

% Diff_subset
thf(fact_1119_double__diff,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
       => ( ( minus_3933957440811877961_state @ B4 @ ( minus_3933957440811877961_state @ C3 @ A4 ) )
          = A4 ) ) ) ).

% double_diff
thf(fact_1120_subset__Compl__self__eq,axiom,
    ! [A4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ ( uminus472742206872269241_state @ A4 ) )
      = ( A4 = bot_bot_set_state ) ) ).

% subset_Compl_self_eq
thf(fact_1121_subset__insert__iff,axiom,
    ! [A4: set_Pr4231240917283394591_state,X: produc7272280185086996969_state,B4: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ A4 @ ( insert175804457004744729_state @ X @ B4 ) )
      = ( ( ( member7461423308196221312_state @ X @ A4 )
         => ( ord_le4032880777312351359_state @ ( minus_2078076265878351864_state @ A4 @ ( insert175804457004744729_state @ X @ bot_bo6430881413863817907_state ) ) @ B4 ) )
        & ( ~ ( member7461423308196221312_state @ X @ A4 )
         => ( ord_le4032880777312351359_state @ A4 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1122_subset__insert__iff,axiom,
    ! [A4: set_Pr7649655576376376530on_val,X: produc9003781588162623004on_val,B4: set_Pr7649655576376376530on_val] :
      ( ( ord_le6900622908513426738on_val @ A4 @ ( insert3030518898131756108on_val @ X @ B4 ) )
      = ( ( ( member2879030624002546611on_val @ X @ A4 )
         => ( ord_le6900622908513426738on_val @ ( minus_9160195963678339755on_val @ A4 @ ( insert3030518898131756108on_val @ X @ bot_bo6722054719108133734on_val ) ) @ B4 ) )
        & ( ~ ( member2879030624002546611on_val @ X @ A4 )
         => ( ord_le6900622908513426738on_val @ A4 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1123_subset__insert__iff,axiom,
    ! [A4: set_Pr2391701600042252046_state,X: produc3882902684156697774_state,B4: set_Pr2391701600042252046_state] :
      ( ( ord_le6483787752022044334_state @ A4 @ ( insert94804854012721790_state @ X @ B4 ) )
      = ( ( ( member6715010751053357271_state @ X @ A4 )
         => ( ord_le6483787752022044334_state @ ( minus_5498279039490143093_state @ A4 @ ( insert94804854012721790_state @ X @ bot_bo3524941057552913786_state ) ) @ B4 ) )
        & ( ~ ( member6715010751053357271_state @ X @ A4 )
         => ( ord_le6483787752022044334_state @ A4 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1124_subset__insert__iff,axiom,
    ! [A4: set_state,X: state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ X @ B4 ) )
      = ( ( ( member_state @ X @ A4 )
         => ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ ( insert_state @ X @ bot_bot_set_state ) ) @ B4 ) )
        & ( ~ ( member_state @ X @ A4 )
         => ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1125_Diff__single__insert,axiom,
    ! [A4: set_state,X: state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ ( insert_state @ X @ bot_bot_set_state ) ) @ B4 )
     => ( ord_le2494988322063910608_state @ A4 @ ( insert_state @ X @ B4 ) ) ) ).

% Diff_single_insert
thf(fact_1126_restrict__complement__singleton__eq,axiom,
    ! [F: state > option_state,X: state] :
      ( ( restri2287918369865870758_state @ F @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) )
      = ( fun_up8843634000204221123_state @ F @ X @ none_state ) ) ).

% restrict_complement_singleton_eq
thf(fact_1127_restrict__complement__singleton__eq,axiom,
    ! [F: state > option_val,X: state] :
      ( ( restri6052284935360306837te_val @ F @ ( uminus472742206872269241_state @ ( insert_state @ X @ bot_bot_set_state ) ) )
      = ( fun_up5073147608505813454on_val @ F @ X @ none_val ) ) ).

% restrict_complement_singleton_eq
thf(fact_1128_compl__le__compl__iff,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ X ) @ ( uminus472742206872269241_state @ Y ) )
      = ( ord_le2494988322063910608_state @ Y @ X ) ) ).

% compl_le_compl_iff
thf(fact_1129_compl__le__swap2,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ Y ) @ X )
     => ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ X ) @ Y ) ) ).

% compl_le_swap2
thf(fact_1130_compl__le__swap1,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ ( uminus472742206872269241_state @ X ) )
     => ( ord_le2494988322063910608_state @ X @ ( uminus472742206872269241_state @ Y ) ) ) ).

% compl_le_swap1
thf(fact_1131_compl__mono,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ Y ) @ ( uminus472742206872269241_state @ X ) ) ) ).

% compl_mono
thf(fact_1132_diff__shunt__var,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ( minus_3933957440811877961_state @ X @ Y )
        = bot_bot_set_state )
      = ( ord_le2494988322063910608_state @ X @ Y ) ) ).

% diff_shunt_var
thf(fact_1133_dom__fun__upd,axiom,
    ! [Y: option_state,F: state > option_state,X: state] :
      ( ( ( Y = none_state )
       => ( ( dom_state_state @ ( fun_up8843634000204221123_state @ F @ X @ Y ) )
          = ( minus_3933957440811877961_state @ ( dom_state_state @ F ) @ ( insert_state @ X @ bot_bot_set_state ) ) ) )
      & ( ( Y != none_state )
       => ( ( dom_state_state @ ( fun_up8843634000204221123_state @ F @ X @ Y ) )
          = ( insert_state @ X @ ( dom_state_state @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_1134_dom__fun__upd,axiom,
    ! [Y: option_val,F: state > option_val,X: state] :
      ( ( ( Y = none_val )
       => ( ( dom_state_val @ ( fun_up5073147608505813454on_val @ F @ X @ Y ) )
          = ( minus_3933957440811877961_state @ ( dom_state_val @ F ) @ ( insert_state @ X @ bot_bot_set_state ) ) ) )
      & ( ( Y != none_val )
       => ( ( dom_state_val @ ( fun_up5073147608505813454on_val @ F @ X @ Y ) )
          = ( insert_state @ X @ ( dom_state_val @ F ) ) ) ) ) ).

% dom_fun_upd
thf(fact_1135_dom__eq__singleton__conv,axiom,
    ! [F: state > option_state,X: state] :
      ( ( ( dom_state_state @ F )
        = ( insert_state @ X @ bot_bot_set_state ) )
      = ( ? [V3: state] :
            ( F
            = ( fun_up8843634000204221123_state
              @ ^ [X2: state] : none_state
              @ X
              @ ( some_state @ V3 ) ) ) ) ) ).

% dom_eq_singleton_conv
thf(fact_1136_dom__eq__singleton__conv,axiom,
    ! [F: state > option_val,X: state] :
      ( ( ( dom_state_val @ F )
        = ( insert_state @ X @ bot_bot_set_state ) )
      = ( ? [V3: val] :
            ( F
            = ( fun_up5073147608505813454on_val
              @ ^ [X2: state] : none_val
              @ X
              @ ( some_val @ V3 ) ) ) ) ) ).

% dom_eq_singleton_conv
thf(fact_1137_dom__eq__empty__conv,axiom,
    ! [F: state > option_state] :
      ( ( ( dom_state_state @ F )
        = bot_bot_set_state )
      = ( F
        = ( ^ [X2: state] : none_state ) ) ) ).

% dom_eq_empty_conv
thf(fact_1138_dom__eq__empty__conv,axiom,
    ! [F: state > option_val] :
      ( ( ( dom_state_val @ F )
        = bot_bot_set_state )
      = ( F
        = ( ^ [X2: state] : none_val ) ) ) ).

% dom_eq_empty_conv
thf(fact_1139_dom__map__add,axiom,
    ! [M: produc1457211279475724562t_char > option_val,N: produc1457211279475724562t_char > option_val] :
      ( ( dom_Pr8989479155164304065ar_val @ ( map_ad2908576761495157028ar_val @ M @ N ) )
      = ( sup_su7899656352754981958t_char @ ( dom_Pr8989479155164304065ar_val @ N ) @ ( dom_Pr8989479155164304065ar_val @ M ) ) ) ).

% dom_map_add
thf(fact_1140_fun__upd__None__if__notin__dom,axiom,
    ! [K: state,M: state > option_state] :
      ( ~ ( member_state @ K @ ( dom_state_state @ M ) )
     => ( ( fun_up8843634000204221123_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1141_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc7272280185086996969_state,M: produc7272280185086996969_state > option_state] :
      ( ~ ( member7461423308196221312_state @ K @ ( dom_Pr5710779687127367671_state @ M ) )
     => ( ( fun_up3650151817091186_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1142_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_state] :
      ( ~ ( member2879030624002546611on_val @ K @ ( dom_Pr4448331044451638570_state @ M ) )
     => ( ( fun_up6681822530636708645_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1143_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc3882902684156697774_state,M: produc3882902684156697774_state > option_state] :
      ( ~ ( member6715010751053357271_state @ K @ ( dom_Pr6427157690771563798_state @ M ) )
     => ( ( fun_up3435231866794294907_state @ M @ K @ none_state )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1144_fun__upd__None__if__notin__dom,axiom,
    ! [K: state,M: state > option_val] :
      ( ~ ( member_state @ K @ ( dom_state_val @ M ) )
     => ( ( fun_up5073147608505813454on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1145_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc7272280185086996969_state,M: produc7272280185086996969_state > option_val] :
      ( ~ ( member7461423308196221312_state @ K @ ( dom_Pr2419751218887380356te_val @ M ) )
     => ( ( fun_up3509650811975514847on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1146_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_val] :
      ( ~ ( member2879030624002546611on_val @ K @ ( dom_Pr7381289304162206737al_val @ M ) )
     => ( ( fun_up8559965269643824108on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1147_fun__upd__None__if__notin__dom,axiom,
    ! [K: produc3882902684156697774_state,M: produc3882902684156697774_state > option_val] :
      ( ~ ( member6715010751053357271_state @ K @ ( dom_Pr7370380374925980453te_val @ M ) )
     => ( ( fun_up3736070447144131606on_val @ M @ K @ none_val )
        = M ) ) ).

% fun_upd_None_if_notin_dom
thf(fact_1148_dom__empty,axiom,
    ( ( dom_state_state
      @ ^ [X2: state] : none_state )
    = bot_bot_set_state ) ).

% dom_empty
thf(fact_1149_dom__empty,axiom,
    ( ( dom_state_val
      @ ^ [X2: state] : none_val )
    = bot_bot_set_state ) ).

% dom_empty
thf(fact_1150_graph__domD,axiom,
    ! [X: produc7272280185086996969_state,M: state > option886743748074664436_state] :
      ( ( member7461423308196221312_state @ X @ ( graph_7551141711029462004_state @ M ) )
     => ( member_state @ ( produc848024588167747631_state @ X ) @ ( dom_st4979949223050981664_state @ M ) ) ) ).

% graph_domD
thf(fact_1151_graph__domD,axiom,
    ! [X: produc3882902684156697774_state,M: state > option_state_state] :
      ( ( member6715010751053357271_state @ X @ ( graph_5871261288037090637_state @ M ) )
     => ( member_state @ ( produc7095885521192019410_state @ X ) @ ( dom_st4905852154126539553_state @ M ) ) ) ).

% graph_domD
thf(fact_1152_graph__domD,axiom,
    ! [X: produc1457211279475724562t_char,M: nat > option_list_char] :
      ( ( member484235747325421115t_char @ X @ ( graph_nat_list_char @ M ) )
     => ( member_nat @ ( produc6204653154488278070t_char @ X ) @ ( dom_nat_list_char @ M ) ) ) ).

% graph_domD
thf(fact_1153_graph__domD,axiom,
    ! [X: produc9003781588162623004on_val,M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( member2879030624002546611on_val @ X @ ( graph_1288227317702120175on_val @ M ) )
     => ( member2336342582916103932r_prat @ ( produc5239619271231976746on_val @ X ) @ ( dom_Pr4152820065153570843on_val @ M ) ) ) ).

% graph_domD
thf(fact_1154_map__add__dom__app__simps_I1_J,axiom,
    ! [M: produc1457211279475724562t_char,L2: produc1457211279475724562t_char > option_val,L1: produc1457211279475724562t_char > option_val] :
      ( ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L2 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L2 @ M ) ) ) ).

% map_add_dom_app_simps(1)
thf(fact_1155_map__add__dom__app__simps_I2_J,axiom,
    ! [M: produc1457211279475724562t_char,L1: produc1457211279475724562t_char > option_val,L2: produc1457211279475724562t_char > option_val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L1 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L2 @ M ) ) ) ).

% map_add_dom_app_simps(2)
thf(fact_1156_map__add__dom__app__simps_I3_J,axiom,
    ! [M: produc1457211279475724562t_char,L2: produc1457211279475724562t_char > option_val,L1: produc1457211279475724562t_char > option_val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ L2 ) )
     => ( ( map_ad2908576761495157028ar_val @ L1 @ L2 @ M )
        = ( L1 @ M ) ) ) ).

% map_add_dom_app_simps(3)
thf(fact_1157_domI,axiom,
    ! [M: state > option_state,A: state,B: state] :
      ( ( ( M @ A )
        = ( some_state @ B ) )
     => ( member_state @ A @ ( dom_state_state @ M ) ) ) ).

% domI
thf(fact_1158_domI,axiom,
    ! [M: produc7272280185086996969_state > option_state,A: produc7272280185086996969_state,B: state] :
      ( ( ( M @ A )
        = ( some_state @ B ) )
     => ( member7461423308196221312_state @ A @ ( dom_Pr5710779687127367671_state @ M ) ) ) ).

% domI
thf(fact_1159_domI,axiom,
    ! [M: produc9003781588162623004on_val > option_state,A: produc9003781588162623004on_val,B: state] :
      ( ( ( M @ A )
        = ( some_state @ B ) )
     => ( member2879030624002546611on_val @ A @ ( dom_Pr4448331044451638570_state @ M ) ) ) ).

% domI
thf(fact_1160_domI,axiom,
    ! [M: produc3882902684156697774_state > option_state,A: produc3882902684156697774_state,B: state] :
      ( ( ( M @ A )
        = ( some_state @ B ) )
     => ( member6715010751053357271_state @ A @ ( dom_Pr6427157690771563798_state @ M ) ) ) ).

% domI
thf(fact_1161_domI,axiom,
    ! [M: state > option_val,A: state,B: val] :
      ( ( ( M @ A )
        = ( some_val @ B ) )
     => ( member_state @ A @ ( dom_state_val @ M ) ) ) ).

% domI
thf(fact_1162_domI,axiom,
    ! [M: produc7272280185086996969_state > option_val,A: produc7272280185086996969_state,B: val] :
      ( ( ( M @ A )
        = ( some_val @ B ) )
     => ( member7461423308196221312_state @ A @ ( dom_Pr2419751218887380356te_val @ M ) ) ) ).

% domI
thf(fact_1163_domI,axiom,
    ! [M: produc9003781588162623004on_val > option_val,A: produc9003781588162623004on_val,B: val] :
      ( ( ( M @ A )
        = ( some_val @ B ) )
     => ( member2879030624002546611on_val @ A @ ( dom_Pr7381289304162206737al_val @ M ) ) ) ).

% domI
thf(fact_1164_domI,axiom,
    ! [M: produc3882902684156697774_state > option_val,A: produc3882902684156697774_state,B: val] :
      ( ( ( M @ A )
        = ( some_val @ B ) )
     => ( member6715010751053357271_state @ A @ ( dom_Pr7370380374925980453te_val @ M ) ) ) ).

% domI
thf(fact_1165_domD,axiom,
    ! [A: state,M: state > option_state] :
      ( ( member_state @ A @ ( dom_state_state @ M ) )
     => ? [B6: state] :
          ( ( M @ A )
          = ( some_state @ B6 ) ) ) ).

% domD
thf(fact_1166_domD,axiom,
    ! [A: produc7272280185086996969_state,M: produc7272280185086996969_state > option_state] :
      ( ( member7461423308196221312_state @ A @ ( dom_Pr5710779687127367671_state @ M ) )
     => ? [B6: state] :
          ( ( M @ A )
          = ( some_state @ B6 ) ) ) ).

% domD
thf(fact_1167_domD,axiom,
    ! [A: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_state] :
      ( ( member2879030624002546611on_val @ A @ ( dom_Pr4448331044451638570_state @ M ) )
     => ? [B6: state] :
          ( ( M @ A )
          = ( some_state @ B6 ) ) ) ).

% domD
thf(fact_1168_domD,axiom,
    ! [A: produc3882902684156697774_state,M: produc3882902684156697774_state > option_state] :
      ( ( member6715010751053357271_state @ A @ ( dom_Pr6427157690771563798_state @ M ) )
     => ? [B6: state] :
          ( ( M @ A )
          = ( some_state @ B6 ) ) ) ).

% domD
thf(fact_1169_domD,axiom,
    ! [A: state,M: state > option_val] :
      ( ( member_state @ A @ ( dom_state_val @ M ) )
     => ? [B6: val] :
          ( ( M @ A )
          = ( some_val @ B6 ) ) ) ).

% domD
thf(fact_1170_domD,axiom,
    ! [A: produc7272280185086996969_state,M: produc7272280185086996969_state > option_val] :
      ( ( member7461423308196221312_state @ A @ ( dom_Pr2419751218887380356te_val @ M ) )
     => ? [B6: val] :
          ( ( M @ A )
          = ( some_val @ B6 ) ) ) ).

% domD
thf(fact_1171_domD,axiom,
    ! [A: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_val] :
      ( ( member2879030624002546611on_val @ A @ ( dom_Pr7381289304162206737al_val @ M ) )
     => ? [B6: val] :
          ( ( M @ A )
          = ( some_val @ B6 ) ) ) ).

% domD
thf(fact_1172_domD,axiom,
    ! [A: produc3882902684156697774_state,M: produc3882902684156697774_state > option_val] :
      ( ( member6715010751053357271_state @ A @ ( dom_Pr7370380374925980453te_val @ M ) )
     => ? [B6: val] :
          ( ( M @ A )
          = ( some_val @ B6 ) ) ) ).

% domD
thf(fact_1173_domIff,axiom,
    ! [A: state,M: state > option_state] :
      ( ( member_state @ A @ ( dom_state_state @ M ) )
      = ( ( M @ A )
       != none_state ) ) ).

% domIff
thf(fact_1174_domIff,axiom,
    ! [A: produc7272280185086996969_state,M: produc7272280185086996969_state > option_state] :
      ( ( member7461423308196221312_state @ A @ ( dom_Pr5710779687127367671_state @ M ) )
      = ( ( M @ A )
       != none_state ) ) ).

% domIff
thf(fact_1175_domIff,axiom,
    ! [A: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_state] :
      ( ( member2879030624002546611on_val @ A @ ( dom_Pr4448331044451638570_state @ M ) )
      = ( ( M @ A )
       != none_state ) ) ).

% domIff
thf(fact_1176_domIff,axiom,
    ! [A: produc3882902684156697774_state,M: produc3882902684156697774_state > option_state] :
      ( ( member6715010751053357271_state @ A @ ( dom_Pr6427157690771563798_state @ M ) )
      = ( ( M @ A )
       != none_state ) ) ).

% domIff
thf(fact_1177_domIff,axiom,
    ! [A: state,M: state > option_val] :
      ( ( member_state @ A @ ( dom_state_val @ M ) )
      = ( ( M @ A )
       != none_val ) ) ).

% domIff
thf(fact_1178_domIff,axiom,
    ! [A: produc7272280185086996969_state,M: produc7272280185086996969_state > option_val] :
      ( ( member7461423308196221312_state @ A @ ( dom_Pr2419751218887380356te_val @ M ) )
      = ( ( M @ A )
       != none_val ) ) ).

% domIff
thf(fact_1179_domIff,axiom,
    ! [A: produc9003781588162623004on_val,M: produc9003781588162623004on_val > option_val] :
      ( ( member2879030624002546611on_val @ A @ ( dom_Pr7381289304162206737al_val @ M ) )
      = ( ( M @ A )
       != none_val ) ) ).

% domIff
thf(fact_1180_domIff,axiom,
    ! [A: produc3882902684156697774_state,M: produc3882902684156697774_state > option_val] :
      ( ( member6715010751053357271_state @ A @ ( dom_Pr7370380374925980453te_val @ M ) )
      = ( ( M @ A )
       != none_val ) ) ).

% domIff
thf(fact_1181_dom__def,axiom,
    ( dom_Pr5710779687127367671_state
    = ( ^ [M5: produc7272280185086996969_state > option_state] :
          ( collec906845016635587262_state
          @ ^ [A2: produc7272280185086996969_state] :
              ( ( M5 @ A2 )
             != none_state ) ) ) ) ).

% dom_def
thf(fact_1182_dom__def,axiom,
    ( dom_Pr4448331044451638570_state
    = ( ^ [M5: produc9003781588162623004on_val > option_state] :
          ( collec7475294502966882545on_val
          @ ^ [A2: produc9003781588162623004on_val] :
              ( ( M5 @ A2 )
             != none_state ) ) ) ) ).

% dom_def
thf(fact_1183_dom__def,axiom,
    ( dom_state_state
    = ( ^ [M5: state > option_state] :
          ( collect_state
          @ ^ [A2: state] :
              ( ( M5 @ A2 )
             != none_state ) ) ) ) ).

% dom_def
thf(fact_1184_dom__def,axiom,
    ( dom_Pr2419751218887380356te_val
    = ( ^ [M5: produc7272280185086996969_state > option_val] :
          ( collec906845016635587262_state
          @ ^ [A2: produc7272280185086996969_state] :
              ( ( M5 @ A2 )
             != none_val ) ) ) ) ).

% dom_def
thf(fact_1185_dom__def,axiom,
    ( dom_Pr7381289304162206737al_val
    = ( ^ [M5: produc9003781588162623004on_val > option_val] :
          ( collec7475294502966882545on_val
          @ ^ [A2: produc9003781588162623004on_val] :
              ( ( M5 @ A2 )
             != none_val ) ) ) ) ).

% dom_def
thf(fact_1186_dom__def,axiom,
    ( dom_state_val
    = ( ^ [M5: state > option_val] :
          ( collect_state
          @ ^ [A2: state] :
              ( ( M5 @ A2 )
             != none_val ) ) ) ) ).

% dom_def
thf(fact_1187_insert__dom,axiom,
    ! [F: state > option_state,X: state,Y: state] :
      ( ( ( F @ X )
        = ( some_state @ Y ) )
     => ( ( insert_state @ X @ ( dom_state_state @ F ) )
        = ( dom_state_state @ F ) ) ) ).

% insert_dom
thf(fact_1188_insert__dom,axiom,
    ! [F: state > option_val,X: state,Y: val] :
      ( ( ( F @ X )
        = ( some_val @ Y ) )
     => ( ( insert_state @ X @ ( dom_state_val @ F ) )
        = ( dom_state_val @ F ) ) ) ).

% insert_dom
thf(fact_1189_dom__minus,axiom,
    ! [F: state > option_state,X: state,A4: set_state] :
      ( ( ( F @ X )
        = none_state )
     => ( ( minus_3933957440811877961_state @ ( dom_state_state @ F ) @ ( insert_state @ X @ A4 ) )
        = ( minus_3933957440811877961_state @ ( dom_state_state @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1190_dom__minus,axiom,
    ! [F: state > option_val,X: state,A4: set_state] :
      ( ( ( F @ X )
        = none_val )
     => ( ( minus_3933957440811877961_state @ ( dom_state_val @ F ) @ ( insert_state @ X @ A4 ) )
        = ( minus_3933957440811877961_state @ ( dom_state_val @ F ) @ A4 ) ) ) ).

% dom_minus
thf(fact_1191_map__add__upd__left,axiom,
    ! [M: state,E2: state > option_state,E1: state > option_state,U1: state] :
      ( ~ ( member_state @ M @ ( dom_state_state @ E2 ) )
     => ( ( map_add_state_state @ ( fun_up8843634000204221123_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up8843634000204221123_state @ ( map_add_state_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1192_map__add__upd__left,axiom,
    ! [M: produc7272280185086996969_state,E2: produc7272280185086996969_state > option_state,E1: produc7272280185086996969_state > option_state,U1: state] :
      ( ~ ( member7461423308196221312_state @ M @ ( dom_Pr5710779687127367671_state @ E2 ) )
     => ( ( map_ad4385406511651772890_state @ ( fun_up3650151817091186_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up3650151817091186_state @ ( map_ad4385406511651772890_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1193_map__add__upd__left,axiom,
    ! [M: produc9003781588162623004on_val,E2: produc9003781588162623004on_val > option_state,E1: produc9003781588162623004on_val > option_state,U1: state] :
      ( ~ ( member2879030624002546611on_val @ M @ ( dom_Pr4448331044451638570_state @ E2 ) )
     => ( ( map_ad2629041965313307917_state @ ( fun_up6681822530636708645_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up6681822530636708645_state @ ( map_ad2629041965313307917_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1194_map__add__upd__left,axiom,
    ! [M: produc3882902684156697774_state,E2: produc3882902684156697774_state > option_state,E1: produc3882902684156697774_state > option_state,U1: state] :
      ( ~ ( member6715010751053357271_state @ M @ ( dom_Pr6427157690771563798_state @ E2 ) )
     => ( ( map_ad1399068676498921971_state @ ( fun_up3435231866794294907_state @ E1 @ M @ ( some_state @ U1 ) ) @ E2 )
        = ( fun_up3435231866794294907_state @ ( map_ad1399068676498921971_state @ E1 @ E2 ) @ M @ ( some_state @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1195_map__add__upd__left,axiom,
    ! [M: state,E2: state > option_val,E1: state > option_val,U1: val] :
      ( ~ ( member_state @ M @ ( dom_state_val @ E2 ) )
     => ( ( map_add_state_val @ ( fun_up5073147608505813454on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up5073147608505813454on_val @ ( map_add_state_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1196_map__add__upd__left,axiom,
    ! [M: produc7272280185086996969_state,E2: produc7272280185086996969_state > option_val,E1: produc7272280185086996969_state > option_val,U1: val] :
      ( ~ ( member7461423308196221312_state @ M @ ( dom_Pr2419751218887380356te_val @ E2 ) )
     => ( ( map_ad7244225162033177441te_val @ ( fun_up3509650811975514847on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up3509650811975514847on_val @ ( map_ad7244225162033177441te_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1197_map__add__upd__left,axiom,
    ! [M: produc9003781588162623004on_val,E2: produc9003781588162623004on_val > option_val,E1: produc9003781588162623004on_val > option_val,U1: val] :
      ( ~ ( member2879030624002546611on_val @ M @ ( dom_Pr7381289304162206737al_val @ E2 ) )
     => ( ( map_ad5466549115852757998al_val @ ( fun_up8559965269643824108on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up8559965269643824108on_val @ ( map_ad5466549115852757998al_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1198_map__add__upd__left,axiom,
    ! [M: produc3882902684156697774_state,E2: produc3882902684156697774_state > option_val,E1: produc3882902684156697774_state > option_val,U1: val] :
      ( ~ ( member6715010751053357271_state @ M @ ( dom_Pr7370380374925980453te_val @ E2 ) )
     => ( ( map_ad4988633262449819272te_val @ ( fun_up3736070447144131606on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up3736070447144131606on_val @ ( map_ad4988633262449819272te_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1199_map__add__upd__left,axiom,
    ! [M: produc1457211279475724562t_char,E2: produc1457211279475724562t_char > option_val,E1: produc1457211279475724562t_char > option_val,U1: val] :
      ( ~ ( member484235747325421115t_char @ M @ ( dom_Pr8989479155164304065ar_val @ E2 ) )
     => ( ( map_ad2908576761495157028ar_val @ ( fun_up5735975307950539954on_val @ E1 @ M @ ( some_val @ U1 ) ) @ E2 )
        = ( fun_up5735975307950539954on_val @ ( map_ad2908576761495157028ar_val @ E1 @ E2 ) @ M @ ( some_val @ U1 ) ) ) ) ).

% map_add_upd_left
thf(fact_1200_fst__graph__eq__dom,axiom,
    ! [M: nat > option_list_char] :
      ( ( image_3548405822317538717ar_nat @ produc6204653154488278070t_char @ ( graph_nat_list_char @ M ) )
      = ( dom_nat_list_char @ M ) ) ).

% fst_graph_eq_dom
thf(fact_1201_fst__graph__eq__dom,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
      ( ( image_3067683418878703216r_prat @ produc5239619271231976746on_val @ ( graph_1288227317702120175on_val @ M ) )
      = ( dom_Pr4152820065153570843on_val @ M ) ) ).

% fst_graph_eq_dom
thf(fact_1202_graph__eq__to__snd__dom,axiom,
    ( graph_628825510059920660_state
    = ( ^ [M5: option_state > option_option_state] :
          ( image_8877801520378654372_state
          @ ^ [X2: option_state] : ( produc9160152616361873709_state @ X2 @ ( the_option_state @ ( M5 @ X2 ) ) )
          @ ( dom_op5824424363013771496_state @ M5 ) ) ) ) ).

% graph_eq_to_snd_dom
thf(fact_1203_graph__eq__to__snd__dom,axiom,
    ( graph_prat_state
    = ( ^ [M5: prat > option_state] :
          ( image_6869036560789213524_state
          @ ^ [X2: prat] : ( produc6205719116230455971_state @ X2 @ ( the_state @ ( M5 @ X2 ) ) )
          @ ( dom_prat_state @ M5 ) ) ) ) ).

% graph_eq_to_snd_dom
thf(fact_1204_graph__eq__to__snd__dom,axiom,
    ( graph_prat_set_state
    = ( ^ [M5: prat > option_set_state] :
          ( image_4988821473515827210_state
          @ ^ [X2: prat] : ( produc9080284787853255769_state @ X2 @ ( the_set_state @ ( M5 @ X2 ) ) )
          @ ( dom_prat_set_state @ M5 ) ) ) ) ).

% graph_eq_to_snd_dom
thf(fact_1205_graph__eq__to__snd__dom,axiom,
    ( graph_nat_list_char
    = ( ^ [M5: nat > option_list_char] :
          ( image_1003422490162143483t_char
          @ ^ [X2: nat] : ( produc120197956887798346t_char @ X2 @ ( the_list_char @ ( M5 @ X2 ) ) )
          @ ( dom_nat_list_char @ M5 ) ) ) ) ).

% graph_eq_to_snd_dom
thf(fact_1206_graph__eq__to__snd__dom,axiom,
    ( graph_1288227317702120175on_val
    = ( ^ [M5: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] :
          ( image_1459058096221225002on_val
          @ ^ [X2: produc1457211279475724562t_char > prat] : ( produc74620467203698198on_val @ X2 @ ( the_Pr646328391962797958on_val @ ( M5 @ X2 ) ) )
          @ ( dom_Pr4152820065153570843on_val @ M5 ) ) ) ) ).

% graph_eq_to_snd_dom
thf(fact_1207_graph__map__add,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( graph_1733029056113894637ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) )
        = ( sup_su5754804325903363146ar_val @ ( graph_1733029056113894637ar_val @ M1 ) @ ( graph_1733029056113894637ar_val @ M2 ) ) ) ) ).

% graph_map_add
thf(fact_1208_graph__map__add,axiom,
    ! [M1: state > option886743748074664436_state,M2: state > option886743748074664436_state] :
      ( ( ( inf_inf_set_state @ ( dom_st4979949223050981664_state @ M1 ) @ ( dom_st4979949223050981664_state @ M2 ) )
        = bot_bot_set_state )
     => ( ( graph_7551141711029462004_state @ ( map_ad9175232245633115645_state @ M1 @ M2 ) )
        = ( sup_su3837536599209510219_state @ ( graph_7551141711029462004_state @ M1 ) @ ( graph_7551141711029462004_state @ M2 ) ) ) ) ).

% graph_map_add
thf(fact_1209_inf_Obounded__iff,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ ( inf_inf_set_state @ B @ C ) )
      = ( ( ord_le2494988322063910608_state @ A @ B )
        & ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_1210_le__inf__iff,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ ( inf_inf_set_state @ Y @ Z2 ) )
      = ( ( ord_le2494988322063910608_state @ X @ Y )
        & ( ord_le2494988322063910608_state @ X @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_1211_Int__subset__iff,axiom,
    ! [C3: set_state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ C3 @ ( inf_inf_set_state @ A4 @ B4 ) )
      = ( ( ord_le2494988322063910608_state @ C3 @ A4 )
        & ( ord_le2494988322063910608_state @ C3 @ B4 ) ) ) ).

% Int_subset_iff
thf(fact_1212_inj__on__map__add__dom,axiom,
    ! [M: produc1457211279475724562t_char > option_val,M6: produc1457211279475724562t_char > option_val] :
      ( ( inj_on4474484569326248358on_val @ ( map_ad2908576761495157028ar_val @ M @ M6 ) @ ( dom_Pr8989479155164304065ar_val @ M6 ) )
      = ( inj_on4474484569326248358on_val @ M6 @ ( dom_Pr8989479155164304065ar_val @ M6 ) ) ) ).

% inj_on_map_add_dom
thf(fact_1213_inj__Some,axiom,
    ! [A4: set_state] : ( inj_on3577428053172332983_state @ some_state @ A4 ) ).

% inj_Some
thf(fact_1214_inj__Some,axiom,
    ! [A4: set_val] : ( inj_on4074814566786472055on_val @ some_val @ A4 ) ).

% inj_Some
thf(fact_1215_inf__sup__ord_I2_J,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_1216_inf__sup__ord_I1_J,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ Y ) @ X ) ).

% inf_sup_ord(1)
thf(fact_1217_inf__le1,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ Y ) @ X ) ).

% inf_le1
thf(fact_1218_inf__le2,axiom,
    ! [X: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ Y ) @ Y ) ).

% inf_le2
thf(fact_1219_le__infE,axiom,
    ! [X: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ ( inf_inf_set_state @ A @ B ) )
     => ~ ( ( ord_le2494988322063910608_state @ X @ A )
         => ~ ( ord_le2494988322063910608_state @ X @ B ) ) ) ).

% le_infE
thf(fact_1220_le__infI,axiom,
    ! [X: set_state,A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ A )
     => ( ( ord_le2494988322063910608_state @ X @ B )
       => ( ord_le2494988322063910608_state @ X @ ( inf_inf_set_state @ A @ B ) ) ) ) ).

% le_infI
thf(fact_1221_inf__mono,axiom,
    ! [A: set_state,C: set_state,B: set_state,D: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ C )
     => ( ( ord_le2494988322063910608_state @ B @ D )
       => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ ( inf_inf_set_state @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_1222_le__infI1,axiom,
    ! [A: set_state,X: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ X )
     => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ X ) ) ).

% le_infI1
thf(fact_1223_le__infI2,axiom,
    ! [B: set_state,X: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ X )
     => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ X ) ) ).

% le_infI2
thf(fact_1224_inf_OorderE,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( A
        = ( inf_inf_set_state @ A @ B ) ) ) ).

% inf.orderE
thf(fact_1225_inf_OorderI,axiom,
    ! [A: set_state,B: set_state] :
      ( ( A
        = ( inf_inf_set_state @ A @ B ) )
     => ( ord_le2494988322063910608_state @ A @ B ) ) ).

% inf.orderI
thf(fact_1226_inf__unique,axiom,
    ! [F: set_state > set_state > set_state,X: set_state,Y: set_state] :
      ( ! [X3: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ ( F @ X3 @ Y3 ) @ X3 )
     => ( ! [X3: set_state,Y3: set_state] : ( ord_le2494988322063910608_state @ ( F @ X3 @ Y3 ) @ Y3 )
       => ( ! [X3: set_state,Y3: set_state,Z4: set_state] :
              ( ( ord_le2494988322063910608_state @ X3 @ Y3 )
             => ( ( ord_le2494988322063910608_state @ X3 @ Z4 )
               => ( ord_le2494988322063910608_state @ X3 @ ( F @ Y3 @ Z4 ) ) ) )
         => ( ( inf_inf_set_state @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_1227_le__iff__inf,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [X2: set_state,Y5: set_state] :
          ( ( inf_inf_set_state @ X2 @ Y5 )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_1228_inf_Oabsorb1,axiom,
    ! [A: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( inf_inf_set_state @ A @ B )
        = A ) ) ).

% inf.absorb1
thf(fact_1229_inf_Oabsorb2,axiom,
    ! [B: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ A )
     => ( ( inf_inf_set_state @ A @ B )
        = B ) ) ).

% inf.absorb2
thf(fact_1230_inf__absorb1,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( inf_inf_set_state @ X @ Y )
        = X ) ) ).

% inf_absorb1
thf(fact_1231_inf__absorb2,axiom,
    ! [Y: set_state,X: set_state] :
      ( ( ord_le2494988322063910608_state @ Y @ X )
     => ( ( inf_inf_set_state @ X @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_1232_inf_OboundedE,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ ( inf_inf_set_state @ B @ C ) )
     => ~ ( ( ord_le2494988322063910608_state @ A @ B )
         => ~ ( ord_le2494988322063910608_state @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_1233_inf_OboundedI,axiom,
    ! [A: set_state,B: set_state,C: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ B )
     => ( ( ord_le2494988322063910608_state @ A @ C )
       => ( ord_le2494988322063910608_state @ A @ ( inf_inf_set_state @ B @ C ) ) ) ) ).

% inf.boundedI
thf(fact_1234_inf__greatest,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ X @ Y )
     => ( ( ord_le2494988322063910608_state @ X @ Z2 )
       => ( ord_le2494988322063910608_state @ X @ ( inf_inf_set_state @ Y @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_1235_inf_Oorder__iff,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A2: set_state,B2: set_state] :
          ( A2
          = ( inf_inf_set_state @ A2 @ B2 ) ) ) ) ).

% inf.order_iff
thf(fact_1236_inf_Ocobounded1,axiom,
    ! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ A ) ).

% inf.cobounded1
thf(fact_1237_inf_Ocobounded2,axiom,
    ! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ B ) ).

% inf.cobounded2
thf(fact_1238_inf_Oabsorb__iff1,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [A2: set_state,B2: set_state] :
          ( ( inf_inf_set_state @ A2 @ B2 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_1239_inf_Oabsorb__iff2,axiom,
    ( ord_le2494988322063910608_state
    = ( ^ [B2: set_state,A2: set_state] :
          ( ( inf_inf_set_state @ A2 @ B2 )
          = B2 ) ) ) ).

% inf.absorb_iff2
thf(fact_1240_inf_OcoboundedI1,axiom,
    ! [A: set_state,C: set_state,B: set_state] :
      ( ( ord_le2494988322063910608_state @ A @ C )
     => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_1241_inf_OcoboundedI2,axiom,
    ! [B: set_state,C: set_state,A: set_state] :
      ( ( ord_le2494988322063910608_state @ B @ C )
     => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_1242_Int__Collect__mono,axiom,
    ! [A4: set_Pr2391701600042252046_state,B4: set_Pr2391701600042252046_state,P2: produc3882902684156697774_state > $o,Q: produc3882902684156697774_state > $o] :
      ( ( ord_le6483787752022044334_state @ A4 @ B4 )
     => ( ! [X3: produc3882902684156697774_state] :
            ( ( member6715010751053357271_state @ X3 @ A4 )
           => ( ( P2 @ X3 )
             => ( Q @ X3 ) ) )
       => ( ord_le6483787752022044334_state @ ( inf_in7073437713476115196_state @ A4 @ ( collec394671971739345689_state @ P2 ) ) @ ( inf_in7073437713476115196_state @ B4 @ ( collec394671971739345689_state @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1243_Int__Collect__mono,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,P2: produc7272280185086996969_state > $o,Q: produc7272280185086996969_state > $o] :
      ( ( ord_le4032880777312351359_state @ A4 @ B4 )
     => ( ! [X3: produc7272280185086996969_state] :
            ( ( member7461423308196221312_state @ X3 @ A4 )
           => ( ( P2 @ X3 )
             => ( Q @ X3 ) ) )
       => ( ord_le4032880777312351359_state @ ( inf_in866569429368772785_state @ A4 @ ( collec906845016635587262_state @ P2 ) ) @ ( inf_in866569429368772785_state @ B4 @ ( collec906845016635587262_state @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1244_Int__Collect__mono,axiom,
    ! [A4: set_Pr7649655576376376530on_val,B4: set_Pr7649655576376376530on_val,P2: produc9003781588162623004on_val > $o,Q: produc9003781588162623004on_val > $o] :
      ( ( ord_le6900622908513426738on_val @ A4 @ B4 )
     => ( ! [X3: produc9003781588162623004on_val] :
            ( ( member2879030624002546611on_val @ X3 @ A4 )
           => ( ( P2 @ X3 )
             => ( Q @ X3 ) ) )
       => ( ord_le6900622908513426738on_val @ ( inf_in1079285664774927716on_val @ A4 @ ( collec7475294502966882545on_val @ P2 ) ) @ ( inf_in1079285664774927716on_val @ B4 @ ( collec7475294502966882545on_val @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1245_Int__Collect__mono,axiom,
    ! [A4: set_state,B4: set_state,P2: state > $o,Q: state > $o] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ! [X3: state] :
            ( ( member_state @ X3 @ A4 )
           => ( ( P2 @ X3 )
             => ( Q @ X3 ) ) )
       => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A4 @ ( collect_state @ P2 ) ) @ ( inf_inf_set_state @ B4 @ ( collect_state @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1246_Int__greatest,axiom,
    ! [C3: set_state,A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ C3 @ A4 )
     => ( ( ord_le2494988322063910608_state @ C3 @ B4 )
       => ( ord_le2494988322063910608_state @ C3 @ ( inf_inf_set_state @ A4 @ B4 ) ) ) ) ).

% Int_greatest
thf(fact_1247_Int__absorb2,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ B4 )
     => ( ( inf_inf_set_state @ A4 @ B4 )
        = A4 ) ) ).

% Int_absorb2
thf(fact_1248_Int__absorb1,axiom,
    ! [B4: set_state,A4: set_state] :
      ( ( ord_le2494988322063910608_state @ B4 @ A4 )
     => ( ( inf_inf_set_state @ A4 @ B4 )
        = B4 ) ) ).

% Int_absorb1
thf(fact_1249_Int__lower2,axiom,
    ! [A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A4 @ B4 ) @ B4 ) ).

% Int_lower2
thf(fact_1250_Int__lower1,axiom,
    ! [A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A4 @ B4 ) @ A4 ) ).

% Int_lower1
thf(fact_1251_Int__mono,axiom,
    ! [A4: set_state,C3: set_state,B4: set_state,D2: set_state] :
      ( ( ord_le2494988322063910608_state @ A4 @ C3 )
     => ( ( ord_le2494988322063910608_state @ B4 @ D2 )
       => ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A4 @ B4 ) @ ( inf_inf_set_state @ C3 @ D2 ) ) ) ) ).

% Int_mono
thf(fact_1252_Un__Int__assoc__eq,axiom,
    ! [A4: set_Pr4231240917283394591_state,B4: set_Pr4231240917283394591_state,C3: set_Pr4231240917283394591_state] :
      ( ( ( sup_su3837536599209510219_state @ ( inf_in866569429368772785_state @ A4 @ B4 ) @ C3 )
        = ( inf_in866569429368772785_state @ A4 @ ( sup_su3837536599209510219_state @ B4 @ C3 ) ) )
      = ( ord_le4032880777312351359_state @ C3 @ A4 ) ) ).

% Un_Int_assoc_eq
thf(fact_1253_Un__Int__assoc__eq,axiom,
    ! [A4: set_state,B4: set_state,C3: set_state] :
      ( ( ( sup_sup_set_state @ ( inf_inf_set_state @ A4 @ B4 ) @ C3 )
        = ( inf_inf_set_state @ A4 @ ( sup_sup_set_state @ B4 @ C3 ) ) )
      = ( ord_le2494988322063910608_state @ C3 @ A4 ) ) ).

% Un_Int_assoc_eq
thf(fact_1254_distrib__inf__le,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ ( inf_in866569429368772785_state @ X @ Y ) @ ( inf_in866569429368772785_state @ X @ Z2 ) ) @ ( inf_in866569429368772785_state @ X @ ( sup_su3837536599209510219_state @ Y @ Z2 ) ) ) ).

% distrib_inf_le
thf(fact_1255_distrib__inf__le,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( inf_inf_set_state @ X @ Y ) @ ( inf_inf_set_state @ X @ Z2 ) ) @ ( inf_inf_set_state @ X @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).

% distrib_inf_le
thf(fact_1256_distrib__sup__le,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] : ( ord_le4032880777312351359_state @ ( sup_su3837536599209510219_state @ X @ ( inf_in866569429368772785_state @ Y @ Z2 ) ) @ ( inf_in866569429368772785_state @ ( sup_su3837536599209510219_state @ X @ Y ) @ ( sup_su3837536599209510219_state @ X @ Z2 ) ) ) ).

% distrib_sup_le
thf(fact_1257_distrib__sup__le,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X @ ( inf_inf_set_state @ Y @ Z2 ) ) @ ( inf_inf_set_state @ ( sup_sup_set_state @ X @ Y ) @ ( sup_sup_set_state @ X @ Z2 ) ) ) ).

% distrib_sup_le
thf(fact_1258_image__Int__subset,axiom,
    ! [F: state > state,A4: set_state,B4: set_state] : ( ord_le2494988322063910608_state @ ( image_state_state @ F @ ( inf_inf_set_state @ A4 @ B4 ) ) @ ( inf_inf_set_state @ ( image_state_state @ F @ A4 ) @ ( image_state_state @ F @ B4 ) ) ) ).

% image_Int_subset
thf(fact_1259_inf__shunt,axiom,
    ! [X: set_state,Y: set_state] :
      ( ( ( inf_inf_set_state @ X @ Y )
        = bot_bot_set_state )
      = ( ord_le2494988322063910608_state @ X @ ( uminus472742206872269241_state @ Y ) ) ) ).

% inf_shunt
thf(fact_1260_shunt1,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( inf_in866569429368772785_state @ X @ Y ) @ Z2 )
      = ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ ( uminus1327639380719934312_state @ Y ) @ Z2 ) ) ) ).

% shunt1
thf(fact_1261_shunt1,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ Y ) @ Z2 )
      = ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ ( uminus472742206872269241_state @ Y ) @ Z2 ) ) ) ).

% shunt1
thf(fact_1262_shunt2,axiom,
    ! [X: set_Pr4231240917283394591_state,Y: set_Pr4231240917283394591_state,Z2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ ( inf_in866569429368772785_state @ X @ ( uminus1327639380719934312_state @ Y ) ) @ Z2 )
      = ( ord_le4032880777312351359_state @ X @ ( sup_su3837536599209510219_state @ Y @ Z2 ) ) ) ).

% shunt2
thf(fact_1263_shunt2,axiom,
    ! [X: set_state,Y: set_state,Z2: set_state] :
      ( ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X @ ( uminus472742206872269241_state @ Y ) ) @ Z2 )
      = ( ord_le2494988322063910608_state @ X @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).

% shunt2
thf(fact_1264_sup__neg__inf,axiom,
    ! [P3: set_Pr4231240917283394591_state,Q2: set_Pr4231240917283394591_state,R2: set_Pr4231240917283394591_state] :
      ( ( ord_le4032880777312351359_state @ P3 @ ( sup_su3837536599209510219_state @ Q2 @ R2 ) )
      = ( ord_le4032880777312351359_state @ ( inf_in866569429368772785_state @ P3 @ ( uminus1327639380719934312_state @ Q2 ) ) @ R2 ) ) ).

% sup_neg_inf
thf(fact_1265_sup__neg__inf,axiom,
    ! [P3: set_state,Q2: set_state,R2: set_state] :
      ( ( ord_le2494988322063910608_state @ P3 @ ( sup_sup_set_state @ Q2 @ R2 ) )
      = ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ P3 @ ( uminus472742206872269241_state @ Q2 ) ) @ R2 ) ) ).

% sup_neg_inf
thf(fact_1266_disjoint__eq__subset__Compl,axiom,
    ! [A4: set_state,B4: set_state] :
      ( ( ( inf_inf_set_state @ A4 @ B4 )
        = bot_bot_set_state )
      = ( ord_le2494988322063910608_state @ A4 @ ( uminus472742206872269241_state @ B4 ) ) ) ).

% disjoint_eq_subset_Compl
thf(fact_1267_map__add__comm,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( map_ad2908576761495157028ar_val @ M1 @ M2 )
        = ( map_ad2908576761495157028ar_val @ M2 @ M1 ) ) ) ).

% map_add_comm
thf(fact_1268_ran__map__add,axiom,
    ! [M1: produc1457211279475724562t_char > option_val,M2: produc1457211279475724562t_char > option_val] :
      ( ( ( inf_in3544766959038609504t_char @ ( dom_Pr8989479155164304065ar_val @ M1 ) @ ( dom_Pr8989479155164304065ar_val @ M2 ) )
        = bot_bo1414094081888755934t_char )
     => ( ( ran_Pr786515303459910110ar_val @ ( map_ad2908576761495157028ar_val @ M1 @ M2 ) )
        = ( sup_sup_set_val @ ( ran_Pr786515303459910110ar_val @ M1 ) @ ( ran_Pr786515303459910110ar_val @ M2 ) ) ) ) ).

% ran_map_add
thf(fact_1269_ran__map__add,axiom,
    ! [M1: state > option2747342629145793465_state,M2: state > option2747342629145793465_state] :
      ( ( ( inf_inf_set_state @ ( dom_st3633639084608838903_state @ M1 ) @ ( dom_st3633639084608838903_state @ M2 ) )
        = bot_bot_set_state )
     => ( ( ran_st3484157348144007316_state @ ( map_ad2308265909133244122_state @ M1 @ M2 ) )
        = ( sup_su3837536599209510219_state @ ( ran_st3484157348144007316_state @ M1 ) @ ( ran_st3484157348144007316_state @ M2 ) ) ) ) ).

% ran_map_add
thf(fact_1270_inj__on__image__set__diff,axiom,
    ! [F: state > state,C3: set_state,A4: set_state,B4: set_state] :
      ( ( inj_on_state_state @ F @ C3 )
     => ( ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A4 @ B4 ) @ C3 )
       => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
         => ( ( image_state_state @ F @ ( minus_3933957440811877961_state @ A4 @ B4 ) )
            = ( minus_3933957440811877961_state @ ( image_state_state @ F @ A4 ) @ ( image_state_state @ F @ B4 ) ) ) ) ) ) ).

% inj_on_image_set_diff
thf(fact_1271_inj__on__image__Int,axiom,
    ! [F: state > state,C3: set_state,A4: set_state,B4: set_state] :
      ( ( inj_on_state_state @ F @ C3 )
     => ( ( ord_le2494988322063910608_state @ A4 @ C3 )
       => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
         => ( ( image_state_state @ F @ ( inf_inf_set_state @ A4 @ B4 ) )
            = ( inf_inf_set_state @ ( image_state_state @ F @ A4 ) @ ( image_state_state @ F @ B4 ) ) ) ) ) ) ).

% inj_on_image_Int
thf(fact_1272_inj__on__fst__graph,axiom,
    ! [M: nat > option_list_char] : ( inj_on2499120878504899377ar_nat @ produc6204653154488278070t_char @ ( graph_nat_list_char @ M ) ) ).

% inj_on_fst_graph
thf(fact_1273_inj__on__fst__graph,axiom,
    ! [M: ( produc1457211279475724562t_char > prat ) > option5747939881698552298on_val] : ( inj_on3812695684120442372r_prat @ produc5239619271231976746on_val @ ( graph_1288227317702120175on_val @ M ) ) ).

% inj_on_fst_graph
thf(fact_1274_inj__on__image__eq__iff,axiom,
    ! [F: state > state,C3: set_state,A4: set_state,B4: set_state] :
      ( ( inj_on_state_state @ F @ C3 )
     => ( ( ord_le2494988322063910608_state @ A4 @ C3 )
       => ( ( ord_le2494988322063910608_state @ B4 @ C3 )
         => ( ( ( image_state_state @ F @ A4 )
              = ( image_state_state @ F @ B4 ) )
            = ( A4 = B4 ) ) ) ) ) ).

% inj_on_image_eq_iff

% Helper facts (10)
thf(help_If_2_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y: prat] :
      ( ( if_prat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PosRat__Oprat_T,axiom,
    ! [X: prat,Y: prat] :
      ( ( if_prat @ $true @ X @ Y )
      = X ) ).

thf(help_fChoice_1_1_fChoice_001t__PosRat__Oprat_T,axiom,
    ! [P2: prat > $o] :
      ( ( P2 @ ( fChoice_prat @ P2 ) )
      = ( ? [X8: prat] : ( P2 @ X8 ) ) ) ).

thf(help_If_2_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ( if_state @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__PartialHeapSA__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ( if_state @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001t__Option__Ooption_It__Mask__Oval_J_T,axiom,
    ! [X: option_val,Y: option_val] :
      ( ( if_option_val @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__Mask__Oval_J_T,axiom,
    ! [X: option_val,Y: option_val] :
      ( ( if_option_val @ $true @ X @ Y )
      = X ) ).

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,
    ! [X: option_state,Y: option_state] :
      ( ( if_option_state @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Option__Ooption_It__PartialHeapSA__Ostate_J_T,axiom,
    ! [X: option_state,Y: option_state] :
      ( ( if_option_state @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( padd @ ( pmult @ alpha @ ( padd @ ( get_m @ ( r @ a2 @ wa ) @ hl ) @ ( get_m @ a2 @ hl ) ) ) @ ( pmult @ beta @ ( padd @ ( get_m @ ( r @ a2 @ wb ) @ hl ) @ ( get_m @ a2 @ hl ) ) ) )
    = ( padd @ ( padd @ ( pmult @ alpha @ ( get_m @ a2 @ hl ) ) @ ( pmult @ beta @ ( get_m @ a2 @ hl ) ) ) @ ( padd @ ( pmult @ alpha @ ( get_m @ ( r @ a2 @ wa ) @ hl ) ) @ ( pmult @ beta @ ( get_m @ ( r @ a2 @ wb ) @ hl ) ) ) ) ) ).

%------------------------------------------------------------------------------