TPTP Problem File: SWW474

TPTP Problem File: SWW474_20.p

%------------------------------------------------------------------------------
% File     : SWW474_20 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Software Verification
% Problem  : Hoare's Logic with Procedures line 440, 500 axioms selected
% Version  : SWW474_2 with the conjecture removed
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [TPTP]
% Names    : 

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    : 1345 ( 286 unt; 532 typ;   0 def)
%            Number of atoms       : 1926 ( 620 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives : 1353 ( 240   ~;  51   |; 108   &)
%                                         ( 116 <=>; 838  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of types       :  177 ( 176 usr)
%            Number of type conns  :  423 ( 245   >; 178   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  355 ( 355 usr; 111 con; 0-2 aty)
%            Number of variables   : 2144 (2096   !;  48   ?;2144   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:46:51
%------------------------------------------------------------------------------
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    hAPP_f891245078_state: ( fun_fu1956604286_state * fun_pn1610849624_state ) > fun_fu2087509785_state ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__fun_Itc__fun_Itc__Hoare____Mirabelle_,type,
    hAPP_f1967984667e_bool: ( fun_fu1543647229e_bool * fun_pn249986828l_bool ) > fun_fu1040518284e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__Obool,type,
    hAPP_f327114704l_bool: ( fun_fu93307442l_bool * fun_state_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Ost,type,
    hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Ost_161,type,
    hAPP_f1863945078e_bool: ( fun_fu1998731480e_bool * fun_state_bool ) > fun_st1506752259e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Ost_162,type,
    hAPP_f1259673775l_bool: ( fun_fu1658206819l_bool * fun_state_bool ) > fun_st2063251938l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_,type,
    hAPP_f1595846909_state: ( fun_fu827928799_state * fun_st1506752259e_bool ) > hoare_1875481847_state ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__163,type,
    hAPP_f1930074316_state: ( fun_fu404278912_state * fun_st1506752259e_bool ) > fun_co879055186_state ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__164,type,
    hAPP_f1012183542e_bool: ( fun_fu2104550360e_bool * fun_st1506752259e_bool ) > fun_state_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__165,type,
    hAPP_f817621513e_bool: ( fun_fu402792811e_bool * fun_st1506752259e_bool ) > fun_st1506752259e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__166,type,
    hAPP_f249262236e_bool: ( fun_fu475229566e_bool * fun_st1506752259e_bool ) > fun_st858662806e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool__167,type,
    hAPP_f1283379615l_bool: ( fun_fu1982748883l_bool * fun_st1506752259e_bool ) > fun_st2116860965l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Co,type,
    hAPP_f1935169308e_bool: ( fun_fu1867913342e_bool * fun_st858662806e_bool ) > fun_st1506752259e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HO,type,
    hAPP_f873506917e_bool: ( fun_fu1454697805e_bool * fun_st2116860965l_bool ) > fun_st1483075957e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HO_168,type,
    hAPP_f1138284024e_bool: ( fun_fu1088452192e_bool * fun_st2116860965l_bool ) > fun_st277393160e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_f167292325e_bool: ( fun_fu1219323149e_bool * fun_st2063251938l_bool ) > fun_bo1936561970e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_169,type,
    hAPP_f644196280e_bool: ( fun_fu1047394976e_bool * fun_st2063251938l_bool ) > fun_fu373216837e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Com,type,
    hAPP_f701449317e_bool: ( fun_fu13754701e_bool * fun_st1483075957e_bool ) > fun_bo898473669e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HO,type,
    hAPP_f915354021e_bool: ( fun_fu1436120077e_bool * fun_st277393160e_bool ) > fun_fu1998731480e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os,type,
    hAPP_f190028117e_bool: ( fun_fu2020320649e_bool * fun_Ho1653816318_pname ) > fun_Ho14659478e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_170,type,
    hAPP_f1542224800_pname: ( fun_fu235184776_pname * fun_Ho1996104121e_bool ) > pname ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_171,type,
    hAPP_f1408815105l_bool: ( fun_fu689207471l_bool * fun_Ho1996104121e_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_172,type,
    hAPP_f890249627_state: ( fun_fu385705929_state * fun_Ho1996104121e_bool ) > hoare_1875481847_state ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_173,type,
    hAPP_f1148778334e_bool: ( fun_fu1040518284e_bool * fun_Ho1996104121e_bool ) > fun_pname_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_174,type,
    hAPP_f78029435l_bool: ( fun_fu854396771l_bool * fun_Ho1996104121e_bool ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_175,type,
    hAPP_f121055253e_bool: ( fun_fu1296727421e_bool * fun_Ho1996104121e_bool ) > fun_Ho1996104121e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_176,type,
    hAPP_f932622461l_bool: ( fun_fu811519275l_bool * fun_Ho1996104121e_bool ) > fun_Ho1896286681l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_177,type,
    hAPP_f56162711e_bool: ( fun_fu775812037e_bool * fun_Ho1996104121e_bool ) > fun_Ho1695028467e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_178,type,
    hAPP_f1628972376l_bool: ( fun_fu1962076352l_bool * fun_Ho1996104121e_bool ) > fun_fu1430349052l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_179,type,
    hAPP_f1873026899l_bool: ( fun_fu1173762305l_bool * fun_Ho1996104121e_bool ) > fun_fu689207471l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_180,type,
    hAPP_f1204759513e_bool: ( fun_fu947547457e_bool * fun_Ho1996104121e_bool ) > fun_fu1296727421e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_181,type,
    hAPP_f640685261l_bool: ( fun_fu2083718837l_bool * fun_Ho1996104121e_bool ) > fun_fu237807729l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_182,type,
    hAPP_f872497439l_bool: ( fun_fu2107095047l_bool * fun_Ho1996104121e_bool ) > fun_fu663891139l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_183,type,
    hAPP_f474907569e_bool: ( fun_fu1653236447e_bool * fun_Ho1455141843_state ) > fun_Ho1695028467e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_184,type,
    hAPP_f1188413809e_bool: ( fun_fu2091051353e_bool * fun_Ho14659478e_bool ) > fun_pn760644914e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_185,type,
    hAPP_f745653815l_bool: ( fun_fu1007240549l_bool * fun_Ho14659478e_bool ) > fun_Ho760178998l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_186,type,
    hAPP_f1300953505e_bool: ( fun_fu1856979029e_bool * fun_Ho1896286681l_bool ) > fun_fu1296727421e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_187,type,
    hAPP_f169892419e_bool: ( fun_fu572183031e_bool * fun_Ho1695028467e_bool ) > fun_Ho1996104121e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_188,type,
    hAPP_f2101312745e_bool: ( fun_fu302189515e_bool * fun_Ho1695028467e_bool ) > fun_Ho1695028467e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_189,type,
    hAPP_f2059405973l_bool: ( fun_fu601378633l_bool * fun_Ho1695028467e_bool ) > fun_Ho1085560331l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_190,type,
    hAPP_f406856233e_bool: ( fun_fu1403260939e_bool * fun_Ho760178998l_bool ) > fun_fu1176632176e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_191,type,
    hAPP_f1795624711e_bool: ( fun_fu1067265135e_bool * fun_Ho1085560331l_bool ) > fun_fu1296727421e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Os_192,type,
    hAPP_f392546175e_bool: ( fun_fu349737825e_bool * fun_Ho1110608055e_bool ) > fun_fu775812037e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__Com__Opnam,type,
    hAPP_f1385420507e_bool: ( fun_fu265667599e_bool * fun_fu1499449723_pname ) > fun_fu410713561e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool,type,
    hAPP_f1935102916l_bool: ( fun_fu399576434l_bool * fun_fu1430349052l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_193,type,
    hAPP_f674760225e_bool: ( fun_fu608906319e_bool * fun_fu1430349052l_bool ) > fun_pname_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_194,type,
    hAPP_f1440968210e_bool: ( fun_fu1333785210e_bool * fun_fu1430349052l_bool ) > fun_Ho1996104121e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_195,type,
    hAPP_f559147733l_bool: ( fun_fu2087345469l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_196,type,
    hAPP_f143162813l_bool: ( fun_fu1747008875l_bool * fun_fu1430349052l_bool ) > fun_fu31783638l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_197,type,
    hAPP_f510955609l_bool: ( fun_fu1911931399l_bool * fun_fu1430349052l_bool ) > fun_fu399576434l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_198,type,
    hAPP_f230953622l_bool: ( fun_fu1759027710l_bool * fun_fu1430349052l_bool ) > fun_fu2087345469l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__Hoare____M,type,
    hAPP_f1703905905e_bool: ( fun_fu764251295e_bool * fun_fu1604182422_state ) > fun_fu1176632176e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__C,type,
    hAPP_f2082757169l_bool: ( fun_fu154623769l_bool * fun_fu410713561e_bool ) > fun_pn422929397l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__H,type,
    hAPP_f624840228l_bool: ( fun_fu502368472l_bool * fun_fu31783638l_bool ) > fun_fu2087345469l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__H_199,type,
    hAPP_f492176169l_bool: ( fun_fu542338571l_bool * fun_fu1176632176e_bool ) > fun_Ho760178998l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f,type,
    hAPP_f1297925993l_bool: ( fun_fu1901728075l_bool * fun_fu802393907l_bool ) > fun_fu802393907l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f_200,type,
    hAPP_f1145991873l_bool: ( fun_fu445680937l_bool * fun_fu931343505l_bool ) > fun_fu2087345469l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc,type,
    hAPP_f585615743e_bool: ( fun_fu372702637e_bool * fun_fu235184776_pname ) > fun_fu1040518284e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_201,type,
    hAPP_f1699935247l_bool: ( fun_fu237807729l_bool * fun_fu689207471l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_202,type,
    hAPP_f75069804e_bool: ( fun_fu2122198606e_bool * fun_fu689207471l_bool ) > fun_pname_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_203,type,
    hAPP_f962122119e_bool: ( fun_fu1163781179e_bool * fun_fu689207471l_bool ) > fun_Ho1996104121e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_204,type,
    hAPP_f900945761l_bool: ( fun_fu663891139l_bool * fun_fu689207471l_bool ) > fun_fu689207471l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_205,type,
    hAPP_f440042033l_bool: ( fun_fu2072024677l_bool * fun_fu689207471l_bool ) > fun_fu854396771l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_206,type,
    hAPP_f1970936639l_bool: ( fun_fu90736755l_bool * fun_fu689207471l_bool ) > fun_fu237807729l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_207,type,
    hAPP_f19215249l_bool: ( fun_fu1415736773l_bool * fun_fu689207471l_bool ) > fun_fu663891139l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_208,type,
    hAPP_f1185879473e_bool: ( fun_fu1900462437e_bool * fun_fu385705929_state ) > fun_fu1296727421e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_209,type,
    hAPP_f662360091l_bool: ( fun_fu262057981l_bool * fun_fu1040518284e_bool ) > fun_pn249986828l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_210,type,
    hAPP_f2051813877l_bool: ( fun_fu1370073565l_bool * fun_fu854396771l_bool ) > fun_fu663891139l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_211,type,
    hAPP_f309954467l_bool: ( fun_fu1703951883l_bool * fun_fu1296727421e_bool ) > fun_Ho1085560331l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_212,type,
    hAPP_f2051277573l_bool: ( fun_fu1923372391l_bool * fun_fu1173762305l_bool ) > fun_fu1173762305l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc_213,type,
    hAPP_f1846363427l_bool: ( fun_fu1805752587l_bool * fun_fu2083718837l_bool ) > fun_fu663891139l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H,type,
    hAPP_f389811538l_bool: ( fun_fu1438281908l_bool * fun_fu399576434l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H_214,type,
    hAPP_f783502055l_bool: ( fun_fu1610316873l_bool * fun_fu399576434l_bool ) > fun_fu399576434l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H_215,type,
    hAPP_f1879335953l_bool: ( fun_fu1787620979l_bool * fun_fu1911931399l_bool ) > fun_fu1911931399l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Ot,type,
    hAPP_f755416249l_bool: ( fun_fu1086366823l_bool * fun_fu237807729l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Ot_216,type,
    hAPP_f57684501l_bool: ( fun_fu2056529149l_bool * fun_fu237807729l_bool ) > fun_fu237807729l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Ot_217,type,
    hAPP_f1475014121l_bool: ( fun_fu544723403l_bool * fun_fu90736755l_bool ) > fun_fu90736755l_bool ).

tff(sy_c_hBOOL,type,
    hBOOL: bool > $o ).

tff(sy_c_member_000tc__Com__Ocom,type,
    member_com: fun_co1633267573l_bool ).

tff(sy_c_member_000tc__Com__Opname,type,
    member_pname: fun_pn422929397l_bool ).

tff(sy_c_member_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate_J,type,
    member618553700_state: fun_Ho1085560331l_bool ).

tff(sy_c_member_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
    member799430823e_bool: fun_fu931343505l_bool ).

tff(sy_c_member_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__,type,
    member1062536460e_bool: fun_fu2083718837l_bool ).

tff(sy_v_Fa,type,
    fa: fun_Ho1996104121e_bool ).

tff(sy_v_pn,type,
    pn: pname ).

tff(sy_v_y,type,
    y: com ).

%----Relevant facts (699)
tff(fact_0_empty,axiom,
    ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)) ).

tff(fact_1_asm,axiom,
    ! [Ts: fun_Ho1996104121e_bool,G_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Ts),G_1))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ).

tff(fact_2_weaken,axiom,
    ! [Ts: fun_Ho1996104121e_bool,G_1: fun_Ho1996104121e_bool,Ts_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Ts),Ts_1))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ) ).

tff(fact_3_thin,axiom,
    ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,G_2),G_1))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ) ).

tff(fact_4_cut,axiom,
    ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ) ).

tff(fact_5_hoare__derivs_Oinsert,axiom,
    ! [Ts: fun_Ho1996104121e_bool,G_1: fun_Ho1996104121e_bool,T: hoare_1875481847_state] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,T),bot_bo1715400655e_bool)))
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,T),Ts))) ) ) ).

tff(fact_6_derivs__insertD,axiom,
    ! [G_1: fun_Ho1996104121e_bool,T: hoare_1875481847_state,Ts: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,T),Ts)))
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,T),bot_bo1715400655e_bool)))
        & hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ) ).

tff(fact_7_MGT__BodyN,axiom,
    ! [Pn_1: pname,G_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_1)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo1715400655e_bool)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo1715400655e_bool))) ) ).

tff(fact_8_finite__Collect__subsets,axiom,
    ! [A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,hAPP_f783502055l_bool(collec1613912337l_bool,hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,ord_le675606854l_bool),A_1)))) ) ).

tff(fact_9_finite__Collect__subsets,axiom,
    ! [A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => hBOOL(hAPP_f755416249l_bool(finite1234242204l_bool,hAPP_f57684501l_bool(collec925828570l_bool,hAPP_f1970936639l_bool(hAPP_f1475014121l_bool(cOMBC_686159718l_bool,ord_le724727525l_bool),A_1)))) ) ).

tff(fact_10_finite__Collect__subsets,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,ord_le233469699e_bool),A_1)))) ) ).

tff(fact_11_finite__Collect__subsets,axiom,
    ! [A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,ord_le313189616e_bool),A_1)))) ) ).

tff(fact_12_finite__imageI,axiom,
    ! [H: fun_Ho14659478e_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1628972376l_bool(image_412748388e_bool(H),Fa))) ) ).

tff(fact_13_finite__imageI,axiom,
    ! [H: fun_Ho1695028467e_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f1873026899l_bool(image_896278159e_bool(H),Fa))) ) ).

tff(fact_14_finite__imageI,axiom,
    ! [H: fun_pn800050071e_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(H),Fa))) ) ).

tff(fact_15_finite__imageI,axiom,
    ! [H: fun_pn760644914e_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f1522632684l_bool(image_1165561978e_bool(H),Fa))) ) ).

tff(fact_16_finite__imageI,axiom,
    ! [H: fun_fu1604182422_state,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f1440968210e_bool(image_1943894628_state(H),Fa))) ) ).

tff(fact_17_finite__imageI,axiom,
    ! [H: fun_fu385705929_state,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f962122119e_bool(image_1669234411_state(H),Fa))) ) ).

tff(fact_18_finite__imageI,axiom,
    ! [H: fun_fu1499449723_pname,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(H),Fa))) ) ).

tff(fact_19_finite__imageI,axiom,
    ! [H: fun_fu235184776_pname,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f75069804e_bool(image_1169820240_pname(H),Fa))) ) ).

tff(fact_20_finite__imageI,axiom,
    ! [H: fun_pn664418900_state,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f1291720380e_bool(image_1283223414_state(H),Fa))) ) ).

tff(fact_21_empty__subsetI,axiom,
    ! [A_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1)) ).

tff(fact_22_empty__subsetI,axiom,
    ! [A_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,bot_bo1715400655e_bool),A_1)) ).

tff(fact_23_finite_OinsertI,axiom,
    ! [A: fun_pname_bool,A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1))) ) ).

tff(fact_24_finite_OinsertI,axiom,
    ! [A: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),A_1))) ) ).

tff(fact_25_finite_OinsertI,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1))) ) ).

tff(fact_26_finite_OinsertI,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1))) ) ).

tff(fact_27_finite_OemptyI,axiom,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ).

tff(fact_28_finite_OemptyI,axiom,
    hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,bot_bo973479705l_bool)) ).

tff(fact_29_finite_OemptyI,axiom,
    hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,bot_bo1715400655e_bool)) ).

tff(fact_30_finite_OemptyI,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).

tff(fact_31_finite__Collect__conjI,axiom,
    ! [Q_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)))) ) ).

tff(fact_32_finite__Collect__conjI,axiom,
    ! [Q_1: fun_fu689207471l_bool,P_1: fun_fu689207471l_bool] :
      ( ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,P_1)))
        | hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,Q_1))) )
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),P_1)),Q_1)))) ) ).

tff(fact_33_finite__Collect__conjI,axiom,
    ! [Q_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,P_1)))
        | hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,Q_1))) )
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),P_1)),Q_1)))) ) ).

tff(fact_34_finite__Collect__conjI,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)))) ) ).

tff(fact_35_image__constant__conv,axiom,
    ! [C: pname,A_1: fun_Ho1996104121e_bool] :
      ( ( ( A_1 = bot_bo1715400655e_bool )
       => ( hAPP_f1148778334e_bool(image_720060442_pname(cOMBK_1595564845_state(C)),A_1) = bot_bo844097828e_bool ) )
      & ( ( A_1 != bot_bo1715400655e_bool )
       => ( hAPP_f1148778334e_bool(image_720060442_pname(cOMBK_1595564845_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ) ).

tff(fact_36_image__constant__conv,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_pname_bool] :
      ( ( ( A_1 = bot_bo844097828e_bool )
       => ( hAPP_f1291720380e_bool(image_1283223414_state(cOMBK_1032401873_pname(C)),A_1) = bot_bo1715400655e_bool ) )
      & ( ( A_1 != bot_bo844097828e_bool )
       => ( hAPP_f1291720380e_bool(image_1283223414_state(cOMBK_1032401873_pname(C)),A_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,C),bot_bo1715400655e_bool) ) ) ) ).

tff(fact_37_image__constant,axiom,
    ! [C: pname,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( hAPP_f1148778334e_bool(image_720060442_pname(cOMBK_1595564845_state(C)),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ).

tff(fact_38_image__constant,axiom,
    ! [C: hoare_1875481847_state,X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( hAPP_f1291720380e_bool(image_1283223414_state(cOMBK_1032401873_pname(C)),A_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,C),bot_bo1715400655e_bool) ) ) ).

tff(fact_39_insert__dom,axiom,
    ! [F: fun_pname_option_com,X_1: pname,Y_1: com] :
      ( ( hAPP_p799580910on_com(F,X_1) = some_com(Y_1) )
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F) ) ) ).

tff(fact_40_finite__surj,axiom,
    ! [B: fun_fu1430349052l_bool,F: fun_Ho14659478e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1628972376l_bool(image_412748388e_bool(F),A_1)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).

tff(fact_41_finite__surj,axiom,
    ! [B: fun_fu689207471l_bool,F: fun_Ho1695028467e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,B),hAPP_f1873026899l_bool(image_896278159e_bool(F),A_1)))
       => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B)) ) ) ).

tff(fact_42_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_43_finite__surj,axiom,
    ! [B: fun_fu1430349052l_bool,F: fun_pn800050071e_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).

tff(fact_44_finite__surj,axiom,
    ! [B: fun_fu689207471l_bool,F: fun_pn760644914e_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,B),hAPP_f1522632684l_bool(image_1165561978e_bool(F),A_1)))
       => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B)) ) ) ).

tff(fact_45_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_pname_pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_46_finite__surj,axiom,
    ! [B: fun_Ho1996104121e_bool,F: fun_fu1604182422_state,A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f1440968210e_bool(image_1943894628_state(F),A_1)))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B)) ) ) ).

tff(fact_47_finite__surj,axiom,
    ! [B: fun_Ho1996104121e_bool,F: fun_fu385705929_state,A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f962122119e_bool(image_1669234411_state(F),A_1)))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B)) ) ) ).

tff(fact_48_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_fu1499449723_pname,A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_49_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_fu235184776_pname,A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f75069804e_bool(image_1169820240_pname(F),A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_50_finite__surj,axiom,
    ! [B: fun_Ho1996104121e_bool,F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B)) ) ) ).

tff(fact_51_subset__singletonD,axiom,
    ! [A_1: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))
     => ( ( A_1 = bot_bo844097828e_bool )
        | ( A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ) ) ) ).

tff(fact_52_subset__singletonD,axiom,
    ! [A_1: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)))
     => ( ( A_1 = bot_bo1715400655e_bool )
        | ( A_1 = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool) ) ) ) ).

tff(fact_53_MGF,axiom,
    ! [C: com] :
      ( hBOOL(hoare_1239590103gleton)
     => ( hBOOL(wT_bodies)
       => ( hBOOL(hAPP_com_bool(wt,C))
         => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) ) ).

tff(fact_54_emptyE,axiom,
    ! [A: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),bot_bo844097828e_bool)) ).

tff(fact_55_emptyE,axiom,
    ! [A: hoare_1875481847_state] : ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),bot_bo1715400655e_bool)) ).

tff(fact_56_insertCI,axiom,
    ! [B_1: pname,A: pname,B: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B))
       => ( A = B_1 ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_57_insertCI,axiom,
    ! [B_1: hoare_1875481847_state,A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),B))
       => ( A = B_1 ) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),B))) ) ).

tff(fact_58_insertE,axiom,
    ! [A: pname,B_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
     => ( ( A != B_1 )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ) ).

tff(fact_59_insertE,axiom,
    ! [A: hoare_1875481847_state,B_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),A_1)))
     => ( ( A != B_1 )
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1)) ) ) ).

tff(fact_60_equalityI,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
       => ( A_1 = B ) ) ) ).

tff(fact_61_equalityI,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1))
       => ( A_1 = B ) ) ) ).

tff(fact_62_subsetD,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_63_subsetD,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_64_image__eqI,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B_1: pname,F: fun_Ho1653816318_pname,X_1: hoare_1875481847_state] :
      ( ( B_1 = hAPP_H139064010_pname(F,X_1) )
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1))) ) ) ).

tff(fact_65_image__eqI,axiom,
    ! [A_1: fun_pname_bool,B_1: hoare_1875481847_state,F: fun_pn664418900_state,X_1: pname] :
      ( ( B_1 = hAPP_p702226982_state(F,X_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,B_1),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1))) ) ) ).

tff(fact_66_equals0D,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( ( A_1 = bot_bo844097828e_bool )
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ).

tff(fact_67_equals0D,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ( A_1 = bot_bo1715400655e_bool )
     => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1)) ) ).

tff(fact_68_Collect__empty__eq,axiom,
    ! [P_1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(collect_pname,P_1) = bot_bo844097828e_bool )
    <=> ! [X_2: pname] : ~ hBOOL(hAPP_pname_bool(P_1,X_2)) ) ).

tff(fact_69_Collect__empty__eq,axiom,
    ! [P_1: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = bot_bo1649642514l_bool )
    <=> ! [X_2: fun_pname_bool] : ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) ) ).

tff(fact_70_Collect__empty__eq,axiom,
    ! [P_1: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool(collec771609166e_bool,P_1) = bot_bo973479705l_bool )
    <=> ! [X_2: fun_Ho1996104121e_bool] : ~ hBOOL(hAPP_f1408815105l_bool(P_1,X_2)) ) ).

tff(fact_71_Collect__empty__eq,axiom,
    ! [P_1: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool(collec1735317154_state,P_1) = bot_bo1715400655e_bool )
    <=> ! [X_2: hoare_1875481847_state] : ~ hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) ) ).

tff(fact_72_empty__iff,axiom,
    ! [C: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).

tff(fact_73_empty__iff,axiom,
    ! [C: hoare_1875481847_state] : ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),bot_bo1715400655e_bool)) ).

tff(fact_74_empty__Collect__eq,axiom,
    ! [P_1: fun_pname_bool] :
      ( ( bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,P_1) )
    <=> ! [X_2: pname] : ~ hBOOL(hAPP_pname_bool(P_1,X_2)) ) ).

tff(fact_75_empty__Collect__eq,axiom,
    ! [P_1: fun_fu1430349052l_bool] :
      ( ( bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,P_1) )
    <=> ! [X_2: fun_pname_bool] : ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_2)) ) ).

tff(fact_76_empty__Collect__eq,axiom,
    ! [P_1: fun_fu689207471l_bool] :
      ( ( bot_bo973479705l_bool = hAPP_f900945761l_bool(collec771609166e_bool,P_1) )
    <=> ! [X_2: fun_Ho1996104121e_bool] : ~ hBOOL(hAPP_f1408815105l_bool(P_1,X_2)) ) ).

tff(fact_77_empty__Collect__eq,axiom,
    ! [P_1: fun_Ho1996104121e_bool] :
      ( ( bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,P_1) )
    <=> ! [X_2: hoare_1875481847_state] : ~ hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) ) ).

tff(fact_78_ex__in__conv,axiom,
    ! [A_1: fun_pname_bool] :
      ( ? [X_2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
    <=> ( A_1 != bot_bo844097828e_bool ) ) ).

tff(fact_79_ex__in__conv,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( ? [X_2: hoare_1875481847_state] : hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
    <=> ( A_1 != bot_bo1715400655e_bool ) ) ).

tff(fact_80_all__not__in__conv,axiom,
    ! [A_1: fun_pname_bool] :
      ( ! [X_2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
    <=> ( A_1 = bot_bo844097828e_bool ) ) ).

tff(fact_81_all__not__in__conv,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] : ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
    <=> ( A_1 = bot_bo1715400655e_bool ) ) ).

tff(fact_82_empty__def,axiom,
    bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,cOMBK_bool_pname(fFalse)) ).

tff(fact_83_empty__def,axiom,
    bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,cOMBK_1857069011e_bool(fFalse)) ).

tff(fact_84_empty__def,axiom,
    bot_bo973479705l_bool = hAPP_f900945761l_bool(collec771609166e_bool,cOMBK_1224513760e_bool(fFalse)) ).

tff(fact_85_empty__def,axiom,
    bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)) ).

tff(fact_86_insert__absorb,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = A_1 ) ) ).

tff(fact_87_insert__absorb,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
     => ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = A_1 ) ) ).

tff(fact_88_insertI2,axiom,
    ! [B_1: pname,A: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_89_insertI2,axiom,
    ! [B_1: hoare_1875481847_state,A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),B))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),B))) ) ).

tff(fact_90_insert__ident,axiom,
    ! [B: fun_pname_bool,X_1: pname,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) )
        <=> ( A_1 = B ) ) ) ) ).

tff(fact_91_insert__ident,axiom,
    ! [B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B))
       => ( ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),B) )
        <=> ( A_1 = B ) ) ) ) ).

tff(fact_92_insert__code,axiom,
    ! [Y_1: pname,A_1: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1),X_1))
    <=> ( ( Y_1 = X_1 )
        | hBOOL(hAPP_pname_bool(A_1,X_1)) ) ) ).

tff(fact_93_insert__code,axiom,
    ! [Y_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,Y_1),A_1),X_1))
    <=> ( ( Y_1 = X_1 )
        | hBOOL(hAPP_H1173941847e_bool(A_1,X_1)) ) ) ).

tff(fact_94_insert__iff,axiom,
    ! [A: pname,B_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A_1)))
    <=> ( ( A = B_1 )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1)) ) ) ).

tff(fact_95_insert__iff,axiom,
    ! [A: hoare_1875481847_state,B_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),A_1)))
    <=> ( ( A = B_1 )
        | hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1)) ) ) ).

tff(fact_96_insert__commute,axiom,
    ! [X_1: pname,Y_1: pname,A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) ) ).

tff(fact_97_insert__commute,axiom,
    ! [X_1: hoare_1875481847_state,Y_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,Y_1),A_1)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,Y_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) ) ).

tff(fact_98_insert__absorb2,axiom,
    ! [X_1: pname,A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1) ) ).

tff(fact_99_insert__absorb2,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1) ) ).

tff(fact_100_insert__Collect,axiom,
    ! [A: pname,P_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(collect_pname,P_1)) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fimplies),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)))),P_1)) ) ).

tff(fact_101_insert__Collect,axiom,
    ! [A: fun_pname_bool,P_1: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),hAPP_f559147733l_bool(collec1974731493e_bool,P_1)) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fimplies),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)))),P_1)) ) ).

tff(fact_102_insert__Collect,axiom,
    ! [A: fun_Ho1996104121e_bool,P_1: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),hAPP_f900945761l_bool(collec771609166e_bool,P_1)) = hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fimplies),hAPP_f900945761l_bool(cOMBB_469839573e_bool(fNot),hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A)))),P_1)) ) ).

tff(fact_103_insert__Collect,axiom,
    ! [A: hoare_1875481847_state,P_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(collec1735317154_state,P_1)) = hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fimplies),hAPP_f121055253e_bool(cOMBB_1424001755_state(fNot),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A)))),P_1)) ) ).

tff(fact_104_insert__compr,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ) ).

tff(fact_105_insert__compr,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ) ).

tff(fact_106_insert__compr,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),B) = hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fdisj),hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A))),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),B))) ) ).

tff(fact_107_insert__compr,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B) = hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fdisj),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A))),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),B))) ) ).

tff(fact_108_insertI1,axiom,
    ! [A: pname,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) ).

tff(fact_109_insertI1,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B))) ).

tff(fact_110_equalityE,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( A_1 = B )
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ) ).

tff(fact_111_equalityE,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A_1 = B )
     => ~ ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
         => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1)) ) ) ).

tff(fact_112_subset__trans,axiom,
    ! [C_1: fun_pname_bool,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1)) ) ) ).

tff(fact_113_subset__trans,axiom,
    ! [C_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),C_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),C_1)) ) ) ).

tff(fact_114_set__mp,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_115_set__mp,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B)) ) ) ).

tff(fact_116_set__rev__mp,axiom,
    ! [B: fun_pname_bool,X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_117_set__rev__mp,axiom,
    ! [B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B)) ) ) ).

tff(fact_118_in__mono,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_119_in__mono,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B)) ) ) ).

tff(fact_120_equalityD2,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( A_1 = B )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ).

tff(fact_121_equalityD2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A_1 = B )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1)) ) ).

tff(fact_122_equalityD1,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( A_1 = B )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ).

tff(fact_123_equalityD1,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A_1 = B )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B)) ) ).

tff(fact_124_set__eq__subset,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( A_1 = B )
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1)) ) ) ).

tff(fact_125_set__eq__subset,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A_1 = B )
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1)) ) ) ).

tff(fact_126_subset__refl,axiom,
    ! [A_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1)) ).

tff(fact_127_subset__refl,axiom,
    ! [A_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),A_1)) ).

tff(fact_128_rev__image__eqI,axiom,
    ! [B_1: pname,F: fun_Ho1653816318_pname,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( ( B_1 = hAPP_H139064010_pname(F,X_1) )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1))) ) ) ).

tff(fact_129_rev__image__eqI,axiom,
    ! [B_1: hoare_1875481847_state,F: fun_pn664418900_state,X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( ( B_1 = hAPP_p702226982_state(F,X_1) )
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,B_1),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1))) ) ) ).

tff(fact_130_imageI,axiom,
    ! [F: fun_Ho1653816318_pname,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H139064010_pname(F,X_1)),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1))) ) ).

tff(fact_131_imageI,axiom,
    ! [F: fun_pn664418900_state,X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,hAPP_p702226982_state(F,X_1)),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1))) ) ).

tff(fact_132_image__iff,axiom,
    ! [Z: hoare_1875481847_state,F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,Z),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
    <=> ? [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
          & ( Z = hAPP_p702226982_state(F,X_2) ) ) ) ).

tff(fact_133_finite__Collect__disjI,axiom,
    ! [P_1: fun_fu1430349052l_bool,Q_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) ) ) ).

tff(fact_134_finite__Collect__disjI,axiom,
    ! [P_1: fun_fu689207471l_bool,Q_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,P_1)))
        & hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,Q_1))) ) ) ).

tff(fact_135_finite__Collect__disjI,axiom,
    ! [P_1: fun_Ho1996104121e_bool,Q_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,P_1)))
        & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,Q_1))) ) ) ).

tff(fact_136_finite__Collect__disjI,axiom,
    ! [P_1: fun_pname_bool,Q_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,P_1)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,Q_1))) ) ) ).

tff(fact_137_insert__compr__raw,axiom,
    ! [X_2: pname,Xa: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),X_2))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),Xa))) ) ).

tff(fact_138_insert__compr__raw,axiom,
    ! [X_2: fun_pname_bool,Xa: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),Xa) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),X_2))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),Xa))) ) ).

tff(fact_139_insert__compr__raw,axiom,
    ! [X_2: fun_Ho1996104121e_bool,Xa: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_2),Xa) = hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fdisj),hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),X_2))),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),Xa))) ) ).

tff(fact_140_insert__compr__raw,axiom,
    ! [X_2: hoare_1875481847_state,Xa: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),Xa) = hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fdisj),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),X_2))),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),Xa))) ) ).

tff(fact_141_singleton__inject,axiom,
    ! [A: pname,B_1: pname] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) )
     => ( A = B_1 ) ) ).

tff(fact_142_singleton__inject,axiom,
    ! [A: hoare_1875481847_state,B_1: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),bot_bo1715400655e_bool) )
     => ( A = B_1 ) ) ).

tff(fact_143_singletonE,axiom,
    ! [B_1: pname,A: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)))
     => ( B_1 = A ) ) ).

tff(fact_144_singletonE,axiom,
    ! [B_1: hoare_1875481847_state,A: hoare_1875481847_state] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,B_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)))
     => ( B_1 = A ) ) ).

tff(fact_145_doubleton__eq__iff,axiom,
    ! [A: pname,B_1: pname,C: pname,D: pname] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,D),bot_bo844097828e_bool)) )
    <=> ( ( ( A = C )
          & ( B_1 = D ) )
        | ( ( A = D )
          & ( B_1 = C ) ) ) ) ).

tff(fact_146_doubleton__eq__iff,axiom,
    ! [A: hoare_1875481847_state,B_1: hoare_1875481847_state,C: hoare_1875481847_state,D: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),bot_bo1715400655e_bool)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,C),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,D),bot_bo1715400655e_bool)) )
    <=> ( ( ( A = C )
          & ( B_1 = D ) )
        | ( ( A = D )
          & ( B_1 = C ) ) ) ) ).

tff(fact_147_singleton__iff,axiom,
    ! [B_1: pname,A: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)))
    <=> ( B_1 = A ) ) ).

tff(fact_148_singleton__iff,axiom,
    ! [B_1: hoare_1875481847_state,A: hoare_1875481847_state] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,B_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)))
    <=> ( B_1 = A ) ) ).

tff(fact_149_insert__not__empty,axiom,
    ! [A: pname,A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) != bot_bo844097828e_bool ) ).

tff(fact_150_insert__not__empty,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) != bot_bo1715400655e_bool ) ).

tff(fact_151_empty__not__insert,axiom,
    ! [A: pname,A_1: fun_pname_bool] : ( bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) ) ).

tff(fact_152_empty__not__insert,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( bot_bo1715400655e_bool != hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) ) ).

tff(fact_153_finite__insert,axiom,
    ! [A: fun_pname_bool,A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),A_1)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ).

tff(fact_154_finite__insert,axiom,
    ! [A: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),A_1)))
    <=> hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1)) ) ).

tff(fact_155_finite__insert,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ).

tff(fact_156_finite__insert,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1)))
    <=> hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1)) ) ).

tff(fact_157_subset__empty,axiom,
    ! [A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool))
    <=> ( A_1 = bot_bo844097828e_bool ) ) ).

tff(fact_158_subset__empty,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),bot_bo1715400655e_bool))
    <=> ( A_1 = bot_bo1715400655e_bool ) ) ).

tff(fact_159_image__is__empty,axiom,
    ! [F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1148778334e_bool(image_720060442_pname(F),A_1) = bot_bo844097828e_bool )
    <=> ( A_1 = bot_bo1715400655e_bool ) ) ).

tff(fact_160_image__is__empty,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool(image_1283223414_state(F),A_1) = bot_bo1715400655e_bool )
    <=> ( A_1 = bot_bo844097828e_bool ) ) ).

tff(fact_161_image__empty,axiom,
    ! [F: fun_Ho1653816318_pname] : ( hAPP_f1148778334e_bool(image_720060442_pname(F),bot_bo1715400655e_bool) = bot_bo844097828e_bool ) ).

tff(fact_162_image__empty,axiom,
    ! [F: fun_pn664418900_state] : ( hAPP_f1291720380e_bool(image_1283223414_state(F),bot_bo844097828e_bool) = bot_bo1715400655e_bool ) ).

tff(fact_163_empty__is__image,axiom,
    ! [F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( ( bot_bo844097828e_bool = hAPP_f1148778334e_bool(image_720060442_pname(F),A_1) )
    <=> ( A_1 = bot_bo1715400655e_bool ) ) ).

tff(fact_164_empty__is__image,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( ( bot_bo1715400655e_bool = hAPP_f1291720380e_bool(image_1283223414_state(F),A_1) )
    <=> ( A_1 = bot_bo844097828e_bool ) ) ).

tff(fact_165_finite__subset,axiom,
    ! [A_1: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ) ).

tff(fact_166_finite__subset,axiom,
    ! [A_1: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,A_1),B))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
       => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1)) ) ) ).

tff(fact_167_finite__subset,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1)) ) ) ).

tff(fact_168_finite__subset,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ) ).

tff(fact_169_rev__finite__subset,axiom,
    ! [A_1: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ) ).

tff(fact_170_rev__finite__subset,axiom,
    ! [A_1: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,A_1),B))
       => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1)) ) ) ).

tff(fact_171_rev__finite__subset,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1)) ) ) ).

tff(fact_172_rev__finite__subset,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ) ).

tff(fact_173_insert__mono,axiom,
    ! [A: pname,C_1: fun_pname_bool,D_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),D_1))) ) ).

tff(fact_174_insert__mono,axiom,
    ! [A: hoare_1875481847_state,C_1: fun_Ho1996104121e_bool,D_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_1),D_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),C_1)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),D_1))) ) ).

tff(fact_175_mem__def,axiom,
    ! [X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
    <=> hBOOL(hAPP_pname_bool(A_1,X_1)) ) ).

tff(fact_176_mem__def,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
    <=> hBOOL(hAPP_H1173941847e_bool(A_1,X_1)) ) ).

tff(fact_177_Collect__def,axiom,
    ! [P_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(collec1735317154_state,P_1) = P_1 ) ).

tff(fact_178_Collect__def,axiom,
    ! [P_1: fun_pname_bool] : ( hAPP_f759274231e_bool(collect_pname,P_1) = P_1 ) ).

tff(fact_179_Collect__def,axiom,
    ! [P_1: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1 ) ).

tff(fact_180_Collect__def,axiom,
    ! [P_1: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(collec771609166e_bool,P_1) = P_1 ) ).

tff(fact_181_subset__insertI2,axiom,
    ! [B_1: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_182_subset__insertI2,axiom,
    ! [B_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,B_1),B))) ) ).

tff(fact_183_subset__insert,axiom,
    ! [B: fun_pname_bool,X_1: pname,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ) ).

tff(fact_184_subset__insert,axiom,
    ! [B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),B)))
      <=> hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B)) ) ) ).

tff(fact_185_insert__subset,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),B))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ) ).

tff(fact_186_insert__subset,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)),B))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B)) ) ) ).

tff(fact_187_subset__insertI,axiom,
    ! [B: fun_pname_bool,A: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B))) ).

tff(fact_188_subset__insertI,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B))) ).

tff(fact_189_insert__image,axiom,
    ! [F: fun_Ho1653816318_pname,X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H139064010_pname(F,X_1)),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)) = hAPP_f1148778334e_bool(image_720060442_pname(F),A_1) ) ) ).

tff(fact_190_insert__image,axiom,
    ! [F: fun_pn664418900_state,X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_p702226982_state(F,X_1)),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)) = hAPP_f1291720380e_bool(image_1283223414_state(F),A_1) ) ) ).

tff(fact_191_image__insert,axiom,
    ! [F: fun_Ho1653816318_pname,A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hAPP_f1148778334e_bool(image_720060442_pname(F),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H139064010_pname(F,A)),hAPP_f1148778334e_bool(image_720060442_pname(F),B)) ) ).

tff(fact_192_image__insert,axiom,
    ! [F: fun_pn664418900_state,A: pname,B: fun_pname_bool] : ( hAPP_f1291720380e_bool(image_1283223414_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_p702226982_state(F,A)),hAPP_f1291720380e_bool(image_1283223414_state(F),B)) ) ).

tff(fact_193_image__mono,axiom,
    ! [F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)),hAPP_f1148778334e_bool(image_720060442_pname(F),B))) ) ).

tff(fact_194_image__mono,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)),hAPP_f1291720380e_bool(image_1283223414_state(F),B))) ) ).

tff(fact_195_subset__image__iff,axiom,
    ! [B: fun_pname_bool,F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)))
    <=> ? [AA: fun_Ho1996104121e_bool] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,AA),A_1))
          & ( B = hAPP_f1148778334e_bool(image_720060442_pname(F),AA) ) ) ) ).

tff(fact_196_subset__image__iff,axiom,
    ! [B: fun_Ho1996104121e_bool,F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
    <=> ? [AA: fun_pname_bool] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1))
          & ( B = hAPP_f1291720380e_bool(image_1283223414_state(F),AA) ) ) ) ).

tff(fact_197_domI,axiom,
    ! [M_1: fun_pname_option_com,A: pname,B_1: com] :
      ( ( hAPP_p799580910on_com(M_1,A) = some_com(B_1) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1))) ) ).

tff(fact_198_Collect__conv__if,axiom,
    ! [P_1: fun_pname_bool,A: pname] :
      ( ( hBOOL(hAPP_pname_bool(P_1,A))
       => ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ) )
      & ( ~ hBOOL(hAPP_pname_bool(P_1,A))
       => ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),P_1)) = bot_bo844097828e_bool ) ) ) ).

tff(fact_199_Collect__conv__if,axiom,
    ! [P_1: fun_fu1430349052l_bool,A: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
       => ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A))
       => ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),P_1)) = bot_bo1649642514l_bool ) ) ) ).

tff(fact_200_Collect__conv__if,axiom,
    ! [P_1: fun_fu689207471l_bool,A: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(P_1,A))
       => ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A))),P_1)) = hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),bot_bo973479705l_bool) ) )
      & ( ~ hBOOL(hAPP_f1408815105l_bool(P_1,A))
       => ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A))),P_1)) = bot_bo973479705l_bool ) ) ) ).

tff(fact_201_Collect__conv__if,axiom,
    ! [P_1: fun_Ho1996104121e_bool,A: hoare_1875481847_state] :
      ( ( hBOOL(hAPP_H1173941847e_bool(P_1,A))
       => ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A))),P_1)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool) ) )
      & ( ~ hBOOL(hAPP_H1173941847e_bool(P_1,A))
       => ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A))),P_1)) = bot_bo1715400655e_bool ) ) ) ).

tff(fact_202_Collect__conv__if2,axiom,
    ! [P_1: fun_pname_bool,A: pname] :
      ( ( hBOOL(hAPP_pname_bool(P_1,A))
       => ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ) )
      & ( ~ hBOOL(hAPP_pname_bool(P_1,A))
       => ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_p61793385e_bool(fequal_pname,A))),P_1)) = bot_bo844097828e_bool ) ) ) ).

tff(fact_203_Collect__conv__if2,axiom,
    ! [P_1: fun_fu1430349052l_bool,A: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
       => ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A))
       => ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f434788991l_bool(fequal533582459e_bool,A))),P_1)) = bot_bo1649642514l_bool ) ) ) ).

tff(fact_204_Collect__conv__if2,axiom,
    ! [P_1: fun_fu689207471l_bool,A: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(P_1,A))
       => ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f1873026899l_bool(fequal259518520e_bool,A))),P_1)) = hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),bot_bo973479705l_bool) ) )
      & ( ~ hBOOL(hAPP_f1408815105l_bool(P_1,A))
       => ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f1873026899l_bool(fequal259518520e_bool,A))),P_1)) = bot_bo973479705l_bool ) ) ) ).

tff(fact_205_Collect__conv__if2,axiom,
    ! [P_1: fun_Ho1996104121e_bool,A: hoare_1875481847_state] :
      ( ( hBOOL(hAPP_H1173941847e_bool(P_1,A))
       => ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_H117293375e_bool(fequal391417144_state,A))),P_1)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool) ) )
      & ( ~ hBOOL(hAPP_H1173941847e_bool(P_1,A))
       => ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_H117293375e_bool(fequal391417144_state,A))),P_1)) = bot_bo1715400655e_bool ) ) ) ).

tff(fact_206_singleton__conv,axiom,
    ! [A: pname] : ( hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ) ).

tff(fact_207_singleton__conv,axiom,
    ! [A: fun_pname_bool] : ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ) ).

tff(fact_208_singleton__conv,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A)) = hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),bot_bo973479705l_bool) ) ).

tff(fact_209_singleton__conv,axiom,
    ! [A: hoare_1875481847_state] : ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool) ) ).

tff(fact_210_singleton__conv2,axiom,
    ! [A: pname] : ( hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool) ) ).

tff(fact_211_singleton__conv2,axiom,
    ! [A: fun_pname_bool] : ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),bot_bo1649642514l_bool) ) ).

tff(fact_212_singleton__conv2,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f1873026899l_bool(fequal259518520e_bool,A)) = hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),bot_bo973479705l_bool) ) ).

tff(fact_213_singleton__conv2,axiom,
    ! [A: hoare_1875481847_state] : ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_H117293375e_bool(fequal391417144_state,A)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool) ) ).

tff(fact_214_MGF__lemma1,axiom,
    ! [C: com,G_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hoare_1239590103gleton)
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body)))
           => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo1715400655e_bool))) )
       => ( hBOOL(hAPP_com_bool(wt,C))
         => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) ) ).

tff(fact_215_WT__bodiesD,axiom,
    ! [Pn: pname,B_4: com] :
      ( hBOOL(wT_bodies)
     => ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
       => hBOOL(hAPP_com_bool(wt,B_4)) ) ) ).

tff(fact_216_imageE,axiom,
    ! [B_1: pname,F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)))
     => ~ ! [X_2: hoare_1875481847_state] :
            ( ( B_1 = hAPP_H139064010_pname(F,X_2) )
           => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1)) ) ) ).

tff(fact_217_imageE,axiom,
    ! [B_1: hoare_1875481847_state,F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,B_1),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
     => ~ ! [X_2: pname] :
            ( ( B_1 = hAPP_p702226982_state(F,X_2) )
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1)) ) ) ).

tff(fact_218_finite__subset__induct,axiom,
    ! [P_1: fun_fu399576434l_bool,A_1: fun_fu1430349052l_bool,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A_1))
       => ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
         => ( ! [A_3: fun_pname_bool,F_1: fun_fu1430349052l_bool] :
                ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
               => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),A_1))
                 => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_3),F_1))
                   => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),F_1))) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_219_finite__subset__induct,axiom,
    ! [P_1: fun_fu237807729l_bool,A_1: fun_fu689207471l_bool,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,Fa),A_1))
       => ( hBOOL(hAPP_f1699935247l_bool(P_1,bot_bo973479705l_bool))
         => ( ! [A_3: fun_Ho1996104121e_bool,F_1: fun_fu689207471l_bool] :
                ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,F_1))
               => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,A_3),A_1))
                 => ( ~ hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,A_3),F_1))
                   => ( hBOOL(hAPP_f1699935247l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1699935247l_bool(P_1,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A_3),F_1))) ) ) ) )
           => hBOOL(hAPP_f1699935247l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_220_finite__subset__induct,axiom,
    ! [P_1: fun_fu1430349052l_bool,A_1: fun_pname_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A_1))
       => ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
         => ( ! [A_3: pname,F_1: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
               => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),F_1))
                   => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),F_1))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_221_finite__subset__induct,axiom,
    ! [P_1: fun_fu689207471l_bool,A_1: fun_Ho1996104121e_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Fa),A_1))
       => ( hBOOL(hAPP_f1408815105l_bool(P_1,bot_bo1715400655e_bool))
         => ( ! [A_3: hoare_1875481847_state,F_1: fun_Ho1996104121e_bool] :
                ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,F_1))
               => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A_3),A_1))
                 => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A_3),F_1))
                   => ( hBOOL(hAPP_f1408815105l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1408815105l_bool(P_1,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A_3),F_1))) ) ) ) )
           => hBOOL(hAPP_f1408815105l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_222_WTs__elim__cases_I7_J,axiom,
    ! [P: pname] :
      ( hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P)))
     => ~ ! [Y_2: com] : ( hAPP_p799580910on_com(body,P) != some_com(Y_2) ) ) ).

tff(fact_223_subsetI,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B)) ) ).

tff(fact_224_subsetI,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
         => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),B)) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B)) ) ).

tff(fact_225_finite__subset__image,axiom,
    ! [F: fun_fu1604182422_state,A_1: fun_fu1430349052l_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f1440968210e_bool(image_1943894628_state(F),A_1)))
       => ? [C_3: fun_fu1430349052l_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1))
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
            & ( B = hAPP_f1440968210e_bool(image_1943894628_state(F),C_3) ) ) ) ) ).

tff(fact_226_finite__subset__image,axiom,
    ! [F: fun_fu385705929_state,A_1: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f962122119e_bool(image_1669234411_state(F),A_1)))
       => ? [C_3: fun_fu689207471l_bool] :
            ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,C_3),A_1))
            & hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,C_3))
            & ( B = hAPP_f962122119e_bool(image_1669234411_state(F),C_3) ) ) ) ) ).

tff(fact_227_finite__subset__image,axiom,
    ! [F: fun_fu1499449723_pname,A_1: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A_1)))
       => ? [C_3: fun_fu1430349052l_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A_1))
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
            & ( B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3) ) ) ) ) ).

tff(fact_228_finite__subset__image,axiom,
    ! [F: fun_fu235184776_pname,A_1: fun_fu689207471l_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f75069804e_bool(image_1169820240_pname(F),A_1)))
       => ? [C_3: fun_fu689207471l_bool] :
            ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,C_3),A_1))
            & hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,C_3))
            & ( B = hAPP_f75069804e_bool(image_1169820240_pname(F),C_3) ) ) ) ) ).

tff(fact_229_finite__subset__image,axiom,
    ! [F: fun_Ho14659478e_bool,A_1: fun_Ho1996104121e_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f1628972376l_bool(image_412748388e_bool(F),A_1)))
       => ? [C_3: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_3),A_1))
            & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,C_3))
            & ( B = hAPP_f1628972376l_bool(image_412748388e_bool(F),C_3) ) ) ) ) ).

tff(fact_230_finite__subset__image,axiom,
    ! [F: fun_Ho1695028467e_bool,A_1: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,B),hAPP_f1873026899l_bool(image_896278159e_bool(F),A_1)))
       => ? [C_3: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_3),A_1))
            & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,C_3))
            & ( B = hAPP_f1873026899l_bool(image_896278159e_bool(F),C_3) ) ) ) ) ).

tff(fact_231_finite__subset__image,axiom,
    ! [F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)))
       => ? [C_3: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_3),A_1))
            & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,C_3))
            & ( B = hAPP_f1148778334e_bool(image_720060442_pname(F),C_3) ) ) ) ) ).

tff(fact_232_finite__subset__image,axiom,
    ! [F: fun_pn800050071e_bool,A_1: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A_1)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3) ) ) ) ) ).

tff(fact_233_finite__subset__image,axiom,
    ! [F: fun_pn760644914e_bool,A_1: fun_pname_bool,B: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
     => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,B),hAPP_f1522632684l_bool(image_1165561978e_bool(F),A_1)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f1522632684l_bool(image_1165561978e_bool(F),C_3) ) ) ) ) ).

tff(fact_234_finite__subset__image,axiom,
    ! [F: fun_pname_pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f759274231e_bool(image_pname_pname(F),C_3) ) ) ) ) ).

tff(fact_235_finite__subset__image,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A_1))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f1291720380e_bool(image_1283223414_state(F),C_3) ) ) ) ) ).

tff(fact_236_finite__dom__body,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))) ).

tff(fact_237_finite__induct,axiom,
    ! [P_1: fun_fu399576434l_bool,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
       => ( ! [X_2: fun_pname_bool,F_1: fun_fu1430349052l_bool] :
              ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
             => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1))
               => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
                 => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))) ) ) )
         => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ).

tff(fact_238_finite__induct,axiom,
    ! [P_1: fun_fu237807729l_bool,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(P_1,bot_bo973479705l_bool))
       => ( ! [X_2: fun_Ho1996104121e_bool,F_1: fun_fu689207471l_bool] :
              ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,F_1))
             => ( ~ hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_2),F_1))
               => ( hBOOL(hAPP_f1699935247l_bool(P_1,F_1))
                 => hBOOL(hAPP_f1699935247l_bool(P_1,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_2),F_1))) ) ) )
         => hBOOL(hAPP_f1699935247l_bool(P_1,Fa)) ) ) ) ).

tff(fact_239_finite__induct,axiom,
    ! [P_1: fun_fu1430349052l_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
       => ( ! [X_2: pname,F_1: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
             => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1))
               => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
                 => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ).

tff(fact_240_finite__induct,axiom,
    ! [P_1: fun_fu689207471l_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(P_1,bot_bo1715400655e_bool))
       => ( ! [X_2: hoare_1875481847_state,F_1: fun_Ho1996104121e_bool] :
              ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,F_1))
             => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),F_1))
               => ( hBOOL(hAPP_f1408815105l_bool(P_1,F_1))
                 => hBOOL(hAPP_f1408815105l_bool(P_1,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),F_1))) ) ) )
         => hBOOL(hAPP_f1408815105l_bool(P_1,Fa)) ) ) ) ).

tff(fact_241_finite_Osimps,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
    <=> ( ( A = bot_bo1649642514l_bool )
        | ? [A_4: fun_fu1430349052l_bool,A_3: fun_pname_bool] :
            ( ( A = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_3),A_4) )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4)) ) ) ) ).

tff(fact_242_finite_Osimps,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A))
    <=> ( ( A = bot_bo973479705l_bool )
        | ? [A_4: fun_fu689207471l_bool,A_3: fun_Ho1996104121e_bool] :
            ( ( A = hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A_3),A_4) )
            & hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_4)) ) ) ) ).

tff(fact_243_finite_Osimps,axiom,
    ! [A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
    <=> ( ( A = bot_bo844097828e_bool )
        | ? [A_4: fun_pname_bool,A_3: pname] :
            ( ( A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_3),A_4) )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4)) ) ) ) ).

tff(fact_244_finite_Osimps,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A))
    <=> ( ( A = bot_bo1715400655e_bool )
        | ? [A_4: fun_Ho1996104121e_bool,A_3: hoare_1875481847_state] :
            ( ( A = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A_3),A_4) )
            & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_4)) ) ) ) ).

tff(fact_245_pigeonhole__infinite,axiom,
    ! [F: fun_pn800050071e_bool,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A_1)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
            & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,hAPP_f567934427l_bool(cOMBB_408569982_pname(fequal533582459e_bool),F)),hAPP_p61793385e_bool(F,X_2)))))) ) ) ) ).

tff(fact_246_pigeonhole__infinite,axiom,
    ! [F: fun_pn760644914e_bool,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f1522632684l_bool(image_1165561978e_bool(F),A_1)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
            & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f1148778334e_bool(hAPP_f1967984667e_bool(cOMBC_1788166607l_bool,hAPP_f98146217l_bool(cOMBB_2094848682_pname(fequal259518520e_bool),F)),hAPP_p1537966538e_bool(F,X_2)))))) ) ) ) ).

tff(fact_247_pigeonhole__infinite,axiom,
    ! [F: fun_Ho1455141843_state,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(image_436941729_state(F),A_1)))
       => ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
            & ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,hAPP_f474907569e_bool(cOMBB_1903241981_state(fequal391417144_state),F)),hAPP_H350317809_state(F,X_2)))))) ) ) ) ).

tff(fact_248_pigeonhole__infinite,axiom,
    ! [F: fun_fu1604182422_state,A_1: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f1440968210e_bool(image_1943894628_state(F),A_1)))
       => ? [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))
            & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_H434980226l_bool(hAPP_f492176169l_bool(cOMBC_620146361e_bool,hAPP_f1703905905e_bool(cOMBB_93797312e_bool(fequal391417144_state),F)),hAPP_f168815540_state(F,X_2)))))) ) ) ) ).

tff(fact_249_pigeonhole__infinite,axiom,
    ! [F: fun_fu385705929_state,A_1: fun_fu689207471l_bool] :
      ( ~ hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f962122119e_bool(image_1669234411_state(F),A_1)))
       => ? [X_2: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_2),A_1))
            & ~ hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),A_1))),hAPP_H810811817l_bool(hAPP_f309954467l_bool(cOMBC_685773310e_bool,hAPP_f1185879473e_bool(cOMBB_1094554675e_bool(fequal391417144_state),F)),hAPP_f890249627_state(F,X_2)))))) ) ) ) ).

tff(fact_250_pigeonhole__infinite,axiom,
    ! [F: fun_pname_pname,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A_1)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
            & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,hAPP_f1336811455e_bool(cOMBB_542850580_pname(fequal_pname),F)),hAPP_pname_pname(F,X_2)))))) ) ) ) ).

tff(fact_251_pigeonhole__infinite,axiom,
    ! [F: fun_Ho1653816318_pname,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)))
       => ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
            & ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_p1537966538e_bool(hAPP_f1188413809e_bool(cOMBC_1259060397e_bool,hAPP_f190028117e_bool(cOMBB_315976743_state(fequal_pname),F)),hAPP_H139064010_pname(F,X_2)))))) ) ) ) ).

tff(fact_252_pigeonhole__infinite,axiom,
    ! [F: fun_fu1499449723_pname,A_1: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A_1)))
       => ? [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))
            & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,hAPP_f1385420507e_bool(cOMBB_598082538e_bool(fequal_pname),F)),hAPP_f1297739591_pname(F,X_2)))))) ) ) ) ).

tff(fact_253_pigeonhole__infinite,axiom,
    ! [F: fun_fu235184776_pname,A_1: fun_fu689207471l_bool] :
      ( ~ hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f75069804e_bool(image_1169820240_pname(F),A_1)))
       => ? [X_2: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_2),A_1))
            & ~ hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),A_1))),hAPP_p1265998686l_bool(hAPP_f662360091l_bool(cOMBC_217340069e_bool,hAPP_f585615743e_bool(cOMBB_184405641e_bool(fequal_pname),F)),hAPP_f1542224800_pname(F,X_2)))))) ) ) ) ).

tff(fact_254_pigeonhole__infinite,axiom,
    ! [F: fun_Ho14659478e_bool,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f1628972376l_bool(image_412748388e_bool(F),A_1)))
       => ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
            & ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_f1291720380e_bool(hAPP_f406856233e_bool(cOMBC_2049654457l_bool,hAPP_f745653815l_bool(cOMBB_582022205_state(fequal533582459e_bool),F)),hAPP_H785152948e_bool(F,X_2)))))) ) ) ) ).

tff(fact_255_pigeonhole__infinite,axiom,
    ! [F: fun_Ho1695028467e_bool,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f1873026899l_bool(image_896278159e_bool(F),A_1)))
       => ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
            & ~ hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,hAPP_f2059405973l_bool(cOMBB_2063006993_state(fequal259518520e_bool),F)),hAPP_H117293375e_bool(F,X_2)))))) ) ) ) ).

tff(fact_256_pigeonhole__infinite,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
            & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_H785152948e_bool(hAPP_f1564627769e_bool(cOMBC_951029257e_bool,hAPP_f1601283355e_bool(cOMBB_2037342654_pname(fequal391417144_state),F)),hAPP_p702226982_state(F,X_2)))))) ) ) ) ).

tff(fact_257_com_Osimps_I6_J,axiom,
    ! [Pname_2: pname,Pname_1: pname] :
      ( ( hAPP_pname_com(body_1,Pname_2) = hAPP_pname_com(body_1,Pname_1) )
    <=> ( Pname_2 = Pname_1 ) ) ).

tff(fact_258_MGT__Body,axiom,
    ! [G_1: fun_Ho1996104121e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs)))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),Procs))) ) ) ).

tff(fact_259_domD,axiom,
    ! [A: pname,M_1: fun_pname_option_com] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),dom_pname_com(M_1)))
     => ? [B_3: com] : ( hAPP_p799580910on_com(M_1,A) = some_com(B_3) ) ) ).

tff(fact_260_the__elem__eq,axiom,
    ! [X_1: pname] : ( hAPP_f1297739591_pname(the_elem_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1 ) ).

tff(fact_261_the__elem__eq,axiom,
    ! [X_1: hoare_1875481847_state] : ( hAPP_f890249627_state(the_el1031305112_state,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) = X_1 ) ).

tff(fact_262_image__subsetI,axiom,
    ! [F: fun_Ho1653816318_pname,B: fun_pname_bool,A_1: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H139064010_pname(F,X_2)),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1148778334e_bool(image_720060442_pname(F),A_1)),B)) ) ).

tff(fact_263_image__subsetI,axiom,
    ! [F: fun_pn664418900_state,B: fun_Ho1996104121e_bool,A_1: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
         => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,hAPP_p702226982_state(F,X_2)),B)) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)),B)) ) ).

tff(fact_264_order__refl,axiom,
    ! [X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1)) ).

tff(fact_265_order__refl,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),X_1)) ).

tff(fact_266_nonempty__iff,axiom,
    ! [A_1: fun_pname_bool] :
      ( ( A_1 != bot_bo844097828e_bool )
    <=> ? [X_2: pname,B_2: fun_pname_bool] :
          ( ( A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_2) )
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_2)) ) ) ).

tff(fact_267_nonempty__iff,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( ( A_1 != bot_bo1715400655e_bool )
    <=> ? [X_2: hoare_1875481847_state,B_2: fun_Ho1996104121e_bool] :
          ( ( A_1 = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),B_2) )
          & ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),B_2)) ) ) ).

tff(fact_268_the_Osimps,axiom,
    ! [X_4: com] : ( hAPP_option_com_com(the_com,some_com(X_4)) = X_4 ) ).

tff(fact_269_weak__Body,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool,Pn_1: pname,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1715400655e_bool)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1715400655e_bool))) ) ).

tff(fact_270_UnCI,axiom,
    ! [A_1: fun_pname_bool,C: pname,B: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ) ).

tff(fact_271_UnCI,axiom,
    ! [A_1: fun_Ho1996104121e_bool,C: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1)) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))) ) ).

tff(fact_272_UnE,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_273_UnE,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)))
     => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_274_Collect__disj__eq,axiom,
    ! [P_1: fun_pname_bool,Q_1: fun_pname_bool] : ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) ) ).

tff(fact_275_Collect__disj__eq,axiom,
    ! [P_1: fun_fu1430349052l_bool,Q_1: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)) ) ).

tff(fact_276_Collect__disj__eq,axiom,
    ! [P_1: fun_fu689207471l_bool,Q_1: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fdisj),P_1)),Q_1)) = hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,hAPP_f900945761l_bool(collec771609166e_bool,P_1)),hAPP_f900945761l_bool(collec771609166e_bool,Q_1)) ) ).

tff(fact_277_Collect__disj__eq,axiom,
    ! [P_1: fun_Ho1996104121e_bool,Q_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fdisj),P_1)),Q_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(collec1735317154_state,P_1)),hAPP_f121055253e_bool(collec1735317154_state,Q_1)) ) ).

tff(fact_278_triple_Oinject,axiom,
    ! [Fun1_2: fun_st1506752259e_bool,Com_2: com,Fun2_2: fun_st1506752259e_bool,Fun1_1: fun_st1506752259e_bool,Com_1: com,Fun2_1: fun_st1506752259e_bool] :
      ( ( hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,Fun1_2),Com_2),Fun2_2) = hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,Fun1_1),Com_1),Fun2_1) )
    <=> ( ( Fun1_2 = Fun1_1 )
        & ( Com_2 = Com_1 )
        & ( Fun2_2 = Fun2_1 ) ) ) ).

tff(fact_279_UnI2,axiom,
    ! [A_1: fun_pname_bool,C: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ) ).

tff(fact_280_UnI2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,C: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))) ) ).

tff(fact_281_UnI1,axiom,
    ! [B: fun_pname_bool,C: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ) ).

tff(fact_282_UnI1,axiom,
    ! [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))) ) ).

tff(fact_283_ball__Un,axiom,
    ! [P_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)))
         => hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) )
    <=> ( ! [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
           => hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) )
        & ! [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),B))
           => hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) ) ) ) ).

tff(fact_284_bex__Un,axiom,
    ! [P_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ? [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)))
          & hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) )
    <=> ( ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
            & hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) )
        | ? [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),B))
            & hBOOL(hAPP_H1173941847e_bool(P_1,X_2)) ) ) ) ).

tff(fact_285_Un__assoc,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)),C_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)) ) ).

tff(fact_286_Un__iff,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_287_Un__iff,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
        | hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_288_Un__left__commute,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),C_1)) ) ).

tff(fact_289_Un__left__absorb,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) ) ).

tff(fact_290_Un__commute,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),A_1) ) ).

tff(fact_291_Un__def,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fdisj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ) ).

tff(fact_292_Un__def,axiom,
    ! [A_1: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fdisj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ) ).

tff(fact_293_Un__def,axiom,
    ! [A_1: fun_fu689207471l_bool,B: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,A_1),B) = hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fdisj),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),A_1))),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),B))) ) ).

tff(fact_294_Un__def,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fdisj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),B))) ) ).

tff(fact_295_Un__absorb,axiom,
    ! [A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),A_1) = A_1 ) ).

tff(fact_296_Un__empty,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = bot_bo844097828e_bool )
    <=> ( ( A_1 = bot_bo844097828e_bool )
        & ( B = bot_bo844097828e_bool ) ) ) ).

tff(fact_297_Un__empty,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = bot_bo1715400655e_bool )
    <=> ( ( A_1 = bot_bo1715400655e_bool )
        & ( B = bot_bo1715400655e_bool ) ) ) ).

tff(fact_298_Un__empty__right,axiom,
    ! [A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),bot_bo844097828e_bool) = A_1 ) ).

tff(fact_299_Un__empty__right,axiom,
    ! [A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),bot_bo1715400655e_bool) = A_1 ) ).

tff(fact_300_Un__empty__left,axiom,
    ! [B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B ) ).

tff(fact_301_Un__empty__left,axiom,
    ! [B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,bot_bo1715400655e_bool),B) = B ) ).

tff(fact_302_finite__UnI,axiom,
    ! [G_1: fun_fu1430349052l_bool,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1))) ) ) ).

tff(fact_303_finite__UnI,axiom,
    ! [G_1: fun_fu689207471l_bool,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,G_1))
       => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,Fa),G_1))) ) ) ).

tff(fact_304_finite__UnI,axiom,
    ! [G_1: fun_pname_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1))) ) ) ).

tff(fact_305_finite__UnI,axiom,
    ! [G_1: fun_Ho1996104121e_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,G_1))
       => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Fa),G_1))) ) ) ).

tff(fact_306_finite__Un,axiom,
    ! [Fa: fun_fu1430349052l_bool,G_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_1)))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) ) ) ).

tff(fact_307_finite__Un,axiom,
    ! [Fa: fun_fu689207471l_bool,G_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,Fa),G_1)))
    <=> ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
        & hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,G_1)) ) ) ).

tff(fact_308_finite__Un,axiom,
    ! [Fa: fun_pname_bool,G_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_1)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) ) ) ).

tff(fact_309_finite__Un,axiom,
    ! [Fa: fun_Ho1996104121e_bool,G_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Fa),G_1)))
    <=> ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
        & hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,G_1)) ) ) ).

tff(fact_310_Un__insert__left,axiom,
    ! [A: pname,B: fun_pname_bool,C_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ) ).

tff(fact_311_Un__insert__left,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)),C_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)) ) ).

tff(fact_312_Un__insert__right,axiom,
    ! [A_1: fun_pname_bool,A: pname,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) ) ).

tff(fact_313_Un__insert__right,axiom,
    ! [A_1: fun_Ho1996104121e_bool,A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)) ) ).

tff(fact_314_Un__mono,axiom,
    ! [B: fun_pname_bool,D_1: fun_pname_bool,A_1: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D_1))) ) ) ).

tff(fact_315_Un__mono,axiom,
    ! [B: fun_Ho1996104121e_bool,D_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),D_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,C_1),D_1))) ) ) ).

tff(fact_316_Un__least,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)),C_1)) ) ) ).

tff(fact_317_Un__least,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),C_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)),C_1)) ) ) ).

tff(fact_318_Un__absorb2,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = A_1 ) ) ).

tff(fact_319_Un__absorb2,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = A_1 ) ) ).

tff(fact_320_Un__absorb1,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B ) ) ).

tff(fact_321_Un__absorb1,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = B ) ) ).

tff(fact_322_subset__Un__eq,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B) = B ) ) ).

tff(fact_323_subset__Un__eq,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
    <=> ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B) = B ) ) ).

tff(fact_324_Un__upper2,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ).

tff(fact_325_Un__upper2,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))) ).

tff(fact_326_Un__upper1,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))) ).

tff(fact_327_Un__upper1,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))) ).

tff(fact_328_image__Un,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool,B: fun_pname_bool] : ( hAPP_f1291720380e_bool(image_1283223414_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)),hAPP_f1291720380e_bool(image_1283223414_state(F),B)) ) ).

tff(fact_329_insert__def,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A))),B) ) ).

tff(fact_330_insert__def,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(collec1735317154_state,hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,fequal391417144_state),A))),B) ) ).

tff(fact_331_insert__def,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A))),B) ) ).

tff(fact_332_insert__def,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,A),B) = hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,fequal259518520e_bool),A))),B) ) ).

tff(fact_333_insert__is__Un,axiom,
    ! [A: pname,A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool)),A_1) ) ).

tff(fact_334_insert__is__Un,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ) ).

tff(fact_335_hoare__derivs_OBody,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),body_1)),Q_1)),Procs))) ) ).

tff(fact_336_xt1_I6_J,axiom,
    ! [Z: fun_pname_bool,Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) ) ) ).

tff(fact_337_xt1_I6_J,axiom,
    ! [Z: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Z),Y_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Z),X_1)) ) ) ).

tff(fact_338_xt1_I5_J,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
       => ( X_1 = Y_1 ) ) ) ).

tff(fact_339_xt1_I5_J,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
       => ( X_1 = Y_1 ) ) ) ).

tff(fact_340_order__trans,axiom,
    ! [Z: fun_pname_bool,X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).

tff(fact_341_order__trans,axiom,
    ! [Z: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),Z))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Z)) ) ) ).

tff(fact_342_order__antisym,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
       => ( X_1 = Y_1 ) ) ) ).

tff(fact_343_order__antisym,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
       => ( X_1 = Y_1 ) ) ) ).

tff(fact_344_xt1_I4_J,axiom,
    ! [C: fun_pname_bool,B_1: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A)) ) ) ).

tff(fact_345_xt1_I4_J,axiom,
    ! [C: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),A))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C),A)) ) ) ).

tff(fact_346_ord__le__eq__trans,axiom,
    ! [C: fun_pname_bool,A: fun_pname_bool,B_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B_1))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) ) ) ).

tff(fact_347_ord__le__eq__trans,axiom,
    ! [C: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),B_1))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),C)) ) ) ).

tff(fact_348_xt1_I3_J,axiom,
    ! [C: fun_pname_bool,A: fun_pname_bool,B_1: fun_pname_bool] :
      ( ( A = B_1 )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A)) ) ) ).

tff(fact_349_xt1_I3_J,axiom,
    ! [C: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] :
      ( ( A = B_1 )
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C),B_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C),A)) ) ) ).

tff(fact_350_ord__eq__le__trans,axiom,
    ! [C: fun_pname_bool,A: fun_pname_bool,B_1: fun_pname_bool] :
      ( ( A = B_1 )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) ) ) ).

tff(fact_351_ord__eq__le__trans,axiom,
    ! [C: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] :
      ( ( A = B_1 )
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),C))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),C)) ) ) ).

tff(fact_352_order__antisym__conv,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
      <=> ( X_1 = Y_1 ) ) ) ).

tff(fact_353_order__antisym__conv,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
      <=> ( X_1 = Y_1 ) ) ) ).

tff(fact_354_order__eq__refl,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( ( X_1 = Y_1 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1)) ) ).

tff(fact_355_order__eq__refl,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( ( X_1 = Y_1 )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1)) ) ).

tff(fact_356_order__eq__iff,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( ( X_1 = Y_1 )
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1)) ) ) ).

tff(fact_357_order__eq__iff,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( ( X_1 = Y_1 )
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1)) ) ) ).

tff(fact_358_option_Oinject,axiom,
    ! [A: com,A_2: com] :
      ( ( some_com(A) = some_com(A_2) )
    <=> ( A = A_2 ) ) ).

tff(fact_359_constant,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool,C_1: bool] :
      ( ( hBOOL(C_1)
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) )
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,hAPP_f873506917e_bool(cOMBB_1757942702_state(cOMBC_231445413l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),C_1)),C),Q_1)),bot_bo1715400655e_bool))) ) ).

tff(fact_360_Body1,axiom,
    ! [Pn_1: pname,G_1: fun_Ho1996104121e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procs))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo1715400655e_bool))) ) ) ).

tff(fact_361_le__bot,axiom,
    ! [A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))
     => ( A = bot_bo844097828e_bool ) ) ).

tff(fact_362_le__bot,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),bot_bo1715400655e_bool))
     => ( A = bot_bo1715400655e_bool ) ) ).

tff(fact_363_bot__unique,axiom,
    ! [A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))
    <=> ( A = bot_bo844097828e_bool ) ) ).

tff(fact_364_bot__unique,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),bot_bo1715400655e_bool))
    <=> ( A = bot_bo1715400655e_bool ) ) ).

tff(fact_365_bot__least,axiom,
    ! [A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)) ).

tff(fact_366_bot__least,axiom,
    ! [A: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,bot_bo1715400655e_bool),A)) ).

tff(fact_367_le__funE,axiom,
    ! [X_1: pname,F: fun_pname_bool,G: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).

tff(fact_368_le__funE,axiom,
    ! [X_1: hoare_1875481847_state,F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1173941847e_bool(F,X_1)),hAPP_H1173941847e_bool(G,X_1))) ) ).

tff(fact_369_le__funD,axiom,
    ! [X_1: pname,F: fun_pname_bool,G: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).

tff(fact_370_le__funD,axiom,
    ! [X_1: hoare_1875481847_state,F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1173941847e_bool(F,X_1)),hAPP_H1173941847e_bool(G,X_1))) ) ).

tff(fact_371_le__fun__def,axiom,
    ! [F: fun_pname_bool,G: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G))
    <=> ! [X_2: pname] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))) ) ).

tff(fact_372_le__fun__def,axiom,
    ! [F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,F),G))
    <=> ! [X_2: hoare_1875481847_state] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1173941847e_bool(F,X_2)),hAPP_H1173941847e_bool(G,X_2))) ) ).

tff(fact_373_bot__apply,axiom,
    ! [X_1: pname] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_374_bot__apply,axiom,
    ! [X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(bot_bo1715400655e_bool,X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_375_bot__fun__def,axiom,
    ! [X_2: pname] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_376_bot__fun__def,axiom,
    ! [X_2: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(bot_bo1715400655e_bool,X_2))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_377_BodyN,axiom,
    ! [P_1: fun_st1506752259e_bool,Pn_1: pname,Q_1: fun_st1506752259e_bool,G_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_1)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo1715400655e_bool)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo1715400655e_bool))) ) ).

tff(fact_378_finite__pointwise,axiom,
    ! [P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,G_1: fun_Ho1996104121e_bool,P_2: fun_pn12888928e_bool,C0_1: fun_pname_com,Q_2: fun_pn12888928e_bool,U_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1))
     => ( ! [P_3: pname] :
            ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_p1637813682e_bool(P_2,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_2,P_3))),bot_bo1715400655e_bool)))
           => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_p1637813682e_bool(P_1,P_3)),hAPP_pname_com(C0_1,P_3)),hAPP_p1637813682e_bool(Q_1,P_3))),bot_bo1715400655e_bool))) )
       => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_2)),C0_1)),Q_2)),U_1)))
         => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).

tff(fact_379_escape,axiom,
    ! [G_1: fun_Ho1996104121e_bool,C: com,Q_1: fun_st1506752259e_bool,P_1: fun_st1506752259e_bool] :
      ( ! [Z_2: state,S_3: state] :
          ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
         => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,cOMBK_631994958_state(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_3))),C),cOMBK_631994958_state(hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo1715400655e_bool))) )
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) ) ).

tff(fact_380_Body__sound__lemma,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_390430481_state(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_390430481_state(G_1),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,hAPP_f275933352_state(cOMBB_718493681_pname(hoare_13225861_state),P_1)),body_1)),Q_1)),Procs))) ) ).

tff(fact_381_conseq1,axiom,
    ! [P_1: fun_st1506752259e_bool,G_1: fun_Ho1996104121e_bool,P_2: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_2),C),Q_1)),bot_bo1715400655e_bool)))
     => ( ! [Z_2: state,S_3: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
           => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S_3)) )
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_382_conseq2,axiom,
    ! [Q_1: fun_st1506752259e_bool,G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool,C: com,Q_2: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_2)),bot_bo1715400655e_bool)))
     => ( ! [Z_2: state,S_3: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_3))
           => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_3)) )
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_383_MGF__complete,axiom,
    ! [P_1: fun_st1506752259e_bool,Q_1: fun_st1506752259e_bool,C: com] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_390430481_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool)))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_384_sup1E,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B),X_1))
     => ( ~ hBOOL(hAPP_H1173941847e_bool(A_1,X_1))
       => hBOOL(hAPP_H1173941847e_bool(B,X_1)) ) ) ).

tff(fact_385_sup1CI,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( ( ~ hBOOL(hAPP_H1173941847e_bool(B,X_1))
       => hBOOL(hAPP_H1173941847e_bool(A_1,X_1)) )
     => hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B),X_1)) ) ).

tff(fact_386_hoare__sound,axiom,
    ! [G_1: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
     => hBOOL(hAPP_f1408815105l_bool(hoare_390430481_state(G_1),Ts)) ) ).

tff(fact_387_bot__empty__eq,axiom,
    ! [X_2: pname] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),bot_bo844097828e_bool)) ) ).

tff(fact_388_bot__empty__eq,axiom,
    ! [X_2: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(bot_bo1715400655e_bool,X_2))
    <=> hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),bot_bo1715400655e_bool)) ) ).

tff(fact_389_rev__predicate1D,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(P_1,X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1))
       => hBOOL(hAPP_pname_bool(Q_1,X_1)) ) ) ).

tff(fact_390_rev__predicate1D,axiom,
    ! [Q_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(P_1,X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,P_1),Q_1))
       => hBOOL(hAPP_H1173941847e_bool(Q_1,X_1)) ) ) ).

tff(fact_391_predicate1D,axiom,
    ! [X_1: pname,P_1: fun_pname_bool,Q_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1))
     => ( hBOOL(hAPP_pname_bool(P_1,X_1))
       => hBOOL(hAPP_pname_bool(Q_1,X_1)) ) ) ).

tff(fact_392_predicate1D,axiom,
    ! [X_1: hoare_1875481847_state,P_1: fun_Ho1996104121e_bool,Q_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,P_1),Q_1))
     => ( hBOOL(hAPP_H1173941847e_bool(P_1,X_1))
       => hBOOL(hAPP_H1173941847e_bool(Q_1,X_1)) ) ) ).

tff(fact_393_sup1I2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(B,X_1))
     => hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B),X_1)) ) ).

tff(fact_394_sup1I1,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(A_1,X_1))
     => hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B),X_1)) ) ).

tff(fact_395_pred__subset__eq,axiom,
    ! [R_1: fun_pname_bool,S: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)))
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,R_1),S)) ) ).

tff(fact_396_pred__subset__eq,axiom,
    ! [R_1: fun_Ho1996104121e_bool,S: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),R_1)),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),S)))
    <=> hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,R_1),S)) ) ).

tff(fact_397_sup__Un__eq,axiom,
    ! [R_1: fun_pname_bool,S: fun_pname_bool,X_2: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2))
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,R_1),S))) ) ).

tff(fact_398_sup__Un__eq,axiom,
    ! [R_1: fun_Ho1996104121e_bool,S: fun_Ho1996104121e_bool,X_2: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),R_1)),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),S)),X_2))
    <=> hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,R_1),S))) ) ).

tff(fact_399_conseq12,axiom,
    ! [Q_1: fun_st1506752259e_bool,P_1: fun_st1506752259e_bool,G_1: fun_Ho1996104121e_bool,P_2: fun_st1506752259e_bool,C: com,Q_2: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_2),C),Q_2)),bot_bo1715400655e_bool)))
     => ( ! [Z_2: state,S_3: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_3))
           => ! [S_4: state] :
                ( ! [Z_3: state] :
                    ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_3))
                   => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_4)) )
               => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_4)) ) )
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_400_le__funI,axiom,
    ! [F: fun_pname_bool,G: fun_pname_bool] :
      ( ! [X_2: pname] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G)) ) ).

tff(fact_401_le__funI,axiom,
    ! [F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1173941847e_bool(F,X_2)),hAPP_H1173941847e_bool(G,X_2)))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,F),G)) ) ).

tff(fact_402_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: pname] : ( set_pname(some_pname(X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ) ).

tff(fact_403_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: hoare_1875481847_state] : ( set_Ho691846255_state(some_H2141159592_state(X_1)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool) ) ).

tff(fact_404_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: com] : ( set_com(some_com(X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ) ).

tff(fact_405_elem__set,axiom,
    ! [X_1: pname,Xo: option_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo)))
    <=> ( Xo = some_pname(X_1) ) ) ).

tff(fact_406_elem__set,axiom,
    ! [X_1: hoare_1875481847_state,Xo: option1681283416_state] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),set_Ho691846255_state(Xo)))
    <=> ( Xo = some_H2141159592_state(X_1) ) ) ).

tff(fact_407_elem__set,axiom,
    ! [X_1: com,Xo: option_com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo)))
    <=> ( Xo = some_com(X_1) ) ) ).

tff(fact_408_ospec,axiom,
    ! [X_1: com,P_1: fun_com_bool,A_1: option_com] :
      ( ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A_1)))
         => hBOOL(hAPP_com_bool(P_1,X_2)) )
     => ( ( A_1 = some_com(X_1) )
       => hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).

tff(fact_409_sup__fun__def,axiom,
    ! [F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool,X_2: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,F),G),X_2))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1173941847e_bool(F,X_2)),hAPP_H1173941847e_bool(G,X_2))) ) ).

tff(fact_410_sup__apply,axiom,
    ! [F: fun_Ho1996104121e_bool,G: fun_Ho1996104121e_bool,X_1: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,F),G),X_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1173941847e_bool(F,X_1)),hAPP_H1173941847e_bool(G,X_1))) ) ).

tff(fact_411_single__stateE,axiom,
    ( hBOOL(hoare_1239590103gleton)
   => ! [T_2: state] :
        ~ ! [S_3: state] : ( S_3 = T_2 ) ) ).

tff(fact_412_state__not__singleton__def,axiom,
    ( hBOOL(hoare_1239590103gleton)
  <=> ? [S_3: state,T_2: state] : ( S_3 != T_2 ) ) ).

tff(fact_413_sup__assoc,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),Z) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) ) ).

tff(fact_414_inf__sup__aci_I6_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),Z) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) ) ).

tff(fact_415_sup_Oassoc,axiom,
    ! [A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1)),C) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B_1),C)) ) ).

tff(fact_416_sup__left__commute,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Z)) ) ).

tff(fact_417_inf__sup__aci_I7_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Z)) ) ).

tff(fact_418_sup_Oleft__commute,axiom,
    ! [B_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),C)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B_1),C)) ) ).

tff(fact_419_sup__left__idem,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) ) ).

tff(fact_420_inf__sup__aci_I8_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) ) ).

tff(fact_421_sup_Oleft__idem,axiom,
    ! [A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1) ) ).

tff(fact_422_sup__commute,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),X_1) ) ).

tff(fact_423_inf__sup__aci_I5_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),X_1) ) ).

tff(fact_424_sup_Ocommute,axiom,
    ! [A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B_1),A) ) ).

tff(fact_425_sup__idem,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),X_1) = X_1 ) ).

tff(fact_426_sup_Oidem,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),A) = A ) ).

tff(fact_427_le__supE,axiom,
    ! [A: fun_pname_bool,B_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) ) ) ).

tff(fact_428_le__supE,axiom,
    ! [A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1)),X_1))
     => ~ ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),X_1))
         => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),X_1)) ) ) ).

tff(fact_429_sup__mono,axiom,
    ! [B_1: fun_pname_bool,D: fun_pname_bool,A: fun_pname_bool,C: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D))) ) ) ).

tff(fact_430_sup__mono,axiom,
    ! [B_1: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),C))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),D))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,C),D))) ) ) ).

tff(fact_431_sup__least,axiom,
    ! [Z: fun_pname_bool,Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z)),X_1)) ) ) ).

tff(fact_432_sup__least,axiom,
    ! [Z: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Z),X_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)),X_1)) ) ) ).

tff(fact_433_le__supI,axiom,
    ! [B_1: fun_pname_bool,A: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1)),X_1)) ) ) ).

tff(fact_434_le__supI,axiom,
    ! [B_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),X_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),X_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1)),X_1)) ) ) ).

tff(fact_435_sup__absorb1,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_436_sup__absorb1,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_437_sup__absorb2,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_438_sup__absorb2,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_439_le__supI2,axiom,
    ! [A: fun_pname_bool,X_1: fun_pname_bool,B_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).

tff(fact_440_le__supI2,axiom,
    ! [A: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),B_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1))) ) ).

tff(fact_441_le__supI1,axiom,
    ! [B_1: fun_pname_bool,X_1: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B_1))) ) ).

tff(fact_442_le__supI1,axiom,
    ! [B_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),A))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A),B_1))) ) ).

tff(fact_443_le__sup__iff,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool,Z: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),Z))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),Z)) ) ) ).

tff(fact_444_le__sup__iff,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),Z))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Z))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),Z)) ) ) ).

tff(fact_445_le__iff__sup,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_446_le__iff__sup,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
    <=> ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_447_sup__ge2,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).

tff(fact_448_sup__ge2,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1))) ).

tff(fact_449_inf__sup__ord_I4_J,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).

tff(fact_450_inf__sup__ord_I4_J,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1))) ).

tff(fact_451_sup__ge1,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).

tff(fact_452_sup__ge1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1))) ).

tff(fact_453_inf__sup__ord_I3_J,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1))) ).

tff(fact_454_inf__sup__ord_I3_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1))) ).

tff(fact_455_sup__eq__bot__iff,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1) = bot_bo844097828e_bool )
    <=> ( ( X_1 = bot_bo844097828e_bool )
        & ( Y_1 = bot_bo844097828e_bool ) ) ) ).

tff(fact_456_sup__eq__bot__iff,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1) = bot_bo1715400655e_bool )
    <=> ( ( X_1 = bot_bo1715400655e_bool )
        & ( Y_1 = bot_bo1715400655e_bool ) ) ) ).

tff(fact_457_sup__bot__right,axiom,
    ! [X_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),bot_bo844097828e_bool) = X_1 ) ).

tff(fact_458_sup__bot__right,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),bot_bo1715400655e_bool) = X_1 ) ).

tff(fact_459_sup__bot__left,axiom,
    ! [X_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),X_1) = X_1 ) ).

tff(fact_460_sup__bot__left,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,bot_bo1715400655e_bool),X_1) = X_1 ) ).

tff(fact_461_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( A_1 != bot_bo1649642514l_bool )
         => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
           => ( ( B != bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ).

tff(fact_462_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite1619424307e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( A_1 != bot_bo973479705l_bool )
         => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
           => ( ( B != bot_bo973479705l_bool )
             => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,A_1),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f962122119e_bool(Fa,A_1)),hAPP_f962122119e_bool(Fa,B)) ) ) ) ) ) ) ).

tff(fact_463_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( A_1 != bot_bo844097828e_bool )
         => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
           => ( ( B != bot_bo844097828e_bool )
             => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ).

tff(fact_464_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1514162941_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( A_1 != bot_bo1715400655e_bool )
         => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
           => ( ( B != bot_bo1715400655e_bool )
             => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)) = hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_f890249627_state(Fa,A_1)),hAPP_f890249627_state(Fa,B)) ) ) ) ) ) ) ).

tff(fact_465_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( B != bot_bo1649642514l_bool )
         => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A_1))
           => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1) ) ) ) ) ) ).

tff(fact_466_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite1619424307e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( B != bot_bo973479705l_bool )
         => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,B),A_1))
           => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f962122119e_bool(Fa,B)),hAPP_f962122119e_bool(Fa,A_1)) = hAPP_f962122119e_bool(Fa,A_1) ) ) ) ) ) ).

tff(fact_467_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( B != bot_bo844097828e_bool )
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
           => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1) ) ) ) ) ) ).

tff(fact_468_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1514162941_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( B != bot_bo1715400655e_bool )
         => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1))
           => ( hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_f890249627_state(Fa,B)),hAPP_f890249627_state(Fa,A_1)) = hAPP_f890249627_state(Fa,A_1) ) ) ) ) ) ).

tff(fact_469_hoare__derivs_OSkip,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),skip),P_1)),bot_bo1715400655e_bool))) ).

tff(fact_470_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( A_1 != bot_bo844097828e_bool )
         => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) ) ) ) ) ).

tff(fact_471_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1514162941_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( A_1 != bot_bo1715400655e_bool )
         => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) = hAPP_H350317809_state(hAPP_H743221337_state(F,X_1),hAPP_f890249627_state(Fa,A_1)) ) ) ) ) ).

tff(fact_472_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( A_1 != bot_bo1649642514l_bool )
         => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) ) ) ) ) ).

tff(fact_473_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite1619424307e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( A_1 != bot_bo973479705l_bool )
         => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),A_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_1),hAPP_f962122119e_bool(Fa,A_1)) ) ) ) ) ).

tff(fact_474_finite__ne__induct,axiom,
    ! [P_1: fun_fu1430349052l_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( ( Fa != bot_bo844097828e_bool )
       => ( ! [X_2: pname] : hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)))
         => ( ! [X_2: pname,F_1: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
               => ( ( F_1 != bot_bo844097828e_bool )
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_1))
                   => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_1))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_475_finite__ne__induct,axiom,
    ! [P_1: fun_fu689207471l_bool,Fa: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
     => ( ( Fa != bot_bo1715400655e_bool )
       => ( ! [X_2: hoare_1875481847_state] : hBOOL(hAPP_f1408815105l_bool(P_1,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),bot_bo1715400655e_bool)))
         => ( ! [X_2: hoare_1875481847_state,F_1: fun_Ho1996104121e_bool] :
                ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,F_1))
               => ( ( F_1 != bot_bo1715400655e_bool )
                 => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),F_1))
                   => ( hBOOL(hAPP_f1408815105l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1408815105l_bool(P_1,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),F_1))) ) ) ) )
           => hBOOL(hAPP_f1408815105l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_476_finite__ne__induct,axiom,
    ! [P_1: fun_fu399576434l_bool,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( ( Fa != bot_bo1649642514l_bool )
       => ( ! [X_2: fun_pname_bool] : hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),bot_bo1649642514l_bool)))
         => ( ! [X_2: fun_pname_bool,F_1: fun_fu1430349052l_bool] :
                ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
               => ( ( F_1 != bot_bo1649642514l_bool )
                 => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_1))
                   => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_1))) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_477_finite__ne__induct,axiom,
    ! [P_1: fun_fu237807729l_bool,Fa: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
     => ( ( Fa != bot_bo973479705l_bool )
       => ( ! [X_2: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1699935247l_bool(P_1,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_2),bot_bo973479705l_bool)))
         => ( ! [X_2: fun_Ho1996104121e_bool,F_1: fun_fu689207471l_bool] :
                ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,F_1))
               => ( ( F_1 != bot_bo973479705l_bool )
                 => ( ~ hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_2),F_1))
                   => ( hBOOL(hAPP_f1699935247l_bool(P_1,F_1))
                     => hBOOL(hAPP_f1699935247l_bool(P_1,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_2),F_1))) ) ) ) )
           => hBOOL(hAPP_f1699935247l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_478_com_Osimps_I19_J,axiom,
    ! [Pname: pname] : ( hAPP_pname_com(body_1,Pname) != skip ) ).

tff(fact_479_com_Osimps_I18_J,axiom,
    ! [Pname: pname] : ( skip != hAPP_pname_com(body_1,Pname) ) ).

tff(fact_480_WT_OSkip,axiom,
    hBOOL(hAPP_com_bool(wt,skip)) ).

tff(fact_481_folding__one__idem_Oin__idem,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
         => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) = hAPP_f1297739591_pname(Fa,A_1) ) ) ) ) ).

tff(fact_482_folding__one__idem_Oin__idem,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1514162941_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
         => ( hAPP_H350317809_state(hAPP_H743221337_state(F,X_1),hAPP_f890249627_state(Fa,A_1)) = hAPP_f890249627_state(Fa,A_1) ) ) ) ) ).

tff(fact_483_folding__one__idem_Oin__idem,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
         => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) = hAPP_f674760225e_bool(Fa,A_1) ) ) ) ) ).

tff(fact_484_folding__one__idem_Oin__idem,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite1619424307e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_1),A_1))
         => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_1),hAPP_f962122119e_bool(Fa,A_1)) = hAPP_f962122119e_bool(Fa,A_1) ) ) ) ) ).

tff(fact_485_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_fu1430349052l_bool,H: fun_fu410713561e_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( ! [X_2: fun_pname_bool,Y_2: fun_pname_bool] : ( hAPP_f759274231e_bool(H,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H,X_2)),hAPP_f759274231e_bool(H,Y_2)) )
       => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N))
         => ( ( N != bot_bo1649642514l_bool )
           => ( hAPP_f759274231e_bool(H,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H),N)) ) ) ) ) ) ).

tff(fact_486_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_fu689207471l_bool,H: fun_fu1296727421e_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite1619424307e_bool(F,Fa))
     => ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(H,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_2),Y_2)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f121055253e_bool(H,X_2)),hAPP_f121055253e_bool(H,Y_2)) )
       => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,N))
         => ( ( N != bot_bo973479705l_bool )
           => ( hAPP_f121055253e_bool(H,hAPP_f962122119e_bool(Fa,N)) = hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(image_1852024517e_bool(H),N)) ) ) ) ) ) ).

tff(fact_487_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_pname_bool,H: fun_pname_pname,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( ! [X_2: pname,Y_2: pname] : ( hAPP_pname_pname(H,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H,X_2)),hAPP_pname_pname(H,Y_2)) )
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N))
         => ( ( N != bot_bo844097828e_bool )
           => ( hAPP_pname_pname(H,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H),N)) ) ) ) ) ) ).

tff(fact_488_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_Ho1996104121e_bool,H: fun_Ho1455141843_state,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1514162941_state(F,Fa))
     => ( ! [X_2: hoare_1875481847_state,Y_2: hoare_1875481847_state] : ( hAPP_H350317809_state(H,hAPP_H350317809_state(hAPP_H743221337_state(F,X_2),Y_2)) = hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_H350317809_state(H,X_2)),hAPP_H350317809_state(H,Y_2)) )
       => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,N))
         => ( ( N != bot_bo1715400655e_bool )
           => ( hAPP_H350317809_state(H,hAPP_f890249627_state(Fa,N)) = hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(image_436941729_state(H),N)) ) ) ) ) ) ).

tff(fact_489_LoopF,axiom,
    ! [G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool,B_1: fun_state_bool,C: com] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fconj)),P_1))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),B_1))),while(B_1,C)),P_1)),bot_bo1715400655e_bool))) ).

tff(fact_490_Comp,axiom,
    ! [D: com,R_1: fun_st1506752259e_bool,G_1: fun_Ho1996104121e_bool,P_1: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),C),Q_1)),bot_bo1715400655e_bool)))
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,Q_1),D),R_1)),bot_bo1715400655e_bool)))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,P_1),semi(C,D)),R_1)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_491_the__elem__def,axiom,
    ! [X_3: fun_pname_bool] : ( hAPP_f1297739591_pname(the_elem_pname,X_3) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_3)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ) ).

tff(fact_492_the__elem__def,axiom,
    ! [X_3: fun_Ho1996104121e_bool] : ( hAPP_f890249627_state(the_el1031305112_state,X_3) = hAPP_f890249627_state(the_Ho1017792262_state,hAPP_f169892419e_bool(cOMBB_1380679615_state(hAPP_f1873026899l_bool(fequal259518520e_bool,X_3)),hAPP_f56162711e_bool(hAPP_f392546175e_bool(cOMBC_483615668e_bool,insert694999549_state),bot_bo1715400655e_bool))) ) ).

tff(fact_493_WTs__elim__cases_I6_J,axiom,
    ! [B_1: fun_state_bool,C: com] :
      ( hBOOL(hAPP_com_bool(wt,while(B_1,C)))
     => hBOOL(hAPP_com_bool(wt,C)) ) ).

tff(fact_494_WTs__elim__cases_I4_J,axiom,
    ! [C1: com,C2: com] :
      ( hBOOL(hAPP_com_bool(wt,semi(C1,C2)))
     => ~ ( hBOOL(hAPP_com_bool(wt,C1))
         => ~ hBOOL(hAPP_com_bool(wt,C2)) ) ) ).

tff(fact_495_com_Osimps_I46_J,axiom,
    ! [Com1_3: com,Com2_3: com,Fun: fun_state_bool,Com_1: com] : ( semi(Com1_3,Com2_3) != while(Fun,Com_1) ) ).

tff(fact_496_com_Osimps_I47_J,axiom,
    ! [Fun: fun_state_bool,Com_1: com,Com1_3: com,Com2_3: com] : ( while(Fun,Com_1) != semi(Com1_3,Com2_3) ) ).

tff(fact_497_com_Osimps_I3_J,axiom,
    ! [Com1_3: com,Com2_3: com,Com1_2: com,Com2_2: com] :
      ( ( semi(Com1_3,Com2_3) = semi(Com1_2,Com2_2) )
    <=> ( ( Com1_3 = Com1_2 )
        & ( Com2_3 = Com2_2 ) ) ) ).

tff(fact_498_com_Osimps_I5_J,axiom,
    ! [Fun_1: fun_state_bool,Com_2: com,Fun: fun_state_bool,Com_1: com] :
      ( ( while(Fun_1,Com_2) = while(Fun,Com_1) )
    <=> ( ( Fun_1 = Fun )
        & ( Com_2 = Com_1 ) ) ) ).

tff(fact_499_com_Osimps_I59_J,axiom,
    ! [Pname_1: pname,Fun_1: fun_state_bool,Com_2: com] : ( hAPP_pname_com(body_1,Pname_1) != while(Fun_1,Com_2) ) ).

tff(fact_500_com_Osimps_I58_J,axiom,
    ! [Fun_1: fun_state_bool,Com_2: com,Pname_1: pname] : ( while(Fun_1,Com_2) != hAPP_pname_com(body_1,Pname_1) ) ).

tff(fact_501_While,axiom,
    ! [B_1: fun_state_bool,C: com] :
      ( hBOOL(hAPP_com_bool(wt,C))
     => hBOOL(hAPP_com_bool(wt,while(B_1,C))) ) ).

tff(fact_502_com_Osimps_I16_J,axiom,
    ! [Fun: fun_state_bool,Com_1: com] : ( skip != while(Fun,Com_1) ) ).

tff(fact_503_com_Osimps_I17_J,axiom,
    ! [Fun: fun_state_bool,Com_1: com] : ( while(Fun,Com_1) != skip ) ).

tff(fact_504_com_Osimps_I49_J,axiom,
    ! [Pname: pname,Com1_1: com,Com2_1: com] : ( hAPP_pname_com(body_1,Pname) != semi(Com1_1,Com2_1) ) ).

tff(fact_505_com_Osimps_I48_J,axiom,
    ! [Com1_1: com,Com2_1: com,Pname: pname] : ( semi(Com1_1,Com2_1) != hAPP_pname_com(body_1,Pname) ) ).

tff(fact_506_WT_OSemi,axiom,
    ! [C1: com,C0: com] :
      ( hBOOL(hAPP_com_bool(wt,C0))
     => ( hBOOL(hAPP_com_bool(wt,C1))
       => hBOOL(hAPP_com_bool(wt,semi(C0,C1))) ) ) ).

tff(fact_507_com_Osimps_I12_J,axiom,
    ! [Com1: com,Com2: com] : ( skip != semi(Com1,Com2) ) ).

tff(fact_508_com_Osimps_I13_J,axiom,
    ! [Com1: com,Com2: com] : ( semi(Com1,Com2) != skip ) ).

tff(fact_509_folding__one_Oinsert,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
         => ( ( A_1 != bot_bo844097828e_bool )
           => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A_1)) ) ) ) ) ) ).

tff(fact_510_folding__one_Oinsert,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
         => ( ( A_1 != bot_bo1715400655e_bool )
           => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) = hAPP_H350317809_state(hAPP_H743221337_state(F,X_1),hAPP_f890249627_state(Fa,A_1)) ) ) ) ) ) ).

tff(fact_511_folding__one_Oinsert,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
         => ( ( A_1 != bot_bo1649642514l_bool )
           => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A_1)) ) ) ) ) ) ).

tff(fact_512_folding__one_Oinsert,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ~ hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_1),A_1))
         => ( ( A_1 != bot_bo973479705l_bool )
           => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),A_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_1),hAPP_f962122119e_bool(Fa,A_1)) ) ) ) ) ) ).

tff(fact_513_folding__one_Osingleton,axiom,
    ! [X_1: pname,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = X_1 ) ) ).

tff(fact_514_folding__one_Osingleton,axiom,
    ! [X_1: hoare_1875481847_state,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) = X_1 ) ) ).

tff(fact_515_folding__one_Oclosed,axiom,
    ! [A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( A_1 != bot_bo844097828e_bool )
         => ( ! [X_2: pname,Y_2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool))))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A_1)),A_1)) ) ) ) ) ).

tff(fact_516_folding__one_Oclosed,axiom,
    ! [A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( A_1 != bot_bo1715400655e_bool )
         => ( ! [X_2: hoare_1875481847_state,Y_2: hoare_1875481847_state] : hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,hAPP_H350317809_state(hAPP_H743221337_state(F,X_2),Y_2)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_2),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,Y_2),bot_bo1715400655e_bool))))
           => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,hAPP_f890249627_state(Fa,A_1)),A_1)) ) ) ) ) ).

tff(fact_517_folding__one_Oclosed,axiom,
    ! [A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( A_1 != bot_bo1649642514l_bool )
         => ( ! [X_2: fun_pname_bool,Y_2: fun_pname_bool] : hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_2)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_2),bot_bo1649642514l_bool))))
           => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A_1)),A_1)) ) ) ) ) ).

tff(fact_518_folding__one_Oclosed,axiom,
    ! [A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( A_1 != bot_bo973479705l_bool )
         => ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_2),Y_2)),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_2),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,Y_2),bot_bo973479705l_bool))))
           => hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,hAPP_f962122119e_bool(Fa,A_1)),A_1)) ) ) ) ) ).

tff(fact_519_triple_Oexhaust,axiom,
    ! [Y_1: hoare_1875481847_state] :
      ~ ! [Fun1: fun_st1506752259e_bool,Com: com,Fun2: fun_st1506752259e_bool] : ( Y_1 != hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,Fun1),Com),Fun2) ) ).

tff(fact_520_image__cong,axiom,
    ! [F: fun_pn664418900_state,G: fun_pn664418900_state,M: fun_pname_bool,N: fun_pname_bool] :
      ( ( M = N )
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N))
           => ( hAPP_p702226982_state(F,X_2) = hAPP_p702226982_state(G,X_2) ) )
       => ( hAPP_f1291720380e_bool(image_1283223414_state(F),M) = hAPP_f1291720380e_bool(image_1283223414_state(G),N) ) ) ) ).

tff(fact_521_Collect__mono,axiom,
    ! [Q_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_H1173941847e_bool(P_1,X_2))
         => hBOOL(hAPP_H1173941847e_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(collec1735317154_state,P_1)),hAPP_f121055253e_bool(collec1735317154_state,Q_1))) ) ).

tff(fact_522_Collect__mono,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_pname_bool(P_1,X_2))
         => hBOOL(hAPP_pname_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1))) ) ).

tff(fact_523_Collect__mono,axiom,
    ! [Q_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool] :
      ( ! [X_2: fun_pname_bool] :
          ( hBOOL(hAPP_f1664156314l_bool(P_1,X_2))
         => hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1))) ) ).

tff(fact_524_Collect__mono,axiom,
    ! [Q_1: fun_fu689207471l_bool,P_1: fun_fu689207471l_bool] :
      ( ! [X_2: fun_Ho1996104121e_bool] :
          ( hBOOL(hAPP_f1408815105l_bool(P_1,X_2))
         => hBOOL(hAPP_f1408815105l_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,hAPP_f900945761l_bool(collec771609166e_bool,P_1)),hAPP_f900945761l_bool(collec771609166e_bool,Q_1))) ) ).

tff(fact_525_predicate1I,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_pname_bool(P_1,X_2))
         => hBOOL(hAPP_pname_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,P_1),Q_1)) ) ).

tff(fact_526_predicate1I,axiom,
    ! [Q_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool] :
      ( ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_H1173941847e_bool(P_1,X_2))
         => hBOOL(hAPP_H1173941847e_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,P_1),Q_1)) ) ).

tff(fact_527_mk__disjoint__insert,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
     => ? [B_2: fun_pname_bool] :
          ( ( A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B_2) )
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),B_2)) ) ) ).

tff(fact_528_mk__disjoint__insert,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
     => ? [B_2: fun_Ho1996104121e_bool] :
          ( ( A_1 = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B_2) )
          & ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),B_2)) ) ) ).

tff(fact_529_Set_Oset__insert,axiom,
    ! [X_1: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ~ ! [B_2: fun_pname_bool] :
            ( ( A_1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B_2) )
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_2)) ) ) ).

tff(fact_530_Set_Oset__insert,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ~ ! [B_2: fun_Ho1996104121e_bool] :
            ( ( A_1 = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),B_2) )
           => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),B_2)) ) ) ).

tff(fact_531_equals0I,axiom,
    ! [A_1: fun_pname_bool] :
      ( ! [Y_2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_2),A_1))
     => ( A_1 = bot_bo844097828e_bool ) ) ).

tff(fact_532_equals0I,axiom,
    ! [A_1: fun_Ho1996104121e_bool] :
      ( ! [Y_2: hoare_1875481847_state] : ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,Y_2),A_1))
     => ( A_1 = bot_bo1715400655e_bool ) ) ).

tff(fact_533_MGT__alternD,axiom,
    ! [G_1: fun_Ho1996104121e_bool,C: com] :
      ( hBOOL(hoare_1239590103gleton)
     => ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1715400655e_bool)))
       => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) ).

tff(fact_534_MGT__alternI,axiom,
    ! [G_1: fun_Ho1996104121e_bool,C: com] :
      ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
     => hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,hAPP_f1935169308e_bool(cOMBB_1036740637_state(cOMBB_1911358915_state(fAll_state)),hAPP_f249262236e_bool(cOMBB_1476898461_state(hAPP_f915354021e_bool(cOMBC_952831051e_bool,hAPP_f1138284024e_bool(cOMBB_20296667_state(cOMBS_1378840469l_bool),hAPP_f1283379615l_bool(cOMBB_1759179140_state(cOMBB_188601460_state(fimplies)),evalc(C))))),fequal_state))),C),fequal_state)),bot_bo1715400655e_bool))) ) ).

tff(fact_535_MGT__def,axiom,
    ! [C: com] : ( hAPP_c406083500_state(hoare_Mirabelle_MGT,C) = hAPP_f1595846909_state(hAPP_c681126378_state(hAPP_f1930074316_state(hoare_13225861_state,fequal_state),C),evalc(C)) ) ).

tff(fact_536_evalc_OBody,axiom,
    ! [Pn: pname,S0: state,S1_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0),S1_1))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0),S1_1)) ) ).

tff(fact_537_evalc__elim__cases_I6_J,axiom,
    ! [P: pname,S_2: state,S1_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_2),S1_1))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_2),S1_1)) ) ).

tff(fact_538_evalc__elim__cases_I1_J,axiom,
    ! [S_2: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),T_1))
     => ( T_1 = S_2 ) ) ).

tff(fact_539_evalc_OWhileFalse,axiom,
    ! [C: com,B_1: fun_state_bool,S_1: state] :
      ( ~ hBOOL(hAPP_state_bool(B_1,S_1))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),S_1)) ) ).

tff(fact_540_evalc_OWhileTrue,axiom,
    ! [S2_1: state,C: com,S1_2: state,B_1: fun_state_bool,S0_1: state] :
      ( hBOOL(hAPP_state_bool(B_1,S0_1))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0_1),S1_2))
       => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1_2),S2_1))
         => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S0_1),S2_1)) ) ) ) ).

tff(fact_541_evalc_OSemi,axiom,
    ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0),S1_1))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_1),S2))
       => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C0,C1)),S0),S2)) ) ) ).

tff(fact_542_evalc_OSkip,axiom,
    ! [S_2: state] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_2),S_2)) ).

tff(fact_543_com__det,axiom,
    ! [U: state,C_2: com,S_2: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),T_1))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_2),U))
       => ( U = T_1 ) ) ) ).

tff(fact_544_evalc__elim__cases_I4_J,axiom,
    ! [C1: com,C2: com,S_2: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(semi(C1,C2)),S_2),T_1))
     => ~ ! [S1: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_2),S1))
           => ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)) ) ) ).

tff(fact_545_evalc__WHILE__case,axiom,
    ! [B_1: fun_state_bool,C: com,S_1: state,T: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S_1),T))
     => ( ( ( T = S_1 )
         => hBOOL(hAPP_state_bool(B_1,S_1)) )
       => ~ ( hBOOL(hAPP_state_bool(B_1,S_1))
           => ! [S1: state] :
                ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_1),S1))
               => ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(while(B_1,C)),S1),T)) ) ) ) ) ).

tff(fact_546_xt1_I15_J,axiom,
    ! [C: fun_pname_bool,A: fun_pname_bool,F: fun_fu410713561e_bool,B_1: fun_pname_bool] :
      ( ( A = hAPP_f759274231e_bool(F,B_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),B_1))
       => ( ! [X_2: fun_pname_bool,Y_2: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2))
             => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2))) )
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A)) ) ) ) ).

tff(fact_547_xt1_I15_J,axiom,
    ! [C: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,F: fun_fu1296727421e_bool,B_1: fun_Ho1996104121e_bool] :
      ( ( A = hAPP_f121055253e_bool(F,B_1) )
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C),B_1))
       => ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool] :
              ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_2),X_2))
             => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(F,Y_2)),hAPP_f121055253e_bool(F,X_2))) )
         => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(F,C)),A)) ) ) ) ).

tff(fact_548_xt1_I16_J,axiom,
    ! [F: fun_fu410713561e_bool,C: fun_pname_bool,B_1: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A))
     => ( ( hAPP_f759274231e_bool(F,B_1) = C )
       => ( ! [X_2: fun_pname_bool,Y_2: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_2))
             => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_2)),hAPP_f759274231e_bool(F,X_2))) )
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A))) ) ) ) ).

tff(fact_549_xt1_I16_J,axiom,
    ! [F: fun_fu1296727421e_bool,C: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),A))
     => ( ( hAPP_f121055253e_bool(F,B_1) = C )
       => ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool] :
              ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_2),X_2))
             => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(F,Y_2)),hAPP_f121055253e_bool(F,X_2))) )
         => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C),hAPP_f121055253e_bool(F,A))) ) ) ) ).

tff(fact_550_folding__one_Ounion__inter,axiom,
    ! [B: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
         => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) != bot_bo1649642514l_bool )
           => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ).

tff(fact_551_folding__one_Ounion__inter,axiom,
    ! [B: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
         => ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),B) != bot_bo973479705l_bool )
           => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,A_1),B))),hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),B))) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f962122119e_bool(Fa,A_1)),hAPP_f962122119e_bool(Fa,B)) ) ) ) ) ) ).

tff(fact_552_folding__one_Ounion__inter,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
         => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) != bot_bo844097828e_bool )
           => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ).

tff(fact_553_folding__one_Ounion__inter,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
         => ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) != bot_bo1715400655e_bool )
           => ( hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B))),hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B))) = hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_f890249627_state(Fa,A_1)),hAPP_f890249627_state(Fa,B)) ) ) ) ) ) ).

tff(fact_554_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( A_1 != bot_bo1649642514l_bool )
         => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
           => ( ( B != bot_bo1649642514l_bool )
             => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = bot_bo1649642514l_bool )
               => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A_1),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A_1)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_555_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( A_1 != bot_bo973479705l_bool )
         => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,B))
           => ( ( B != bot_bo973479705l_bool )
             => ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),B) = bot_bo973479705l_bool )
               => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1703230395l_bool,A_1),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,hAPP_f962122119e_bool(Fa,A_1)),hAPP_f962122119e_bool(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_556_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( A_1 != bot_bo844097828e_bool )
         => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
           => ( ( B != bot_bo844097828e_bool )
             => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool )
               => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_1),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A_1)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_557_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( A_1 != bot_bo1715400655e_bool )
         => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,B))
           => ( ( B != bot_bo1715400655e_bool )
             => ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) = bot_bo1715400655e_bool )
               => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)) = hAPP_H350317809_state(hAPP_H743221337_state(F,hAPP_f890249627_state(Fa,A_1)),hAPP_f890249627_state(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_558_IntI,axiom,
    ! [B: fun_pname_bool,C: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) ) ) ).

tff(fact_559_IntI,axiom,
    ! [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B))) ) ) ).

tff(fact_560_IntE,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_561_IntE,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)))
     => ~ ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
         => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_562_finite__Int,axiom,
    ! [G_1: fun_fu1430349052l_bool,Fa: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_1)) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_1))) ) ).

tff(fact_563_finite__Int,axiom,
    ! [G_1: fun_fu689207471l_bool,Fa: fun_fu689207471l_bool] :
      ( ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,Fa))
        | hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,G_1)) )
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,Fa),G_1))) ) ).

tff(fact_564_finite__Int,axiom,
    ! [G_1: fun_pname_bool,Fa: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_1)) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_1))) ) ).

tff(fact_565_finite__Int,axiom,
    ! [G_1: fun_Ho1996104121e_bool,Fa: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,Fa))
        | hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,G_1)) )
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Fa),G_1))) ) ).

tff(fact_566_disjoint__iff__not__equal,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = bot_bo844097828e_bool )
    <=> ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
         => ! [Xa: pname] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B))
             => ( X_2 != Xa ) ) ) ) ).

tff(fact_567_disjoint__iff__not__equal,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) = bot_bo1715400655e_bool )
    <=> ! [X_2: hoare_1875481847_state] :
          ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
         => ! [Xa: hoare_1875481847_state] :
              ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,Xa),B))
             => ( X_2 != Xa ) ) ) ) ).

tff(fact_568_Int__empty__right,axiom,
    ! [A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),bot_bo844097828e_bool) = bot_bo844097828e_bool ) ).

tff(fact_569_Int__empty__right,axiom,
    ! [A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),bot_bo1715400655e_bool) = bot_bo1715400655e_bool ) ).

tff(fact_570_Int__empty__left,axiom,
    ! [B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),B) = bot_bo844097828e_bool ) ).

tff(fact_571_Int__empty__left,axiom,
    ! [B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,bot_bo1715400655e_bool),B) = bot_bo1715400655e_bool ) ).

tff(fact_572_Int__def,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),A_1))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ) ).

tff(fact_573_Int__def,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) = hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),A_1))),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),B))) ) ).

tff(fact_574_Int__def,axiom,
    ! [A_1: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),B) = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A_1))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ) ).

tff(fact_575_Int__def,axiom,
    ! [A_1: fun_fu689207471l_bool,B: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),B) = hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),A_1))),hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,member1062536460e_bool),B))) ) ).

tff(fact_576_Int__iff,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_577_Int__iff,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_578_IntD1,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1)) ) ).

tff(fact_579_IntD1,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1)) ) ).

tff(fact_580_IntD2,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).

tff(fact_581_IntD2,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ).

tff(fact_582_Collect__conj__eq,axiom,
    ! [P_1: fun_Ho1996104121e_bool,Q_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(collec1735317154_state,hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,hAPP_f932622461l_bool(cOMBB_242064253_state(fconj),P_1)),Q_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(collec1735317154_state,P_1)),hAPP_f121055253e_bool(collec1735317154_state,Q_1)) ) ).

tff(fact_583_Collect__conj__eq,axiom,
    ! [P_1: fun_pname_bool,Q_1: fun_pname_bool] : ( hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,hAPP_f1402196763l_bool(cOMBB_675860798_pname(fconj),P_1)),Q_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(collect_pname,P_1)),hAPP_f759274231e_bool(collect_pname,Q_1)) ) ).

tff(fact_584_Collect__conj__eq,axiom,
    ! [P_1: fun_fu1430349052l_bool,Q_1: fun_fu1430349052l_bool] : ( hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,hAPP_f143162813l_bool(cOMBB_2095475776e_bool(fconj),P_1)),Q_1)) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,hAPP_f559147733l_bool(collec1974731493e_bool,P_1)),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)) ) ).

tff(fact_585_Collect__conj__eq,axiom,
    ! [P_1: fun_fu689207471l_bool,Q_1: fun_fu689207471l_bool] : ( hAPP_f900945761l_bool(collec771609166e_bool,hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,hAPP_f440042033l_bool(cOMBB_532710323e_bool(fconj),P_1)),Q_1)) = hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,hAPP_f900945761l_bool(collec771609166e_bool,P_1)),hAPP_f900945761l_bool(collec771609166e_bool,Q_1)) ) ).

tff(fact_586_Int__Collect,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,P_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
        & hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).

tff(fact_587_Int__Collect,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(collec1735317154_state,P_1))))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
        & hBOOL(hAPP_H1173941847e_bool(P_1,X_1)) ) ) ).

tff(fact_588_Int__Collect,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
        & hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ) ).

tff(fact_589_Int__Collect,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,P_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_1),hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),hAPP_f900945761l_bool(collec771609166e_bool,P_1))))
    <=> ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_1),A_1))
        & hBOOL(hAPP_f1408815105l_bool(P_1,X_1)) ) ) ).

tff(fact_590_inf__Int__eq,axiom,
    ! [R_1: fun_pname_bool,S: fun_pname_bool,X_2: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),R_1)),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),S)),X_2))
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,R_1),S))) ) ).

tff(fact_591_inf__Int__eq,axiom,
    ! [R_1: fun_Ho1996104121e_bool,S: fun_Ho1996104121e_bool,X_2: hoare_1875481847_state] :
      ( hBOOL(hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),R_1)),hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,member618553700_state),S)),X_2))
    <=> hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,R_1),S))) ) ).

tff(fact_592_Un__Int__crazy,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,C_1),A_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,C_1),A_1)) ) ).

tff(fact_593_Un__Int__distrib2,axiom,
    ! [B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1)),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),A_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,C_1),A_1)) ) ).

tff(fact_594_Int__Un__distrib2,axiom,
    ! [B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),A_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,C_1),A_1)) ) ).

tff(fact_595_Un__Int__distrib,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,A_1),C_1)) ) ).

tff(fact_596_Int__Un__distrib,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),C_1)) ) ).

tff(fact_597_Int__mono,axiom,
    ! [B: fun_pname_bool,D_1: fun_pname_bool,A_1: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D_1))) ) ) ).

tff(fact_598_Int__mono,axiom,
    ! [B: fun_Ho1996104121e_bool,D_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),C_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),D_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,C_1),D_1))) ) ) ).

tff(fact_599_Int__greatest,axiom,
    ! [B: fun_pname_bool,C_1: fun_pname_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))) ) ) ).

tff(fact_600_Int__greatest,axiom,
    ! [B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_1),A_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_1),B))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B))) ) ) ).

tff(fact_601_Int__absorb1,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = B ) ) ).

tff(fact_602_Int__absorb1,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B),A_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) = B ) ) ).

tff(fact_603_Int__absorb2,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) = A_1 ) ) ).

tff(fact_604_Int__absorb2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) = A_1 ) ) ).

tff(fact_605_Int__lower2,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),B)) ).

tff(fact_606_Int__lower2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),B)) ).

tff(fact_607_Int__lower1,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),A_1)) ).

tff(fact_608_Int__lower1,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),A_1)) ).

tff(fact_609_Int__insert__left__if1,axiom,
    ! [B: fun_pname_bool,A: pname,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) ) ).

tff(fact_610_Int__insert__left__if1,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,C_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),C_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)),C_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1)) ) ) ).

tff(fact_611_Int__insert__right__if1,axiom,
    ! [B: fun_pname_bool,A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) ) ) ).

tff(fact_612_Int__insert__right__if1,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)) ) ) ).

tff(fact_613_Int__insert__left__if0,axiom,
    ! [B: fun_pname_bool,A: pname,C_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ).

tff(fact_614_Int__insert__left__if0,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,C_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),C_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)),C_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1) ) ) ).

tff(fact_615_Int__insert__right__if0,axiom,
    ! [B: fun_pname_bool,A: pname,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) ) ) ).

tff(fact_616_Int__insert__right__if0,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) ) ) ).

tff(fact_617_insert__inter__insert,axiom,
    ! [A: pname,A_1: fun_pname_bool,B: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) ) ).

tff(fact_618_insert__inter__insert,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)) ) ).

tff(fact_619_Int__insert__left,axiom,
    ! [B: fun_pname_bool,A: pname,C_1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),C_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ) ).

tff(fact_620_Int__insert__left,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,C_1: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),C_1))
       => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)),C_1) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1)) ) )
      & ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),C_1))
       => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)),C_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),C_1) ) ) ) ).

tff(fact_621_Int__insert__right,axiom,
    ! [B: fun_pname_bool,A: pname,A_1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B) ) ) ) ).

tff(fact_622_Int__insert__right,axiom,
    ! [B: fun_Ho1996104121e_bool,A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
       => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)) ) )
      & ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
       => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B) ) ) ) ).

tff(fact_623_inf__sup__ord_I1_J,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1)) ).

tff(fact_624_inf__sup__ord_I1_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),X_1)) ).

tff(fact_625_inf__le1,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),X_1)) ).

tff(fact_626_inf__le1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),X_1)) ).

tff(fact_627_inf__sup__ord_I2_J,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1)) ).

tff(fact_628_inf__sup__ord_I2_J,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),Y_1)) ).

tff(fact_629_inf__le2,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),Y_1)) ).

tff(fact_630_inf__le2,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),Y_1)) ).

tff(fact_631_le__iff__inf,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_632_le__iff__inf,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
    <=> ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_633_le__inf__iff,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool,Z: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).

tff(fact_634_le__inf__iff,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z)))
    <=> ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
        & hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Z)) ) ) ).

tff(fact_635_le__infI1,axiom,
    ! [B_1: fun_pname_bool,A: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),X_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)) ) ).

tff(fact_636_le__infI1,axiom,
    ! [B_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),X_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A),B_1)),X_1)) ) ).

tff(fact_637_le__infI2,axiom,
    ! [A: fun_pname_bool,B_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),X_1)) ) ).

tff(fact_638_le__infI2,axiom,
    ! [A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),X_1))
     => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A),B_1)),X_1)) ) ).

tff(fact_639_inf__absorb1,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_640_inf__absorb1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1) = X_1 ) ) ).

tff(fact_641_inf__absorb2,axiom,
    ! [Y_1: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_1),X_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_642_inf__absorb2,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,Y_1),X_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1) = Y_1 ) ) ).

tff(fact_643_le__infI,axiom,
    ! [B_1: fun_pname_bool,X_1: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1))) ) ) ).

tff(fact_644_le__infI,axiom,
    ! [B_1: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),A))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),B_1))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A),B_1))) ) ) ).

tff(fact_645_inf__greatest,axiom,
    ! [Z: fun_pname_bool,X_1: fun_pname_bool,Y_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))) ) ) ).

tff(fact_646_inf__greatest,axiom,
    ! [Z: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),Z))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z))) ) ) ).

tff(fact_647_inf__mono,axiom,
    ! [B_1: fun_pname_bool,D: fun_pname_bool,A: fun_pname_bool,C: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D))) ) ) ).

tff(fact_648_inf__mono,axiom,
    ! [B_1: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A),C))
     => ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,B_1),D))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A),B_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,C),D))) ) ) ).

tff(fact_649_le__infE,axiom,
    ! [X_1: fun_pname_bool,A: fun_pname_bool,B_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B_1)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) ) ) ).

tff(fact_650_le__infE,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A: fun_Ho1996104121e_bool,B_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A),B_1)))
     => ~ ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),A))
         => ~ hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,X_1),B_1)) ) ) ).

tff(fact_651_inf__sup__absorb,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)) = X_1 ) ).

tff(fact_652_sup__inf__absorb,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)) = X_1 ) ).

tff(fact_653_inf__sup__distrib1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Z)) ) ).

tff(fact_654_sup__inf__distrib1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Z)) ) ).

tff(fact_655_inf__sup__distrib2,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)),X_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),X_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Z),X_1)) ) ).

tff(fact_656_sup__inf__distrib2,axiom,
    ! [Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool,X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z)),X_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),X_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Z),X_1)) ) ).

tff(fact_657_inf__bot__right,axiom,
    ! [X_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),bot_bo844097828e_bool) = bot_bo844097828e_bool ) ).

tff(fact_658_inf__bot__right,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),bot_bo1715400655e_bool) = bot_bo1715400655e_bool ) ).

tff(fact_659_inf__bot__left,axiom,
    ! [X_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,bot_bo844097828e_bool),X_1) = bot_bo844097828e_bool ) ).

tff(fact_660_inf__bot__left,axiom,
    ! [X_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,bot_bo1715400655e_bool),X_1) = bot_bo1715400655e_bool ) ).

tff(fact_661_distrib__sup__le,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool,Z: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)))) ).

tff(fact_662_distrib__sup__le,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Z)))) ).

tff(fact_663_distrib__inf__le,axiom,
    ! [X_1: fun_pname_bool,Y_1: fun_pname_bool,Z: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_1),Z)))) ).

tff(fact_664_distrib__inf__le,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Z))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)))) ).

tff(fact_665_image__Int__subset,axiom,
    ! [F: fun_pn664418900_state,A_1: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),A_1)),hAPP_f1291720380e_bool(image_1283223414_state(F),B)))) ).

tff(fact_666_Un__Int__assoc__eq,axiom,
    ! [A_1: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) )
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_1)) ) ).

tff(fact_667_Un__Int__assoc__eq,axiom,
    ! [A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C_1: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),B)),C_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,B),C_1)) )
    <=> hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,C_1),A_1)) ) ).

tff(fact_668_if__image__distrib,axiom,
    ! [P_1: fun_pname_bool,F: fun_pn664418900_state,G: fun_pn664418900_state,S: fun_pname_bool] : ( hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f1981552043_state(hAPP_f1875279510_state(cOMBS_629630867_state,hAPP_f1087244981_state(hAPP_f294490838_state(cOMBS_602905655_state,hAPP_f980169511_state(cOMBB_1989814576_pname(if_Hoa1541320583_state),P_1)),F)),G)),S) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f1291720380e_bool(image_1283223414_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f1291720380e_bool(image_1283223414_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1))))) ) ).

tff(fact_669_dom__if,axiom,
    ! [P_1: fun_pname_bool,F: fun_pname_option_com,G: fun_pname_option_com] : ( dom_pname_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,hAPP_f755519727on_com(cOMBB_1394247784_pname(if_option_com),P_1)),F)),G)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(G)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),P_1)))) ) ).

tff(fact_670_Int__Collect__mono,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B))
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
           => ( hBOOL(hAPP_pname_bool(P_1,X_2))
             => hBOOL(hAPP_pname_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_1),hAPP_f759274231e_bool(collect_pname,P_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),hAPP_f759274231e_bool(collect_pname,Q_1)))) ) ) ).

tff(fact_671_Int__Collect__mono,axiom,
    ! [Q_1: fun_Ho1996104121e_bool,P_1: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,A_1),B))
     => ( ! [X_2: hoare_1875481847_state] :
            ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_2),A_1))
           => ( hBOOL(hAPP_H1173941847e_bool(P_1,X_2))
             => hBOOL(hAPP_H1173941847e_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,A_1),hAPP_f121055253e_bool(collec1735317154_state,P_1))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,B),hAPP_f121055253e_bool(collec1735317154_state,Q_1)))) ) ) ).

tff(fact_672_Int__Collect__mono,axiom,
    ! [Q_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B))
     => ( ! [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A_1))
           => ( hBOOL(hAPP_f1664156314l_bool(P_1,X_2))
             => hBOOL(hAPP_f1664156314l_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A_1),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))),hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,B),hAPP_f559147733l_bool(collec1974731493e_bool,Q_1)))) ) ) ).

tff(fact_673_Int__Collect__mono,axiom,
    ! [Q_1: fun_fu689207471l_bool,P_1: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,A_1),B))
     => ( ! [X_2: fun_Ho1996104121e_bool] :
            ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_2),A_1))
           => ( hBOOL(hAPP_f1408815105l_bool(P_1,X_2))
             => hBOOL(hAPP_f1408815105l_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(ord_le724727525l_bool,hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,A_1),hAPP_f900945761l_bool(collec771609166e_bool,P_1))),hAPP_f900945761l_bool(hAPP_f19215249l_bool(semila1058800161l_bool,B),hAPP_f900945761l_bool(collec771609166e_bool,Q_1)))) ) ) ).

tff(fact_674_distrib__imp1,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] :
      ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool,Z_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_2),Z_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_2),Y_2)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_2),Z_1)) )
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_1),Z)) ) ) ).

tff(fact_675_distrib__imp2,axiom,
    ! [X_1: fun_Ho1996104121e_bool,Y_1: fun_Ho1996104121e_bool,Z: fun_Ho1996104121e_bool] :
      ( ! [X_2: fun_Ho1996104121e_bool,Y_2: fun_Ho1996104121e_bool,Z_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_2),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,Y_2),Z_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_2),Y_2)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,X_2),Z_1)) )
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,Y_1),Z)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Y_1)),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila657954503e_bool,X_1),Z)) ) ) ).

tff(fact_676_folding__one_Oremove,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
         => ( ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
             => ( hAPP_f1297739591_pname(Fa,A_1) = X_1 ) )
            & ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool )
             => ( hAPP_f1297739591_pname(Fa,A_1) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ) ).

tff(fact_677_folding__one_Oremove,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
         => ( ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) = bot_bo1715400655e_bool )
             => ( hAPP_f890249627_state(Fa,A_1) = X_1 ) )
            & ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) != bot_bo1715400655e_bool )
             => ( hAPP_f890249627_state(Fa,A_1) = hAPP_H350317809_state(hAPP_H743221337_state(F,X_1),hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)))) ) ) ) ) ) ) ).

tff(fact_678_folding__one_Oremove,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
         => ( ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(Fa,A_1) = X_1 ) )
            & ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(Fa,A_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ) ).

tff(fact_679_folding__one_Oremove,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( hBOOL(hAPP_f1699935247l_bool(hAPP_f640685261l_bool(member1062536460e_bool,X_1),A_1))
         => ( ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)) = bot_bo973479705l_bool )
             => ( hAPP_f962122119e_bool(Fa,A_1) = X_1 ) )
            & ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)) != bot_bo973479705l_bool )
             => ( hAPP_f962122119e_bool(Fa,A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_1),hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)))) ) ) ) ) ) ) ).

tff(fact_680_folding__one_Oinsert__remove,axiom,
    ! [X_1: pname,A_1: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
       => ( ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
           => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = X_1 ) )
          & ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool )
           => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ).

tff(fact_681_folding__one_Oinsert__remove,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,F: fun_Ho784854669_state,Fa: fun_fu385705929_state] :
      ( hBOOL(finite1782051386_state(F,Fa))
     => ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
       => ( ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) = bot_bo1715400655e_bool )
           => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) = X_1 ) )
          & ( ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) != bot_bo1715400655e_bool )
           => ( hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)) = hAPP_H350317809_state(hAPP_H743221337_state(F,X_1),hAPP_f890249627_state(Fa,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)))) ) ) ) ) ) ).

tff(fact_682_folding__one_Oinsert__remove,axiom,
    ! [X_1: fun_pname_bool,A_1: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
       => ( ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool )
           => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = X_1 ) )
          & ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool )
           => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ).

tff(fact_683_folding__one_Oinsert__remove,axiom,
    ! [X_1: fun_Ho1996104121e_bool,A_1: fun_fu689207471l_bool,F: fun_fu947547457e_bool,Fa: fun_fu1163781179e_bool] :
      ( hBOOL(finite792754358e_bool(F,Fa))
     => ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
       => ( ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)) = bot_bo973479705l_bool )
           => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),A_1)) = X_1 ) )
          & ( ( hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)) != bot_bo973479705l_bool )
           => ( hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),A_1)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(F,X_1),hAPP_f962122119e_bool(Fa,hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),hAPP_f900945761l_bool(hAPP_f872497439l_bool(insert504309043e_bool,X_1),bot_bo973479705l_bool)))) ) ) ) ) ) ).

tff(fact_684_DiffI,axiom,
    ! [B: fun_pname_bool,C: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))) ) ) ).

tff(fact_685_DiffI,axiom,
    ! [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
     => ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B))
       => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),B))) ) ) ).

tff(fact_686_DiffE,axiom,
    ! [C: pname,A_1: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A_1))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_687_DiffE,axiom,
    ! [C: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),B)))
     => ~ ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),A_1))
         => hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,C),B)) ) ) ).

tff(fact_688_finite__Diff,axiom,
    ! [B: fun_fu1430349052l_bool,A_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_1),B))) ) ).

tff(fact_689_finite__Diff,axiom,
    ! [B: fun_fu689207471l_bool,A_1: fun_fu689207471l_bool] :
      ( hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,A_1))
     => hBOOL(hAPP_f1699935247l_bool(finite1559130124e_bool,hAPP_f900945761l_bool(hAPP_f19215249l_bool(minus_1959767774l_bool,A_1),B))) ) ).

tff(fact_690_finite__Diff,axiom,
    ! [B: fun_pname_bool,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),B))) ) ).

tff(fact_691_finite__Diff,axiom,
    ! [B: fun_Ho1996104121e_bool,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,A_1))
     => hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),B))) ) ).

tff(fact_692_insert__Diff,axiom,
    ! [A: pname,A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A),A_1))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = A_1 ) ) ).

tff(fact_693_insert__Diff,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,A),A_1))
     => ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool))) = A_1 ) ) ).

tff(fact_694_Diff__insert__absorb,axiom,
    ! [X_1: pname,A_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A_1 ) ) ).

tff(fact_695_Diff__insert__absorb,axiom,
    ! [X_1: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,X_1),A_1))
     => ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),A_1)),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,X_1),bot_bo1715400655e_bool)) = A_1 ) ) ).

tff(fact_696_insert__Diff__single,axiom,
    ! [A: pname,A_1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A),A_1) ) ).

tff(fact_697_insert__Diff__single,axiom,
    ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool))) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) ) ).

tff(fact_698_Diff__insert2,axiom,
    ! [A_1: fun_Ho1996104121e_bool,A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),B)) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,hAPP_f121055253e_bool(hAPP_f1204759513e_bool(minus_589155914e_bool,A_1),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool))),B) ) ).

%----Helper facts (107)
tff(help_fNot_1_1_U,axiom,
    ! [P: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fNot,P))
      | ~ hBOOL(P) ) ).

tff(help_fNot_2_1_U,axiom,
    ! [P: bool] :
      ( hBOOL(P)
      | hBOOL(hAPP_bool_bool(fNot,P)) ) ).

tff(help_fconj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).

tff(help_fconj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(P) ) ).

tff(help_fconj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(Q) ) ).

tff(help_fdisj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).

tff(help_fdisj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).

tff(help_fdisj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | hBOOL(P)
      | hBOOL(Q) ) ).

tff(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse) ).

tff(help_fFalse_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fimplies_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( hBOOL(P)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).

tff(help_fimplies_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).

tff(help_fimplies_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
      | ~ hBOOL(P)
      | hBOOL(Q) ) ).

tff(help_fAll_1_1_fAll_000tc__Com__Ostate_U,axiom,
    ! [X: state,P: fun_state_bool] :
      ( ~ hBOOL(hAPP_f327114704l_bool(fAll_state,P))
      | hBOOL(hAPP_state_bool(P,X)) ) ).

tff(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
    ! [X: pname,Y: pname] :
      ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
    ! [X: pname,Y: pname] :
      ( ( X != Y )
      | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
    ! [X: state,Y: state] :
      ( ( X != Y )
      | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
    ! [P: bool,Q: pname] : ( hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P ) ).

tff(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
    ! [X: option_com,Y: option_com] : ( hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fTrue),X),Y) = X ) ).

tff(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
    ! [X: option_com,Y: option_com] : ( hAPP_o356497025on_com(hAPP_o334540577on_com(hAPP_b1679505845on_com(if_option_com,fFalse),X),Y) = Y ) ).

tff(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
    ! [X: fun_pname_bool,Y: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
    ! [X: fun_pname_bool,Y: fun_pname_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
    ! [P: fun_bool_bool,Q: fun_pname_bool,R: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBB_647938656_pname(P),Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
    ! [P: fun_bool_bool,Q: fun_state_bool,R: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_st2063251938l_bool,Q: bool,R: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_pn250273176l_bool,Q: fun_pname_bool,R: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f649174806e_bool(cOMBS_568398431l_bool,P),Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_st2063251938l_bool,Q: fun_state_bool,R: state] : ( hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
    ! [P: fun_pn800050071e_bool,Q: pname,R: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U,axiom,
    ! [P: fun_st1506752259e_bool,Q: state,R: state] : ( hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
    ! [P: bool,Q: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
    ! [P: fun_state_bool,Q: state] : ( hAPP_s1806633685e_bool(cOMBK_631994958_state(P),Q) = P ) ).

tff(help_If_1_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate,axiom,
    ! [X: hoare_1875481847_state,Y: hoare_1875481847_state] : ( hAPP_H350317809_state(hAPP_H743221337_state(hAPP_b1347637997_state(if_Hoa1541320583_state,fTrue),X),Y) = X ) ).

tff(help_If_2_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate,axiom,
    ! [X: hoare_1875481847_state,Y: hoare_1875481847_state] : ( hAPP_H350317809_state(hAPP_H743221337_state(hAPP_b1347637997_state(if_Hoa1541320583_state,fFalse),X),Y) = Y ) ).

tff(help_If_3_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com,axiom,
    ! [X: hoare_1875481847_state,Y: hoare_1875481847_state] :
      ( ~ hBOOL(hAPP_H1173941847e_bool(hAPP_H117293375e_bool(fequal391417144_state,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com,axiom,
    ! [X: hoare_1875481847_state,Y: hoare_1875481847_state] :
      ( ( X != Y )
      | hBOOL(hAPP_H1173941847e_bool(hAPP_H117293375e_bool(fequal391417144_state,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00,axiom,
    ! [P: fun_option_com_com,Q: fun_pname_option_com,R: pname] : ( hAPP_pname_com(hAPP_f96342628me_com(cOMBB_923936821_pname(P),Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBB_307249310e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_pname_bool,R: pname] : ( hAPP_p393069232l_bool(hAPP_f1402196763l_bool(cOMBB_675860798_pname(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_218,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_state_bool,R: state] : ( hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
    ! [P: fun_fu31783638l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f624840228l_bool(cOMBS_350070575l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
    ! [P: fun_fu1430349052l_bool,Q: fun_pn800050071e_bool,R: pname] : ( hAPP_pname_bool(hAPP_f42430548e_bool(cOMBB_530759491_pname(P),Q),R) = hAPP_f1664156314l_bool(P,hAPP_p61793385e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
    ! [P: fun_fu93307442l_bool,Q: fun_st1506752259e_bool,R: state] : ( hAPP_state_bool(hAPP_f1012183542e_bool(cOMBB_1911358915_state(P),Q),R) = hAPP_f327114704l_bool(P,hAPP_s1806633685e_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P: fun_pn422929397l_bool,Q: fun_pname_bool,R: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O,axiom,
    ! [P: fun_st1483075957e_bool,Q: bool,R: state] : ( hAPP_s1806633685e_bool(hAPP_b1095269219e_bool(hAPP_f701449317e_bool(cOMBC_471052088e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_s1874344717e_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
    ! [P: fun_fu410713561e_bool,Q: pname,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_p338031245l_bool(hAPP_f2082757169l_bool(cOMBC_1004116266e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_pname_pname,R: pname] : ( hAPP_p61793385e_bool(hAPP_f1336811455e_bool(cOMBB_542850580_pname(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____xlrqixeqwe__,axiom,
    ! [P: bool,Q: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(cOMBK_2086958736_state(P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_,axiom,
    ! [P: pname,Q: hoare_1875481847_state] : ( hAPP_H139064010_pname(cOMBK_1595564845_state(P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__,axiom,
    ! [P: hoare_1875481847_state,Q: pname] : ( hAPP_p702226982_state(cOMBK_1032401873_pname(P),Q) = P ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple,axiom,
    ! [X: fun_Ho1996104121e_bool,Y: fun_Ho1996104121e_bool] :
      ( ~ hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(fequal259518520e_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple,axiom,
    ! [X: fun_Ho1996104121e_bool,Y: fun_Ho1996104121e_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(fequal259518520e_bool,X),Y)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_,axiom,
    ! [P: fun_pn1580610524on_com,Q: fun_pname_option_com,R: pname] : ( hAPP_p799580910on_com(hAPP_f2123220539on_com(hAPP_f1673966486on_com(cOMBS_904531235on_com,P),Q),R) = hAPP_o356497025on_com(hAPP_p1086945780on_com(P,R),hAPP_p799580910on_com(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____xlrqixeqwe__O,axiom,
    ! [P: fun_co2032091866_state,Q: fun_pname_com,R: pname] : ( hAPP_p702226982_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(P),Q),R) = hAPP_c406083500_state(P,hAPP_pname_com(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
    ! [P: fun_bool_bool,Q: fun_Ho1996104121e_bool,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_f121055253e_bool(cOMBB_1424001755_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H1173941847e_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho1896286681l_bool,Q: fun_Ho1996104121e_bool,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1300953505e_bool(cOMBS_896408300l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H377399461l_bool(P,R),hAPP_H1173941847e_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_,axiom,
    ! [P: fun_pn760644914e_bool,Q: hoare_1875481847_state,R: pname] : ( hAPP_pname_bool(hAPP_H785152948e_bool(hAPP_f1564627769e_bool(cOMBC_951029257e_bool,P),Q),R) = hAPP_H1173941847e_bool(hAPP_p1537966538e_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho14659478e_bool,Q: pname,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_p1537966538e_bool(hAPP_f1188413809e_bool(cOMBC_1259060397e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H785152948e_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_219,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : ( hAPP_f1476298914l_bool(hAPP_f143162813l_bool(cOMBB_2095475776e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P: fun_fu802393907l_bool,Q: fun_pname_bool,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_220,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_fu1499449723_pname,R: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1385420507e_bool(cOMBB_598082538e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_221,axiom,
    ! [P: fun_pn479984722e_bool,Q: fun_pname_bool,R: pname] : ( hAPP_p61793385e_bool(hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob,axiom,
    ! [P: fun_st277393160e_bool,Q: fun_state_bool,R: state] : ( hAPP_s1806633685e_bool(hAPP_f1863945078e_bool(hAPP_f915354021e_bool(cOMBC_952831051e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_s1226857760e_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____xlr,axiom,
    ! [P: bool,Q: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(cOMBK_1224513760e_bool(P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
    ! [P: fun_bool_bool,Q: fun_fu689207471l_bool,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_f900945761l_bool(cOMBB_469839573e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f1408815105l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_222,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Ho1996104121e_bool,R: hoare_1875481847_state] : ( hAPP_H377399461l_bool(hAPP_f932622461l_bool(cOMBB_242064253_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1173941847e_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I,axiom,
    ! [P: fun_fu854396771l_bool,Q: fun_fu689207471l_bool,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_f900945761l_bool(hAPP_f2051813877l_bool(cOMBS_1451994324l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f78029435l_bool(P,R),hAPP_f1408815105l_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____xl,axiom,
    ! [P: fun_pn249986828l_bool,Q: fun_Ho1996104121e_bool,R: pname] : ( hAPP_pname_bool(hAPP_f1148778334e_bool(hAPP_f1967984667e_bool(cOMBC_1788166607l_bool,P),Q),R) = hAPP_f1408815105l_bool(hAPP_p1265998686l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___223,axiom,
    ! [P: fun_Ho760178998l_bool,Q: fun_pname_bool,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_f1291720380e_bool(hAPP_f406856233e_bool(cOMBC_2049654457l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H434980226l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,axiom,
    ! [P: fun_fu1176632176e_bool,Q: hoare_1875481847_state,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_H434980226l_bool(hAPP_f492176169l_bool(cOMBC_620146361e_bool,P),Q),R) = hAPP_H1173941847e_bool(hAPP_f1291720380e_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I,axiom,
    ! [P: fun_fu1040518284e_bool,Q: pname,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_p1265998686l_bool(hAPP_f662360091l_bool(cOMBC_217340069e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f1148778334e_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_224,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_Ho1653816318_pname,R: hoare_1875481847_state] : ( hAPP_H785152948e_bool(hAPP_f190028117e_bool(cOMBB_315976743_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H139064010_pname(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_225,axiom,
    ! [P: fun_fu931343505l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P: fun_fu802393907l_bool,Q: fun_pn800050071e_bool,R: pname] : ( hAPP_p338031245l_bool(hAPP_f567934427l_bool(cOMBB_408569982_pname(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P: fun_fu1658206819l_bool,Q: fun_st1506752259e_bool,R: state] : ( hAPP_s2001034685l_bool(hAPP_f1283379615l_bool(cOMBB_1759179140_state(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_s1806633685e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_226,axiom,
    ! [P: fun_fu1998731480e_bool,Q: fun_st1506752259e_bool,R: state] : ( hAPP_s336103912e_bool(hAPP_f249262236e_bool(cOMBB_1476898461_state(P),Q),R) = hAPP_f1863945078e_bool(P,hAPP_s1806633685e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__,axiom,
    ! [P: fun_fu2104550360e_bool,Q: fun_st858662806e_bool,R: state] : ( hAPP_s1806633685e_bool(hAPP_f1935169308e_bool(cOMBB_1036740637_state(P),Q),R) = hAPP_f1012183542e_bool(P,hAPP_s336103912e_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__227,axiom,
    ! [P: fun_pn1673019570on_com,Q: fun_pname_option_com,R: pname] : ( hAPP_p1086945780on_com(hAPP_f648377725on_com(hAPP_f2093196134on_com(cOMBS_1529518335on_com,P),Q),R) = hAPP_o334540577on_com(hAPP_p1164893188on_com(P,R),hAPP_p799580910on_com(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___228,axiom,
    ! [P: fun_Ho1695028467e_bool,Q: hoare_1875481847_state,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_H117293375e_bool(hAPP_f2101312745e_bool(cOMBC_1972244470e_bool,P),Q),R) = hAPP_H1173941847e_bool(hAPP_H117293375e_bool(P,R),Q) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_,axiom,
    ! [P: fun_pn1776597836_state,Q: fun_pn664418900_state,R: pname] : ( hAPP_p702226982_state(hAPP_f1981552043_state(hAPP_f1875279510_state(cOMBS_629630867_state,P),Q),R) = hAPP_H350317809_state(hAPP_p1279250276_state(P,R),hAPP_p702226982_state(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_229,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_fu689207471l_bool,R: fun_Ho1996104121e_bool] : ( hAPP_f78029435l_bool(hAPP_f440042033l_bool(cOMBB_532710323e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f1408815105l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_230,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_fu235184776_pname,R: fun_Ho1996104121e_bool] : ( hAPP_f1148778334e_bool(hAPP_f585615743e_bool(cOMBB_184405641e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1542224800_pname(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc,axiom,
    ! [P: fun_pn1610849624_state,Q: fun_pn12888928e_bool,R: pname] : ( hAPP_p702226982_state(hAPP_f1568887991_state(hAPP_f891245078_state(cOMBS_475568287_state,P),Q),R) = hAPP_f1595846909_state(hAPP_p1985340144_state(P,R),hAPP_p1637813682e_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
    ! [P: fun_fu1911931399l_bool,Q: fun_fu1430349052l_bool,R: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(hAPP_f1879335953l_bool(cOMBC_7971162l_bool,P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H,axiom,
    ! [P: fun_fu1219323149e_bool,Q: fun_st2116860965l_bool,R: state] : ( hAPP_s1874344717e_bool(hAPP_f873506917e_bool(cOMBB_1757942702_state(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_s2001034685l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_,axiom,
    ! [P: fun_bo79750167on_com,Q: fun_pname_bool,R: pname] : ( hAPP_p1164893188on_com(hAPP_f755519727on_com(cOMBB_1394247784_pname(P),Q),R) = hAPP_b1679505845on_com(P,hAPP_pname_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I,axiom,
    ! [P: fun_fu689207471l_bool,Q: fun_Ho1695028467e_bool,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_f169892419e_bool(cOMBB_1380679615_state(P),Q),R) = hAPP_f1408815105l_bool(P,hAPP_H117293375e_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___231,axiom,
    ! [P: fun_Ho1085560331l_bool,Q: fun_Ho1996104121e_bool,R: hoare_1875481847_state] : ( hAPP_H1173941847e_bool(hAPP_f121055253e_bool(hAPP_f1795624711e_bool(cOMBC_1099403170l_bool,P),Q),R) = hAPP_f1408815105l_bool(hAPP_H810811817l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_232,axiom,
    ! [P: fun_fu1296727421e_bool,Q: hoare_1875481847_state,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_H810811817l_bool(hAPP_f309954467l_bool(cOMBC_685773310e_bool,P),Q),R) = hAPP_H1173941847e_bool(hAPP_f121055253e_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho1695028467e_bool,Q: fun_pn664418900_state,R: pname] : ( hAPP_p1537966538e_bool(hAPP_f1601283355e_bool(cOMBB_2037342654_pname(P),Q),R) = hAPP_H117293375e_bool(P,hAPP_p702226982_state(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_233,axiom,
    ! [P: fun_fu802393907l_bool,Q: fun_Ho14659478e_bool,R: hoare_1875481847_state] : ( hAPP_H434980226l_bool(hAPP_f745653815l_bool(cOMBB_582022205_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H785152948e_bool(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc,axiom,
    ! [P: fun_pn92346699_state,Q: fun_pname_com,R: pname] : ( hAPP_p1985340144_state(hAPP_f2116202538_state(hAPP_f1339343196_state(cOMBS_1674056844_state,P),Q),R) = hAPP_c681126378_state(hAPP_p2012996835_state(P,R),hAPP_pname_com(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_234,axiom,
    ! [P: fun_fu1047394976e_bool,Q: fun_st2116860965l_bool,R: state] : ( hAPP_s1226857760e_bool(hAPP_f1138284024e_bool(cOMBB_20296667_state(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_s2001034685l_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_235,axiom,
    ! [P: fun_fu1173762305l_bool,Q: fun_Ho1996104121e_bool,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(hAPP_f2051277573l_bool(cOMBC_195806106l_bool,P),Q),R) = hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___236,axiom,
    ! [P: fun_Ho1695028467e_bool,Q: fun_fu1604182422_state,R: fun_pname_bool] : ( hAPP_f1291720380e_bool(hAPP_f1703905905e_bool(cOMBB_93797312e_bool(P),Q),R) = hAPP_H117293375e_bool(P,hAPP_f168815540_state(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___237,axiom,
    ! [P: fun_Ho1695028467e_bool,Q: fun_Ho1455141843_state,R: hoare_1875481847_state] : ( hAPP_H117293375e_bool(hAPP_f474907569e_bool(cOMBB_1903241981_state(P),Q),R) = hAPP_H117293375e_bool(P,hAPP_H350317809_state(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe__238,axiom,
    ! [P: fun_pn1243268074_state,Q: fun_pn664418900_state,R: pname] : ( hAPP_p1279250276_state(hAPP_f1087244981_state(hAPP_f294490838_state(cOMBS_602905655_state,P),Q),R) = hAPP_H743221337_state(hAPP_p1513527868_state(P,R),hAPP_p702226982_state(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_239,axiom,
    ! [P: fun_fu2083718837l_bool,Q: fun_fu689207471l_bool,R: fun_Ho1996104121e_bool] : ( hAPP_f1408815105l_bool(hAPP_f900945761l_bool(hAPP_f1846363427l_bool(cOMBC_1909905718l_bool,P),Q),R) = hAPP_f1699935247l_bool(hAPP_f640685261l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_240,axiom,
    ! [P: fun_fu1173762305l_bool,Q: fun_pn760644914e_bool,R: pname] : ( hAPP_p1265998686l_bool(hAPP_f98146217l_bool(cOMBB_2094848682_pname(P),Q),R) = hAPP_f1873026899l_bool(P,hAPP_p1537966538e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___241,axiom,
    ! [P: fun_Ho1695028467e_bool,Q: fun_fu385705929_state,R: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_f1185879473e_bool(cOMBB_1094554675e_bool(P),Q),R) = hAPP_H117293375e_bool(P,hAPP_f890249627_state(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___242,axiom,
    ! [P: fun_Ho1110608055e_bool,Q: fun_Ho1996104121e_bool,R: hoare_1875481847_state] : ( hAPP_H117293375e_bool(hAPP_f56162711e_bool(hAPP_f392546175e_bool(cOMBC_483615668e_bool,P),Q),R) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____xlr,axiom,
    ! [P: fun_bo840793679_state,Q: fun_pname_bool,R: pname] : ( hAPP_p1513527868_state(hAPP_f980169511_state(cOMBB_1989814576_pname(P),Q),R) = hAPP_b1347637997_state(P,hAPP_pname_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__,axiom,
    ! [P: fun_fu90736755l_bool,Q: fun_fu689207471l_bool,R: fun_fu689207471l_bool] : ( hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(hAPP_f1475014121l_bool(cOMBC_686159718l_bool,P),Q),R) = hAPP_f1699935247l_bool(hAPP_f1970936639l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___243,axiom,
    ! [P: fun_fu404278912_state,Q: fun_pn12888928e_bool,R: pname] : ( hAPP_p2012996835_state(hAPP_f275933352_state(cOMBB_718493681_pname(P),Q),R) = hAPP_f1930074316_state(P,hAPP_p1637813682e_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_244,axiom,
    ! [P: fun_fu1173762305l_bool,Q: fun_Ho1695028467e_bool,R: hoare_1875481847_state] : ( hAPP_H810811817l_bool(hAPP_f2059405973l_bool(cOMBB_2063006993_state(P),Q),R) = hAPP_f1873026899l_bool(P,hAPP_H117293375e_bool(Q,R)) ) ).

%----Conjectures (8)
tff(conj_0,hypothesis,
    hBOOL(hoare_1239590103gleton) ).

tff(conj_1,hypothesis,
    hBOOL(wT_bodies) ).

tff(conj_2,hypothesis,
    hBOOL(hAPP_f1408815105l_bool(finite1792194148_state,fa)) ).

tff(conj_3,hypothesis,
    ~ hBOOL(hAPP_f1408815105l_bool(hAPP_H810811817l_bool(member618553700_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),fa)) ).

tff(conj_4,hypothesis,
    hBOOL(hAPP_f1408815105l_bool(hAPP_f1873026899l_bool(ord_le233469699e_bool,fa),hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),dom_pname_com(body)))) ).

tff(conj_5,hypothesis,
    hAPP_p799580910on_com(body,pn) = some_com(y) ).

tff(conj_6,hypothesis,
    hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),fa)) ).

% tff(conj_7,conjecture,
%     hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ).

%------------------------------------------------------------------------------