TPTP Problem File: SWW474

TPTP Problem File: SWW474_3.p

%------------------------------------------------------------------------------
% File     : SWW474_3 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Hoare's Logic with Procedures line 440, 1000 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : hoare_1000_tff_l440 [Bla11]

% Status   : Theorem
% Rating   : 0.44 v8.2.0, 0.40 v8.1.0, 0.64 v7.5.0, 0.62 v7.4.0, 0.20 v7.3.0, 0.17 v7.1.0, 0.00 v6.0.0, 0.60 v5.5.0, 0.00 v5.4.0, 0.33 v5.3.0
% Syntax   : Number of formulae    : 2199 ( 483 unt; 840 typ;   0 def)
%            Number of atoms       : 3170 (1044 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives : 2186 ( 375   ~;  64   |; 164   &)
%                                         ( 250 <=>;1333  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of types       :  274 ( 273 usr)
%            Number of type conns  :  681 ( 395   >; 286   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  566 ( 566 usr; 172 con; 0-4 aty)
%            Number of variables   : 3552 (3474   !;  78   ?;3552   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:54:53
%------------------------------------------------------------------------------
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tff(sy_c_Com_Ocom_OSKIP,type,
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tff(sy_c_Com_Ocom_OSemi,type,
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tff(sy_c_Com_Ocom_OWhile,type,
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tff(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
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tff(sy_c_Option_Ois__none_000tc__Com__Ocom,type,
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tff(sy_c_Partial__Function_Oflat__lub_000tc__Com__Ocom,type,
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tff(sy_c_Partial__Function_Oflat__lub_000tc__Com__Opname,type,
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tff(sy_c_Set_OCollect_000tc__Com__Ocom,type,
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tff(sy_c_Set_OCollect_000tc__Com__Opname,type,
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tff(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Ocom,type,
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tff(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Opname,type,
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tff(sy_c_Set_Oinsert_000tc__Com__Ocom,type,
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tff(sy_c_Set_Oinsert_000tc__Com__Opname,type,
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tff(sy_c_Set_Oinsert_000tc__HOL__Obool,type,
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tff(sy_c_fTrue,type,
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    hAPP_f726209793l_bool: ( fun_fu2036837167l_bool * fun_Ho320143120e_bool ) > fun_fu1996308102l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_300,type,
    hAPP_f1043393922e_bool: ( fun_fu531943146e_bool * fun_Ho320143120e_bool ) > fun_fu1066574909e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_301,type,
    hAPP_f1610329741l_bool: ( fun_fu1467933941l_bool * fun_Ho320143120e_bool ) > fun_fu1972704968l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_302,type,
    hAPP_f644061942e_bool: ( fun_fu1271036068e_bool * fun_Ho320143120e_bool ) > fun_fu1671561851e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_303,type,
    hAPP_f1941218614l_bool: ( fun_fu1997055262l_bool * fun_Ho320143120e_bool ) > fun_fu1858490225l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_304,type,
    hAPP_f355123231e_bool: ( fun_fu513998669e_bool * fun_Ho901937921_state ) > fun_Ho424838195e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_305,type,
    hAPP_f626747953e_bool: ( fun_fu323425945e_bool * fun_Ho1262521325e_bool ) > fun_pn1521100553e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_306,type,
    hAPP_f399561463l_bool: ( fun_fu1117089189l_bool * fun_Ho1262521325e_bool ) > fun_Ho769804319l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_307,type,
    hAPP_f1612626488e_bool: ( fun_fu1914413292e_bool * fun_Ho544647106l_bool ) > fun_fu1066574909e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_308,type,
    hAPP_f265222234e_bool: ( fun_fu956445838e_bool * fun_Ho424838195e_bool ) > fun_Ho320143120e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_309,type,
    hAPP_f114072425e_bool: ( fun_fu1590463051e_bool * fun_Ho424838195e_bool ) > fun_Ho424838195e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_310,type,
    hAPP_f565239043l_bool: ( fun_fu390015671l_bool * fun_Ho424838195e_bool ) > fun_Ho177530809l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_311,type,
    hAPP_f306007574e_bool: ( fun_fu708272248e_bool * fun_Ho424838195e_bool ) > fun_Ho1500656352e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_312,type,
    hAPP_f1421439337e_bool: ( fun_fu1211884491e_bool * fun_Ho769804319l_bool ) > fun_fu1937087815e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_313,type,
    hAPP_f1072682137e_bool: ( fun_fu90083841e_bool * fun_Ho177530809l_bool ) > fun_fu1066574909e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Os_314,type,
    hAPP_f961492031e_bool: ( fun_fu739615905e_bool * fun_Ho1500656352e_bool ) > fun_fu296346460e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_Mtc__fun_Itc__fun,type,
    hAPP_f1898485935m_bool: ( fun_fu1004917649m_bool * fun_fu1107293590m_bool ) > fun_fu1107293590m_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__Com__Ocom_,type,
    hAPP_f926121585_state: ( fun_fu2101253843_state * fun_fu78728705ol_com ) > fun_fu1476767085_state ).

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_315,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_316,type,
    hAPP_f1912490857e_bool: ( fun_fu2094240849e_bool * fun_fu1430349052l_bool ) > fun_Ho320143120e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_317,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_318,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_319,type,
    hAPP_f417341722l_bool: ( fun_fu1201163592l_bool * fun_fu1430349052l_bool ) > fun_fu802393907l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_320,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_321,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_f272807711e_bool: ( fun_fu274677197e_bool * fun_fu54631149_state ) > fun_fu1937087815e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__C,type,
    hAPP_f907647536_state: ( fun_fu319306468_state * fun_fu121404128_state ) > fun_fu2101253843_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__C_322,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__C_323,type,
    hAPP_f2070959648_state: ( fun_fu411634056_state * fun_fu1022316450e_bool ) > fun_fu54631149_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__C_324,type,
    hAPP_f1215319405_state: ( fun_fu717443355_state * fun_fu1022316450e_bool ) > fun_fu121404128_state ).

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_325,type,
    hAPP_f1075942761l_bool: ( fun_fu1582046155l_bool * fun_fu1937087815e_bool ) > fun_Ho769804319l_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_326,type,
    hAPP_f1149191722l_bool: ( fun_fu1914144780l_bool * fun_fu802393907l_bool ) > fun_fu1232732404l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f_327,type,
    hAPP_f182188835e_bool: ( fun_fu532860805e_bool * fun_fu2101097872e_bool ) > fun_fu2101097872e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f_328,type,
    hAPP_f820078872_state: ( fun_fu1061167308_state * fun_fu1476767085_state ) > fun_fu411634056_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f_329,type,
    hAPP_f1145991873l_bool: ( fun_fu445680937l_bool * fun_fu931343505l_bool ) > fun_fu2087345469l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__fun_Itc__f_330,type,
    hAPP_f836143551l_bool: ( fun_fu1958014113l_bool * fun_fu1232732404l_bool ) > fun_fu1201163592l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc,type,
    hAPP_f153770241_state: ( fun_fu1414752361_state * fun_fu1203007991ol_com ) > fun_fu422494307_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_331,type,
    hAPP_f1544555711e_bool: ( fun_fu333202797e_bool * fun_fu2380401_pname ) > fun_fu665342307e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_332,type,
    hAPP_f1287348838l_bool: ( fun_fu1972704968l_bool * fun_fu1996308102l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_333,type,
    hAPP_f1892738755e_bool: ( fun_fu1792383909e_bool * fun_fu1996308102l_bool ) > fun_pname_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_334,type,
    hAPP_f1180969799e_bool: ( fun_fu1671561851e_bool * fun_fu1996308102l_bool ) > fun_Ho320143120e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_335,type,
    hAPP_f85652879l_bool: ( fun_fu1858490225l_bool * fun_fu1996308102l_bool ) > fun_fu1996308102l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_336,type,
    hAPP_f945781379l_bool: ( fun_fu253717047l_bool * fun_fu1996308102l_bool ) > fun_fu24650956l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_337,type,
    hAPP_f434845752l_bool: ( fun_fu2118416282l_bool * fun_fu1996308102l_bool ) > fun_fu2036837167l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_338,type,
    hAPP_f746351743l_bool: ( fun_fu1575689779l_bool * fun_fu1996308102l_bool ) > fun_fu1972704968l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_339,type,
    hAPP_f1175211816l_bool: ( fun_fu1392972380l_bool * fun_fu1996308102l_bool ) > fun_fu1858490225l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_340,type,
    hAPP_f440040771e_bool: ( fun_fu900385015e_bool * fun_fu700438391_state ) > fun_fu1066574909e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_341,type,
    hAPP_f2014973160_state: ( fun_fu1698101968_state * fun_fu47394518_state ) > fun_fu1414752361_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_342,type,
    hAPP_f883421385l_bool: ( fun_fu765334827l_bool * fun_fu665342307e_bool ) > fun_pn1419495779l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_343,type,
    hAPP_f605405862_state: ( fun_fu543459464_state * fun_fu1232608556e_bool ) > fun_fu700438391_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_344,type,
    hAPP_f1323754599_state: ( fun_fu2064421403_state * fun_fu1232608556e_bool ) > fun_fu47394518_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_345,type,
    hAPP_f927797370l_bool: ( fun_fu1214779746l_bool * fun_fu24650956l_bool ) > fun_fu1858490225l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_346,type,
    hAPP_f1585300113l_bool: ( fun_fu2114617849l_bool * fun_fu1066574909e_bool ) > fun_Ho177530809l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_347,type,
    hAPP_f1593397690_state: ( fun_fu720446882_state * fun_fu422494307_state ) > fun_fu543459464_state ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_348,type,
    hAPP_f205303905l_bool: ( fun_fu103205827l_bool * fun_fu2036837167l_bool ) > fun_fu2036837167l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_349,type,
    hAPP_f471491948l_bool: ( fun_fu1005788192l_bool * fun_fu2036837167l_bool ) > fun_fu1997055262l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_350,type,
    hAPP_f1873524693e_bool: ( fun_fu1281251517e_bool * fun_fu531943146e_bool ) > fun_fu531943146e_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_351,type,
    hAPP_f1854331281l_bool: ( fun_fu634959481l_bool * fun_fu1467933941l_bool ) > fun_fu1858490225l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc_352,type,
    hAPP_f1793815761l_bool: ( fun_fu1987524409l_bool * fun_fu1997055262l_bool ) > fun_fu2118416282l_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_353,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_354,type,
    hAPP_f1879335953l_bool: ( fun_fu1787620979l_bool * fun_fu1911931399l_bool ) > fun_fu1911931399l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H_355,type,
    hAPP_f1477350485l_bool: ( fun_fu427611837l_bool * fun_fu1759027710l_bool ) > fun_fu1759027710l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Ot,type,
    hAPP_f834704272l_bool: ( fun_fu1165654846l_bool * fun_fu1972704968l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Ot_356,type,
    hAPP_f891779797l_bool: ( fun_fu1305195069l_bool * fun_fu1972704968l_bool ) > fun_fu1972704968l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Ot_357,type,
    hAPP_f992844137l_bool: ( fun_fu541826379l_bool * fun_fu1575689779l_bool ) > fun_fu1575689779l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Ot_358,type,
    hAPP_f103280059l_bool: ( fun_fu357036829l_bool * fun_fu1392972380l_bool ) > fun_fu1392972380l_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__HOL__Obool,type,
    member_bool: fun_bo492988759l_bool ).

tff(sy_c_member_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Ostate_J,type,
    member1253905979_state: fun_Ho177530809l_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____wdcyoqcnvy__Otriple_Itc__Com__,type,
    member1534059107e_bool: fun_fu1467933941l_bool ).

tff(sy_v_Fa,type,
    fa: fun_Ho320143120e_bool ).

tff(sy_v_pn,type,
    pn: pname ).

tff(sy_v_y,type,
    y: com ).

%----Relevant facts (1199)
tff(fact_0_empty,axiom,
    ! [G_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),bot_bo39439654e_bool)) ).

tff(fact_1_asm,axiom,
    ! [Ts: fun_Ho320143120e_bool,G_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Ts),G_2))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts)) ) ).

tff(fact_2_weaken,axiom,
    ! [Ts: fun_Ho320143120e_bool,G_2: fun_Ho320143120e_bool,Ts_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Ts),Ts_1))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts)) ) ) ).

tff(fact_3_thin,axiom,
    ! [G_2: fun_Ho320143120e_bool,G_3: fun_Ho320143120e_bool,Ts: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_3),Ts))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,G_3),G_2))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts)) ) ) ).

tff(fact_4_cut,axiom,
    ! [G_2: fun_Ho320143120e_bool,G_3: fun_Ho320143120e_bool,Ts: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_3),Ts))
     => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),G_3))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts)) ) ) ).

tff(fact_5_hoare__derivs_Oinsert,axiom,
    ! [Ts: fun_Ho320143120e_bool,G_2: fun_Ho320143120e_bool,T: hoare_363350478_state] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,T),bot_bo39439654e_bool)))
     => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,T),Ts))) ) ) ).

tff(fact_6_derivs__insertD,axiom,
    ! [G_2: fun_Ho320143120e_bool,T: hoare_363350478_state,Ts: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,T),Ts)))
     => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,T),bot_bo39439654e_bool)))
        & hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts)) ) ) ).

tff(fact_7_MGT__BodyN,axiom,
    ! [Pn_1: pname,G_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),G_2)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1)))),bot_bo39439654e_bool)))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1))),bot_bo39439654e_bool))) ) ).

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

tff(fact_9_finite__Collect__subsets,axiom,
    ! [A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => hBOOL(hAPP_f834704272l_bool(finite393859187l_bool,hAPP_f891779797l_bool(collec85445553l_bool,hAPP_f746351743l_bool(hAPP_f992844137l_bool(cOMBC_736208532l_bool,ord_le2031828156l_bool),A)))) ) ).

tff(fact_10_finite__Collect__subsets,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,ord_le704992346e_bool),A)))) ) ).

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

tff(fact_12_finite__imageI,axiom,
    ! [H_1: fun_Ho1262521325e_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f766639041l_bool(image_1660610235e_bool(H_1),Fa))) ) ).

tff(fact_13_finite__imageI,axiom,
    ! [H_1: fun_Ho424838195e_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f726209793l_bool(image_1484638543e_bool(H_1),Fa))) ) ).

tff(fact_14_finite__imageI,axiom,
    ! [H_1: 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_1),Fa))) ) ).

tff(fact_15_finite__imageI,axiom,
    ! [H_1: fun_pn1521100553e_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f682249667l_bool(image_1637084625e_bool(H_1),Fa))) ) ).

tff(fact_16_finite__imageI,axiom,
    ! [H_1: fun_fu54631149_state,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1912490857e_bool(image_431763259_state(H_1),Fa))) ) ).

tff(fact_17_finite__imageI,axiom,
    ! [H_1: fun_fu700438391_state,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1180969799e_bool(image_2021386777_state(H_1),Fa))) ) ).

tff(fact_18_finite__imageI,axiom,
    ! [H_1: 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_1),Fa))) ) ).

tff(fact_19_finite__imageI,axiom,
    ! [H_1: fun_fu2380401_pname,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1892738755e_bool(image_937015865_pname(H_1),Fa))) ) ).

tff(fact_20_finite__imageI,axiom,
    ! [H_1: fun_pn1262351275_state,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1763243027e_bool(image_1918575693_state(H_1),Fa))) ) ).

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

tff(fact_22_empty__subsetI,axiom,
    ! [A: fun_com_bool] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A)) ).

tff(fact_23_empty__subsetI,axiom,
    ! [A: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,bot_bo39439654e_bool),A)) ).

tff(fact_24_finite_OinsertI,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A))) ) ).

tff(fact_25_finite_OinsertI,axiom,
    ! [A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A))) ) ).

tff(fact_26_finite_OinsertI,axiom,
    ! [A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),A))) ) ).

tff(fact_27_finite_OinsertI,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A))) ) ).

tff(fact_28_finite_OinsertI,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A))) ) ).

tff(fact_29_finite_OemptyI,axiom,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ).

tff(fact_30_finite_OemptyI,axiom,
    hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,bot_bo133096688l_bool)) ).

tff(fact_31_finite_OemptyI,axiom,
    hBOOL(hAPP_f990396704l_bool(finite_finite_com,bot_bot_fun_com_bool)) ).

tff(fact_32_finite_OemptyI,axiom,
    hBOOL(hAPP_f568432088l_bool(finite280062779_state,bot_bo39439654e_bool)) ).

tff(fact_33_finite_OemptyI,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).

tff(fact_34_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_35_finite__Collect__conjI,axiom,
    ! [Q_1: fun_fu1996308102l_bool,P_1: fun_fu1996308102l_bool] :
      ( ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,P_1)))
        | hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,Q_1))) )
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),P_1)),Q_1)))) ) ).

tff(fact_36_finite__Collect__conjI,axiom,
    ! [Q_1: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,P_1)))
        | hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,Q_1))) )
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),P_1)),Q_1)))) ) ).

tff(fact_37_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_38_image__constant__conv,axiom,
    ! [C: pname,A: fun_Ho320143120e_bool] :
      ( ( ( A = bot_bo39439654e_bool )
       => ( hAPP_f773602357e_bool(image_1927198851_pname(hAPP_p1379817622_pname(cOMBK_83433476_state,C)),A) = bot_bo844097828e_bool ) )
      & ( ( A != bot_bo39439654e_bool )
       => ( hAPP_f773602357e_bool(image_1927198851_pname(hAPP_p1379817622_pname(cOMBK_83433476_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ) ).

tff(fact_39_image__constant__conv,axiom,
    ! [C: com,A: fun_Ho320143120e_bool] :
      ( ( ( A = bot_bo39439654e_bool )
       => ( hAPP_f497466683m_bool(image_689867145te_com(hAPP_c6662434te_com(cOMBK_1864507658_state,C)),A) = bot_bot_fun_com_bool ) )
      & ( ( A != bot_bo39439654e_bool )
       => ( hAPP_f497466683m_bool(image_689867145te_com(hAPP_c6662434te_com(cOMBK_1864507658_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ) ) ).

tff(fact_40_image__constant__conv,axiom,
    ! [C: hoare_363350478_state,A: fun_com_bool] :
      ( ( ( A = bot_bot_fun_com_bool )
       => ( hAPP_f1859782925e_bool(image_1736049107_state(hAPP_H154362754_state(cOMBK_818325696te_com,C)),A) = bot_bo39439654e_bool ) )
      & ( ( A != bot_bot_fun_com_bool )
       => ( hAPP_f1859782925e_bool(image_1736049107_state(hAPP_H154362754_state(cOMBK_818325696te_com,C)),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,C),bot_bo39439654e_bool) ) ) ) ).

tff(fact_41_image__constant__conv,axiom,
    ! [C: hoare_363350478_state,A: fun_pname_bool] :
      ( ( ( A = bot_bo844097828e_bool )
       => ( hAPP_f1763243027e_bool(image_1918575693_state(hAPP_H1607320188_state(cOMBK_92056634_pname,C)),A) = bot_bo39439654e_bool ) )
      & ( ( A != bot_bo844097828e_bool )
       => ( hAPP_f1763243027e_bool(image_1918575693_state(hAPP_H1607320188_state(cOMBK_92056634_pname,C)),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,C),bot_bo39439654e_bool) ) ) ) ).

tff(fact_42_image__constant,axiom,
    ! [C: pname,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hAPP_f773602357e_bool(image_1927198851_pname(hAPP_p1379817622_pname(cOMBK_83433476_state,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ).

tff(fact_43_image__constant,axiom,
    ! [C: com,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hAPP_f497466683m_bool(image_689867145te_com(hAPP_c6662434te_com(cOMBK_1864507658_state,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ) ).

tff(fact_44_image__constant,axiom,
    ! [C: pname,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f759274231e_bool(image_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,C)),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,C),bot_bo844097828e_bool) ) ) ).

tff(fact_45_image__constant,axiom,
    ! [C: com,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f1206115581m_bool(image_pname_com(hAPP_c1494068046me_com(cOMBK_com_pname,C)),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),bot_bot_fun_com_bool) ) ) ).

tff(fact_46_image__constant,axiom,
    ! [C: hoare_363350478_state,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( hAPP_f1859782925e_bool(image_1736049107_state(hAPP_H154362754_state(cOMBK_818325696te_com,C)),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,C),bot_bo39439654e_bool) ) ) ).

tff(fact_47_image__constant,axiom,
    ! [C: hoare_363350478_state,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f1763243027e_bool(image_1918575693_state(hAPP_H1607320188_state(cOMBK_92056634_pname,C)),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,C),bot_bo39439654e_bool) ) ) ).

tff(fact_48_insert__dom,axiom,
    ! [F: fun_com_option_com,X_1: com,Y_2: com] :
      ( ( hAPP_com_option_com(F,X_1) = hAPP_com_option_com(some_com,Y_2) )
     => ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),dom_com_com(F)) = dom_com_com(F) ) ) ).

tff(fact_49_insert__dom,axiom,
    ! [F: fun_Ho12798188_pname,X_1: hoare_363350478_state,Y_2: pname] :
      ( ( hAPP_H134270346_pname(F,X_1) = hAPP_p1252095976_pname(some_pname,Y_2) )
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),dom_Ho75493366_pname(F)) = dom_Ho75493366_pname(F) ) ) ).

tff(fact_50_insert__dom,axiom,
    ! [F: fun_Ho382349394_state,X_1: hoare_363350478_state,Y_2: hoare_363350478_state] :
      ( ( hAPP_H1942146718_state(F,X_1) = hAPP_H1942146718_state(some_H629028223_state,Y_2) )
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),dom_Ho867270556_state(F)) = dom_Ho867270556_state(F) ) ) ).

tff(fact_51_insert__dom,axiom,
    ! [F: fun_pname_option_com,X_1: pname,Y_2: com] :
      ( ( hAPP_p799580910on_com(F,X_1) = hAPP_com_option_com(some_com,Y_2) )
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) = dom_pname_com(F) ) ) ).

tff(fact_52_finite__surj,axiom,
    ! [B: fun_fu1430349052l_bool,F: fun_Ho1262521325e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f766639041l_bool(image_1660610235e_bool(F),A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).

tff(fact_53_finite__surj,axiom,
    ! [B: fun_fu1996308102l_bool,F: fun_Ho424838195e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,B),hAPP_f726209793l_bool(image_1484638543e_bool(F),A)))
       => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B)) ) ) ).

tff(fact_54_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f773602357e_bool(image_1927198851_pname(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_55_finite__surj,axiom,
    ! [B: fun_fu1430349052l_bool,F: fun_pn800050071e_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f434788991l_bool(image_47868345e_bool(F),A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).

tff(fact_56_finite__surj,axiom,
    ! [B: fun_fu1996308102l_bool,F: fun_pn1521100553e_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,B),hAPP_f682249667l_bool(image_1637084625e_bool(F),A)))
       => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B)) ) ) ).

tff(fact_57_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_pname_pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(image_pname_pname(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_58_finite__surj,axiom,
    ! [B: fun_Ho320143120e_bool,F: fun_fu54631149_state,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1912490857e_bool(image_431763259_state(F),A)))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,B)) ) ) ).

tff(fact_59_finite__surj,axiom,
    ! [B: fun_Ho320143120e_bool,F: fun_fu700438391_state,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1180969799e_bool(image_2021386777_state(F),A)))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,B)) ) ) ).

tff(fact_60_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_fu1499449723_pname,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f674760225e_bool(image_1283814551_pname(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_61_finite__surj,axiom,
    ! [B: fun_pname_bool,F: fun_fu2380401_pname,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f1892738755e_bool(image_937015865_pname(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).

tff(fact_62_finite__surj,axiom,
    ! [B: fun_Ho320143120e_bool,F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,B)) ) ) ).

tff(fact_63_subset__singletonD,axiom,
    ! [A: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))
     => ( ( A = bot_bo844097828e_bool )
        | ( A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ) ) ) ).

tff(fact_64_subset__singletonD,axiom,
    ! [A: fun_com_bool,X_1: com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))
     => ( ( A = bot_bot_fun_com_bool )
        | ( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ) ) ) ).

tff(fact_65_subset__singletonD,axiom,
    ! [A: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)))
     => ( ( A = bot_bo39439654e_bool )
        | ( A = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool) ) ) ) ).

tff(fact_66_MGF,axiom,
    ! [C: com] :
      ( hBOOL(hoare_265376576gleton)
     => ( hBOOL(wT_bodies)
       => ( hBOOL(hAPP_com_bool(wt,C))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(bot_bo39439654e_bool),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,C)),bot_bo39439654e_bool))) ) ) ) ).

tff(fact_67_emptyE,axiom,
    ! [A_4: com] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),bot_bot_fun_com_bool)) ).

tff(fact_68_emptyE,axiom,
    ! [A_4: hoare_363350478_state] : ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),bot_bo39439654e_bool)) ).

tff(fact_69_emptyE,axiom,
    ! [A_4: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),bot_bo844097828e_bool)) ).

tff(fact_70_insertCI,axiom,
    ! [B_1: com,A_4: com,B: fun_com_bool] :
      ( ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B))
       => ( A_4 = B_1 ) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).

tff(fact_71_insertCI,axiom,
    ! [B_1: pname,A_4: pname,B: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B))
       => ( A_4 = B_1 ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_72_insertCI,axiom,
    ! [B_1: hoare_363350478_state,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),B))
       => ( A_4 = B_1 ) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),B))) ) ).

tff(fact_73_insertE,axiom,
    ! [A_4: com,B_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A)))
     => ( ( A_4 != B_1 )
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ) ).

tff(fact_74_insertE,axiom,
    ! [A_4: pname,B_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A)))
     => ( ( A_4 != B_1 )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ) ).

tff(fact_75_insertE,axiom,
    ! [A_4: hoare_363350478_state,B_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),A)))
     => ( ( A_4 != B_1 )
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A)) ) ) ).

tff(fact_76_equalityI,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_77_equalityI,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_78_subsetD,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_79_subsetD,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_80_subsetD,axiom,
    ! [C: pname,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_81_image__eqI,axiom,
    ! [A: fun_Ho320143120e_bool,B_1: com,F: fun_Ho938602221te_com,X_1: hoare_363350478_state] :
      ( ( B_1 = hAPP_H2142737465te_com(F,X_1) )
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f497466683m_bool(image_689867145te_com(F),A))) ) ) ).

tff(fact_82_image__eqI,axiom,
    ! [A: fun_pname_bool,B_1: com,F: fun_pname_com,X_1: pname] :
      ( ( B_1 = hAPP_pname_com(F,X_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ) ).

tff(fact_83_image__eqI,axiom,
    ! [A: fun_com_bool,B_1: hoare_363350478_state,F: fun_co482540593_state,X_1: com] :
      ( ( B_1 = hAPP_c1041435779_state(F,X_1) )
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1859782925e_bool(image_1736049107_state(F),A))) ) ) ).

tff(fact_84_image__eqI,axiom,
    ! [A: fun_com_bool,B_1: pname,F: fun_com_pname,X_1: com] :
      ( ( B_1 = hAPP_com_pname(F,X_1) )
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ) ).

tff(fact_85_image__eqI,axiom,
    ! [A: fun_pname_bool,B_1: hoare_363350478_state,F: fun_pn1262351275_state,X_1: pname] :
      ( ( B_1 = hAPP_p1337579261_state(F,X_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1763243027e_bool(image_1918575693_state(F),A))) ) ) ).

tff(fact_86_equals0D,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( ( A = bot_bot_fun_com_bool )
     => ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ).

tff(fact_87_equals0D,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ( A = bot_bo39439654e_bool )
     => ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A)) ) ).

tff(fact_88_equals0D,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( ( A = bot_bo844097828e_bool )
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ).

tff(fact_89_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_90_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_91_Collect__empty__eq,axiom,
    ! [P_1: fun_fu1996308102l_bool] :
      ( ( hAPP_f85652879l_bool(collec1243131813e_bool,P_1) = bot_bo133096688l_bool )
    <=> ! [X_2: fun_Ho320143120e_bool] : ~ hBOOL(hAPP_f568432088l_bool(P_1,X_2)) ) ).

tff(fact_92_Collect__empty__eq,axiom,
    ! [P_1: fun_com_bool] :
      ( ( hAPP_f1682609283m_bool(collect_com,P_1) = bot_bot_fun_com_bool )
    <=> ! [X_2: com] : ~ hBOOL(hAPP_com_bool(P_1,X_2)) ) ).

tff(fact_93_Collect__empty__eq,axiom,
    ! [P_1: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(collec223185785_state,P_1) = bot_bo39439654e_bool )
    <=> ! [X_2: hoare_363350478_state] : ~ hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) ) ).

tff(fact_94_empty__iff,axiom,
    ! [C: com] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),bot_bot_fun_com_bool)) ).

tff(fact_95_empty__iff,axiom,
    ! [C: hoare_363350478_state] : ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),bot_bo39439654e_bool)) ).

tff(fact_96_empty__iff,axiom,
    ! [C: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool)) ).

tff(fact_97_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_98_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_99_empty__Collect__eq,axiom,
    ! [P_1: fun_fu1996308102l_bool] :
      ( ( bot_bo133096688l_bool = hAPP_f85652879l_bool(collec1243131813e_bool,P_1) )
    <=> ! [X_2: fun_Ho320143120e_bool] : ~ hBOOL(hAPP_f568432088l_bool(P_1,X_2)) ) ).

tff(fact_100_empty__Collect__eq,axiom,
    ! [P_1: fun_com_bool] :
      ( ( bot_bot_fun_com_bool = hAPP_f1682609283m_bool(collect_com,P_1) )
    <=> ! [X_2: com] : ~ hBOOL(hAPP_com_bool(P_1,X_2)) ) ).

tff(fact_101_empty__Collect__eq,axiom,
    ! [P_1: fun_Ho320143120e_bool] :
      ( ( bot_bo39439654e_bool = hAPP_f1749453397e_bool(collec223185785_state,P_1) )
    <=> ! [X_2: hoare_363350478_state] : ~ hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) ) ).

tff(fact_102_ex__in__conv,axiom,
    ! [A: fun_com_bool] :
      ( ? [X_2: com] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
    <=> ( A != bot_bot_fun_com_bool ) ) ).

tff(fact_103_ex__in__conv,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( ? [X_2: hoare_363350478_state] : hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
    <=> ( A != bot_bo39439654e_bool ) ) ).

tff(fact_104_ex__in__conv,axiom,
    ! [A: fun_pname_bool] :
      ( ? [X_2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
    <=> ( A != bot_bo844097828e_bool ) ) ).

tff(fact_105_all__not__in__conv,axiom,
    ! [A: fun_com_bool] :
      ( ! [X_2: com] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
    <=> ( A = bot_bot_fun_com_bool ) ) ).

tff(fact_106_all__not__in__conv,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] : ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_107_all__not__in__conv,axiom,
    ! [A: fun_pname_bool] :
      ( ! [X_2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
    <=> ( A = bot_bo844097828e_bool ) ) ).

tff(fact_108_empty__def,axiom,
    bot_bo844097828e_bool = hAPP_f759274231e_bool(collect_pname,hAPP_b76515610e_bool(cOMBK_bool_pname,fFalse)) ).

tff(fact_109_empty__def,axiom,
    bot_bo1649642514l_bool = hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_b357632156l_bool(cOMBK_1857069011e_bool,fFalse)) ).

tff(fact_110_empty__def,axiom,
    bot_bo133096688l_bool = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_b1504838374l_bool(cOMBK_1696036407e_bool,fFalse)) ).

tff(fact_111_empty__def,axiom,
    bot_bot_fun_com_bool = hAPP_f1682609283m_bool(collect_com,hAPP_b1153789088m_bool(cOMBK_bool_com,fFalse)) ).

tff(fact_112_empty__def,axiom,
    bot_bo39439654e_bool = hAPP_f1749453397e_bool(collec223185785_state,hAPP_b230077104e_bool(cOMBK_574827367_state,fFalse)) ).

tff(fact_113_insert__absorb,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
     => ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = A ) ) ).

tff(fact_114_insert__absorb,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = A ) ) ).

tff(fact_115_insert__absorb,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A) = A ) ) ).

tff(fact_116_insertI2,axiom,
    ! [B_1: com,A_4: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).

tff(fact_117_insertI2,axiom,
    ! [B_1: pname,A_4: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_118_insertI2,axiom,
    ! [B_1: hoare_363350478_state,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),B))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),B))) ) ).

tff(fact_119_insert__ident,axiom,
    ! [B: fun_com_bool,X_1: com,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
       => ( ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B) )
        <=> ( A = B ) ) ) ) ).

tff(fact_120_insert__ident,axiom,
    ! [B: fun_pname_bool,X_1: pname,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) )
        <=> ( A = B ) ) ) ) ).

tff(fact_121_insert__ident,axiom,
    ! [B: fun_Ho320143120e_bool,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B))
       => ( ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),B) )
        <=> ( A = B ) ) ) ) ).

tff(fact_122_insert__code,axiom,
    ! [Y_2: pname,A: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A),X_1))
    <=> ( ( Y_2 = X_1 )
        | hBOOL(hAPP_pname_bool(A,X_1)) ) ) ).

tff(fact_123_insert__code,axiom,
    ! [Y_2: com,A: fun_com_bool,X_1: com] :
      ( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A),X_1))
    <=> ( ( Y_2 = X_1 )
        | hBOOL(hAPP_com_bool(A,X_1)) ) ) ).

tff(fact_124_insert__code,axiom,
    ! [Y_2: hoare_363350478_state,A: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,Y_2),A),X_1))
    <=> ( ( Y_2 = X_1 )
        | hBOOL(hAPP_H1645464494e_bool(A,X_1)) ) ) ).

tff(fact_125_insert__iff,axiom,
    ! [A_4: com,B_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),A)))
    <=> ( ( A_4 = B_1 )
        | hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A)) ) ) ).

tff(fact_126_insert__iff,axiom,
    ! [A_4: pname,B_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),A)))
    <=> ( ( A_4 = B_1 )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A)) ) ) ).

tff(fact_127_insert__iff,axiom,
    ! [A_4: hoare_363350478_state,B_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),A)))
    <=> ( ( A_4 = B_1 )
        | hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A)) ) ) ).

tff(fact_128_insert__commute,axiom,
    ! [X_1: pname,Y_2: pname,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) ).

tff(fact_129_insert__commute,axiom,
    ! [X_1: com,Y_2: com,A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) ).

tff(fact_130_insert__commute,axiom,
    ! [X_1: hoare_363350478_state,Y_2: hoare_363350478_state,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,Y_2),A)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,Y_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) ).

tff(fact_131_insert__absorb2,axiom,
    ! [X_1: pname,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) ).

tff(fact_132_insert__absorb2,axiom,
    ! [X_1: com,A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A) ).

tff(fact_133_insert__absorb2,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A) ).

tff(fact_134_insert__Collect,axiom,
    ! [A_4: pname,P_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),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_4)))),P_1)) ).

tff(fact_135_insert__Collect,axiom,
    ! [A_4: com,P_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(collect_com,P_1)) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fimplies),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)))),P_1)) ).

tff(fact_136_insert__Collect,axiom,
    ! [A_4: fun_pname_bool,P_1: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),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_4)))),P_1)) ).

tff(fact_137_insert__Collect,axiom,
    ! [A_4: fun_Ho320143120e_bool,P_1: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),hAPP_f85652879l_bool(collec1243131813e_bool,P_1)) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fimplies),hAPP_f85652879l_bool(cOMBB_941362220e_bool(fNot),hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4)))),P_1)) ).

tff(fact_138_insert__Collect,axiom,
    ! [A_4: hoare_363350478_state,P_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(collec223185785_state,P_1)) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fimplies),hAPP_f1749453397e_bool(cOMBB_2059354034_state(fNot),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4)))),P_1)) ).

tff(fact_139_insert__compr,axiom,
    ! [A_4: com,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).

tff(fact_140_insert__compr,axiom,
    ! [A_4: fun_pname_bool,B: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),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_4))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).

tff(fact_141_insert__compr,axiom,
    ! [A_4: fun_Ho320143120e_bool,B: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),B) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fdisj),hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4))),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),B))) ).

tff(fact_142_insert__compr,axiom,
    ! [A_4: pname,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),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_4))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).

tff(fact_143_insert__compr,axiom,
    ! [A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fdisj),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4))),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),B))) ).

tff(fact_144_insertI1,axiom,
    ! [A_4: com,B: fun_com_bool] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))) ).

tff(fact_145_insertI1,axiom,
    ! [A_4: pname,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))) ).

tff(fact_146_insertI1,axiom,
    ! [A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B))) ).

tff(fact_147_equalityE,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ).

tff(fact_148_equalityE,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( A = B )
     => ~ ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
         => ~ hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A)) ) ) ).

tff(fact_149_subset__trans,axiom,
    ! [C_1: fun_pname_bool,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),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),C_1)) ) ) ).

tff(fact_150_subset__trans,axiom,
    ! [C_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),C_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),C_1)) ) ) ).

tff(fact_151_set__mp,axiom,
    ! [X_1: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).

tff(fact_152_set__mp,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B)) ) ) ).

tff(fact_153_set__mp,axiom,
    ! [X_1: pname,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_154_set__rev__mp,axiom,
    ! [B: fun_com_bool,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).

tff(fact_155_set__rev__mp,axiom,
    ! [B: fun_Ho320143120e_bool,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B)) ) ) ).

tff(fact_156_set__rev__mp,axiom,
    ! [B: fun_pname_bool,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_157_in__mono,axiom,
    ! [X_1: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B)) ) ) ).

tff(fact_158_in__mono,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B)) ) ) ).

tff(fact_159_in__mono,axiom,
    ! [X_1: pname,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ) ).

tff(fact_160_equalityD2,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ).

tff(fact_161_equalityD2,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A)) ) ).

tff(fact_162_equalityD1,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).

tff(fact_163_equalityD1,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B)) ) ).

tff(fact_164_set__eq__subset,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ).

tff(fact_165_set__eq__subset,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( A = B )
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
        & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A)) ) ) ).

tff(fact_166_subset__refl,axiom,
    ! [A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)) ).

tff(fact_167_subset__refl,axiom,
    ! [A: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),A)) ).

tff(fact_168_rev__image__eqI,axiom,
    ! [B_1: com,F: fun_Ho938602221te_com,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( ( B_1 = hAPP_H2142737465te_com(F,X_1) )
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f497466683m_bool(image_689867145te_com(F),A))) ) ) ).

tff(fact_169_rev__image__eqI,axiom,
    ! [B_1: com,F: fun_pname_com,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( ( B_1 = hAPP_pname_com(F,X_1) )
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ) ).

tff(fact_170_rev__image__eqI,axiom,
    ! [B_1: hoare_363350478_state,F: fun_co482540593_state,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( ( B_1 = hAPP_c1041435779_state(F,X_1) )
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1859782925e_bool(image_1736049107_state(F),A))) ) ) ).

tff(fact_171_rev__image__eqI,axiom,
    ! [B_1: pname,F: fun_com_pname,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( ( B_1 = hAPP_com_pname(F,X_1) )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ) ).

tff(fact_172_rev__image__eqI,axiom,
    ! [B_1: hoare_363350478_state,F: fun_pn1262351275_state,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( ( B_1 = hAPP_p1337579261_state(F,X_1) )
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1763243027e_bool(image_1918575693_state(F),A))) ) ) ).

tff(fact_173_imageI,axiom,
    ! [F: fun_Ho938602221te_com,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H2142737465te_com(F,X_1)),hAPP_f497466683m_bool(image_689867145te_com(F),A))) ) ).

tff(fact_174_imageI,axiom,
    ! [F: fun_pname_com,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A))) ) ).

tff(fact_175_imageI,axiom,
    ! [F: fun_co482540593_state,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_c1041435779_state(F,X_1)),hAPP_f1859782925e_bool(image_1736049107_state(F),A))) ) ).

tff(fact_176_imageI,axiom,
    ! [F: fun_com_pname,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_1)),hAPP_f1438183293e_bool(image_com_pname(F),A))) ) ).

tff(fact_177_imageI,axiom,
    ! [F: fun_pn1262351275_state,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_p1337579261_state(F,X_1)),hAPP_f1763243027e_bool(image_1918575693_state(F),A))) ) ).

tff(fact_178_image__iff,axiom,
    ! [Z: hoare_363350478_state,F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,Z),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
    <=> ? [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
          & ( Z = hAPP_p1337579261_state(F,X_2) ) ) ) ).

tff(fact_179_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_180_finite__Collect__disjI,axiom,
    ! [P_1: fun_fu1996308102l_bool,Q_1: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,P_1)))
        & hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,Q_1))) ) ) ).

tff(fact_181_finite__Collect__disjI,axiom,
    ! [P_1: fun_Ho320143120e_bool,Q_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fdisj),P_1)),Q_1))))
    <=> ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,P_1)))
        & hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,Q_1))) ) ) ).

tff(fact_182_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_183_insert__compr__raw,axiom,
    ! [X_2: com,Xa: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),Xa) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),X_2))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),Xa))) ).

tff(fact_184_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_185_insert__compr__raw,axiom,
    ! [X_2: fun_Ho320143120e_bool,Xa: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_2),Xa) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fdisj),hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),X_2))),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),Xa))) ).

tff(fact_186_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_187_insert__compr__raw,axiom,
    ! [X_2: hoare_363350478_state,Xa: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),Xa) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fdisj),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),X_2))),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),Xa))) ).

tff(fact_188_singleton__inject,axiom,
    ! [A_4: pname,B_1: pname] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool) )
     => ( A_4 = B_1 ) ) ).

tff(fact_189_singleton__inject,axiom,
    ! [A_4: com,B_1: com] :
      ( ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool) )
     => ( A_4 = B_1 ) ) ).

tff(fact_190_singleton__inject,axiom,
    ! [A_4: hoare_363350478_state,B_1: hoare_363350478_state] :
      ( ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),bot_bo39439654e_bool) )
     => ( A_4 = B_1 ) ) ).

tff(fact_191_singletonE,axiom,
    ! [B_1: com,A_4: com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)))
     => ( B_1 = A_4 ) ) ).

tff(fact_192_singletonE,axiom,
    ! [B_1: pname,A_4: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)))
     => ( B_1 = A_4 ) ) ).

tff(fact_193_singletonE,axiom,
    ! [B_1: hoare_363350478_state,A_4: hoare_363350478_state] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool)))
     => ( B_1 = A_4 ) ) ).

tff(fact_194_doubleton__eq__iff,axiom,
    ! [A_4: pname,B_1: pname,C: pname,D_1: pname] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),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_1),bot_bo844097828e_bool)) )
    <=> ( ( ( A_4 = C )
          & ( B_1 = D_1 ) )
        | ( ( A_4 = D_1 )
          & ( B_1 = C ) ) ) ) ).

tff(fact_195_doubleton__eq__iff,axiom,
    ! [A_4: com,B_1: com,C: com,D_1: com] :
      ( ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,C),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,D_1),bot_bot_fun_com_bool)) )
    <=> ( ( ( A_4 = C )
          & ( B_1 = D_1 ) )
        | ( ( A_4 = D_1 )
          & ( B_1 = C ) ) ) ) ).

tff(fact_196_doubleton__eq__iff,axiom,
    ! [A_4: hoare_363350478_state,B_1: hoare_363350478_state,C: hoare_363350478_state,D_1: hoare_363350478_state] :
      ( ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),bot_bo39439654e_bool)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,C),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,D_1),bot_bo39439654e_bool)) )
    <=> ( ( ( A_4 = C )
          & ( B_1 = D_1 ) )
        | ( ( A_4 = D_1 )
          & ( B_1 = C ) ) ) ) ).

tff(fact_197_singleton__iff,axiom,
    ! [B_1: com,A_4: com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)))
    <=> ( B_1 = A_4 ) ) ).

tff(fact_198_singleton__iff,axiom,
    ! [B_1: pname,A_4: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)))
    <=> ( B_1 = A_4 ) ) ).

tff(fact_199_singleton__iff,axiom,
    ! [B_1: hoare_363350478_state,A_4: hoare_363350478_state] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool)))
    <=> ( B_1 = A_4 ) ) ).

tff(fact_200_insert__not__empty,axiom,
    ! [A_4: pname,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) != bot_bo844097828e_bool ).

tff(fact_201_insert__not__empty,axiom,
    ! [A_4: com,A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) != bot_bot_fun_com_bool ).

tff(fact_202_insert__not__empty,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A) != bot_bo39439654e_bool ).

tff(fact_203_empty__not__insert,axiom,
    ! [A_4: pname,A: fun_pname_bool] : bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) ).

tff(fact_204_empty__not__insert,axiom,
    ! [A_4: com,A: fun_com_bool] : bot_bot_fun_com_bool != hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) ).

tff(fact_205_empty__not__insert,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] : bot_bo39439654e_bool != hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A) ).

tff(fact_206_finite__insert,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)))
    <=> hBOOL(hAPP_f990396704l_bool(finite_finite_com,A)) ) ).

tff(fact_207_finite__insert,axiom,
    ! [A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ).

tff(fact_208_finite__insert,axiom,
    ! [A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),A)))
    <=> hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A)) ) ).

tff(fact_209_finite__insert,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ).

tff(fact_210_finite__insert,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A)))
    <=> hBOOL(hAPP_f568432088l_bool(finite280062779_state,A)) ) ).

tff(fact_211_subset__empty,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_212_subset__empty,axiom,
    ! [A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),bot_bot_fun_com_bool))
    <=> ( A = bot_bot_fun_com_bool ) ) ).

tff(fact_213_subset__empty,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),bot_bo39439654e_bool))
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_214_image__is__empty,axiom,
    ! [F: fun_co482540593_state,A: fun_com_bool] :
      ( ( hAPP_f1859782925e_bool(image_1736049107_state(F),A) = bot_bo39439654e_bool )
    <=> ( A = bot_bot_fun_com_bool ) ) ).

tff(fact_215_image__is__empty,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
      ( ( hAPP_f773602357e_bool(image_1927198851_pname(F),A) = bot_bo844097828e_bool )
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_216_image__is__empty,axiom,
    ! [F: fun_Ho938602221te_com,A: fun_Ho320143120e_bool] :
      ( ( hAPP_f497466683m_bool(image_689867145te_com(F),A) = bot_bot_fun_com_bool )
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_217_image__is__empty,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( ( hAPP_f1763243027e_bool(image_1918575693_state(F),A) = bot_bo39439654e_bool )
    <=> ( A = bot_bo844097828e_bool ) ) ).

tff(fact_218_image__empty,axiom,
    ! [F: fun_Ho713471079_pname] : hAPP_f773602357e_bool(image_1927198851_pname(F),bot_bo39439654e_bool) = bot_bo844097828e_bool ).

tff(fact_219_image__empty,axiom,
    ! [F: fun_Ho938602221te_com] : hAPP_f497466683m_bool(image_689867145te_com(F),bot_bo39439654e_bool) = bot_bot_fun_com_bool ).

tff(fact_220_image__empty,axiom,
    ! [F: fun_co482540593_state] : hAPP_f1859782925e_bool(image_1736049107_state(F),bot_bot_fun_com_bool) = bot_bo39439654e_bool ).

tff(fact_221_image__empty,axiom,
    ! [F: fun_pn1262351275_state] : hAPP_f1763243027e_bool(image_1918575693_state(F),bot_bo844097828e_bool) = bot_bo39439654e_bool ).

tff(fact_222_empty__is__image,axiom,
    ! [F: fun_co482540593_state,A: fun_com_bool] :
      ( ( bot_bo39439654e_bool = hAPP_f1859782925e_bool(image_1736049107_state(F),A) )
    <=> ( A = bot_bot_fun_com_bool ) ) ).

tff(fact_223_empty__is__image,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
      ( ( bot_bo844097828e_bool = hAPP_f773602357e_bool(image_1927198851_pname(F),A) )
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_224_empty__is__image,axiom,
    ! [F: fun_Ho938602221te_com,A: fun_Ho320143120e_bool] :
      ( ( bot_bot_fun_com_bool = hAPP_f497466683m_bool(image_689867145te_com(F),A) )
    <=> ( A = bot_bo39439654e_bool ) ) ).

tff(fact_225_empty__is__image,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( ( bot_bo39439654e_bool = hAPP_f1763243027e_bool(image_1918575693_state(F),A) )
    <=> ( A = bot_bo844097828e_bool ) ) ).

tff(fact_226_finite__subset,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).

tff(fact_227_finite__subset,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,A),B))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
       => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A)) ) ) ).

tff(fact_228_finite__subset,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,A)) ) ) ).

tff(fact_229_finite__subset,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).

tff(fact_230_rev__finite__subset,axiom,
    ! [A: 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),B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).

tff(fact_231_rev__finite__subset,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,A),B))
       => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A)) ) ) ).

tff(fact_232_rev__finite__subset,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,A)) ) ) ).

tff(fact_233_rev__finite__subset,axiom,
    ! [A: 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),B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).

tff(fact_234_insert__mono,axiom,
    ! [A_4: pname,C_1: fun_pname_bool,D: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),D))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),C_1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),D))) ) ).

tff(fact_235_insert__mono,axiom,
    ! [A_4: com,C_1: fun_com_bool,D: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,C_1),D))
     => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),C_1)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),D))) ) ).

tff(fact_236_insert__mono,axiom,
    ! [A_4: hoare_363350478_state,C_1: fun_Ho320143120e_bool,D: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_1),D))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),C_1)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),D))) ) ).

tff(fact_237_mem__def,axiom,
    ! [X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
    <=> hBOOL(hAPP_com_bool(A,X_1)) ) ).

tff(fact_238_mem__def,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
    <=> hBOOL(hAPP_H1645464494e_bool(A,X_1)) ) ).

tff(fact_239_mem__def,axiom,
    ! [X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
    <=> hBOOL(hAPP_pname_bool(A,X_1)) ) ).

tff(fact_240_Collect__def,axiom,
    ! [P_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(collec223185785_state,P_1) = P_1 ).

tff(fact_241_Collect__def,axiom,
    ! [P_1: fun_pname_bool] : hAPP_f759274231e_bool(collect_pname,P_1) = P_1 ).

tff(fact_242_Collect__def,axiom,
    ! [P_1: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(collec1974731493e_bool,P_1) = P_1 ).

tff(fact_243_Collect__def,axiom,
    ! [P_1: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(collec1243131813e_bool,P_1) = P_1 ).

tff(fact_244_subset__insertI2,axiom,
    ! [B_1: pname,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),B))) ) ).

tff(fact_245_subset__insertI2,axiom,
    ! [B_1: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
     => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),B))) ) ).

tff(fact_246_subset__insertI2,axiom,
    ! [B_1: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),B))) ) ).

tff(fact_247_subset__insert,axiom,
    ! [B: fun_com_bool,X_1: com,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)))
      <=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ).

tff(fact_248_subset__insert,axiom,
    ! [B: fun_pname_bool,X_1: pname,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).

tff(fact_249_subset__insert,axiom,
    ! [B: fun_Ho320143120e_bool,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),B)))
      <=> hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B)) ) ) ).

tff(fact_250_insert__subset,axiom,
    ! [X_1: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B))
    <=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
        & hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ).

tff(fact_251_insert__subset,axiom,
    ! [X_1: pname,A: 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)),B))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).

tff(fact_252_insert__subset,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)),B))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B))
        & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B)) ) ) ).

tff(fact_253_subset__insertI,axiom,
    ! [B: fun_pname_bool,A_4: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))) ).

tff(fact_254_subset__insertI,axiom,
    ! [B: fun_com_bool,A_4: com] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))) ).

tff(fact_255_subset__insertI,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B))) ).

tff(fact_256_insert__image,axiom,
    ! [F: fun_Ho713471079_pname,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1346202419_pname(F,X_1)),hAPP_f773602357e_bool(image_1927198851_pname(F),A)) = hAPP_f773602357e_bool(image_1927198851_pname(F),A) ) ) ).

tff(fact_257_insert__image,axiom,
    ! [F: fun_Ho938602221te_com,X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H2142737465te_com(F,X_1)),hAPP_f497466683m_bool(image_689867145te_com(F),A)) = hAPP_f497466683m_bool(image_689867145te_com(F),A) ) ) ).

tff(fact_258_insert__image,axiom,
    ! [F: fun_pname_pname,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_pname_pname(F,X_1)),hAPP_f759274231e_bool(image_pname_pname(F),A)) = hAPP_f759274231e_bool(image_pname_pname(F),A) ) ) ).

tff(fact_259_insert__image,axiom,
    ! [F: fun_pname_com,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_pname_com(F,X_1)),hAPP_f1206115581m_bool(image_pname_com(F),A)) = hAPP_f1206115581m_bool(image_pname_com(F),A) ) ) ).

tff(fact_260_insert__image,axiom,
    ! [F: fun_co482540593_state,X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(F,X_1)),hAPP_f1859782925e_bool(image_1736049107_state(F),A)) = hAPP_f1859782925e_bool(image_1736049107_state(F),A) ) ) ).

tff(fact_261_insert__image,axiom,
    ! [F: fun_pn1262351275_state,X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_p1337579261_state(F,X_1)),hAPP_f1763243027e_bool(image_1918575693_state(F),A)) = hAPP_f1763243027e_bool(image_1918575693_state(F),A) ) ) ).

tff(fact_262_image__insert,axiom,
    ! [F: fun_Ho713471079_pname,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f773602357e_bool(image_1927198851_pname(F),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,hAPP_H1346202419_pname(F,A_4)),hAPP_f773602357e_bool(image_1927198851_pname(F),B)) ).

tff(fact_263_image__insert,axiom,
    ! [F: fun_Ho938602221te_com,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f497466683m_bool(image_689867145te_com(F),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,hAPP_H2142737465te_com(F,A_4)),hAPP_f497466683m_bool(image_689867145te_com(F),B)) ).

tff(fact_264_image__insert,axiom,
    ! [F: fun_co482540593_state,A_4: com,B: fun_com_bool] : hAPP_f1859782925e_bool(image_1736049107_state(F),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(F,A_4)),hAPP_f1859782925e_bool(image_1736049107_state(F),B)) ).

tff(fact_265_image__insert,axiom,
    ! [F: fun_pn1262351275_state,A_4: pname,B: fun_pname_bool] : hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_p1337579261_state(F,A_4)),hAPP_f1763243027e_bool(image_1918575693_state(F),B)) ).

tff(fact_266_image__mono,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f773602357e_bool(image_1927198851_pname(F),A)),hAPP_f773602357e_bool(image_1927198851_pname(F),B))) ) ).

tff(fact_267_image__mono,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B))) ) ).

tff(fact_268_subset__image__iff,axiom,
    ! [B: fun_pname_bool,F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f773602357e_bool(image_1927198851_pname(F),A)))
    <=> ? [AA: fun_Ho320143120e_bool] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,AA),A))
          & ( B = hAPP_f773602357e_bool(image_1927198851_pname(F),AA) ) ) ) ).

tff(fact_269_subset__image__iff,axiom,
    ! [B: fun_Ho320143120e_bool,F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
    <=> ? [AA: fun_pname_bool] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
          & ( B = hAPP_f1763243027e_bool(image_1918575693_state(F),AA) ) ) ) ).

tff(fact_270_domI,axiom,
    ! [M: fun_com_option_com,A_4: com,B_1: com] :
      ( ( hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_1) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M))) ) ).

tff(fact_271_domI,axiom,
    ! [M: fun_Ho12798188_pname,A_4: hoare_363350478_state,B_1: pname] :
      ( ( hAPP_H134270346_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),dom_Ho75493366_pname(M))) ) ).

tff(fact_272_domI,axiom,
    ! [M: fun_Ho382349394_state,A_4: hoare_363350478_state,B_1: hoare_363350478_state] :
      ( ( hAPP_H1942146718_state(M,A_4) = hAPP_H1942146718_state(some_H629028223_state,B_1) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),dom_Ho867270556_state(M))) ) ).

tff(fact_273_domI,axiom,
    ! [M: fun_pn1342468758_pname,A_4: pname,B_1: pname] :
      ( ( hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_1) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M))) ) ).

tff(fact_274_domI,axiom,
    ! [M: fun_pn1405249832_state,A_4: pname,B_1: hoare_363350478_state] :
      ( ( hAPP_p1737106368_state(M,A_4) = hAPP_H1942146718_state(some_H629028223_state,B_1) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn66870208_state(M))) ) ).

tff(fact_275_domI,axiom,
    ! [M: fun_pname_option_com,A_4: pname,B_1: com] :
      ( ( hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_1) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M))) ) ).

tff(fact_276_Collect__conv__if,axiom,
    ! [P_1: fun_pname_bool,A_4: pname] :
      ( ( hBOOL(hAPP_pname_bool(P_1,A_4))
       => ( 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_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ) )
      & ( ~ hBOOL(hAPP_pname_bool(P_1,A_4))
       => ( 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_4))),P_1)) = bot_bo844097828e_bool ) ) ) ).

tff(fact_277_Collect__conv__if,axiom,
    ! [P_1: fun_com_bool,A_4: com] :
      ( ( hBOOL(hAPP_com_bool(P_1,A_4))
       => ( hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ) )
      & ( ~ hBOOL(hAPP_com_bool(P_1,A_4))
       => ( hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),P_1)) = bot_bot_fun_com_bool ) ) ) ).

tff(fact_278_Collect__conv__if,axiom,
    ! [P_1: fun_fu1430349052l_bool,A_4: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
       => ( 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_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
       => ( 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_4))),P_1)) = bot_bo1649642514l_bool ) ) ) ).

tff(fact_279_Collect__conv__if,axiom,
    ! [P_1: fun_fu1996308102l_bool,A_4: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(P_1,A_4))
       => ( hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4))),P_1)) = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),bot_bo133096688l_bool) ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(P_1,A_4))
       => ( hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4))),P_1)) = bot_bo133096688l_bool ) ) ) ).

tff(fact_280_Collect__conv__if,axiom,
    ! [P_1: fun_Ho320143120e_bool,A_4: hoare_363350478_state] :
      ( ( hBOOL(hAPP_H1645464494e_bool(P_1,A_4))
       => ( hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4))),P_1)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool) ) )
      & ( ~ hBOOL(hAPP_H1645464494e_bool(P_1,A_4))
       => ( hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4))),P_1)) = bot_bo39439654e_bool ) ) ) ).

tff(fact_281_Collect__conv__if2,axiom,
    ! [P_1: fun_pname_bool,A_4: pname] :
      ( ( hBOOL(hAPP_pname_bool(P_1,A_4))
       => ( 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_4))),P_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ) )
      & ( ~ hBOOL(hAPP_pname_bool(P_1,A_4))
       => ( 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_4))),P_1)) = bot_bo844097828e_bool ) ) ) ).

tff(fact_282_Collect__conv__if2,axiom,
    ! [P_1: fun_com_bool,A_4: com] :
      ( ( hBOOL(hAPP_com_bool(P_1,A_4))
       => ( hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ) )
      & ( ~ hBOOL(hAPP_com_bool(P_1,A_4))
       => ( hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_c1396316405m_bool(fequal_com,A_4))),P_1)) = bot_bot_fun_com_bool ) ) ) ).

tff(fact_283_Collect__conv__if2,axiom,
    ! [P_1: fun_fu1430349052l_bool,A_4: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
       => ( 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_4))),P_1)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_4))
       => ( 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_4))),P_1)) = bot_bo1649642514l_bool ) ) ) ).

tff(fact_284_Collect__conv__if2,axiom,
    ! [P_1: fun_fu1996308102l_bool,A_4: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(P_1,A_4))
       => ( hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f726209793l_bool(fequal731041167e_bool,A_4))),P_1)) = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),bot_bo133096688l_bool) ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(P_1,A_4))
       => ( hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f726209793l_bool(fequal731041167e_bool,A_4))),P_1)) = bot_bo133096688l_bool ) ) ) ).

tff(fact_285_Collect__conv__if2,axiom,
    ! [P_1: fun_Ho320143120e_bool,A_4: hoare_363350478_state] :
      ( ( hBOOL(hAPP_H1645464494e_bool(P_1,A_4))
       => ( hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_H705653759e_bool(fequal1026769423_state,A_4))),P_1)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool) ) )
      & ( ~ hBOOL(hAPP_H1645464494e_bool(P_1,A_4))
       => ( hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_H705653759e_bool(fequal1026769423_state,A_4))),P_1)) = bot_bo39439654e_bool ) ) ) ).

tff(fact_286_singleton__conv,axiom,
    ! [A_4: pname] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(hAPP_f22061361e_bool(cOMBC_1149511130e_bool,fequal_pname),A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ).

tff(fact_287_singleton__conv,axiom,
    ! [A_4: com] : hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ).

tff(fact_288_singleton__conv,axiom,
    ! [A_4: fun_pname_bool] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(hAPP_f1297925993l_bool(cOMBC_1284144636l_bool,fequal533582459e_bool),A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ).

tff(fact_289_singleton__conv,axiom,
    ! [A_4: fun_Ho320143120e_bool] : hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4)) = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),bot_bo133096688l_bool) ).

tff(fact_290_singleton__conv,axiom,
    ! [A_4: hoare_363350478_state] : hAPP_f1749453397e_bool(collec223185785_state,hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool) ).

tff(fact_291_singleton__conv2,axiom,
    ! [A_4: pname] : hAPP_f759274231e_bool(collect_pname,hAPP_p61793385e_bool(fequal_pname,A_4)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool) ).

tff(fact_292_singleton__conv2,axiom,
    ! [A_4: com] : hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(fequal_com,A_4)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool) ).

tff(fact_293_singleton__conv2,axiom,
    ! [A_4: fun_pname_bool] : hAPP_f559147733l_bool(collec1974731493e_bool,hAPP_f434788991l_bool(fequal533582459e_bool,A_4)) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),bot_bo1649642514l_bool) ).

tff(fact_294_singleton__conv2,axiom,
    ! [A_4: fun_Ho320143120e_bool] : hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f726209793l_bool(fequal731041167e_bool,A_4)) = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),bot_bo133096688l_bool) ).

tff(fact_295_singleton__conv2,axiom,
    ! [A_4: hoare_363350478_state] : hAPP_f1749453397e_bool(collec223185785_state,hAPP_H705653759e_bool(fequal1026769423_state,A_4)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool) ).

tff(fact_296_MGF__lemma1,axiom,
    ! [C: com,G_2: fun_Ho320143120e_bool] :
      ( hBOOL(hoare_265376576gleton)
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),dom_pname_com(body)))
           => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_2))),bot_bo39439654e_bool))) )
       => ( hBOOL(hAPP_com_bool(wt,C))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,C)),bot_bo39439654e_bool))) ) ) ) ).

tff(fact_297_WT__bodiesD,axiom,
    ! [Pn: pname,B_4: com] :
      ( hBOOL(wT_bodies)
     => ( ( hAPP_p799580910on_com(body,Pn) = hAPP_com_option_com(some_com,B_4) )
       => hBOOL(hAPP_com_bool(wt,B_4)) ) ) ).

tff(fact_298_imageE,axiom,
    ! [B_1: hoare_363350478_state,F: fun_co482540593_state,A: fun_com_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1859782925e_bool(image_1736049107_state(F),A)))
     => ~ ! [X_2: com] :
            ( ( B_1 = hAPP_c1041435779_state(F,X_2) )
           => ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) ) ) ).

tff(fact_299_imageE,axiom,
    ! [B_1: pname,F: fun_com_pname,A: fun_com_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),hAPP_f1438183293e_bool(image_com_pname(F),A)))
     => ~ ! [X_2: com] :
            ( ( B_1 = hAPP_com_pname(F,X_2) )
           => ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A)) ) ) ).

tff(fact_300_imageE,axiom,
    ! [B_1: com,F: fun_Ho938602221te_com,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f497466683m_bool(image_689867145te_com(F),A)))
     => ~ ! [X_2: hoare_363350478_state] :
            ( ( B_1 = hAPP_H2142737465te_com(F,X_2) )
           => ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A)) ) ) ).

tff(fact_301_imageE,axiom,
    ! [B_1: com,F: fun_pname_com,A: fun_pname_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,B_1),hAPP_f1206115581m_bool(image_pname_com(F),A)))
     => ~ ! [X_2: pname] :
            ( ( B_1 = hAPP_pname_com(F,X_2) )
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ) ).

tff(fact_302_imageE,axiom,
    ! [B_1: hoare_363350478_state,F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,B_1),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
     => ~ ! [X_2: pname] :
            ( ( B_1 = hAPP_p1337579261_state(F,X_2) )
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ) ).

tff(fact_303_finite__subset__induct,axiom,
    ! [P_1: fun_fu1362071682l_bool,A: fun_com_bool,Fa: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,Fa),A))
       => ( hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool))
         => ( ! [A_2: com,F_2: fun_com_bool] :
                ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
               => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A))
                 => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),F_2))
                   => ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
                     => hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_304_finite__subset__induct,axiom,
    ! [P_1: fun_fu399576434l_bool,A: 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))
       => ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
         => ( ! [A_2: fun_pname_bool,F_2: fun_fu1430349052l_bool] :
                ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
               => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A))
                 => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2))
                   => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_305_finite__subset__induct,axiom,
    ! [P_1: fun_fu1972704968l_bool,A: fun_fu1996308102l_bool,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,Fa),A))
       => ( hBOOL(hAPP_f1287348838l_bool(P_1,bot_bo133096688l_bool))
         => ( ! [A_2: fun_Ho320143120e_bool,F_2: fun_fu1996308102l_bool] :
                ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,F_2))
               => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,A_2),A))
                 => ( ~ hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,A_2),F_2))
                   => ( hBOOL(hAPP_f1287348838l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1287348838l_bool(P_1,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1287348838l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_306_finite__subset__induct,axiom,
    ! [P_1: fun_fu1430349052l_bool,A: 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))
       => ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
         => ( ! [A_2: pname,F_2: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
               => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2))
                   => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_307_finite__subset__induct,axiom,
    ! [P_1: fun_fu1996308102l_bool,A: fun_Ho320143120e_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Fa),A))
       => ( hBOOL(hAPP_f568432088l_bool(P_1,bot_bo39439654e_bool))
         => ( ! [A_2: hoare_363350478_state,F_2: fun_Ho320143120e_bool] :
                ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,F_2))
               => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_2),A))
                 => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_2),F_2))
                   => ( hBOOL(hAPP_f568432088l_bool(P_1,F_2))
                     => hBOOL(hAPP_f568432088l_bool(P_1,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f568432088l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_308_WTs__elim__cases_I7_J,axiom,
    ! [P: pname] :
      ( hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,P)))
     => ~ ! [Y_3: com] : hAPP_p799580910on_com(body,P) != hAPP_com_option_com(some_com,Y_3) ) ).

tff(fact_309_subsetI,axiom,
    ! [B: fun_com_bool,A: fun_com_bool] :
      ( ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B)) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ).

tff(fact_310_subsetI,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),B)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B)) ) ).

tff(fact_311_subsetI,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).

tff(fact_312_finite__subset__image,axiom,
    ! [F: fun_fu54631149_state,A: fun_fu1430349052l_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1912490857e_bool(image_431763259_state(F),A)))
       => ? [C_3: fun_fu1430349052l_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A))
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
            & ( B = hAPP_f1912490857e_bool(image_431763259_state(F),C_3) ) ) ) ) ).

tff(fact_313_finite__subset__image,axiom,
    ! [F: fun_fu700438391_state,A: fun_fu1996308102l_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1180969799e_bool(image_2021386777_state(F),A)))
       => ? [C_3: fun_fu1996308102l_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,C_3),A))
            & hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,C_3))
            & ( B = hAPP_f1180969799e_bool(image_2021386777_state(F),C_3) ) ) ) ) ).

tff(fact_314_finite__subset__image,axiom,
    ! [F: fun_fu1499449723_pname,A: 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)))
       => ? [C_3: fun_fu1430349052l_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_3),A))
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_3))
            & ( B = hAPP_f674760225e_bool(image_1283814551_pname(F),C_3) ) ) ) ) ).

tff(fact_315_finite__subset__image,axiom,
    ! [F: fun_fu2380401_pname,A: fun_fu1996308102l_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_f1892738755e_bool(image_937015865_pname(F),A)))
       => ? [C_3: fun_fu1996308102l_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,C_3),A))
            & hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,C_3))
            & ( B = hAPP_f1892738755e_bool(image_937015865_pname(F),C_3) ) ) ) ) ).

tff(fact_316_finite__subset__image,axiom,
    ! [F: fun_Ho1262521325e_bool,A: fun_Ho320143120e_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),hAPP_f766639041l_bool(image_1660610235e_bool(F),A)))
       => ? [C_3: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_3),A))
            & hBOOL(hAPP_f568432088l_bool(finite280062779_state,C_3))
            & ( B = hAPP_f766639041l_bool(image_1660610235e_bool(F),C_3) ) ) ) ) ).

tff(fact_317_finite__subset__image,axiom,
    ! [F: fun_Ho424838195e_bool,A: fun_Ho320143120e_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,B),hAPP_f726209793l_bool(image_1484638543e_bool(F),A)))
       => ? [C_3: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_3),A))
            & hBOOL(hAPP_f568432088l_bool(finite280062779_state,C_3))
            & ( B = hAPP_f726209793l_bool(image_1484638543e_bool(F),C_3) ) ) ) ) ).

tff(fact_318_finite__subset__image,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_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_f773602357e_bool(image_1927198851_pname(F),A)))
       => ? [C_3: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_3),A))
            & hBOOL(hAPP_f568432088l_bool(finite280062779_state,C_3))
            & ( B = hAPP_f773602357e_bool(image_1927198851_pname(F),C_3) ) ) ) ) ).

tff(fact_319_finite__subset__image,axiom,
    ! [F: fun_pn800050071e_bool,A: 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)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f434788991l_bool(image_47868345e_bool(F),C_3) ) ) ) ) ).

tff(fact_320_finite__subset__image,axiom,
    ! [F: fun_pn1521100553e_bool,A: fun_pname_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,B),hAPP_f682249667l_bool(image_1637084625e_bool(F),A)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f682249667l_bool(image_1637084625e_bool(F),C_3) ) ) ) ) ).

tff(fact_321_finite__subset__image,axiom,
    ! [F: fun_pname_pname,A: 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)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f759274231e_bool(image_pname_pname(F),C_3) ) ) ) ) ).

tff(fact_322_finite__subset__image,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
       => ? [C_3: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_3),A))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_3))
            & ( B = hAPP_f1763243027e_bool(image_1918575693_state(F),C_3) ) ) ) ) ).

tff(fact_323_finite__dom__body,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))) ).

tff(fact_324_finite__induct,axiom,
    ! [P_1: fun_fu1362071682l_bool,Fa: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool))
       => ( ! [X_2: com,F_2: fun_com_bool] :
              ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
             => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2))
               => ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
                 => hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ).

tff(fact_325_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_2: fun_fu1430349052l_bool] :
              ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
             => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2))
               => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
                 => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ).

tff(fact_326_finite__induct,axiom,
    ! [P_1: fun_fu1972704968l_bool,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(P_1,bot_bo133096688l_bool))
       => ( ! [X_2: fun_Ho320143120e_bool,F_2: fun_fu1996308102l_bool] :
              ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,F_2))
             => ( ~ hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),F_2))
               => ( hBOOL(hAPP_f1287348838l_bool(P_1,F_2))
                 => hBOOL(hAPP_f1287348838l_bool(P_1,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f1287348838l_bool(P_1,Fa)) ) ) ) ).

tff(fact_327_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_2: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
             => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
               => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
                 => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ).

tff(fact_328_finite__induct,axiom,
    ! [P_1: fun_fu1996308102l_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(P_1,bot_bo39439654e_bool))
       => ( ! [X_2: hoare_363350478_state,F_2: fun_Ho320143120e_bool] :
              ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,F_2))
             => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),F_2))
               => ( hBOOL(hAPP_f568432088l_bool(P_1,F_2))
                 => hBOOL(hAPP_f568432088l_bool(P_1,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f568432088l_bool(P_1,Fa)) ) ) ) ).

tff(fact_329_finite_Osimps,axiom,
    ! [A_4: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_4))
    <=> ( ( A_4 = bot_bot_fun_com_bool )
        | ? [A_7: fun_com_bool,A_2: com] :
            ( ( A_4 = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),A_7) )
            & hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7)) ) ) ) ).

tff(fact_330_finite_Osimps,axiom,
    ! [A_4: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_4))
    <=> ( ( A_4 = bot_bo1649642514l_bool )
        | ? [A_7: fun_fu1430349052l_bool,A_2: fun_pname_bool] :
            ( ( A_4 = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A_7) )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7)) ) ) ) ).

tff(fact_331_finite_Osimps,axiom,
    ! [A_4: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A_4))
    <=> ( ( A_4 = bot_bo133096688l_bool )
        | ? [A_7: fun_fu1996308102l_bool,A_2: fun_Ho320143120e_bool] :
            ( ( A_4 = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_2),A_7) )
            & hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A_7)) ) ) ) ).

tff(fact_332_finite_Osimps,axiom,
    ! [A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_4))
    <=> ( ( A_4 = bot_bo844097828e_bool )
        | ? [A_7: fun_pname_bool,A_2: pname] :
            ( ( A_4 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A_7) )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7)) ) ) ) ).

tff(fact_333_finite_Osimps,axiom,
    ! [A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A_4))
    <=> ( ( A_4 = bot_bo39439654e_bool )
        | ? [A_7: fun_Ho320143120e_bool,A_2: hoare_363350478_state] :
            ( ( A_4 = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_2),A_7) )
            & hBOOL(hAPP_f568432088l_bool(finite280062779_state,A_7)) ) ) ) ).

tff(fact_334_pigeonhole__infinite,axiom,
    ! [F: fun_co482540593_state,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1859782925e_bool(image_1736049107_state(F),A)))
       => ? [X_2: com] :
            ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
            & ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_H176808977m_bool(hAPP_f1375689733m_bool(cOMBC_1517337958e_bool,hAPP_f1813061839e_bool(cOMBB_147383684ol_com(fequal1026769423_state),F)),hAPP_c1041435779_state(F,X_2)))))) ) ) ) ).

tff(fact_335_pigeonhole__infinite,axiom,
    ! [F: fun_Ho901937921_state,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(image_2068641359_state(F),A)))
       => ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
            & ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,hAPP_f355123231e_bool(cOMBB_496159380_state(fequal1026769423_state),F)),hAPP_H1982017439_state(F,X_2)))))) ) ) ) ).

tff(fact_336_pigeonhole__infinite,axiom,
    ! [F: fun_fu54631149_state,A: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1912490857e_bool(image_431763259_state(F),A)))
       => ? [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
            & ~ 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))),hAPP_H444605547l_bool(hAPP_f1075942761l_bool(cOMBC_1091669008e_bool,hAPP_f272807711e_bool(cOMBB_543245952e_bool(fequal1026769423_state),F)),hAPP_f804167819_state(F,X_2)))))) ) ) ) ).

tff(fact_337_pigeonhole__infinite,axiom,
    ! [F: fun_fu700438391_state,A: fun_fu1996308102l_bool] :
      ( ~ hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1180969799e_bool(image_2021386777_state(F),A)))
       => ? [X_2: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),A))
            & ~ hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),A))),hAPP_H40373975l_bool(hAPP_f1585300113l_bool(cOMBC_497487404e_bool,hAPP_f440040771e_bool(cOMBB_238163658e_bool(fequal1026769423_state),F)),hAPP_f1242401993_state(F,X_2)))))) ) ) ) ).

tff(fact_338_pigeonhole__infinite,axiom,
    ! [F: fun_com_pname,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1438183293e_bool(image_com_pname(F),A)))
       => ? [X_2: com] :
            ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
            & ~ hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,hAPP_f835719487e_bool(cOMBB_1083901850ol_com(fequal_pname),F)),hAPP_com_pname(F,X_2)))))) ) ) ) ).

tff(fact_339_pigeonhole__infinite,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f773602357e_bool(image_1927198851_pname(F),A)))
       => ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
            & ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_p2009489185e_bool(hAPP_f626747953e_bool(cOMBC_1026256022e_bool,hAPP_f875047427e_bool(cOMBB_951329022_state(fequal_pname),F)),hAPP_H1346202419_pname(F,X_2)))))) ) ) ) ).

tff(fact_340_pigeonhole__infinite,axiom,
    ! [F: fun_pname_pname,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(image_pname_pname(F),A)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & ~ 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))),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_341_pigeonhole__infinite,axiom,
    ! [F: fun_fu1499449723_pname,A: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f674760225e_bool(image_1283814551_pname(F),A)))
       => ? [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
            & ~ 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))),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_342_pigeonhole__infinite,axiom,
    ! [F: fun_fu2380401_pname,A: fun_fu1996308102l_bool] :
      ( ~ hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f1892738755e_bool(image_937015865_pname(F),A)))
       => ? [X_2: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),A))
            & ~ hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),A))),hAPP_p425615669l_bool(hAPP_f883421385l_bool(cOMBC_1845395470e_bool,hAPP_f1544555711e_bool(cOMBB_655928288e_bool(fequal_pname),F)),hAPP_f1309420425_pname(F,X_2)))))) ) ) ) ).

tff(fact_343_pigeonhole__infinite,axiom,
    ! [F: fun_Ho1262521325e_bool,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f766639041l_bool(image_1660610235e_bool(F),A)))
       => ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
            & ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_f1763243027e_bool(hAPP_f1421439337e_bool(cOMBC_1674478480l_bool,hAPP_f399561463l_bool(cOMBB_1217374484_state(fequal533582459e_bool),F)),hAPP_H2033014795e_bool(F,X_2)))))) ) ) ) ).

tff(fact_344_pigeonhole__infinite,axiom,
    ! [F: fun_Ho424838195e_bool,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f726209793l_bool(image_1484638543e_bool(F),A)))
       => ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
            & ~ hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,hAPP_f565239043l_bool(cOMBB_867654038_state(fequal731041167e_bool),F)),hAPP_H705653759e_bool(F,X_2)))))) ) ) ) ).

tff(fact_345_pigeonhole__infinite,axiom,
    ! [F: fun_pn800050071e_bool,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f434788991l_bool(image_47868345e_bool(F),A)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & ~ 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))),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_346_pigeonhole__infinite,axiom,
    ! [F: fun_pn1521100553e_bool,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f682249667l_bool(image_1637084625e_bool(F),A)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & ~ 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))),hAPP_f773602357e_bool(hAPP_f1863577801e_bool(cOMBC_947783590l_bool,hAPP_f1841796439l_bool(cOMBB_343228284_pname(fequal731041167e_bool),F)),hAPP_p2009489185e_bool(F,X_2)))))) ) ) ) ).

tff(fact_347_pigeonhole__infinite,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
       => ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & ~ 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))),hAPP_H2033014795e_bool(hAPP_f443781369e_bool(cOMBC_1422551904e_bool,hAPP_f1284518107e_bool(cOMBB_1755629310_pname(fequal1026769423_state),F)),hAPP_p1337579261_state(F,X_2)))))) ) ) ) ).

tff(fact_348_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_349_MGT__Body,axiom,
    ! [G_2: fun_Ho320143120e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_pname(hoare_Mirabelle_MGT),body_1)),Procs))),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_pname(hoare_Mirabelle_MGT),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Procs)))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Procs))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_pname(hoare_Mirabelle_MGT),body_1)),Procs))) ) ) ).

tff(fact_350_domD,axiom,
    ! [A_4: com,M: fun_com_option_com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),dom_com_com(M)))
     => ? [B_3: com] : hAPP_com_option_com(M,A_4) = hAPP_com_option_com(some_com,B_3) ) ).

tff(fact_351_domD,axiom,
    ! [A_4: hoare_363350478_state,M: fun_Ho12798188_pname] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),dom_Ho75493366_pname(M)))
     => ? [B_3: pname] : hAPP_H134270346_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3) ) ).

tff(fact_352_domD,axiom,
    ! [A_4: hoare_363350478_state,M: fun_Ho382349394_state] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),dom_Ho867270556_state(M)))
     => ? [B_3: hoare_363350478_state] : hAPP_H1942146718_state(M,A_4) = hAPP_H1942146718_state(some_H629028223_state,B_3) ) ).

tff(fact_353_domD,axiom,
    ! [A_4: pname,M: fun_pn1342468758_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_pname(M)))
     => ? [B_3: pname] : hAPP_p1252095976_pname(M,A_4) = hAPP_p1252095976_pname(some_pname,B_3) ) ).

tff(fact_354_domD,axiom,
    ! [A_4: pname,M: fun_pn1405249832_state] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pn66870208_state(M)))
     => ? [B_3: hoare_363350478_state] : hAPP_p1737106368_state(M,A_4) = hAPP_H1942146718_state(some_H629028223_state,B_3) ) ).

tff(fact_355_domD,axiom,
    ! [A_4: pname,M: fun_pname_option_com] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M)))
     => ? [B_3: com] : hAPP_p799580910on_com(M,A_4) = hAPP_com_option_com(some_com,B_3) ) ).

tff(fact_356_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_357_the__elem__eq,axiom,
    ! [X_1: com] : hAPP_f1276420679ol_com(the_elem_com,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1 ).

tff(fact_358_the__elem__eq,axiom,
    ! [X_1: hoare_363350478_state] : hAPP_f1242401993_state(the_el1666657391_state,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) = X_1 ).

tff(fact_359_image__subsetI,axiom,
    ! [F: fun_Ho938602221te_com,B: fun_com_bool,A: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_H2142737465te_com(F,X_2)),B)) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f497466683m_bool(image_689867145te_com(F),A)),B)) ) ).

tff(fact_360_image__subsetI,axiom,
    ! [F: fun_Ho713471079_pname,B: fun_pname_bool,A: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1346202419_pname(F,X_2)),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f773602357e_bool(image_1927198851_pname(F),A)),B)) ) ).

tff(fact_361_image__subsetI,axiom,
    ! [F: fun_pname_com,B: fun_com_bool,A: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_pname_com(F,X_2)),B)) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1206115581m_bool(image_pname_com(F),A)),B)) ) ).

tff(fact_362_image__subsetI,axiom,
    ! [F: fun_pname_pname,B: fun_pname_bool,A: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_2)),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),B)) ) ).

tff(fact_363_image__subsetI,axiom,
    ! [F: fun_co482540593_state,B: fun_Ho320143120e_bool,A: fun_com_bool] :
      ( ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_c1041435779_state(F,X_2)),B)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1859782925e_bool(image_1736049107_state(F),A)),B)) ) ).

tff(fact_364_image__subsetI,axiom,
    ! [F: fun_com_pname,B: fun_pname_bool,A: fun_com_bool] :
      ( ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_com_pname(F,X_2)),B)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f1438183293e_bool(image_com_pname(F),A)),B)) ) ).

tff(fact_365_image__subsetI,axiom,
    ! [F: fun_pn1262351275_state,B: fun_Ho320143120e_bool,A: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_p1337579261_state(F,X_2)),B)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),B)) ) ).

tff(fact_366_order__refl,axiom,
    ! [X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),X_1)) ).

tff(fact_367_order__refl,axiom,
    ! [X_1: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),X_1)) ).

tff(fact_368_order__refl,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),X_1)) ).

tff(fact_369_nonempty__iff,axiom,
    ! [A: fun_com_bool] :
      ( ( A != bot_bot_fun_com_bool )
    <=> ? [X_2: com,B_2: fun_com_bool] :
          ( ( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),B_2) )
          & ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),B_2)) ) ) ).

tff(fact_370_nonempty__iff,axiom,
    ! [A: fun_pname_bool] :
      ( ( A != bot_bo844097828e_bool )
    <=> ? [X_2: pname,B_2: fun_pname_bool] :
          ( ( A = 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_371_nonempty__iff,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( ( A != bot_bo39439654e_bool )
    <=> ? [X_2: hoare_363350478_state,B_2: fun_Ho320143120e_bool] :
          ( ( A = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),B_2) )
          & ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),B_2)) ) ) ).

tff(fact_372_the_Osimps,axiom,
    ! [X_5: pname] : hAPP_o593586696_pname(the_pname_1,hAPP_p1252095976_pname(some_pname,X_5)) = X_5 ).

tff(fact_373_the_Osimps,axiom,
    ! [X_5: hoare_363350478_state] : hAPP_o1390191976_state(the_Ho1765868149_state,hAPP_H1942146718_state(some_H629028223_state,X_5)) = X_5 ).

tff(fact_374_the_Osimps,axiom,
    ! [X_5: com] : hAPP_option_com_com(the_com,hAPP_com_option_com(some_com,X_5)) = X_5 ).

tff(fact_375_weak__Body,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool,Pn_1: pname,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo39439654e_bool)))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo39439654e_bool))) ) ).

tff(fact_376_BodyN,axiom,
    ! [P_1: fun_st1506752259e_bool,Pn_1: pname,Q_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),G_2)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),Q_1)),bot_bo39439654e_bool)))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_pname_com(body_1,Pn_1)),Q_1)),bot_bo39439654e_bool))) ) ).

tff(fact_377_state__not__singleton__def,axiom,
    ( hBOOL(hoare_265376576gleton)
  <=> ? [S_1: state,T_2: state] : S_1 != T_2 ) ).

tff(fact_378_UnCI,axiom,
    ! [A: fun_com_bool,C: com,B: fun_com_bool] :
      ( ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) )
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).

tff(fact_379_UnCI,axiom,
    ! [A: fun_Ho320143120e_bool,C: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))) ) ).

tff(fact_380_UnCI,axiom,
    ! [A: 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)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ) ).

tff(fact_381_UnE,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)))
     => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_382_UnE,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)))
     => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_383_UnE,axiom,
    ! [C: pname,A: 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),B)))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_384_triple_Oinject,axiom,
    ! [Fun1_2: fun_st1506752259e_bool,Com_1: com,Fun2_2: fun_st1506752259e_bool,Fun1_1: fun_st1506752259e_bool,Com_2: com,Fun2_1: fun_st1506752259e_bool] :
      ( ( hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,Fun1_2),Com_1),Fun2_2) = hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,Fun1_1),Com_2),Fun2_1) )
    <=> ( ( Fun1_2 = Fun1_1 )
        & ( Com_1 = Com_2 )
        & ( Fun2_2 = Fun2_1 ) ) ) ).

tff(fact_385_UnI2,axiom,
    ! [A: fun_com_bool,C: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).

tff(fact_386_UnI2,axiom,
    ! [A: fun_Ho320143120e_bool,C: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))) ) ).

tff(fact_387_UnI2,axiom,
    ! [A: 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),B))) ) ).

tff(fact_388_UnI1,axiom,
    ! [B: fun_com_bool,C: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))) ) ).

tff(fact_389_UnI1,axiom,
    ! [B: fun_Ho320143120e_bool,C: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))) ) ).

tff(fact_390_UnI1,axiom,
    ! [B: fun_pname_bool,C: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ) ).

tff(fact_391_ball__Un,axiom,
    ! [P_1: fun_pname_bool,A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
         => hBOOL(hAPP_pname_bool(P_1,X_2)) )
    <=> ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
           => hBOOL(hAPP_pname_bool(P_1,X_2)) )
        & ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
           => hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ) ).

tff(fact_392_ball__Un,axiom,
    ! [P_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)))
         => hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) )
    <=> ( ! [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
           => hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) )
        & ! [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),B))
           => hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) ) ) ) ).

tff(fact_393_bex__Un,axiom,
    ! [P_1: fun_pname_bool,A: fun_pname_bool,B: fun_pname_bool] :
      ( ? [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
          & hBOOL(hAPP_pname_bool(P_1,X_2)) )
    <=> ( ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & hBOOL(hAPP_pname_bool(P_1,X_2)) )
        | ? [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
            & hBOOL(hAPP_pname_bool(P_1,X_2)) ) ) ) ).

tff(fact_394_bex__Un,axiom,
    ! [P_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ? [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)))
          & hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) )
    <=> ( ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
            & hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) )
        | ? [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),B))
            & hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) ) ) ) ).

tff(fact_395_Un__assoc,axiom,
    ! [A: 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(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ).

tff(fact_396_Un__assoc,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),C_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) ).

tff(fact_397_Un__iff,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)))
    <=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
        | hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_398_Un__iff,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
        | hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_399_Un__iff,axiom,
    ! [C: pname,A: 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),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_400_Un__left__commute,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).

tff(fact_401_Un__left__commute,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),C_1)) ).

tff(fact_402_Un__left__absorb,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) ).

tff(fact_403_Un__left__absorb,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) ).

tff(fact_404_Un__commute,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A) ).

tff(fact_405_Un__commute,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),A) ).

tff(fact_406_Un__def,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fdisj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).

tff(fact_407_Un__def,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_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_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),A))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).

tff(fact_408_Un__def,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fdisj),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),A))),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),B))) ).

tff(fact_409_Un__def,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fdisj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),B))) ).

tff(fact_410_Un__def,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),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))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).

tff(fact_411_Un__absorb,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),A) = A ).

tff(fact_412_Un__absorb,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),A) = A ).

tff(fact_413_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_414_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_415_Collect__disj__eq,axiom,
    ! [P_1: fun_fu1996308102l_bool,Q_1: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fdisj),P_1)),Q_1)) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,hAPP_f85652879l_bool(collec1243131813e_bool,P_1)),hAPP_f85652879l_bool(collec1243131813e_bool,Q_1)) ).

tff(fact_416_Collect__disj__eq,axiom,
    ! [P_1: fun_Ho320143120e_bool,Q_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fdisj),P_1)),Q_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(collec223185785_state,P_1)),hAPP_f1749453397e_bool(collec223185785_state,Q_1)) ).

tff(fact_417_Un__empty,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = bot_bo844097828e_bool )
    <=> ( ( A = bot_bo844097828e_bool )
        & ( B = bot_bo844097828e_bool ) ) ) ).

tff(fact_418_Un__empty,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] :
      ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = bot_bot_fun_com_bool )
    <=> ( ( A = bot_bot_fun_com_bool )
        & ( B = bot_bot_fun_com_bool ) ) ) ).

tff(fact_419_Un__empty,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = bot_bo39439654e_bool )
    <=> ( ( A = bot_bo39439654e_bool )
        & ( B = bot_bo39439654e_bool ) ) ) ).

tff(fact_420_Un__empty__right,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),bot_bo844097828e_bool) = A ).

tff(fact_421_Un__empty__right,axiom,
    ! [A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),bot_bot_fun_com_bool) = A ).

tff(fact_422_Un__empty__right,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),bot_bo39439654e_bool) = A ).

tff(fact_423_Un__empty__left,axiom,
    ! [B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,bot_bo844097828e_bool),B) = B ).

tff(fact_424_Un__empty__left,axiom,
    ! [B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),B) = B ).

tff(fact_425_Un__empty__left,axiom,
    ! [B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,bot_bo39439654e_bool),B) = B ).

tff(fact_426_finite__UnI,axiom,
    ! [G_2: fun_fu1430349052l_bool,Fa: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2))) ) ) ).

tff(fact_427_finite__UnI,axiom,
    ! [G_2: fun_fu1996308102l_bool,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,G_2))
       => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,Fa),G_2))) ) ) ).

tff(fact_428_finite__UnI,axiom,
    ! [G_2: fun_Ho320143120e_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,G_2))
       => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Fa),G_2))) ) ) ).

tff(fact_429_finite__UnI,axiom,
    ! [G_2: fun_pname_bool,Fa: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2))) ) ) ).

tff(fact_430_finite__Un,axiom,
    ! [Fa: fun_fu1430349052l_bool,G_2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,Fa),G_2)))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) ) ) ).

tff(fact_431_finite__Un,axiom,
    ! [Fa: fun_fu1996308102l_bool,G_2: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,Fa),G_2)))
    <=> ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
        & hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,G_2)) ) ) ).

tff(fact_432_finite__Un,axiom,
    ! [Fa: fun_Ho320143120e_bool,G_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Fa),G_2)))
    <=> ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
        & hBOOL(hAPP_f568432088l_bool(finite280062779_state,G_2)) ) ) ).

tff(fact_433_finite__Un,axiom,
    ! [Fa: fun_pname_bool,G_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Fa),G_2)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) ) ) ).

tff(fact_434_Un__insert__left,axiom,
    ! [A_4: 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_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) ).

tff(fact_435_Un__insert__left,axiom,
    ! [A_4: com,B: fun_com_bool,C_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,B),C_1)) ).

tff(fact_436_Un__insert__left,axiom,
    ! [A_4: hoare_363350478_state,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)),C_1) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) ).

tff(fact_437_Un__insert__right,axiom,
    ! [A: fun_pname_bool,A_4: pname,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) ).

tff(fact_438_Un__insert__right,axiom,
    ! [A: fun_com_bool,A_4: com,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) ).

tff(fact_439_Un__insert__right,axiom,
    ! [A: fun_Ho320143120e_bool,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)) ).

tff(fact_440_Un__mono,axiom,
    ! [B: fun_pname_bool,D: fun_pname_bool,A: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),D))) ) ) ).

tff(fact_441_Un__mono,axiom,
    ! [B: fun_Ho320143120e_bool,D: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),C_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),D))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,C_1),D))) ) ) ).

tff(fact_442_Un__least,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),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),B)),C_1)) ) ) ).

tff(fact_443_Un__least,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),C_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),C_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),C_1)) ) ) ).

tff(fact_444_Un__absorb2,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = A ) ) ).

tff(fact_445_Un__absorb2,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = A ) ) ).

tff(fact_446_Un__absorb1,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B ) ) ).

tff(fact_447_Un__absorb1,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = B ) ) ).

tff(fact_448_subset__Un__eq,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = B ) ) ).

tff(fact_449_subset__Un__eq,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
    <=> ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = B ) ) ).

tff(fact_450_Un__upper2,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ).

tff(fact_451_Un__upper2,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))) ).

tff(fact_452_Un__upper1,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))) ).

tff(fact_453_Un__upper1,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))) ).

tff(fact_454_image__Un,axiom,
    ! [F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f773602357e_bool(image_1927198851_pname(F),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f773602357e_bool(image_1927198851_pname(F),A)),hAPP_f773602357e_bool(image_1927198851_pname(F),B)) ).

tff(fact_455_image__Un,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] : hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B)) ).

tff(fact_456_insert__def,axiom,
    ! [A_4: pname,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),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_4))),B) ).

tff(fact_457_insert__def,axiom,
    ! [A_4: com,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(collect_com,hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,fequal_com),A_4))),B) ).

tff(fact_458_insert__def,axiom,
    ! [A_4: fun_pname_bool,B: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),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_4))),B) ).

tff(fact_459_insert__def,axiom,
    ! [A_4: fun_Ho320143120e_bool,B: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),B) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,fequal731041167e_bool),A_4))),B) ).

tff(fact_460_insert__def,axiom,
    ! [A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(collec223185785_state,hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,fequal1026769423_state),A_4))),B) ).

tff(fact_461_insert__is__Un,axiom,
    ! [A_4: pname,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)),A) ).

tff(fact_462_insert__is__Un,axiom,
    ! [A_4: com,A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)),A) ).

tff(fact_463_insert__is__Un,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool)),A) ).

tff(fact_464_hoare__derivs_OBody,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),body_1)),Q_1)),Procs))) ) ).

tff(fact_465_xt1_I6_J,axiom,
    ! [Z: fun_pname_bool,Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),Y_2))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z),X_1)) ) ) ).

tff(fact_466_xt1_I6_J,axiom,
    ! [Z: bool,Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1)) ) ) ).

tff(fact_467_xt1_I6_J,axiom,
    ! [Z: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Z),Y_2))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Z),X_1)) ) ) ).

tff(fact_468_xt1_I5_J,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
       => ( X_1 = Y_2 ) ) ) ).

tff(fact_469_xt1_I5_J,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
       => ( hBOOL(X_1)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_470_xt1_I5_J,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
       => ( X_1 = Y_2 ) ) ) ).

tff(fact_471_order__trans,axiom,
    ! [Z: fun_pname_bool,X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).

tff(fact_472_order__trans,axiom,
    ! [Z: bool,X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) ) ) ).

tff(fact_473_order__trans,axiom,
    ! [Z: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),Z))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Z)) ) ) ).

tff(fact_474_order__antisym,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
       => ( X_1 = Y_2 ) ) ) ).

tff(fact_475_order__antisym,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
       => ( hBOOL(X_1)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_476_order__antisym,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
       => ( X_1 = Y_2 ) ) ) ).

tff(fact_477_xt1_I4_J,axiom,
    ! [C: fun_pname_bool,B_1: fun_pname_bool,A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A_4)) ) ) ).

tff(fact_478_xt1_I4_J,axiom,
    ! [C: bool,B_1: bool,A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4))
     => ( ( hBOOL(B_1)
        <=> hBOOL(C) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4)) ) ) ).

tff(fact_479_xt1_I4_J,axiom,
    ! [C: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),A_4))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C),A_4)) ) ) ).

tff(fact_480_ord__le__eq__trans,axiom,
    ! [C: fun_pname_bool,A_4: fun_pname_bool,B_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),B_1))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C)) ) ) ).

tff(fact_481_ord__le__eq__trans,axiom,
    ! [C: bool,A_4: bool,B_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),B_1))
     => ( ( hBOOL(B_1)
        <=> hBOOL(C) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) ) ) ).

tff(fact_482_ord__le__eq__trans,axiom,
    ! [C: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),B_1))
     => ( ( B_1 = C )
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),C)) ) ) ).

tff(fact_483_xt1_I3_J,axiom,
    ! [C: fun_pname_bool,A_4: fun_pname_bool,B_1: fun_pname_bool] :
      ( ( A_4 = 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_4)) ) ) ).

tff(fact_484_xt1_I3_J,axiom,
    ! [C: bool,B_1: bool,A_4: bool] :
      ( ( hBOOL(A_4)
      <=> hBOOL(B_1) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),A_4)) ) ) ).

tff(fact_485_xt1_I3_J,axiom,
    ! [C: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] :
      ( ( A_4 = B_1 )
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C),B_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C),A_4)) ) ) ).

tff(fact_486_ord__eq__le__trans,axiom,
    ! [C: fun_pname_bool,A_4: fun_pname_bool,B_1: fun_pname_bool] :
      ( ( A_4 = 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_4),C)) ) ) ).

tff(fact_487_ord__eq__le__trans,axiom,
    ! [C: bool,B_1: bool,A_4: bool] :
      ( ( hBOOL(A_4)
      <=> hBOOL(B_1) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C)) ) ) ).

tff(fact_488_ord__eq__le__trans,axiom,
    ! [C: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] :
      ( ( A_4 = B_1 )
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),C))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),C)) ) ) ).

tff(fact_489_order__antisym__conv,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
      <=> ( X_1 = Y_2 ) ) ) ).

tff(fact_490_order__antisym__conv,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
      <=> ( hBOOL(X_1)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_491_order__antisym__conv,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
      <=> ( X_1 = Y_2 ) ) ) ).

tff(fact_492_order__eq__refl,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( ( X_1 = Y_2 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2)) ) ).

tff(fact_493_order__eq__refl,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( ( hBOOL(X_1)
      <=> hBOOL(Y_2) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2)) ) ).

tff(fact_494_order__eq__refl,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( ( X_1 = Y_2 )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2)) ) ).

tff(fact_495_order__eq__iff,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( ( X_1 = Y_2 )
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1)) ) ) ).

tff(fact_496_order__eq__iff,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( ( hBOOL(X_1)
      <=> hBOOL(Y_2) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1)) ) ) ).

tff(fact_497_order__eq__iff,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( ( X_1 = Y_2 )
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
        & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1)) ) ) ).

tff(fact_498_option_Oinject,axiom,
    ! [A_4: pname,A_8: pname] :
      ( ( hAPP_p1252095976_pname(some_pname,A_4) = hAPP_p1252095976_pname(some_pname,A_8) )
    <=> ( A_4 = A_8 ) ) ).

tff(fact_499_option_Oinject,axiom,
    ! [A_4: hoare_363350478_state,A_8: hoare_363350478_state] :
      ( ( hAPP_H1942146718_state(some_H629028223_state,A_4) = hAPP_H1942146718_state(some_H629028223_state,A_8) )
    <=> ( A_4 = A_8 ) ) ).

tff(fact_500_option_Oinject,axiom,
    ! [A_4: com,A_8: com] :
      ( ( hAPP_com_option_com(some_com,A_4) = hAPP_com_option_com(some_com,A_8) )
    <=> ( A_4 = A_8 ) ) ).

tff(fact_501_constant,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool,C_1: bool] :
      ( ( hBOOL(C_1)
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) )
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_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_bo39439654e_bool))) ) ).

tff(fact_502_Body1,axiom,
    ! [Pn_1: pname,G_2: fun_Ho320143120e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_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_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_p1637813682e_bool(P_1,Pn_1)),hAPP_pname_com(body_1,Pn_1)),hAPP_p1637813682e_bool(Q_1,Pn_1))),bot_bo39439654e_bool))) ) ) ).

tff(fact_503_le__bot,axiom,
    ! [A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool))
     => ( A_4 = bot_bo844097828e_bool ) ) ).

tff(fact_504_le__bot,axiom,
    ! [A_4: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool))
     => ( A_4 = bot_bot_fun_com_bool ) ) ).

tff(fact_505_le__bot,axiom,
    ! [A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool))
     => ( hBOOL(A_4)
      <=> hBOOL(bot_bot_bool) ) ) ).

tff(fact_506_le__bot,axiom,
    ! [A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),bot_bo39439654e_bool))
     => ( A_4 = bot_bo39439654e_bool ) ) ).

tff(fact_507_bot__unique,axiom,
    ! [A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),bot_bo844097828e_bool))
    <=> ( A_4 = bot_bo844097828e_bool ) ) ).

tff(fact_508_bot__unique,axiom,
    ! [A_4: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A_4),bot_bot_fun_com_bool))
    <=> ( A_4 = bot_bot_fun_com_bool ) ) ).

tff(fact_509_bot__unique,axiom,
    ! [A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),bot_bot_bool))
    <=> ( hBOOL(A_4)
      <=> hBOOL(bot_bot_bool) ) ) ).

tff(fact_510_bot__unique,axiom,
    ! [A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),bot_bo39439654e_bool))
    <=> ( A_4 = bot_bo39439654e_bool ) ) ).

tff(fact_511_bot__least,axiom,
    ! [A_4: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_4)) ).

tff(fact_512_bot__least,axiom,
    ! [A_4: fun_com_bool] : hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,bot_bot_fun_com_bool),A_4)) ).

tff(fact_513_bot__least,axiom,
    ! [A_4: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_4)) ).

tff(fact_514_bot__least,axiom,
    ! [A_4: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,bot_bo39439654e_bool),A_4)) ).

tff(fact_515_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_516_le__funE,axiom,
    ! [X_1: hoare_363350478_state,F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1645464494e_bool(F,X_1)),hAPP_H1645464494e_bool(G,X_1))) ) ).

tff(fact_517_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_518_le__funD,axiom,
    ! [X_1: hoare_363350478_state,F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1645464494e_bool(F,X_1)),hAPP_H1645464494e_bool(G,X_1))) ) ).

tff(fact_519_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_520_le__fun__def,axiom,
    ! [F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,F),G))
    <=> ! [X_2: hoare_363350478_state] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1645464494e_bool(F,X_2)),hAPP_H1645464494e_bool(G,X_2))) ) ).

tff(fact_521_bot__apply,axiom,
    ! [X_1: pname] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_522_bot__apply,axiom,
    ! [X_1: com] :
      ( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_523_bot__apply,axiom,
    ! [X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(bot_bo39439654e_bool,X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_524_bot__fun__def,axiom,
    ! [X_2: pname] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_2))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_525_bot__fun__def,axiom,
    ! [X_2: com] :
      ( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_526_bot__fun__def,axiom,
    ! [X_2: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(bot_bo39439654e_bool,X_2))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_527_finite__pointwise,axiom,
    ! [P_1: fun_fu1022316450e_bool,Q_1: fun_fu1022316450e_bool,G_2: fun_Ho320143120e_bool,P_3: fun_fu1022316450e_bool,C0_1: fun_fu78728705ol_com,Q_3: fun_fu1022316450e_bool,U_1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1))
     => ( ! [P_4: fun_pname_bool] :
            ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_f887530048e_bool(P_3,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_3,P_4))),bot_bo39439654e_bool)))
           => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_f887530048e_bool(P_1,P_4)),hAPP_f792846925ol_com(C0_1,P_4)),hAPP_f887530048e_bool(Q_1,P_4))),bot_bo39439654e_bool))) )
       => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1912490857e_bool(image_431763259_state(hAPP_f2070959648_state(hAPP_f820078872_state(cOMBS_444947014_state,hAPP_f926121585_state(hAPP_f907647536_state(cOMBS_1636274867_state,hAPP_f1215319405_state(cOMBB_151548708e_bool(hoare_608330478_state),P_3)),C0_1)),Q_3)),U_1)))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1912490857e_bool(image_431763259_state(hAPP_f2070959648_state(hAPP_f820078872_state(cOMBS_444947014_state,hAPP_f926121585_state(hAPP_f907647536_state(cOMBS_1636274867_state,hAPP_f1215319405_state(cOMBB_151548708e_bool(hoare_608330478_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).

tff(fact_528_finite__pointwise,axiom,
    ! [P_1: fun_fu1232608556e_bool,Q_1: fun_fu1232608556e_bool,G_2: fun_Ho320143120e_bool,P_3: fun_fu1232608556e_bool,C0_1: fun_fu1203007991ol_com,Q_3: fun_fu1232608556e_bool,U_1: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,U_1))
     => ( ! [P_4: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_f877220222e_bool(P_3,P_4)),hAPP_f1577230223ol_com(C0_1,P_4)),hAPP_f877220222e_bool(Q_3,P_4))),bot_bo39439654e_bool)))
           => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_f877220222e_bool(P_1,P_4)),hAPP_f1577230223ol_com(C0_1,P_4)),hAPP_f877220222e_bool(Q_1,P_4))),bot_bo39439654e_bool))) )
       => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1180969799e_bool(image_2021386777_state(hAPP_f605405862_state(hAPP_f1593397690_state(cOMBS_1452472386_state,hAPP_f153770241_state(hAPP_f2014973160_state(cOMBS_319359663_state,hAPP_f1323754599_state(cOMBB_188465958e_bool(hoare_608330478_state),P_3)),C0_1)),Q_3)),U_1)))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1180969799e_bool(image_2021386777_state(hAPP_f605405862_state(hAPP_f1593397690_state(cOMBS_1452472386_state,hAPP_f153770241_state(hAPP_f2014973160_state(cOMBS_319359663_state,hAPP_f1323754599_state(cOMBB_188465958e_bool(hoare_608330478_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).

tff(fact_529_finite__pointwise,axiom,
    ! [P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,G_2: fun_Ho320143120e_bool,P_3: fun_pn12888928e_bool,C0_1: fun_pname_com,Q_3: fun_pn12888928e_bool,U_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1))
     => ( ! [P_4: pname] :
            ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_p1637813682e_bool(P_3,P_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_3,P_4))),bot_bo39439654e_bool)))
           => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_p1637813682e_bool(P_1,P_4)),hAPP_pname_com(C0_1,P_4)),hAPP_p1637813682e_bool(Q_1,P_4))),bot_bo39439654e_bool))) )
       => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_3)),C0_1)),Q_3)),U_1)))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),C0_1)),Q_1)),U_1))) ) ) ) ).

tff(fact_530_escape,axiom,
    ! [G_2: fun_Ho320143120e_bool,C: com,Q_1: fun_st1506752259e_bool,P_1: fun_st1506752259e_bool] :
      ( ! [Z_2: state,S_1: state] :
          ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
         => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S_1))),C),hAPP_f1863945078e_bool(cOMBK_631994958_state,hAPP_s1806633685e_bool(Q_1,Z_2)))),bot_bo39439654e_bool))) )
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ).

tff(fact_531_Body__sound__lemma,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_pn12888928e_bool,Q_1: fun_pn12888928e_bool,Procs: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_501514600_state(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),body_1)),Q_1)),Procs))),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),hAPP_f96342628me_com(cOMBB_923936821_pname(the_com),body))),Q_1)),Procs)))
     => hBOOL(hAPP_f568432088l_bool(hoare_501514600_state(G_2),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,hAPP_f387017471_state(cOMBB_1212270426_pname(hoare_608330478_state),P_1)),body_1)),Q_1)),Procs))) ) ).

tff(fact_532_conseq1,axiom,
    ! [P_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool,P_3: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_3),C),Q_1)),bot_bo39439654e_bool)))
     => ( ! [Z_2: state,S_1: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
           => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_2),S_1)) )
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ) ).

tff(fact_533_conseq2,axiom,
    ! [Q_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool,C: com,Q_3: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_3)),bot_bo39439654e_bool)))
     => ( ! [Z_2: state,S_1: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_2),S_1))
           => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_1)) )
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ) ).

tff(fact_534_MGF__complete,axiom,
    ! [P_1: fun_st1506752259e_bool,Q_1: fun_st1506752259e_bool,C: com] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(bot_bo39439654e_bool),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,C)),bot_bo39439654e_bool)))
     => ( hBOOL(hAPP_f568432088l_bool(hoare_501514600_state(bot_bo39439654e_bool),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool)))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(bot_bo39439654e_bool),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ) ).

tff(fact_535_sup1E,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1))
     => ( ~ hBOOL(hAPP_pname_bool(A,X_1))
       => hBOOL(hAPP_pname_bool(B,X_1)) ) ) ).

tff(fact_536_sup1E,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B),X_1))
     => ( ~ hBOOL(hAPP_H1645464494e_bool(A,X_1))
       => hBOOL(hAPP_H1645464494e_bool(B,X_1)) ) ) ).

tff(fact_537_sup1CI,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,X_1: pname] :
      ( ( ~ hBOOL(hAPP_pname_bool(B,X_1))
       => hBOOL(hAPP_pname_bool(A,X_1)) )
     => hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).

tff(fact_538_sup1CI,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( ( ~ hBOOL(hAPP_H1645464494e_bool(B,X_1))
       => hBOOL(hAPP_H1645464494e_bool(A,X_1)) )
     => hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B),X_1)) ) ).

tff(fact_539_conseq12,axiom,
    ! [Q_1: fun_st1506752259e_bool,P_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool,P_3: fun_st1506752259e_bool,C: com,Q_3: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_3),C),Q_3)),bot_bo39439654e_bool)))
     => ( ! [Z_2: state,S_1: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
           => ! [S_2: state] :
                ( ! [Z_3: state] :
                    ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_3,Z_3),S_1))
                   => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_3,Z_3),S_2)) )
               => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)) ) )
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ) ).

tff(fact_540_hoare__sound,axiom,
    ! [G_2: fun_Ho320143120e_bool,Ts: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),Ts))
     => hBOOL(hAPP_f568432088l_bool(hoare_501514600_state(G_2),Ts)) ) ).

tff(fact_541_bot__empty__eq,axiom,
    ! [X_2: com] :
      ( hBOOL(hAPP_com_bool(bot_bot_fun_com_bool,X_2))
    <=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),bot_bot_fun_com_bool)) ) ).

tff(fact_542_bot__empty__eq,axiom,
    ! [X_2: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(bot_bo39439654e_bool,X_2))
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),bot_bo39439654e_bool)) ) ).

tff(fact_543_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_544_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_545_rev__predicate1D,axiom,
    ! [Q_1: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(P_1,X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,P_1),Q_1))
       => hBOOL(hAPP_H1645464494e_bool(Q_1,X_1)) ) ) ).

tff(fact_546_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_547_predicate1D,axiom,
    ! [X_1: hoare_363350478_state,P_1: fun_Ho320143120e_bool,Q_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,P_1),Q_1))
     => ( hBOOL(hAPP_H1645464494e_bool(P_1,X_1))
       => hBOOL(hAPP_H1645464494e_bool(Q_1,X_1)) ) ) ).

tff(fact_548_sup1I2,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(B,X_1))
     => hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).

tff(fact_549_sup1I2,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(B,X_1))
     => hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B),X_1)) ) ).

tff(fact_550_sup1I1,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(A,X_1))
     => hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B),X_1)) ) ).

tff(fact_551_sup1I1,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(A,X_1))
     => hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B),X_1)) ) ).

tff(fact_552_pred__subset__eq,axiom,
    ! [R_1: fun_com_bool,S: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)))
    <=> hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,R_1),S)) ) ).

tff(fact_553_pred__subset__eq,axiom,
    ! [R_1: fun_Ho320143120e_bool,S: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),R_1)),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),S)))
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,R_1),S)) ) ).

tff(fact_554_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_555_sup__Un__eq,axiom,
    ! [R_1: fun_com_bool,S: fun_com_bool,X_2: com] :
      ( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2))
    <=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,R_1),S))) ) ).

tff(fact_556_sup__Un__eq,axiom,
    ! [R_1: fun_Ho320143120e_bool,S: fun_Ho320143120e_bool,X_2: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),R_1)),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),S)),X_2))
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,R_1),S))) ) ).

tff(fact_557_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_558_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_559_le__funI,axiom,
    ! [F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H1645464494e_bool(F,X_2)),hAPP_H1645464494e_bool(G,X_2)))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,F),G)) ) ).

tff(fact_560_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: pname] : set_pname(hAPP_p1252095976_pname(some_pname,X_1)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) ).

tff(fact_561_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: com] : set_com(hAPP_com_option_com(some_com,X_1)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool) ).

tff(fact_562_Option_Oset_Osimps_I2_J,axiom,
    ! [X_1: hoare_363350478_state] : set_Ho1327198534_state(hAPP_H1942146718_state(some_H629028223_state,X_1)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool) ).

tff(fact_563_sup__apply,axiom,
    ! [F: fun_pname_bool,G: fun_pname_bool,X_1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G,X_1))) ) ).

tff(fact_564_sup__apply,axiom,
    ! [F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool,X_1: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,F),G),X_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1645464494e_bool(F,X_1)),hAPP_H1645464494e_bool(G,X_1))) ) ).

tff(fact_565_sup__fun__def,axiom,
    ! [F: fun_pname_bool,G: fun_pname_bool,X_2: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,F),G),X_2))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_pname_bool(F,X_2)),hAPP_pname_bool(G,X_2))) ) ).

tff(fact_566_sup__fun__def,axiom,
    ! [F: fun_Ho320143120e_bool,G: fun_Ho320143120e_bool,X_2: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,F),G),X_2))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_H1645464494e_bool(F,X_2)),hAPP_H1645464494e_bool(G,X_2))) ) ).

tff(fact_567_single__stateE,axiom,
    ( hBOOL(hoare_265376576gleton)
   => ! [T_2: state] :
        ~ ! [S_1: state] : S_1 = T_2 ) ).

tff(fact_568_sup__eq__bot__iff,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = bot_bo844097828e_bool )
    <=> ( ( X_1 = bot_bo844097828e_bool )
        & ( Y_2 = bot_bo844097828e_bool ) ) ) ).

tff(fact_569_sup__eq__bot__iff,axiom,
    ! [X_1: fun_com_bool,Y_2: fun_com_bool] :
      ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),Y_2) = bot_bot_fun_com_bool )
    <=> ( ( X_1 = bot_bot_fun_com_bool )
        & ( Y_2 = bot_bot_fun_com_bool ) ) ) ).

tff(fact_570_sup__eq__bot__iff,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
      <=> hBOOL(bot_bot_bool) )
    <=> ( ( hBOOL(X_1)
        <=> hBOOL(bot_bot_bool) )
        & ( hBOOL(Y_2)
        <=> hBOOL(bot_bot_bool) ) ) ) ).

tff(fact_571_sup__eq__bot__iff,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = bot_bo39439654e_bool )
    <=> ( ( X_1 = bot_bo39439654e_bool )
        & ( Y_2 = bot_bo39439654e_bool ) ) ) ).

tff(fact_572_elem__set,axiom,
    ! [X_1: com,Xo: option_com] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),set_com(Xo)))
    <=> ( Xo = hAPP_com_option_com(some_com,X_1) ) ) ).

tff(fact_573_elem__set,axiom,
    ! [X_1: hoare_363350478_state,Xo: option131732143_state] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),set_Ho1327198534_state(Xo)))
    <=> ( Xo = hAPP_H1942146718_state(some_H629028223_state,X_1) ) ) ).

tff(fact_574_elem__set,axiom,
    ! [X_1: pname,Xo: option_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),set_pname(Xo)))
    <=> ( Xo = hAPP_p1252095976_pname(some_pname,X_1) ) ) ).

tff(fact_575_sup_Oidem,axiom,
    ! [A_4: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),A_4) = A_4 ).

tff(fact_576_sup_Oidem,axiom,
    ! [A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),A_4))
    <=> hBOOL(A_4) ) ).

tff(fact_577_sup_Oidem,axiom,
    ! [A_4: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),A_4) = A_4 ).

tff(fact_578_sup__idem,axiom,
    ! [X_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1 ).

tff(fact_579_sup__idem,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1))
    <=> hBOOL(X_1) ) ).

tff(fact_580_sup__idem,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),X_1) = X_1 ).

tff(fact_581_sup_Ocommute,axiom,
    ! [A_4: fun_pname_bool,B_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),A_4) ).

tff(fact_582_sup_Ocommute,axiom,
    ! [A_4: bool,B_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),A_4)) ) ).

tff(fact_583_sup_Ocommute,axiom,
    ! [A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B_1),A_4) ).

tff(fact_584_inf__sup__aci_I5_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1) ).

tff(fact_585_inf__sup__aci_I5_J,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)) ) ).

tff(fact_586_inf__sup__aci_I5_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),X_1) ).

tff(fact_587_sup__commute,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1) ).

tff(fact_588_sup__commute,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)) ) ).

tff(fact_589_sup__commute,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),X_1) ).

tff(fact_590_sup_Oleft__idem,axiom,
    ! [A_4: fun_pname_bool,B_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1) ).

tff(fact_591_sup_Oleft__idem,axiom,
    ! [A_4: bool,B_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)) ) ).

tff(fact_592_sup_Oleft__idem,axiom,
    ! [A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1) ).

tff(fact_593_inf__sup__aci_I8_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) ).

tff(fact_594_inf__sup__aci_I8_J,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) ) ).

tff(fact_595_inf__sup__aci_I8_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) ).

tff(fact_596_sup__left__idem,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) ).

tff(fact_597_sup__left__idem,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)) ) ).

tff(fact_598_sup__left__idem,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) ).

tff(fact_599_sup_Oleft__commute,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,C: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),C)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C)) ).

tff(fact_600_sup_Oleft__commute,axiom,
    ! [B_1: bool,A_4: bool,C: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),C)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ).

tff(fact_601_sup_Oleft__commute,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,C: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),C)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B_1),C)) ).

tff(fact_602_inf__sup__aci_I7_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).

tff(fact_603_inf__sup__aci_I7_J,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).

tff(fact_604_inf__sup__aci_I7_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Z)) ).

tff(fact_605_sup__left__commute,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).

tff(fact_606_sup__left__commute,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).

tff(fact_607_sup__left__commute,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Z)) ).

tff(fact_608_sup_Oassoc,axiom,
    ! [A_4: fun_pname_bool,B_1: fun_pname_bool,C: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),C) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C)) ).

tff(fact_609_sup_Oassoc,axiom,
    ! [A_4: bool,B_1: bool,C: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),C))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ).

tff(fact_610_sup_Oassoc,axiom,
    ! [A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,C: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)),C) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B_1),C)) ).

tff(fact_611_inf__sup__aci_I6_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) ).

tff(fact_612_inf__sup__aci_I6_J,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) ) ).

tff(fact_613_inf__sup__aci_I6_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),Z) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) ).

tff(fact_614_sup__assoc,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),Z) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) ).

tff(fact_615_sup__assoc,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z))) ) ).

tff(fact_616_sup__assoc,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),Z) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) ).

tff(fact_617_inf__sup__ord_I3_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2))) ).

tff(fact_618_inf__sup__ord_I3_J,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).

tff(fact_619_inf__sup__ord_I3_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2))) ).

tff(fact_620_sup__ge1,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2))) ).

tff(fact_621_sup__ge1,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).

tff(fact_622_sup__ge1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2))) ).

tff(fact_623_inf__sup__ord_I4_J,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).

tff(fact_624_inf__sup__ord_I4_J,axiom,
    ! [Y_2: bool,X_1: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).

tff(fact_625_inf__sup__ord_I4_J,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2))) ).

tff(fact_626_sup__ge2,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2))) ).

tff(fact_627_sup__ge2,axiom,
    ! [Y_2: bool,X_1: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))) ).

tff(fact_628_sup__ge2,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2))) ).

tff(fact_629_le__iff__sup,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_630_le__iff__sup,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
      <=> hBOOL(Y_2) ) ) ).

tff(fact_631_le__iff__sup,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
    <=> ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_632_le__sup__iff,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2)),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_2),Z)) ) ) ).

tff(fact_633_le__sup__iff,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),Z))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)) ) ) ).

tff(fact_634_le__sup__iff,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),Z))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Z))
        & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),Z)) ) ) ).

tff(fact_635_le__supI1,axiom,
    ! [B_1: fun_pname_bool,X_1: fun_pname_bool,A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1))) ) ).

tff(fact_636_le__supI1,axiom,
    ! [B_1: bool,X_1: bool,A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))) ) ).

tff(fact_637_le__supI1,axiom,
    ! [B_1: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),A_4))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1))) ) ).

tff(fact_638_le__supI2,axiom,
    ! [A_4: 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_4),B_1))) ) ).

tff(fact_639_le__supI2,axiom,
    ! [A_4: bool,X_1: bool,B_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1))) ) ).

tff(fact_640_le__supI2,axiom,
    ! [A_4: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),B_1))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1))) ) ).

tff(fact_641_sup__absorb2,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_642_sup__absorb2,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
      <=> hBOOL(Y_2) ) ) ).

tff(fact_643_sup__absorb2,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_644_sup__absorb1,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_645_sup__absorb1,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2))
      <=> hBOOL(X_1) ) ) ).

tff(fact_646_sup__absorb1,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_647_le__supI,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),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_4),B_1)),X_1)) ) ) ).

tff(fact_648_le__supI,axiom,
    ! [B_1: bool,A_4: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1)) ) ) ).

tff(fact_649_le__supI,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),X_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)),X_1)) ) ) ).

tff(fact_650_sup__least,axiom,
    ! [Z: fun_pname_bool,Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),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_2),Z)),X_1)) ) ) ).

tff(fact_651_sup__least,axiom,
    ! [Z: bool,Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1)) ) ) ).

tff(fact_652_sup__least,axiom,
    ! [Z: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Z),X_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)),X_1)) ) ) ).

tff(fact_653_sup__mono,axiom,
    ! [B_1: fun_pname_bool,D_1: fun_pname_bool,A_4: fun_pname_bool,C: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C),D_1))) ) ) ).

tff(fact_654_sup__mono,axiom,
    ! [B_1: bool,D_1: bool,A_4: bool,C: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,C),D_1))) ) ) ).

tff(fact_655_sup__mono,axiom,
    ! [B_1: fun_Ho320143120e_bool,D_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,C: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),C))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),D_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,C),D_1))) ) ) ).

tff(fact_656_le__supE,axiom,
    ! [A_4: 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_4),B_1)),X_1))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_1)) ) ) ).

tff(fact_657_le__supE,axiom,
    ! [A_4: bool,B_1: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),X_1))
     => ~ ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
         => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1)) ) ) ).

tff(fact_658_le__supE,axiom,
    ! [A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)),X_1))
     => ~ ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),X_1))
         => ~ hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),X_1)) ) ) ).

tff(fact_659_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_660_sup__bot__left,axiom,
    ! [X_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,bot_bot_fun_com_bool),X_1) = X_1 ).

tff(fact_661_sup__bot__left,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,bot_bot_bool),X_1))
    <=> hBOOL(X_1) ) ).

tff(fact_662_sup__bot__left,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,bot_bo39439654e_bool),X_1) = X_1 ).

tff(fact_663_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_664_sup__bot__right,axiom,
    ! [X_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,X_1),bot_bot_fun_com_bool) = X_1 ).

tff(fact_665_sup__bot__right,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),bot_bot_bool))
    <=> hBOOL(X_1) ) ).

tff(fact_666_sup__bot__right,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),bot_bo39439654e_bool) = X_1 ).

tff(fact_667_ospec,axiom,
    ! [X_1: pname,P_1: fun_pname_bool,A: option_pname] :
      ( ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),set_pname(A)))
         => hBOOL(hAPP_pname_bool(P_1,X_2)) )
     => ( ( A = hAPP_p1252095976_pname(some_pname,X_1) )
       => hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).

tff(fact_668_ospec,axiom,
    ! [X_1: hoare_363350478_state,P_1: fun_Ho320143120e_bool,A: option131732143_state] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),set_Ho1327198534_state(A)))
         => hBOOL(hAPP_H1645464494e_bool(P_1,X_2)) )
     => ( ( A = hAPP_H1942146718_state(some_H629028223_state,X_1) )
       => hBOOL(hAPP_H1645464494e_bool(P_1,X_1)) ) ) ).

tff(fact_669_ospec,axiom,
    ! [X_1: com,P_1: fun_com_bool,A: option_com] :
      ( ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),set_com(A)))
         => hBOOL(hAPP_com_bool(P_1,X_2)) )
     => ( ( A = hAPP_com_option_com(some_com,X_1) )
       => hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).

tff(fact_670_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( A != 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),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ).

tff(fact_671_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( A != bot_bo133096688l_bool )
         => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
           => ( ( B != bot_bo133096688l_bool )
             => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1180969799e_bool(Fa,A)),hAPP_f1180969799e_bool(Fa,B)) ) ) ) ) ) ) ).

tff(fact_672_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_com_bool,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( A != bot_bot_fun_com_bool )
         => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
           => ( ( B != bot_bot_fun_com_bool )
             => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ) ) ).

tff(fact_673_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( A != bot_bo39439654e_bool )
         => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
           => ( ( B != bot_bo39439654e_bool )
             => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_f1242401993_state(Fa,A)),hAPP_f1242401993_state(Fa,B)) ) ) ) ) ) ) ).

tff(fact_674_folding__one__idem_Ounion__idem,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( A != 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),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ).

tff(fact_675_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( B != bot_bo1649642514l_bool )
         => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A))
           => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,B)),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A) ) ) ) ) ) ).

tff(fact_676_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( B != bot_bo133096688l_bool )
         => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,B),A))
           => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1180969799e_bool(Fa,B)),hAPP_f1180969799e_bool(Fa,A)) = hAPP_f1180969799e_bool(Fa,A) ) ) ) ) ) ).

tff(fact_677_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_com_bool,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( B != bot_bot_fun_com_bool )
         => ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,B),A))
           => ( hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,B)),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A) ) ) ) ) ) ).

tff(fact_678_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( B != bot_bo39439654e_bool )
         => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A))
           => ( hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_f1242401993_state(Fa,B)),hAPP_f1242401993_state(Fa,A)) = hAPP_f1242401993_state(Fa,A) ) ) ) ) ) ).

tff(fact_679_folding__one__idem_Osubset__idem,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( B != bot_bo844097828e_bool )
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
           => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,B)),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A) ) ) ) ) ) ).

tff(fact_680_hoare__derivs_OSkip,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool] : hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),skip),P_1)),bot_bo39439654e_bool))) ).

tff(fact_681_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( A != bot_bot_fun_com_bool )
         => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) ) ) ) ) ).

tff(fact_682_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( A != bot_bo1649642514l_bool )
         => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) ) ) ) ) ).

tff(fact_683_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( A != bot_bo133096688l_bool )
         => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_1),hAPP_f1180969799e_bool(Fa,A)) ) ) ) ) ).

tff(fact_684_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( A != bot_bo844097828e_bool )
         => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) ) ) ) ) ).

tff(fact_685_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( A != bot_bo39439654e_bool )
         => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),hAPP_f1242401993_state(Fa,A)) ) ) ) ) ).

tff(fact_686_finite__ne__induct,axiom,
    ! [P_1: fun_fu1362071682l_bool,Fa: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,Fa))
     => ( ( Fa != bot_bot_fun_com_bool )
       => ( ! [X_2: com] : hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),bot_bot_fun_com_bool)))
         => ( ! [X_2: com,F_2: fun_com_bool] :
                ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,F_2))
               => ( ( F_2 != bot_bot_fun_com_bool )
                 => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),F_2))
                   => ( hBOOL(hAPP_f990396704l_bool(P_1,F_2))
                     => hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f990396704l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_687_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_2: fun_fu1430349052l_bool] :
                ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
               => ( ( F_2 != bot_bo1649642514l_bool )
                 => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),F_2))
                   => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_688_finite__ne__induct,axiom,
    ! [P_1: fun_fu1972704968l_bool,Fa: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
     => ( ( Fa != bot_bo133096688l_bool )
       => ( ! [X_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f1287348838l_bool(P_1,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_2),bot_bo133096688l_bool)))
         => ( ! [X_2: fun_Ho320143120e_bool,F_2: fun_fu1996308102l_bool] :
                ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,F_2))
               => ( ( F_2 != bot_bo133096688l_bool )
                 => ( ~ hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),F_2))
                   => ( hBOOL(hAPP_f1287348838l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1287348838l_bool(P_1,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1287348838l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_689_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_2: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
               => ( ( F_2 != bot_bo844097828e_bool )
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
                   => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_2))
                     => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_690_finite__ne__induct,axiom,
    ! [P_1: fun_fu1996308102l_bool,Fa: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
     => ( ( Fa != bot_bo39439654e_bool )
       => ( ! [X_2: hoare_363350478_state] : hBOOL(hAPP_f568432088l_bool(P_1,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),bot_bo39439654e_bool)))
         => ( ! [X_2: hoare_363350478_state,F_2: fun_Ho320143120e_bool] :
                ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,F_2))
               => ( ( F_2 != bot_bo39439654e_bool )
                 => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),F_2))
                   => ( hBOOL(hAPP_f568432088l_bool(P_1,F_2))
                     => hBOOL(hAPP_f568432088l_bool(P_1,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f568432088l_bool(P_1,Fa)) ) ) ) ) ).

tff(fact_691_LoopF,axiom,
    ! [G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool,B_1: fun_state_bool,C: com] : hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_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))),hAPP_com_com(while(B_1),C)),P_1)),bot_bo39439654e_bool))) ).

tff(fact_692_Comp,axiom,
    ! [D_1: com,R_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool,P_1: fun_st1506752259e_bool,C: com,Q_1: fun_st1506752259e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool)))
     => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,Q_1),D_1),R_1)),bot_bo39439654e_bool)))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),hAPP_com_com(hAPP_com_fun_com_com(semi,C),D_1)),R_1)),bot_bo39439654e_bool))) ) ) ).

tff(fact_693_WTs__elim__cases_I6_J,axiom,
    ! [B_1: fun_state_bool,C: com] :
      ( hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C)))
     => hBOOL(hAPP_com_bool(wt,C)) ) ).

tff(fact_694_WTs__elim__cases_I4_J,axiom,
    ! [C1: com,C2: com] :
      ( hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2)))
     => ~ ( hBOOL(hAPP_com_bool(wt,C1))
         => ~ hBOOL(hAPP_com_bool(wt,C2)) ) ) ).

tff(fact_695_folding__one__idem_Oidem,axiom,
    ! [X_1: hoare_363350478_state,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),X_1) = X_1 ) ) ).

tff(fact_696_folding__one__idem_Oidem,axiom,
    ! [X_1: pname,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),X_1) = X_1 ) ) ).

tff(fact_697_com_Osimps_I12_J,axiom,
    ! [Com1_3: com,Com2_3: com] : skip != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3) ).

tff(fact_698_com_Osimps_I16_J,axiom,
    ! [Fun_1: fun_state_bool,Com_2: com] : skip != hAPP_com_com(while(Fun_1),Com_2) ).

tff(fact_699_com_Osimps_I13_J,axiom,
    ! [Com1_3: com,Com2_3: com] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_3),Com2_3) != skip ).

tff(fact_700_com_Osimps_I17_J,axiom,
    ! [Fun_1: fun_state_bool,Com_2: com] : hAPP_com_com(while(Fun_1),Com_2) != skip ).

tff(fact_701_com_Osimps_I46_J,axiom,
    ! [Com1_2: com,Com2_2: com,Fun_1: fun_state_bool,Com_2: com] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) != hAPP_com_com(while(Fun_1),Com_2) ).

tff(fact_702_com_Osimps_I47_J,axiom,
    ! [Fun_1: fun_state_bool,Com_2: com,Com1_2: com,Com2_2: com] : hAPP_com_com(while(Fun_1),Com_2) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) ).

tff(fact_703_com_Osimps_I3_J,axiom,
    ! [Com1_2: com,Com2_2: com,Com1_1: com,Com2_1: com] :
      ( ( hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_2),Com2_2) = hAPP_com_com(hAPP_com_fun_com_com(semi,Com1_1),Com2_1) )
    <=> ( ( Com1_2 = Com1_1 )
        & ( Com2_2 = Com2_1 ) ) ) ).

tff(fact_704_com_Osimps_I5_J,axiom,
    ! [Fun: fun_state_bool,Com_1: com,Fun_1: fun_state_bool,Com_2: com] :
      ( ( hAPP_com_com(while(Fun),Com_1) = hAPP_com_com(while(Fun_1),Com_2) )
    <=> ( ( Fun = Fun_1 )
        & ( Com_1 = Com_2 ) ) ) ).

tff(fact_705_com_Osimps_I59_J,axiom,
    ! [Pname_1: pname,Fun: fun_state_bool,Com_1: com] : hAPP_pname_com(body_1,Pname_1) != hAPP_com_com(while(Fun),Com_1) ).

tff(fact_706_com_Osimps_I58_J,axiom,
    ! [Fun: fun_state_bool,Com_1: com,Pname_1: pname] : hAPP_com_com(while(Fun),Com_1) != hAPP_pname_com(body_1,Pname_1) ).

tff(fact_707_While,axiom,
    ! [B_1: fun_state_bool,C: com] :
      ( hBOOL(hAPP_com_bool(wt,C))
     => hBOOL(hAPP_com_bool(wt,hAPP_com_com(while(B_1),C))) ) ).

tff(fact_708_com_Osimps_I49_J,axiom,
    ! [Pname: pname,Com1: com,Com2: com] : hAPP_pname_com(body_1,Pname) != hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2) ).

tff(fact_709_com_Osimps_I48_J,axiom,
    ! [Com1: com,Com2: com,Pname: pname] : hAPP_com_com(hAPP_com_fun_com_com(semi,Com1),Com2) != hAPP_pname_com(body_1,Pname) ).

tff(fact_710_WT_OSemi,axiom,
    ! [C1: com,C0: com] :
      ( hBOOL(hAPP_com_bool(wt,C0))
     => ( hBOOL(hAPP_com_bool(wt,C1))
       => hBOOL(hAPP_com_bool(wt,hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1))) ) ) ).

tff(fact_711_com_Osimps_I18_J,axiom,
    ! [Pname: pname] : skip != hAPP_pname_com(body_1,Pname) ).

tff(fact_712_com_Osimps_I19_J,axiom,
    ! [Pname: pname] : hAPP_pname_com(body_1,Pname) != skip ).

tff(fact_713_WT_OSkip,axiom,
    hBOOL(hAPP_com_bool(wt,skip)) ).

tff(fact_714_folding__one__idem_Oin__idem,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => ( hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) = hAPP_f1276420679ol_com(Fa,A) ) ) ) ) ).

tff(fact_715_folding__one__idem_Oin__idem,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) = hAPP_f1297739591_pname(Fa,A) ) ) ) ) ).

tff(fact_716_folding__one__idem_Oin__idem,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => ( hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),hAPP_f1242401993_state(Fa,A)) = hAPP_f1242401993_state(Fa,A) ) ) ) ) ).

tff(fact_717_folding__one__idem_Oin__idem,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) = hAPP_f674760225e_bool(Fa,A) ) ) ) ) ).

tff(fact_718_folding__one__idem_Oin__idem,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),A))
         => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_1),hAPP_f1180969799e_bool(Fa,A)) = hAPP_f1180969799e_bool(Fa,A) ) ) ) ) ).

tff(fact_719_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_fu1430349052l_bool,H_1: fun_fu410713561e_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( ! [X_2: fun_pname_bool,Y_3: fun_pname_bool] : hAPP_f759274231e_bool(H_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f759274231e_bool(H_1,X_2)),hAPP_f759274231e_bool(H_1,Y_3))
       => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,N))
         => ( ( N != bot_bo1649642514l_bool )
           => ( hAPP_f759274231e_bool(H_1,hAPP_f674760225e_bool(Fa,N)) = hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(image_2063528359e_bool(H_1),N)) ) ) ) ) ) ).

tff(fact_720_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_fu1996308102l_bool,H_1: fun_fu1066574909e_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(H_1,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_2),Y_3)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1749453397e_bool(H_1,X_2)),hAPP_f1749453397e_bool(H_1,Y_3))
       => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,N))
         => ( ( N != bot_bo133096688l_bool )
           => ( hAPP_f1749453397e_bool(H_1,hAPP_f1180969799e_bool(Fa,N)) = hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(image_1332939013e_bool(H_1),N)) ) ) ) ) ) ).

tff(fact_721_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_pname_bool,H_1: fun_pname_pname,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( ! [X_2: pname,Y_3: pname] : hAPP_pname_pname(H_1,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_pname_pname(H_1,X_2)),hAPP_pname_pname(H_1,Y_3))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,N))
         => ( ( N != bot_bo844097828e_bool )
           => ( hAPP_pname_pname(H_1,hAPP_f1297739591_pname(Fa,N)) = hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(image_pname_pname(H_1),N)) ) ) ) ) ) ).

tff(fact_722_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_Ho320143120e_bool,H_1: fun_Ho901937921_state,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( ! [X_2: hoare_363350478_state,Y_3: hoare_363350478_state] : hAPP_H1982017439_state(H_1,hAPP_H1982017439_state(hAPP_H230141040_state(F,X_2),Y_3)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_H1982017439_state(H_1,X_2)),hAPP_H1982017439_state(H_1,Y_3))
       => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,N))
         => ( ( N != bot_bo39439654e_bool )
           => ( hAPP_H1982017439_state(H_1,hAPP_f1242401993_state(Fa,N)) = hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(image_2068641359_state(H_1),N)) ) ) ) ) ) ).

tff(fact_723_folding__one__idem_Ohom__commute,axiom,
    ! [N: fun_com_bool,H_1: fun_com_com,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( ! [X_2: com,Y_3: com] : hAPP_com_com(H_1,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_com_com(H_1,X_2)),hAPP_com_com(H_1,Y_3))
       => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,N))
         => ( ( N != bot_bot_fun_com_bool )
           => ( hAPP_com_com(H_1,hAPP_f1276420679ol_com(Fa,N)) = hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(image_com_com(H_1),N)) ) ) ) ) ) ).

tff(fact_724_the__elem__def,axiom,
    ! [X_4: fun_com_bool] : hAPP_f1276420679ol_com(the_elem_com,X_4) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1998868198m_bool(cOMBB_298914627ol_com(hAPP_f273696895l_bool(fequal_fun_com_bool,X_4)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool))) ).

tff(fact_725_the__elem__def,axiom,
    ! [X_4: fun_pname_bool] : hAPP_f1297739591_pname(the_elem_pname,X_4) = hAPP_f1297739591_pname(the_pname,hAPP_f42430548e_bool(cOMBB_530759491_pname(hAPP_f434788991l_bool(fequal533582459e_bool,X_4)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))) ).

tff(fact_726_the__elem__def,axiom,
    ! [X_4: fun_Ho320143120e_bool] : hAPP_f1242401993_state(the_el1666657391_state,X_4) = hAPP_f1242401993_state(the_Ho1653144541_state,hAPP_f265222234e_bool(cOMBB_1356223341_state(hAPP_f726209793l_bool(fequal731041167e_bool,X_4)),hAPP_f596150574e_bool(hAPP_f961492031e_bool(cOMBC_1774708299e_bool,insert1330351828_state),bot_bo39439654e_bool))) ).

tff(fact_727_folding__one_Oinsert,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => ( ( A != bot_bot_fun_com_bool )
           => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,A)) ) ) ) ) ) ).

tff(fact_728_folding__one_Oinsert,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => ( ( A != bot_bo844097828e_bool )
           => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,A)) ) ) ) ) ) ).

tff(fact_729_folding__one_Oinsert,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => ( ( A != bot_bo39439654e_bool )
           => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),hAPP_f1242401993_state(Fa,A)) ) ) ) ) ) ).

tff(fact_730_folding__one_Oinsert,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => ( ( A != bot_bo1649642514l_bool )
           => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,A)) ) ) ) ) ) ).

tff(fact_731_folding__one_Oinsert,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ~ hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),A))
         => ( ( A != bot_bo133096688l_bool )
           => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_1),hAPP_f1180969799e_bool(Fa,A)) ) ) ) ) ) ).

tff(fact_732_triple_Oexhaust,axiom,
    ! [Y_2: hoare_363350478_state] :
      ~ ! [Fun1: fun_st1506752259e_bool,Com: com,Fun2: fun_st1506752259e_bool] : Y_2 != hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,Fun1),Com),Fun2) ).

tff(fact_733_folding__one_Osingleton,axiom,
    ! [X_1: com,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = X_1 ) ) ).

tff(fact_734_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_735_folding__one_Osingleton,axiom,
    ! [X_1: hoare_363350478_state,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) = X_1 ) ) ).

tff(fact_736_folding__one_Oclosed,axiom,
    ! [A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( A != bot_bot_fun_com_bool )
         => ( ! [X_2: com,Y_3: com] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_com_com(hAPP_com_fun_com_com(F,X_2),Y_3)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_2),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,Y_3),bot_bot_fun_com_bool))))
           => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,hAPP_f1276420679ol_com(Fa,A)),A)) ) ) ) ) ).

tff(fact_737_folding__one_Oclosed,axiom,
    ! [A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( A != bot_bo844097828e_bool )
         => ( ! [X_2: pname,Y_3: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_3),bot_bo844097828e_bool))))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(Fa,A)),A)) ) ) ) ) ).

tff(fact_738_folding__one_Oclosed,axiom,
    ! [A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( A != bot_bo39439654e_bool )
         => ( ! [X_2: hoare_363350478_state,Y_3: hoare_363350478_state] : hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_H1982017439_state(hAPP_H230141040_state(F,X_2),Y_3)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,Y_3),bot_bo39439654e_bool))))
           => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_f1242401993_state(Fa,A)),A)) ) ) ) ) ).

tff(fact_739_folding__one_Oclosed,axiom,
    ! [A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( A != bot_bo1649642514l_bool )
         => ( ! [X_2: fun_pname_bool,Y_3: fun_pname_bool] : hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_2),Y_3)),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_2),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,Y_3),bot_bo1649642514l_bool))))
           => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,hAPP_f674760225e_bool(Fa,A)),A)) ) ) ) ) ).

tff(fact_740_folding__one_Oclosed,axiom,
    ! [A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( A != bot_bo133096688l_bool )
         => ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool] : hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_2),Y_3)),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_2),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,Y_3),bot_bo133096688l_bool))))
           => hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,hAPP_f1180969799e_bool(Fa,A)),A)) ) ) ) ) ).

tff(fact_741_image__cong,axiom,
    ! [F: fun_pn1262351275_state,G: fun_pn1262351275_state,M_1: fun_pname_bool,N: fun_pname_bool] :
      ( ( M_1 = N )
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),N))
           => ( hAPP_p1337579261_state(F,X_2) = hAPP_p1337579261_state(G,X_2) ) )
       => ( hAPP_f1763243027e_bool(image_1918575693_state(F),M_1) = hAPP_f1763243027e_bool(image_1918575693_state(G),N) ) ) ) ).

tff(fact_742_Collect__mono,axiom,
    ! [Q_1: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_H1645464494e_bool(P_1,X_2))
         => hBOOL(hAPP_H1645464494e_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(collec223185785_state,P_1)),hAPP_f1749453397e_bool(collec223185785_state,Q_1))) ) ).

tff(fact_743_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_744_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_745_Collect__mono,axiom,
    ! [Q_1: fun_fu1996308102l_bool,P_1: fun_fu1996308102l_bool] :
      ( ! [X_2: fun_Ho320143120e_bool] :
          ( hBOOL(hAPP_f568432088l_bool(P_1,X_2))
         => hBOOL(hAPP_f568432088l_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,hAPP_f85652879l_bool(collec1243131813e_bool,P_1)),hAPP_f85652879l_bool(collec1243131813e_bool,Q_1))) ) ).

tff(fact_746_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_747_predicate1I,axiom,
    ! [Q_1: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool] :
      ( ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_H1645464494e_bool(P_1,X_2))
         => hBOOL(hAPP_H1645464494e_bool(Q_1,X_2)) )
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,P_1),Q_1)) ) ).

tff(fact_748_mk__disjoint__insert,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
     => ? [B_2: fun_com_bool] :
          ( ( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B_2) )
          & ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),B_2)) ) ) ).

tff(fact_749_mk__disjoint__insert,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
     => ? [B_2: fun_pname_bool] :
          ( ( A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B_2) )
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),B_2)) ) ) ).

tff(fact_750_mk__disjoint__insert,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
     => ? [B_2: fun_Ho320143120e_bool] :
          ( ( A = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B_2) )
          & ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),B_2)) ) ) ).

tff(fact_751_Set_Oset__insert,axiom,
    ! [X_1: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ~ ! [B_2: fun_com_bool] :
            ( ( A = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B_2) )
           => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B_2)) ) ) ).

tff(fact_752_Set_Oset__insert,axiom,
    ! [X_1: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ~ ! [B_2: fun_pname_bool] :
            ( ( A = 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_753_Set_Oset__insert,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ~ ! [B_2: fun_Ho320143120e_bool] :
            ( ( A = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),B_2) )
           => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B_2)) ) ) ).

tff(fact_754_equals0I,axiom,
    ! [A: fun_com_bool] :
      ( ! [Y_3: com] : ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Y_3),A))
     => ( A = bot_bot_fun_com_bool ) ) ).

tff(fact_755_equals0I,axiom,
    ! [A: fun_pname_bool] :
      ( ! [Y_3: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Y_3),A))
     => ( A = bot_bo844097828e_bool ) ) ).

tff(fact_756_equals0I,axiom,
    ! [A: fun_Ho320143120e_bool] :
      ( ! [Y_3: hoare_363350478_state] : ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,Y_3),A))
     => ( A = bot_bo39439654e_bool ) ) ).

tff(fact_757_MGT__alternD,axiom,
    ! [G_2: fun_Ho320143120e_bool,C: com] :
      ( hBOOL(hoare_265376576gleton)
     => ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_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_bo39439654e_bool)))
       => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,C)),bot_bo39439654e_bool))) ) ) ).

tff(fact_758_xt1_I15_J,axiom,
    ! [C: bool,F: fun_bool_bool,B_1: bool,A_4: bool] :
      ( ( hBOOL(A_4)
      <=> hBOOL(hAPP_bool_bool(F,B_1)) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),B_1))
       => ( ! [X_2: bool,Y_3: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,C)),A_4)) ) ) ) ).

tff(fact_759_xt1_I15_J,axiom,
    ! [C: fun_pname_bool,A_4: fun_pname_bool,F: fun_fu410713561e_bool,B_1: fun_pname_bool] :
      ( ( A_4 = 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_3: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2))
             => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2))) )
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,C)),A_4)) ) ) ) ).

tff(fact_760_xt1_I15_J,axiom,
    ! [C: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,F: fun_fu1066574909e_bool,B_1: fun_Ho320143120e_bool] :
      ( ( A_4 = hAPP_f1749453397e_bool(F,B_1) )
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C),B_1))
       => ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool] :
              ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_3),X_2))
             => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(F,Y_3)),hAPP_f1749453397e_bool(F,X_2))) )
         => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(F,C)),A_4)) ) ) ) ).

tff(fact_761_MGT__alternI,axiom,
    ! [G_2: fun_Ho320143120e_bool,C: com] :
      ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,C)),bot_bo39439654e_bool)))
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_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_bo39439654e_bool))) ) ).

tff(fact_762_MGT__def,axiom,
    ! [C: com] : hAPP_c1041435779_state(hoare_Mirabelle_MGT,C) = hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,fequal_state),C),evalc(C)) ).

tff(fact_763_evalc__elim__cases_I6_J,axiom,
    ! [P: pname,S_4: state,S1_2: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,P)),S_4),S1_2))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,P))),S_4),S1_2)) ) ).

tff(fact_764_evalc_OBody,axiom,
    ! [Pn: pname,S0_1: state,S1_2: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn))),S0_1),S1_2))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_pname_com(body_1,Pn)),S0_1),S1_2)) ) ).

tff(fact_765_evalc__elim__cases_I1_J,axiom,
    ! [S_4: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),T_1))
     => ( T_1 = S_4 ) ) ).

tff(fact_766_evalc_OSkip,axiom,
    ! [S_4: state] : hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(skip),S_4),S_4)) ).

tff(fact_767_evalc_OSemi,axiom,
    ! [C1: com,S2_1: state,C0: com,S0_1: state,S1_2: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C0),S0_1),S1_2))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S1_2),S2_1))
       => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C0),C1)),S0_1),S2_1)) ) ) ).

tff(fact_768_evalc_OWhileTrue,axiom,
    ! [S2: state,C: com,S1_1: state,B_1: fun_state_bool,S0: state] :
      ( hBOOL(hAPP_state_bool(B_1,S0))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S0),S1_1))
       => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1_1),S2))
         => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S0),S2)) ) ) ) ).

tff(fact_769_evalc_OWhileFalse,axiom,
    ! [C: com,B_1: fun_state_bool,S_3: state] :
      ( ~ hBOOL(hAPP_state_bool(B_1,S_3))
     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),S_3)) ) ).

tff(fact_770_com__det,axiom,
    ! [U: state,C_2: com,S_4: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),T_1))
     => ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C_2),S_4),U))
       => ( U = T_1 ) ) ) ).

tff(fact_771_evalc__elim__cases_I4_J,axiom,
    ! [C1: com,C2: com,S_4: state,T_1: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(hAPP_com_fun_com_com(semi,C1),C2)),S_4),T_1))
     => ~ ! [S1: state] :
            ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C1),S_4),S1))
           => ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C2),S1),T_1)) ) ) ).

tff(fact_772_evalc__WHILE__case,axiom,
    ! [B_1: fun_state_bool,C: com,S_3: state,T: state] :
      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S_3),T))
     => ( ( ( T = S_3 )
         => hBOOL(hAPP_state_bool(B_1,S_3)) )
       => ~ ( hBOOL(hAPP_state_bool(B_1,S_3))
           => ! [S1: state] :
                ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(C),S_3),S1))
               => ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(evalc(hAPP_com_com(while(B_1),C)),S1),T)) ) ) ) ) ).

tff(fact_773_xt1_I16_J,axiom,
    ! [C: bool,F: fun_bool_bool,B_1: bool,A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_4))
     => ( ( hBOOL(hAPP_bool_bool(F,B_1))
        <=> hBOOL(C) )
       => ( ! [X_2: bool,Y_3: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_3),X_2))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_3)),hAPP_bool_bool(F,X_2))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C),hAPP_bool_bool(F,A_4))) ) ) ) ).

tff(fact_774_xt1_I16_J,axiom,
    ! [F: fun_fu410713561e_bool,C: fun_pname_bool,B_1: fun_pname_bool,A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_4))
     => ( ( hAPP_f759274231e_bool(F,B_1) = C )
       => ( ! [X_2: fun_pname_bool,Y_3: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_3),X_2))
             => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(F,Y_3)),hAPP_f759274231e_bool(F,X_2))) )
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),hAPP_f759274231e_bool(F,A_4))) ) ) ) ).

tff(fact_775_xt1_I16_J,axiom,
    ! [F: fun_fu1066574909e_bool,C: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),A_4))
     => ( ( hAPP_f1749453397e_bool(F,B_1) = C )
       => ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool] :
              ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_3),X_2))
             => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(F,Y_3)),hAPP_f1749453397e_bool(F,X_2))) )
         => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C),hAPP_f1749453397e_bool(F,A_4))) ) ) ) ).

tff(fact_776_folding__one_Ounion__inter,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
         => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool )
           => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ).

tff(fact_777_folding__one_Ounion__inter,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
         => ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B) != bot_bo133096688l_bool )
           => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B))),hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B))) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1180969799e_bool(Fa,A)),hAPP_f1180969799e_bool(Fa,B)) ) ) ) ) ) ).

tff(fact_778_folding__one_Ounion__inter,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
         => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) != bot_bo844097828e_bool )
           => ( hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B))),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ).

tff(fact_779_folding__one_Ounion__inter,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
         => ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) != bot_bo39439654e_bool )
           => ( hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B))),hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B))) = hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_f1242401993_state(Fa,A)),hAPP_f1242401993_state(Fa,B)) ) ) ) ) ) ).

tff(fact_780_folding__one_Ounion__inter,axiom,
    ! [B: fun_com_bool,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
         => ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) != bot_bot_fun_com_bool )
           => ( hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B))),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ) ).

tff(fact_781_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( A != bot_bo1649642514l_bool )
         => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
           => ( ( B != bot_bo1649642514l_bool )
             => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool )
               => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,hAPP_f674760225e_bool(Fa,A)),hAPP_f674760225e_bool(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_782_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( A != bot_bo133096688l_bool )
         => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
           => ( ( B != bot_bo133096688l_bool )
             => ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B) = bot_bo133096688l_bool )
               => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,hAPP_f1180969799e_bool(Fa,A)),hAPP_f1180969799e_bool(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_783_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( A != bot_bo844097828e_bool )
         => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
           => ( ( B != bot_bo844097828e_bool )
             => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool )
               => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(Fa,A)),hAPP_f1297739591_pname(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_784_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( A != bot_bo39439654e_bool )
         => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
           => ( ( B != bot_bo39439654e_bool )
             => ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = bot_bo39439654e_bool )
               => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,hAPP_f1242401993_state(Fa,A)),hAPP_f1242401993_state(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_785_folding__one_Ounion__disjoint,axiom,
    ! [B: fun_com_bool,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( A != bot_bot_fun_com_bool )
         => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,B))
           => ( ( B != bot_bot_fun_com_bool )
             => ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool )
               => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B)) = hAPP_com_com(hAPP_com_fun_com_com(F,hAPP_f1276420679ol_com(Fa,A)),hAPP_f1276420679ol_com(Fa,B)) ) ) ) ) ) ) ) ).

tff(fact_786_folding__one_Oinsert__remove,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool )
           => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = X_1 ) )
          & ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool )
           => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))) ) ) ) ) ) ).

tff(fact_787_folding__one_Oinsert__remove,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),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)) = X_1 ) )
          & ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),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)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ).

tff(fact_788_folding__one_Oinsert__remove,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) = bot_bo39439654e_bool )
           => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = X_1 ) )
          & ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) != bot_bo39439654e_bool )
           => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)))) ) ) ) ) ) ).

tff(fact_789_folding__one_Oinsert__remove,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),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)) = X_1 ) )
          & ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),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)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ).

tff(fact_790_folding__one_Oinsert__remove,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)) = bot_bo133096688l_bool )
           => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),A)) = X_1 ) )
          & ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)) != bot_bo133096688l_bool )
           => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_1),hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)))) ) ) ) ) ) ).

tff(fact_791_folding__one_Oremove,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => ( ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = bot_bot_fun_com_bool )
             => ( hAPP_f1276420679ol_com(Fa,A) = X_1 ) )
            & ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) != bot_bot_fun_com_bool )
             => ( hAPP_f1276420679ol_com(Fa,A) = hAPP_com_com(hAPP_com_fun_com_com(F,X_1),hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)))) ) ) ) ) ) ) ).

tff(fact_792_folding__one_Oremove,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => ( ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
             => ( hAPP_f1297739591_pname(Fa,A) = X_1 ) )
            & ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool )
             => ( hAPP_f1297739591_pname(Fa,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ) ) ) ) ) ).

tff(fact_793_folding__one_Oremove,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => ( ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) = bot_bo39439654e_bool )
             => ( hAPP_f1242401993_state(Fa,A) = X_1 ) )
            & ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) != bot_bo39439654e_bool )
             => ( hAPP_f1242401993_state(Fa,A) = hAPP_H1982017439_state(hAPP_H230141040_state(F,X_1),hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)))) ) ) ) ) ) ) ).

tff(fact_794_folding__one_Oremove,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => ( ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) = bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(Fa,A) = X_1 ) )
            & ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)) != bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(Fa,A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(F,X_1),hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),bot_bo1649642514l_bool)))) ) ) ) ) ) ) ).

tff(fact_795_folding__one_Oremove,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),A))
         => ( ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)) = bot_bo133096688l_bool )
             => ( hAPP_f1180969799e_bool(Fa,A) = X_1 ) )
            & ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)) != bot_bo133096688l_bool )
             => ( hAPP_f1180969799e_bool(Fa,A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(F,X_1),hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),bot_bo133096688l_bool)))) ) ) ) ) ) ) ).

tff(fact_796_is__none__code_I2_J,axiom,
    ! [X_3: pname] : ~ hBOOL(is_none_pname(hAPP_p1252095976_pname(some_pname,X_3))) ).

tff(fact_797_is__none__code_I2_J,axiom,
    ! [X_3: hoare_363350478_state] : ~ hBOOL(is_non965104584_state(hAPP_H1942146718_state(some_H629028223_state,X_3))) ).

tff(fact_798_is__none__code_I2_J,axiom,
    ! [X_3: com] : ~ hBOOL(is_none_com(hAPP_com_option_com(some_com,X_3))) ).

tff(fact_799_conseq,axiom,
    ! [Q_1: fun_st1506752259e_bool,G_2: fun_Ho320143120e_bool,C: com,P_1: fun_st1506752259e_bool] :
      ( ! [Z_2: state,S_1: state] :
          ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S_1))
         => ? [P_2: fun_st1506752259e_bool,Q_2: fun_st1506752259e_bool] :
              ( hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_2),C),Q_2)),bot_bo39439654e_bool)))
              & ! [S_2: state] :
                  ( ! [Z_3: state] :
                      ( hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_3),S_1))
                     => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_3),S_2)) )
                 => hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_2)) ) ) )
     => hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(G_2),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_f83715540_state(hAPP_c1279058753_state(hAPP_f960042659_state(hoare_608330478_state,P_1),C),Q_1)),bot_bo39439654e_bool))) ) ).

tff(fact_800_IntE,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
     => ~ ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
         => ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_801_IntE,axiom,
    ! [C: pname,A: 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),B)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_802_IntE,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)))
     => ~ ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
         => ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_803_IntI,axiom,
    ! [B: fun_com_bool,C: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B))) ) ) ).

tff(fact_804_IntI,axiom,
    ! [B: fun_pname_bool,C: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
     => ( 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),B))) ) ) ).

tff(fact_805_IntI,axiom,
    ! [B: fun_Ho320143120e_bool,C: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B))) ) ) ).

tff(fact_806_DiffE,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
     => ~ ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_807_DiffE,axiom,
    ! [C: pname,A: 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),B)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_808_DiffE,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)))
     => ~ ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_809_DiffI,axiom,
    ! [B: fun_com_bool,C: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
     => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B))
       => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) ) ) ).

tff(fact_810_DiffI,axiom,
    ! [B: fun_pname_bool,C: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
     => ( ~ 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),B))) ) ) ).

tff(fact_811_DiffI,axiom,
    ! [B: fun_Ho320143120e_bool,C: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
     => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B))) ) ) ).

tff(fact_812_finite__Int,axiom,
    ! [G_2: fun_fu1430349052l_bool,Fa: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,G_2)) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,Fa),G_2))) ) ).

tff(fact_813_finite__Int,axiom,
    ! [G_2: fun_fu1996308102l_bool,Fa: fun_fu1996308102l_bool] :
      ( ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,Fa))
        | hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,G_2)) )
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,Fa),G_2))) ) ).

tff(fact_814_finite__Int,axiom,
    ! [G_2: fun_pname_bool,Fa: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,G_2)) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Fa),G_2))) ) ).

tff(fact_815_finite__Int,axiom,
    ! [G_2: fun_Ho320143120e_bool,Fa: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,Fa))
        | hBOOL(hAPP_f568432088l_bool(finite280062779_state,G_2)) )
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Fa),G_2))) ) ).

tff(fact_816_finite__Diff,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))) ) ).

tff(fact_817_finite__Diff,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),B))) ) ).

tff(fact_818_finite__Diff,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ).

tff(fact_819_finite__Diff,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B))) ) ).

tff(fact_820_inf__Int__eq,axiom,
    ! [R_1: fun_com_bool,S: fun_com_bool,X_2: com] :
      ( hBOOL(hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),R_1)),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),S)),X_2))
    <=> hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,R_1),S))) ) ).

tff(fact_821_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_822_inf__Int__eq,axiom,
    ! [R_1: fun_Ho320143120e_bool,S: fun_Ho320143120e_bool,X_2: hoare_363350478_state] :
      ( hBOOL(hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),R_1)),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),S)),X_2))
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,R_1),S))) ) ).

tff(fact_823_Diff__disjoint,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A)) = bot_bot_fun_com_bool ).

tff(fact_824_Diff__disjoint,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = bot_bo844097828e_bool ).

tff(fact_825_Diff__disjoint,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),A)) = bot_bo39439654e_bool ).

tff(fact_826_Diff__triv,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] :
      ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool )
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = A ) ) ).

tff(fact_827_Diff__triv,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool )
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = A ) ) ).

tff(fact_828_Diff__triv,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = bot_bo39439654e_bool )
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B) = A ) ) ).

tff(fact_829_DiffD2,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
     => ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ).

tff(fact_830_DiffD2,axiom,
    ! [C: pname,A: 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),B)))
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).

tff(fact_831_DiffD2,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)))
     => ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ).

tff(fact_832_IntD2,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ).

tff(fact_833_IntD2,axiom,
    ! [C: pname,A: 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),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ).

tff(fact_834_IntD2,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ).

tff(fact_835_IntD1,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) ) ).

tff(fact_836_IntD1,axiom,
    ! [C: pname,A: 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),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).

tff(fact_837_IntD1,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A)) ) ).

tff(fact_838_DiffD1,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
     => hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A)) ) ).

tff(fact_839_DiffD1,axiom,
    ! [C: pname,A: 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),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) ) ).

tff(fact_840_DiffD1,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)))
     => hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A)) ) ).

tff(fact_841_Int__iff,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)))
    <=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
        & hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_842_Int__iff,axiom,
    ! [C: pname,A: 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),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_843_Int__iff,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
        & hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_844_Diff__iff,axiom,
    ! [C: com,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)))
    <=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),A))
        & ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,C),B)) ) ) ).

tff(fact_845_Diff__iff,axiom,
    ! [C: pname,A: 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),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B)) ) ) ).

tff(fact_846_Diff__iff,axiom,
    ! [C: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),A))
        & ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,C),B)) ) ) ).

tff(fact_847_Int__def,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B))) ).

tff(fact_848_Int__def,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),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))),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B))) ).

tff(fact_849_Int__def,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),B))) ).

tff(fact_850_Int__def,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),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))),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B))) ).

tff(fact_851_Int__def,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),A))),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),B))) ).

tff(fact_852_set__diff__eq,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) = hAPP_f1682609283m_bool(collect_com,hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,hAPP_f954469007l_bool(cOMBB_886968260ol_com(fconj),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),A))),hAPP_f1682609283m_bool(cOMBB_bool_bool_com(fNot),hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),B)))) ).

tff(fact_853_set__diff__eq,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),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))),hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),B)))) ).

tff(fact_854_set__diff__eq,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B) = hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),A))),hAPP_f1749453397e_bool(cOMBB_2059354034_state(fNot),hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),B)))) ).

tff(fact_855_set__diff__eq,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),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))),hAPP_f559147733l_bool(cOMBB_307249310e_bool(fNot),hAPP_f559147733l_bool(hAPP_f1145991873l_bool(cOMBC_1988546018l_bool,member799430823e_bool),B)))) ).

tff(fact_856_set__diff__eq,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),B) = hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),A))),hAPP_f85652879l_bool(cOMBB_941362220e_bool(fNot),hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,member1534059107e_bool),B)))) ).

tff(fact_857_Int__Collect,axiom,
    ! [X_1: com,A: fun_com_bool,P_1: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1))))
    <=> ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
        & hBOOL(hAPP_com_bool(P_1,X_1)) ) ) ).

tff(fact_858_Int__Collect,axiom,
    ! [X_1: pname,A: 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),hAPP_f759274231e_bool(collect_pname,P_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
        & hBOOL(hAPP_pname_bool(P_1,X_1)) ) ) ).

tff(fact_859_Int__Collect,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(collec223185785_state,P_1))))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
        & hBOOL(hAPP_H1645464494e_bool(P_1,X_1)) ) ) ).

tff(fact_860_Int__Collect,axiom,
    ! [X_1: fun_pname_bool,A: 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),hAPP_f559147733l_bool(collec1974731493e_bool,P_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
        & hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ) ).

tff(fact_861_Int__Collect,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,P_1: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),hAPP_f85652879l_bool(collec1243131813e_bool,P_1))))
    <=> ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),A))
        & hBOOL(hAPP_f568432088l_bool(P_1,X_1)) ) ) ).

tff(fact_862_Collect__conj__eq,axiom,
    ! [P_1: fun_Ho320143120e_bool,Q_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(collec223185785_state,hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,hAPP_f1422032445l_bool(cOMBB_877416532_state(fconj),P_1)),Q_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(collec223185785_state,P_1)),hAPP_f1749453397e_bool(collec223185785_state,Q_1)) ).

tff(fact_863_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_864_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_865_Collect__conj__eq,axiom,
    ! [P_1: fun_fu1996308102l_bool,Q_1: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(collec1243131813e_bool,hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,hAPP_f945781379l_bool(cOMBB_1004232970e_bool(fconj),P_1)),Q_1)) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,hAPP_f85652879l_bool(collec1243131813e_bool,P_1)),hAPP_f85652879l_bool(collec1243131813e_bool,Q_1)) ).

tff(fact_866_Diff__Int,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)) ).

tff(fact_867_Diff__Int,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),C_1)) ).

tff(fact_868_Diff__Un,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)) ).

tff(fact_869_Diff__Un,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),C_1)) ).

tff(fact_870_Un__Diff__Int,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = A ).

tff(fact_871_Un__Diff__Int,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)) = A ).

tff(fact_872_inf__sup__ord_I1_J,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1)) ).

tff(fact_873_inf__sup__ord_I1_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1)) ).

tff(fact_874_inf__sup__ord_I1_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),X_1)) ).

tff(fact_875_inf__le1,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),X_1)) ).

tff(fact_876_inf__le1,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),X_1)) ).

tff(fact_877_inf__le1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),X_1)) ).

tff(fact_878_inf__sup__ord_I2_J,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2)) ).

tff(fact_879_inf__sup__ord_I2_J,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2)) ).

tff(fact_880_inf__sup__ord_I2_J,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),Y_2)) ).

tff(fact_881_inf__le2,axiom,
    ! [X_1: bool,Y_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),Y_2)) ).

tff(fact_882_inf__le2,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),Y_2)) ).

tff(fact_883_inf__le2,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),Y_2)) ).

tff(fact_884_le__iff__inf,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
      <=> hBOOL(X_1) ) ) ).

tff(fact_885_le__iff__inf,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
    <=> ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_886_le__iff__inf,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
    <=> ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_887_le__inf__iff,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z)) ) ) ).

tff(fact_888_le__inf__iff,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2),Z)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Z)) ) ) ).

tff(fact_889_le__inf__iff,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z)))
    <=> ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
        & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Z)) ) ) ).

tff(fact_890_le__infI1,axiom,
    ! [B_1: bool,A_4: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),X_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)) ) ).

tff(fact_891_le__infI1,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),X_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),X_1)) ) ).

tff(fact_892_le__infI1,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),X_1))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1)),X_1)) ) ).

tff(fact_893_le__infI2,axiom,
    ! [A_4: bool,B_1: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),X_1)) ) ).

tff(fact_894_le__infI2,axiom,
    ! [A_4: 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_4),B_1)),X_1)) ) ).

tff(fact_895_le__infI2,axiom,
    ! [A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),X_1))
     => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1)),X_1)) ) ).

tff(fact_896_inf__absorb1,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
      <=> hBOOL(X_1) ) ) ).

tff(fact_897_inf__absorb1,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_898_inf__absorb1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2) = X_1 ) ) ).

tff(fact_899_inf__absorb2,axiom,
    ! [Y_2: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_1))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2))
      <=> hBOOL(Y_2) ) ) ).

tff(fact_900_inf__absorb2,axiom,
    ! [Y_2: fun_pname_bool,X_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_901_inf__absorb2,axiom,
    ! [Y_2: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,Y_2),X_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2) = Y_2 ) ) ).

tff(fact_902_le__infI,axiom,
    ! [B_1: bool,X_1: bool,A_4: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1))) ) ) ).

tff(fact_903_le__infI,axiom,
    ! [B_1: fun_pname_bool,X_1: fun_pname_bool,A_4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
     => ( 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_4),B_1))) ) ) ).

tff(fact_904_le__infI,axiom,
    ! [B_1: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),A_4))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),B_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1))) ) ) ).

tff(fact_905_inf__greatest,axiom,
    ! [Z: bool,X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Z))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))) ) ) ).

tff(fact_906_inf__greatest,axiom,
    ! [Z: fun_pname_bool,X_1: fun_pname_bool,Y_2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),Y_2))
     => ( 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_2),Z))) ) ) ).

tff(fact_907_inf__greatest,axiom,
    ! [Z: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Y_2))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),Z))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z))) ) ) ).

tff(fact_908_inf__mono,axiom,
    ! [B_1: bool,D_1: bool,A_4: bool,C: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_4),C))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),D_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,C),D_1))) ) ) ).

tff(fact_909_inf__mono,axiom,
    ! [B_1: fun_pname_bool,D_1: fun_pname_bool,A_4: fun_pname_bool,C: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_4),C))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),D_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C),D_1))) ) ) ).

tff(fact_910_inf__mono,axiom,
    ! [B_1: fun_Ho320143120e_bool,D_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,C: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_4),C))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),D_1))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,C),D_1))) ) ) ).

tff(fact_911_le__infE,axiom,
    ! [X_1: bool,A_4: bool,B_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1)))
     => ~ ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),A_4))
         => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),B_1)) ) ) ).

tff(fact_912_le__infE,axiom,
    ! [X_1: fun_pname_bool,A_4: 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_4),B_1)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),A_4))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_1),B_1)) ) ) ).

tff(fact_913_le__infE,axiom,
    ! [X_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1)))
     => ~ ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),A_4))
         => ~ hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_1),B_1)) ) ) ).

tff(fact_914_inf__bot__right,axiom,
    ! [X_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,X_1),bot_bot_fun_com_bool) = bot_bot_fun_com_bool ).

tff(fact_915_inf__bot__right,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),bot_bot_bool))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_916_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_917_inf__bot__right,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),bot_bo39439654e_bool) = bot_bo39439654e_bool ).

tff(fact_918_inf__bot__left,axiom,
    ! [X_1: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),X_1) = bot_bot_fun_com_bool ).

tff(fact_919_inf__bot__left,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,bot_bot_bool),X_1))
    <=> hBOOL(bot_bot_bool) ) ).

tff(fact_920_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_921_inf__bot__left,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,bot_bo39439654e_bool),X_1) = bot_bo39439654e_bool ).

tff(fact_922_inf__sup__absorb,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)))
    <=> hBOOL(X_1) ) ).

tff(fact_923_inf__sup__absorb,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)) = X_1 ).

tff(fact_924_inf__sup__absorb,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)) = X_1 ).

tff(fact_925_sup__inf__absorb,axiom,
    ! [X_1: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)))
    <=> hBOOL(X_1) ) ).

tff(fact_926_sup__inf__absorb,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)) = X_1 ).

tff(fact_927_sup__inf__absorb,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)) = X_1 ).

tff(fact_928_inf__sup__distrib1,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))) ) ).

tff(fact_929_inf__sup__distrib1,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z)) ).

tff(fact_930_inf__sup__distrib1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Z)) ).

tff(fact_931_sup__inf__distrib1,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ).

tff(fact_932_sup__inf__distrib1,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ).

tff(fact_933_sup__inf__distrib1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Z)) ).

tff(fact_934_inf__sup__distrib2,axiom,
    ! [Y_2: bool,Z: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)),X_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Z),X_1))) ) ).

tff(fact_935_inf__sup__distrib2,axiom,
    ! [Y_2: fun_pname_bool,Z: fun_pname_bool,X_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Z),X_1)) ).

tff(fact_936_inf__sup__distrib2,axiom,
    ! [Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)),X_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),X_1)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Z),X_1)) ).

tff(fact_937_sup__inf__distrib2,axiom,
    ! [Y_2: bool,Z: bool,X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)),X_1))
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),X_1)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Z),X_1))) ) ).

tff(fact_938_sup__inf__distrib2,axiom,
    ! [Y_2: fun_pname_bool,Z: fun_pname_bool,X_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)),X_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),X_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Z),X_1)) ).

tff(fact_939_sup__inf__distrib2,axiom,
    ! [Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool,X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z)),X_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),X_1)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Z),X_1)) ).

tff(fact_940_Diff__cancel,axiom,
    ! [A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),A) = bot_bot_fun_com_bool ).

tff(fact_941_Diff__cancel,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A) = bot_bo844097828e_bool ).

tff(fact_942_Diff__cancel,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),A) = bot_bo39439654e_bool ).

tff(fact_943_Diff__empty,axiom,
    ! [A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),bot_bot_fun_com_bool) = A ).

tff(fact_944_Diff__empty,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),bot_bo844097828e_bool) = A ).

tff(fact_945_Diff__empty,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),bot_bo39439654e_bool) = A ).

tff(fact_946_empty__Diff,axiom,
    ! [A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,bot_bot_fun_com_bool),A) = bot_bot_fun_com_bool ).

tff(fact_947_empty__Diff,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,bot_bo844097828e_bool),A) = bot_bo844097828e_bool ).

tff(fact_948_empty__Diff,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,bot_bo39439654e_bool),A) = bot_bo39439654e_bool ).

tff(fact_949_finite__Diff2,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B)))
      <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).

tff(fact_950_finite__Diff2,axiom,
    ! [A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),B)))
      <=> hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A)) ) ) ).

tff(fact_951_finite__Diff2,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
      <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).

tff(fact_952_finite__Diff2,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,B))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)))
      <=> hBOOL(hAPP_f568432088l_bool(finite280062779_state,A)) ) ) ).

tff(fact_953_insert__Diff1,axiom,
    ! [A: fun_com_bool,X_1: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) ) ) ).

tff(fact_954_insert__Diff1,axiom,
    ! [A: fun_pname_bool,X_1: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) ) ) ).

tff(fact_955_insert__Diff1,axiom,
    ! [A: fun_Ho320143120e_bool,X_1: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)),B) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B) ) ) ).

tff(fact_956_insert__Diff__if,axiom,
    ! [A: fun_com_bool,X_1: com,B: fun_com_bool] :
      ( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B) ) )
      & ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),B))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),B) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)) ) ) ) ).

tff(fact_957_insert__Diff__if,axiom,
    ! [A: fun_pname_bool,X_1: pname,B: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) ) ) ) ).

tff(fact_958_insert__Diff__if,axiom,
    ! [A: fun_Ho320143120e_bool,X_1: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)),B) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B) ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),B))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)),B) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)) ) ) ) ).

tff(fact_959_disjoint__iff__not__equal,axiom,
    ! [A: fun_com_bool,B: fun_com_bool] :
      ( ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) = bot_bot_fun_com_bool )
    <=> ! [X_2: com] :
          ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
         => ! [Xa: com] :
              ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,Xa),B))
             => ( X_2 != Xa ) ) ) ) ).

tff(fact_960_disjoint__iff__not__equal,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = bot_bo844097828e_bool )
    <=> ! [X_2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => ! [Xa: pname] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Xa),B))
             => ( X_2 != Xa ) ) ) ) ).

tff(fact_961_disjoint__iff__not__equal,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = bot_bo39439654e_bool )
    <=> ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
         => ! [Xa: hoare_363350478_state] :
              ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,Xa),B))
             => ( X_2 != Xa ) ) ) ) ).

tff(fact_962_Int__empty__right,axiom,
    ! [A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),bot_bot_fun_com_bool) = bot_bot_fun_com_bool ).

tff(fact_963_Int__empty__right,axiom,
    ! [A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),bot_bo844097828e_bool) = bot_bo844097828e_bool ).

tff(fact_964_Int__empty__right,axiom,
    ! [A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),bot_bo39439654e_bool) = bot_bo39439654e_bool ).

tff(fact_965_Int__empty__left,axiom,
    ! [B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,bot_bot_fun_com_bool),B) = bot_bot_fun_com_bool ).

tff(fact_966_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_967_Int__empty__left,axiom,
    ! [B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,bot_bo39439654e_bool),B) = bot_bo39439654e_bool ).

tff(fact_968_double__diff,axiom,
    ! [C_1: fun_pname_bool,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),A)) = A ) ) ) ).

tff(fact_969_double__diff,axiom,
    ! [C_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),C_1))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,C_1),A)) = A ) ) ) ).

tff(fact_970_Diff__mono,axiom,
    ! [D: fun_pname_bool,B: fun_pname_bool,A: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,D),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,C_1),D))) ) ) ).

tff(fact_971_Diff__mono,axiom,
    ! [D: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),C_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,D),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,C_1),D))) ) ) ).

tff(fact_972_Diff__subset,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),A)) ).

tff(fact_973_Diff__subset,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),A)) ).

tff(fact_974_Un__Diff,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),C_1)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),C_1)) ).

tff(fact_975_Un__Diff,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),C_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),C_1)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),C_1)) ).

tff(fact_976_Un__Diff__cancel2,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A) ).

tff(fact_977_Un__Diff__cancel2,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),A)),A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),A) ).

tff(fact_978_Un__Diff__cancel,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) ).

tff(fact_979_Un__Diff__cancel,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) ).

tff(fact_980_Int__insert__left__if1,axiom,
    ! [B: fun_com_bool,A_4: com,C_1: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)) ) ) ).

tff(fact_981_Int__insert__left__if1,axiom,
    ! [B: fun_pname_bool,A_4: pname,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) ) ).

tff(fact_982_Int__insert__left__if1,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),C_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)),C_1) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1)) ) ) ).

tff(fact_983_Int__insert__right__if1,axiom,
    ! [B: fun_com_bool,A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) ) ) ).

tff(fact_984_Int__insert__right__if1,axiom,
    ! [B: fun_pname_bool,A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) ) ) ).

tff(fact_985_Int__insert__right__if1,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)) ) ) ).

tff(fact_986_Int__insert__left__if0,axiom,
    ! [B: fun_com_bool,A_4: com,C_1: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1) ) ) ).

tff(fact_987_Int__insert__left__if0,axiom,
    ! [B: fun_pname_bool,A_4: pname,C_1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ).

tff(fact_988_Int__insert__left__if0,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,C_1: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),C_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)),C_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1) ) ) ).

tff(fact_989_Int__insert__right__if0,axiom,
    ! [B: fun_com_bool,A_4: com,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) ) ) ).

tff(fact_990_Int__insert__right__if0,axiom,
    ! [B: fun_pname_bool,A_4: pname,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) ) ) ).

tff(fact_991_Int__insert__right__if0,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) ) ) ).

tff(fact_992_insert__inter__insert,axiom,
    ! [A_4: com,A: fun_com_bool,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) ).

tff(fact_993_insert__inter__insert,axiom,
    ! [A_4: pname,A: fun_pname_bool,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) ).

tff(fact_994_insert__inter__insert,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)) ).

tff(fact_995_Int__insert__left,axiom,
    ! [B: fun_com_bool,A_4: com,C_1: fun_com_bool] :
      ( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1)) ) )
      & ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),C_1))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)),C_1) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),C_1) ) ) ) ).

tff(fact_996_Int__insert__left,axiom,
    ! [B: fun_pname_bool,A_4: pname,C_1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),C_1))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1) ) ) ) ).

tff(fact_997_Int__insert__left,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,C_1: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),C_1))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)),C_1) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1)) ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),C_1))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)),C_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1) ) ) ) ).

tff(fact_998_Int__insert__right,axiom,
    ! [B: fun_com_bool,A_4: com,A: fun_com_bool] :
      ( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B)) ) )
      & ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
       => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),B) ) ) ) ).

tff(fact_999_Int__insert__right,axiom,
    ! [B: fun_pname_bool,A_4: pname,A: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) ) ) ) ).

tff(fact_1000_Int__insert__right,axiom,
    ! [B: fun_Ho320143120e_bool,A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)) ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
       => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) ) ) ) ).

tff(fact_1001_Int__mono,axiom,
    ! [B: fun_pname_bool,D: fun_pname_bool,A: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),D))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),D))) ) ) ).

tff(fact_1002_Int__mono,axiom,
    ! [B: fun_Ho320143120e_bool,D: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),C_1))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),D))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,C_1),D))) ) ) ).

tff(fact_1003_Int__greatest,axiom,
    ! [B: fun_pname_bool,C_1: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A))
     => ( 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),B))) ) ) ).

tff(fact_1004_Int__greatest,axiom,
    ! [B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_1),A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_1),B))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B))) ) ) ).

tff(fact_1005_Int__absorb1,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = B ) ) ).

tff(fact_1006_Int__absorb1,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B),A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = B ) ) ).

tff(fact_1007_Int__absorb2,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B) = A ) ) ).

tff(fact_1008_Int__absorb2,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B) = A ) ) ).

tff(fact_1009_Int__lower2,axiom,
    ! [A: 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),B)),B)) ).

tff(fact_1010_Int__lower2,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),B)) ).

tff(fact_1011_Int__lower1,axiom,
    ! [A: 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),B)),A)) ).

tff(fact_1012_Int__lower1,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),A)) ).

tff(fact_1013_Un__Int__crazy,axiom,
    ! [A: 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(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).

tff(fact_1014_Un__Int__crazy,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,C_1),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,C_1),A)) ).

tff(fact_1015_Un__Int__distrib2,axiom,
    ! [B: fun_pname_bool,C_1: fun_pname_bool,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,C_1),A)) ).

tff(fact_1016_Un__Int__distrib2,axiom,
    ! [B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1)),A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),A)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,C_1),A)) ).

tff(fact_1017_Int__Un__distrib2,axiom,
    ! [B: fun_pname_bool,C_1: fun_pname_bool,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,C_1),A)) ).

tff(fact_1018_Int__Un__distrib2,axiom,
    ! [B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)),A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),A)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,C_1),A)) ).

tff(fact_1019_Un__Int__distrib,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),C_1)) ).

tff(fact_1020_Un__Int__distrib,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),C_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),C_1)) ).

tff(fact_1021_Int__Un__distrib,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),C_1)) ).

tff(fact_1022_Int__Un__distrib,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),C_1)) ).

tff(fact_1023_distrib__inf__le,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))) ).

tff(fact_1024_distrib__inf__le,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2)),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_2),Z)))) ).

tff(fact_1025_distrib__inf__le,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Z))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)))) ).

tff(fact_1026_distrib__sup__le,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z))),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z)))) ).

tff(fact_1027_distrib__sup__le,axiom,
    ! [X_1: fun_pname_bool,Y_2: 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_2),Z))),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)))) ).

tff(fact_1028_distrib__sup__le,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Z)))) ).

tff(fact_1029_insert__Diff,axiom,
    ! [A_4: com,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_4),A))
     => ( hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = A ) ) ).

tff(fact_1030_insert__Diff,axiom,
    ! [A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),A))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = A ) ) ).

tff(fact_1031_insert__Diff,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_4),A))
     => ( hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool))) = A ) ) ).

tff(fact_1032_Diff__insert__absorb,axiom,
    ! [X_1: com,A: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool)) = A ) ) ).

tff(fact_1033_Diff__insert__absorb,axiom,
    ! [X_1: pname,A: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A ) ) ).

tff(fact_1034_Diff__insert__absorb,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool)) = A ) ) ).

tff(fact_1035_insert__Diff__single,axiom,
    ! [A_4: com,A: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A) ).

tff(fact_1036_insert__Diff__single,axiom,
    ! [A_4: pname,A: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A) ).

tff(fact_1037_insert__Diff__single,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool))) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A) ).

tff(fact_1038_Diff__insert2,axiom,
    ! [A: fun_com_bool,A_4: com,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool))),B) ).

tff(fact_1039_Diff__insert2,axiom,
    ! [A: fun_pname_bool,A_4: pname,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))),B) ).

tff(fact_1040_Diff__insert2,axiom,
    ! [A: fun_Ho320143120e_bool,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool))),B) ).

tff(fact_1041_Diff__insert,axiom,
    ! [A: fun_com_bool,A_4: com,B: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B)) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B)),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),bot_bot_fun_com_bool)) ).

tff(fact_1042_Diff__insert,axiom,
    ! [A: fun_pname_bool,A_4: pname,B: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool)) ).

tff(fact_1043_Diff__insert,axiom,
    ! [A: fun_Ho320143120e_bool,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),bot_bo39439654e_bool)) ).

tff(fact_1044_finite__Diff__insert,axiom,
    ! [A: fun_com_bool,A_4: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),B))))
    <=> hBOOL(hAPP_f990396704l_bool(finite_finite_com,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),B))) ) ).

tff(fact_1045_finite__Diff__insert,axiom,
    ! [A: fun_pname_bool,A_4: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),B))))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ).

tff(fact_1046_finite__Diff__insert,axiom,
    ! [A: fun_Ho320143120e_bool,A_4: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),B))))
    <=> hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B))) ) ).

tff(fact_1047_finite__Diff__insert,axiom,
    ! [A: fun_fu1430349052l_bool,A_4: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),B))))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A),B))) ) ).

tff(fact_1048_finite__Diff__insert,axiom,
    ! [A: fun_fu1996308102l_bool,A_4: fun_Ho320143120e_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),B))))
    <=> hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A),B))) ) ).

tff(fact_1049_image__diff__subset,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B))),hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))) ).

tff(fact_1050_Diff__partition,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A)) = B ) ) ).

tff(fact_1051_Diff__partition,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),A)) = B ) ) ).

tff(fact_1052_Diff__subset__conv,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)),C_1))
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1))) ) ).

tff(fact_1053_Diff__subset__conv,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),B)),C_1))
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1))) ) ).

tff(fact_1054_image__Int__subset,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B)))) ).

tff(fact_1055_Un__Int__assoc__eq,axiom,
    ! [A: 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),B)),C_1) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B),C_1)) )
    <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A)) ) ).

tff(fact_1056_Un__Int__assoc__eq,axiom,
    ! [A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool,C_1: fun_Ho320143120e_bool] :
      ( ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),B)),C_1) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B),C_1)) )
    <=> hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,C_1),A)) ) ).

tff(fact_1057_if__image__distrib,axiom,
    ! [P_1: fun_pname_bool,F: fun_pn1262351275_state,G: fun_pn1262351275_state,S: fun_pname_bool] : hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f901668953_state(hAPP_f1521026326_state(cOMBS_113846849_state,hAPP_f1180972108_state(hAPP_f1993951364_state(cOMBS_89825358_state,hAPP_f1418159294_state(cOMBB_1777678681_pname(if_Hoa29189214_state),P_1)),F)),G)),S) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,S),hAPP_f759274231e_bool(collect_pname,P_1)))),hAPP_f1763243027e_bool(image_1918575693_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_1058_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_1059_diff__single__insert,axiom,
    ! [A: fun_com_bool,X_1: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B))
     => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
       => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B))) ) ) ).

tff(fact_1060_diff__single__insert,axiom,
    ! [A: fun_pname_bool,X_1: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) ) ) ).

tff(fact_1061_diff__single__insert,axiom,
    ! [A: fun_Ho320143120e_bool,X_1: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool))),B))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),B))) ) ) ).

tff(fact_1062_subset__insert__iff,axiom,
    ! [A: fun_com_bool,X_1: com,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),B)))
    <=> ( ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),bot_bot_fun_com_bool))),B)) )
        & ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B)) ) ) ) ).

tff(fact_1063_subset__insert__iff,axiom,
    ! [A: fun_pname_bool,X_1: pname,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
    <=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) )
        & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ) ).

tff(fact_1064_subset__insert__iff,axiom,
    ! [A: fun_Ho320143120e_bool,X_1: hoare_363350478_state,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),B)))
    <=> ( ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),bot_bo39439654e_bool))),B)) )
        & ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B)) ) ) ) ).

tff(fact_1065_finite__empty__induct,axiom,
    ! [P_1: fun_fu1362071682l_bool,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => ( hBOOL(hAPP_f990396704l_bool(P_1,A))
       => ( ! [A_2: com,A_7: fun_com_bool] :
              ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A_7))
             => ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,A_2),A_7))
               => ( hBOOL(hAPP_f990396704l_bool(P_1,A_7))
                 => hBOOL(hAPP_f990396704l_bool(P_1,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A_7),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_2),bot_bot_fun_com_bool)))) ) ) )
         => hBOOL(hAPP_f990396704l_bool(P_1,bot_bot_fun_com_bool)) ) ) ) ).

tff(fact_1066_finite__empty__induct,axiom,
    ! [P_1: fun_fu1430349052l_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(P_1,A))
       => ( ! [A_2: pname,A_7: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_7))
             => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_7))
               => ( hBOOL(hAPP_f1664156314l_bool(P_1,A_7))
                 => hBOOL(hAPP_f1664156314l_bool(P_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_7),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool)) ) ) ) ).

tff(fact_1067_finite__empty__induct,axiom,
    ! [P_1: fun_fu1996308102l_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f568432088l_bool(P_1,A))
       => ( ! [A_2: hoare_363350478_state,A_7: fun_Ho320143120e_bool] :
              ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A_7))
             => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,A_2),A_7))
               => ( hBOOL(hAPP_f568432088l_bool(P_1,A_7))
                 => hBOOL(hAPP_f568432088l_bool(P_1,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A_7),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_2),bot_bo39439654e_bool)))) ) ) )
         => hBOOL(hAPP_f568432088l_bool(P_1,bot_bo39439654e_bool)) ) ) ) ).

tff(fact_1068_finite__empty__induct,axiom,
    ! [P_1: fun_fu399576434l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(P_1,A))
       => ( ! [A_2: fun_pname_bool,A_7: fun_fu1430349052l_bool] :
              ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_7))
             => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_7))
               => ( hBOOL(hAPP_f1935102916l_bool(P_1,A_7))
                 => hBOOL(hAPP_f1935102916l_bool(P_1,hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,A_7),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),bot_bo1649642514l_bool)))) ) ) )
         => hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool)) ) ) ) ).

tff(fact_1069_finite__empty__induct,axiom,
    ! [P_1: fun_fu1972704968l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(P_1,A))
       => ( ! [A_2: fun_Ho320143120e_bool,A_7: fun_fu1996308102l_bool] :
              ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A_7))
             => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,A_2),A_7))
               => ( hBOOL(hAPP_f1287348838l_bool(P_1,A_7))
                 => hBOOL(hAPP_f1287348838l_bool(P_1,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,A_7),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_2),bot_bo133096688l_bool)))) ) ) )
         => hBOOL(hAPP_f1287348838l_bool(P_1,bot_bo133096688l_bool)) ) ) ) ).

tff(fact_1070_dom__override__on,axiom,
    ! [F: fun_pname_option_com,G: fun_pname_option_com,A: fun_pname_bool] : dom_pname_com(overri1496249029on_com(F,G,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),dom_pname_com(G)))))),hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),dom_pname_com(G))))) ).

tff(fact_1071_Int__Collect__mono,axiom,
    ! [Q_1: fun_com_bool,P_1: fun_com_bool,A: fun_com_bool,B: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),B))
     => ( ! [X_2: com] :
            ( hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_2),A))
           => ( hBOOL(hAPP_com_bool(P_1,X_2))
             => hBOOL(hAPP_com_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,A),hAPP_f1682609283m_bool(collect_com,P_1))),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila980496562m_bool,B),hAPP_f1682609283m_bool(collect_com,Q_1)))) ) ) ).

tff(fact_1072_Int__Collect__mono,axiom,
    ! [Q_1: fun_pname_bool,P_1: fun_pname_bool,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( ! [X_2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
           => ( 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),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_1073_Int__Collect__mono,axiom,
    ! [Q_1: fun_Ho320143120e_bool,P_1: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool,B: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),B))
     => ( ! [X_2: hoare_363350478_state] :
            ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A))
           => ( hBOOL(hAPP_H1645464494e_bool(P_1,X_2))
             => hBOOL(hAPP_H1645464494e_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A),hAPP_f1749453397e_bool(collec223185785_state,P_1))),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B),hAPP_f1749453397e_bool(collec223185785_state,Q_1)))) ) ) ).

tff(fact_1074_Int__Collect__mono,axiom,
    ! [Q_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
     => ( ! [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
           => ( 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),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_1075_Int__Collect__mono,axiom,
    ! [Q_1: fun_fu1996308102l_bool,P_1: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool,B: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,A),B))
     => ( ! [X_2: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),A))
           => ( hBOOL(hAPP_f568432088l_bool(P_1,X_2))
             => hBOOL(hAPP_f568432088l_bool(Q_1,X_2)) ) )
       => hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),hAPP_f85652879l_bool(collec1243131813e_bool,P_1))),hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,B),hAPP_f85652879l_bool(collec1243131813e_bool,Q_1)))) ) ) ).

tff(fact_1076_distrib__imp2,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( ! [X_2: bool,Y_3: bool,Z_1: bool] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_3),Z_1)))
        <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_2),Z_1))) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_2),Z)))
      <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_1),Z))) ) ) ).

tff(fact_1077_distrib__imp2,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] :
      ( ! [X_2: fun_pname_bool,Y_3: fun_pname_bool,Z_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_2),Z_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_1),Z)) ) ) ).

tff(fact_1078_distrib__imp2,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] :
      ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool,Z_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_3),Z_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_2),Y_3)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_2),Z_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_1),Z)) ) ) ).

tff(fact_1079_distrib__imp1,axiom,
    ! [X_1: bool,Y_2: bool,Z: bool] :
      ( ! [X_2: bool,Y_3: bool,Z_1: bool] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,Y_3),Z_1)))
        <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Y_3)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,X_2),Z_1))) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,Y_2),Z)))
      <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Y_2)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),Z))) ) ) ).

tff(fact_1080_distrib__imp1,axiom,
    ! [X_1: fun_pname_bool,Y_2: fun_pname_bool,Z: fun_pname_bool] :
      ( ! [X_2: fun_pname_bool,Y_3: fun_pname_bool,Z_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,Y_3),Z_1)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Y_3)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,X_2),Z_1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,Y_2),Z)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Y_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),Z)) ) ) ).

tff(fact_1081_distrib__imp1,axiom,
    ! [X_1: fun_Ho320143120e_bool,Y_2: fun_Ho320143120e_bool,Z: fun_Ho320143120e_bool] :
      ( ! [X_2: fun_Ho320143120e_bool,Y_3: fun_Ho320143120e_bool,Z_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,Y_3),Z_1)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_2),Y_3)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,X_2),Z_1))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,Y_2),Z)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Y_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),Z)) ) ) ).

tff(fact_1082_flat__lub__def,axiom,
    ! [A: fun_com_bool,B_1: com] :
      ( ( hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))
       => ( hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = B_1 ) )
      & ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(ord_le1708315510m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))
       => ( hAPP_f1276420679ol_com(partial_flat_lub_com(B_1),A) = hAPP_f1276420679ol_com(the_com_1,hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,member_com),hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,A),hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,B_1),bot_bot_fun_com_bool)))) ) ) ) ).

tff(fact_1083_flat__lub__def,axiom,
    ! [A: fun_pname_bool,B_1: pname] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))
       => ( hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = B_1 ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))
       => ( hAPP_f1297739591_pname(partia752020666_pname(B_1),A) = hAPP_f1297739591_pname(the_pname,hAPP_f759274231e_bool(hAPP_f661147897e_bool(cOMBC_1058051404l_bool,member_pname),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_1),bot_bo844097828e_bool)))) ) ) ) ).

tff(fact_1084_flat__lub__def,axiom,
    ! [A: fun_Ho320143120e_bool,B_1: hoare_363350478_state] :
      ( ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),bot_bo39439654e_bool)))
       => ( hAPP_f1242401993_state(partia2058675160_state(B_1),A) = B_1 ) )
      & ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),bot_bo39439654e_bool)))
       => ( hAPP_f1242401993_state(partia2058675160_state(B_1),A) = hAPP_f1242401993_state(the_Ho1653144541_state,hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,member1253905979_state),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,B_1),bot_bo39439654e_bool)))) ) ) ) ).

tff(fact_1085_comp__fun__idem__remove,axiom,
    hBOOL(finite1653727294m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,minus_59609839m_bool)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool)))) ).

tff(fact_1086_comp__fun__idem__remove,axiom,
    hBOOL(finite2017903282e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,minus_1015773161e_bool)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool)))) ).

tff(fact_1087_comp__fun__idem__remove,axiom,
    hBOOL(finite377806280e_bool(hAPP_f306007574e_bool(cOMBB_1253415543_state(hAPP_f1873524693e_bool(cOMBC_1626046675e_bool,minus_1060678561e_bool)),hAPP_f596150574e_bool(hAPP_f961492031e_bool(cOMBC_1774708299e_bool,insert1330351828_state),bot_bo39439654e_bool)))) ).

tff(fact_1088_fun__upd__image,axiom,
    ! [F: fun_pn1262351275_state,Y_2: hoare_363350478_state,X_1: pname,A: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => ( hAPP_f1763243027e_bool(image_1918575693_state(fun_up641226197_state(F,X_1,Y_2)),A) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,Y_2),hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) )
      & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => ( hAPP_f1763243027e_bool(image_1918575693_state(fun_up641226197_state(F,X_1,Y_2)),A) = hAPP_f1763243027e_bool(image_1918575693_state(F),A) ) ) ) ).

tff(fact_1089_comp__fun__idem__insert,axiom,
    hBOOL(finite1653727294m_bool(insert_com)) ).

tff(fact_1090_comp__fun__idem__insert,axiom,
    hBOOL(finite2017903282e_bool(insert_pname)) ).

tff(fact_1091_comp__fun__idem__insert,axiom,
    hBOOL(finite377806280e_bool(insert1330351828_state)) ).

tff(fact_1092_comp__fun__idem__sup,axiom,
    hBOOL(finite318301748l_bool(semila1168014441p_bool)) ).

tff(fact_1093_comp__fun__idem__sup,axiom,
    hBOOL(finite367769966e_bool(semila278973382e_bool)) ).

tff(fact_1094_comp__fun__idem__sup,axiom,
    hBOOL(finite560903500e_bool(semila1579166468e_bool)) ).

tff(fact_1095_inj__on__Un,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),A))
        & hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),B))
        & ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A))) = bot_bo39439654e_bool ) ) ) ).

tff(fact_1096_dom__eq__singleton__conv,axiom,
    ! [F: fun_pname_option_com,X_1: pname] :
      ( ( dom_pname_com(F) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool) )
    <=> ? [V: com] : F = fun_up879233478on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,none_com),X_1,hAPP_com_option_com(some_com,V)) ) ).

tff(fact_1097_minus__fold__remove,axiom,
    ! [B: fun_com_bool,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(minus_59609839m_bool,B),A) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,minus_59609839m_bool)),hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,insert_com),bot_bot_fun_com_bool))),B),A) ) ) ).

tff(fact_1098_minus__fold__remove,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),A) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,minus_1015773161e_bool)),hAPP_f180827860e_bool(hAPP_f698292281e_bool(cOMBC_1123258281e_bool,insert_pname),bot_bo844097828e_bool))),B),A) ) ) ).

tff(fact_1099_minus__fold__remove,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),A) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(finite1720034636e_bool(hAPP_f306007574e_bool(cOMBB_1253415543_state(hAPP_f1873524693e_bool(cOMBC_1626046675e_bool,minus_1060678561e_bool)),hAPP_f596150574e_bool(hAPP_f961492031e_bool(cOMBC_1774708299e_bool,insert1330351828_state),bot_bo39439654e_bool))),B),A) ) ) ).

tff(fact_1100_minus__fold__remove,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(minus_1290075917l_bool,B),A) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,minus_1290075917l_bool)),hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,insert1325755072e_bool),bot_bo1649642514l_bool))),B),A) ) ) ).

tff(fact_1101_minus__fold__remove,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(minus_1119384757l_bool,B),A) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(finite1820487374l_bool(hAPP_f471491948l_bool(cOMBB_460931425e_bool(hAPP_f103280059l_bool(cOMBC_646647229l_bool,minus_1119384757l_bool)),hAPP_f434845752l_bool(hAPP_f1793815761l_bool(cOMBC_2079418125l_bool,insert975831690e_bool),bot_bo133096688l_bool))),B),A) ) ) ).

tff(fact_1102_image__eq__fold__image,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hAPP_f1763243027e_bool(image_1918575693_state(F),A) = finite517504007_pname(semila1579166468e_bool,hAPP_f265219918e_bool(hAPP_f1853922773e_bool(cOMBC_1001821703e_bool,hAPP_f43306888e_bool(cOMBB_1717464465_pname(insert1330351828_state),F)),bot_bo39439654e_bool),bot_bo39439654e_bool,A) ) ) ).

tff(fact_1103_inj__Some,axiom,
    ! [A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(inj_on737724108_pname(some_pname),A)) ).

tff(fact_1104_inj__Some,axiom,
    ! [A: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(inj_on574065538_state(some_H629028223_state),A)) ).

tff(fact_1105_inj__Some,axiom,
    ! [A: fun_com_bool] : hBOOL(hAPP_f990396704l_bool(inj_on11367768on_com(some_com),A)) ).

tff(fact_1106_option_Osimps_I2_J,axiom,
    ! [A_6: com] : none_com != hAPP_com_option_com(some_com,A_6) ).

tff(fact_1107_option_Osimps_I2_J,axiom,
    ! [A_6: pname] : none_pname != hAPP_p1252095976_pname(some_pname,A_6) ).

tff(fact_1108_option_Osimps_I2_J,axiom,
    ! [A_6: hoare_363350478_state] : none_H1908530691_state != hAPP_H1942146718_state(some_H629028223_state,A_6) ).

tff(fact_1109_option_Osimps_I3_J,axiom,
    ! [A_5: com] : hAPP_com_option_com(some_com,A_5) != none_com ).

tff(fact_1110_option_Osimps_I3_J,axiom,
    ! [A_5: pname] : hAPP_p1252095976_pname(some_pname,A_5) != none_pname ).

tff(fact_1111_option_Osimps_I3_J,axiom,
    ! [A_5: hoare_363350478_state] : hAPP_H1942146718_state(some_H629028223_state,A_5) != none_H1908530691_state ).

tff(fact_1112_not__Some__eq,axiom,
    ! [X_1: option_com] :
      ( ! [Y_3: com] : X_1 != hAPP_com_option_com(some_com,Y_3)
    <=> ( X_1 = none_com ) ) ).

tff(fact_1113_not__Some__eq,axiom,
    ! [X_1: option_pname] :
      ( ! [Y_3: pname] : X_1 != hAPP_p1252095976_pname(some_pname,Y_3)
    <=> ( X_1 = none_pname ) ) ).

tff(fact_1114_not__Some__eq,axiom,
    ! [X_1: option131732143_state] :
      ( ! [Y_3: hoare_363350478_state] : X_1 != hAPP_H1942146718_state(some_H629028223_state,Y_3)
    <=> ( X_1 = none_H1908530691_state ) ) ).

tff(fact_1115_not__None__eq,axiom,
    ! [X_1: option_com] :
      ( ( X_1 != none_com )
    <=> ? [Y_3: com] : X_1 = hAPP_com_option_com(some_com,Y_3) ) ).

tff(fact_1116_not__None__eq,axiom,
    ! [X_1: option_pname] :
      ( ( X_1 != none_pname )
    <=> ? [Y_3: pname] : X_1 = hAPP_p1252095976_pname(some_pname,Y_3) ) ).

tff(fact_1117_not__None__eq,axiom,
    ! [X_1: option131732143_state] :
      ( ( X_1 != none_H1908530691_state )
    <=> ? [Y_3: hoare_363350478_state] : X_1 = hAPP_H1942146718_state(some_H629028223_state,Y_3) ) ).

tff(fact_1118_dom__def,axiom,
    ! [M: fun_pname_option_com] : dom_pname_com(M) = hAPP_f759274231e_bool(collect_pname,hAPP_f759274231e_bool(cOMBB_647938656_pname(fNot),hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,hAPP_f919496731m_bool(cOMBB_418828222_pname(fequal_option_com),M)),none_com))) ).

tff(fact_1119_domIff,axiom,
    ! [A_4: pname,M: fun_pname_option_com] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_4),dom_pname_com(M)))
    <=> ( hAPP_p799580910on_com(M,A_4) != none_com ) ) ).

tff(fact_1120_finite__imageD,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
     => ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),A))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).

tff(fact_1121_inj__on__Un__image__eq__iff,axiom,
    ! [F: fun_pn1262351275_state,A: fun_pname_bool,B: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B)))
     => ( ( hAPP_f1763243027e_bool(image_1918575693_state(F),A) = hAPP_f1763243027e_bool(image_1918575693_state(F),B) )
      <=> ( A = B ) ) ) ).

tff(fact_1122_is__none__def,axiom,
    ! [X_1: option_com] :
      ( hBOOL(is_none_com(X_1))
    <=> ( X_1 = none_com ) ) ).

tff(fact_1123_is__none__code_I1_J,axiom,
    hBOOL(is_none_com(none_com)) ).

tff(fact_1124_inj__on__fun__updI,axiom,
    ! [X_1: pname,Y_2: hoare_363350478_state,F: fun_pn1262351275_state,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),A))
     => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,Y_2),hAPP_f1763243027e_bool(image_1918575693_state(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(fun_up641226197_state(F,X_1,Y_2)),A)) ) ) ).

tff(fact_1125_sup__le__fold__sup,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),B_1)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A))) ) ) ).

tff(fact_1126_sup__le__fold__sup,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,A_4),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),B_1)),hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1579166468e_bool),B_1),A))) ) ) ).

tff(fact_1127_sup__le__fold__sup,axiom,
    ! [B_1: bool,A_4: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),B_1)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A))) ) ) ).

tff(fact_1128_fold__inf__le__inf,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_4),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),B_1))) ) ) ).

tff(fact_1129_fold__inf__le__inf,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,A_4),A))
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1129477150e_bool),B_1),A)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),B_1))) ) ) ).

tff(fact_1130_fold__inf__le__inf,axiom,
    ! [B_1: bool,A_4: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,A_4),A))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),B_1),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,A_4),B_1))) ) ) ).

tff(fact_1131_fold__sup__insert,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),B_1),A)) ) ) ).

tff(fact_1132_fold__sup__insert,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1579166468e_bool),B_1),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A_4),hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1579166468e_bool),B_1),A)) ) ) ).

tff(fact_1133_fold__sup__insert,axiom,
    ! [B_1: bool,A_4: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),hAPP_f961197973l_bool(hAPP_b496459037l_bool(insert_bool,A_4),A)))
      <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,A_4),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),B_1),A))) ) ) ).

tff(fact_1134_fold__inf__insert,axiom,
    ! [B_1: fun_pname_bool,A_4: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A_4),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),B_1),A)) ) ) ).

tff(fact_1135_fold__inf__insert,axiom,
    ! [B_1: fun_Ho320143120e_bool,A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1129477150e_bool),B_1),hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),A)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,A_4),hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1129477150e_bool),B_1),A)) ) ) ).

tff(fact_1136_dom__eq__empty__conv,axiom,
    ! [F: fun_pname_option_com] :
      ( ( dom_pname_com(F) = bot_bo844097828e_bool )
    <=> ! [X_2: pname] : hAPP_p799580910on_com(F,X_2) = none_com ) ).

tff(fact_1137_dom__empty,axiom,
    dom_pname_com(hAPP_o129566686on_com(cOMBK_413306633_pname,none_com)) = bot_bo844097828e_bool ).

tff(fact_1138_Option_Oset_Osimps_I1_J,axiom,
    set_com(none_com) = bot_bot_fun_com_bool ).

tff(fact_1139_Option_Oset_Osimps_I1_J,axiom,
    set_pname(none_pname) = bot_bo844097828e_bool ).

tff(fact_1140_Option_Oset_Osimps_I1_J,axiom,
    set_Ho1327198534_state(none_H1908530691_state) = bot_bo39439654e_bool ).

tff(fact_1141_set__empty__eq,axiom,
    ! [Xo: option_com] :
      ( ( set_com(Xo) = bot_bot_fun_com_bool )
    <=> ( Xo = none_com ) ) ).

tff(fact_1142_set__empty__eq,axiom,
    ! [Xo: option_pname] :
      ( ( set_pname(Xo) = bot_bo844097828e_bool )
    <=> ( Xo = none_pname ) ) ).

tff(fact_1143_set__empty__eq,axiom,
    ! [Xo: option131732143_state] :
      ( ( set_Ho1327198534_state(Xo) = bot_bo39439654e_bool )
    <=> ( Xo = none_H1908530691_state ) ) ).

tff(fact_1144_endo__inj__surj,axiom,
    ! [F: fun_fu410713561e_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,hAPP_f559147733l_bool(image_2063528359e_bool(F),A)),A))
       => ( hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A))
         => ( hAPP_f559147733l_bool(image_2063528359e_bool(F),A) = A ) ) ) ) ).

tff(fact_1145_endo__inj__surj,axiom,
    ! [F: fun_fu1066574909e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,hAPP_f85652879l_bool(image_1332939013e_bool(F),A)),A))
       => ( hBOOL(hAPP_f1287348838l_bool(inj_on938701937e_bool(F),A))
         => ( hAPP_f85652879l_bool(image_1332939013e_bool(F),A) = A ) ) ) ) ).

tff(fact_1146_endo__inj__surj,axiom,
    ! [F: fun_pname_pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(image_pname_pname(F),A)),A))
       => ( hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A))
         => ( hAPP_f759274231e_bool(image_pname_pname(F),A) = A ) ) ) ) ).

tff(fact_1147_endo__inj__surj,axiom,
    ! [F: fun_Ho901937921_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(image_2068641359_state(F),A)),A))
       => ( hBOOL(hAPP_f568432088l_bool(inj_on1943491515_state(F),A))
         => ( hAPP_f1749453397e_bool(image_2068641359_state(F),A) = A ) ) ) ) ).

tff(fact_1148_finite__surj__inj,axiom,
    ! [F: fun_fu410713561e_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),hAPP_f559147733l_bool(image_2063528359e_bool(F),A)))
       => hBOOL(hAPP_f1935102916l_bool(inj_on1490514707e_bool(F),A)) ) ) ).

tff(fact_1149_finite__surj__inj,axiom,
    ! [F: fun_fu1066574909e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(hAPP_f746351743l_bool(ord_le2031828156l_bool,A),hAPP_f85652879l_bool(image_1332939013e_bool(F),A)))
       => hBOOL(hAPP_f1287348838l_bool(inj_on938701937e_bool(F),A)) ) ) ).

tff(fact_1150_finite__surj__inj,axiom,
    ! [F: fun_pname_pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(image_pname_pname(F),A)))
       => hBOOL(hAPP_f1664156314l_bool(inj_on_pname_pname(F),A)) ) ) ).

tff(fact_1151_finite__surj__inj,axiom,
    ! [F: fun_Ho901937921_state,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A),hAPP_f1749453397e_bool(image_2068641359_state(F),A)))
       => hBOOL(hAPP_f568432088l_bool(inj_on1943491515_state(F),A)) ) ) ).

tff(fact_1152_inj__on__image__Int,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1262351275_state,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
         => ( hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B)) ) ) ) ) ).

tff(fact_1153_inj__on__image__set__diff,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool,F: fun_pn1262351275_state,C_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),C_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_1))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_1))
         => ( hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),A)),hAPP_f1763243027e_bool(image_1918575693_state(F),B)) ) ) ) ) ).

tff(fact_1154_union__fold__insert,axiom,
    ! [B: fun_com_bool,A: fun_com_bool] :
      ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
     => ( hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(semila605046092m_bool,A),B) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(finite1275301314m_bool(insert_com),B),A) ) ) ).

tff(fact_1155_union__fold__insert,axiom,
    ! [B: fun_pname_bool,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,A),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(finite315386934e_bool(insert_pname),B),A) ) ) ).

tff(fact_1156_union__fold__insert,axiom,
    ! [B: fun_Ho320143120e_bool,A: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
     => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,A),B) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(finite1720034636e_bool(insert1330351828_state),B),A) ) ) ).

tff(fact_1157_union__fold__insert,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(finite1627341516l_bool(insert1325755072e_bool),B),A) ) ) ).

tff(fact_1158_union__fold__insert,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(finite1820487374l_bool(insert975831690e_bool),B),A) ) ) ).

tff(fact_1159_dom__minus,axiom,
    ! [A: fun_pname_bool,F: fun_pname_option_com,X_1: pname] :
      ( ( hAPP_p799580910on_com(F,X_1) = none_com )
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),A) ) ) ).

tff(fact_1160_Sup__fin_Oidem,axiom,
    ! [X_1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,X_1),X_1))
    <=> hBOOL(X_1) ) ).

tff(fact_1161_Sup__fin_Oidem,axiom,
    ! [X_1: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,X_1),X_1) = X_1 ).

tff(fact_1162_Sup__fin_Oidem,axiom,
    ! [X_1: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,X_1),X_1) = X_1 ).

tff(fact_1163_folding__one_Oeq__fold_H,axiom,
    ! [X_1: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite860057415ne_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),A))
         => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,X_1),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),X_1),A) ) ) ) ) ).

tff(fact_1164_folding__one_Oeq__fold_H,axiom,
    ! [X_1: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite1282449217_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),X_1),A) ) ) ) ) ).

tff(fact_1165_folding__one_Oeq__fold_H,axiom,
    ! [X_1: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite269920017_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),A))
         => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,X_1),A)) = hAPP_f1242401993_state(hAPP_H2108048200_state(finite1620577938_state(F),X_1),A) ) ) ) ) ).

tff(fact_1166_folding__one_Oeq__fold_H,axiom,
    ! [X_1: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1626890877e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),X_1),A) ) ) ) ) ).

tff(fact_1167_folding__one_Oeq__fold_H,axiom,
    ! [X_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite1264277005e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( ~ hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_1),A))
         => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,X_1),A)) = hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(F),X_1),A) ) ) ) ) ).

tff(fact_1168_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [A_4: com,A: fun_com_bool,F: fun_com_fun_com_com,Fa: fun_fun_com_bool_com] :
      ( hBOOL(finite666746948em_com(F,Fa))
     => ( hBOOL(hAPP_f990396704l_bool(finite_finite_com,A))
       => ( hAPP_f1276420679ol_com(Fa,hAPP_f1682609283m_bool(hAPP_c566651504m_bool(insert_com,A_4),A)) = hAPP_f1276420679ol_com(hAPP_c1546426672ol_com(finite_fold_com_com(F),A_4),A) ) ) ) ).

tff(fact_1169_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [A_4: pname,A: fun_pname_bool,F: fun_pn1208287926_pname,Fa: fun_fu1499449723_pname] :
      ( hBOOL(finite89670078_pname(F,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
       => ( hAPP_f1297739591_pname(Fa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)) = hAPP_f1297739591_pname(hAPP_p1630511146_pname(finite1657623752_pname(F),A_4),A) ) ) ) ).

tff(fact_1170_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [A_4: hoare_363350478_state,A: fun_Ho320143120e_bool,F: fun_Ho31865764_state,Fa: fun_fu700438391_state] :
      ( hBOOL(finite2031572_state(F,Fa))
     => ( hBOOL(hAPP_f568432088l_bool(finite280062779_state,A))
       => ( hAPP_f1242401993_state(Fa,hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,A_4),A)) = hAPP_f1242401993_state(hAPP_H2108048200_state(finite1620577938_state(F),A_4),A) ) ) ) ).

tff(fact_1171_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [A_4: fun_pname_bool,A: fun_fu1430349052l_bool,F: fun_fu2101097872e_bool,Fa: fun_fu608906319e_bool] :
      ( hBOOL(finite1268145088e_bool(F,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
       => ( hAPP_f674760225e_bool(Fa,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_4),A)) = hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(F),A_4),A) ) ) ) ).

tff(fact_1172_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [A_4: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool,F: fun_fu531943146e_bool,Fa: fun_fu1671561851e_bool] :
      ( hBOOL(finite2090946954e_bool(F,Fa))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
       => ( hAPP_f1180969799e_bool(Fa,hAPP_f85652879l_bool(hAPP_f1941218614l_bool(insert975831690e_bool,A_4),A)) = hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(F),A_4),A) ) ) ) ).

tff(fact_1173_WT_OBody,axiom,
    ! [Pn: pname] :
      ( ( hAPP_p799580910on_com(body,Pn) != none_com )
     => hBOOL(hAPP_com_bool(wt,hAPP_pname_com(body_1,Pn))) ) ).

tff(fact_1174_inj__on__insert,axiom,
    ! [F: fun_pn1262351275_state,A_4: pname,A: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),A)))
    <=> ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F),A))
        & ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_p1337579261_state(F,A_4)),hAPP_f1763243027e_bool(image_1918575693_state(F),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_4),bot_bo844097828e_bool))))) ) ) ).

tff(fact_1175_dom__fun__upd,axiom,
    ! [F: fun_pname_option_com,X_1: pname,Y_2: option_com] :
      ( ( ( Y_2 = none_com )
       => ( dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,dom_pname_com(F)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) ) )
      & ( ( Y_2 != none_com )
       => ( dom_pname_com(fun_up879233478on_com(F,X_1,Y_2)) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),dom_pname_com(F)) ) ) ) ).

tff(fact_1176_inf__le__fold__inf,axiom,
    ! [C: fun_pname_bool,B_1: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ! [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),X_2)) )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,B_1),C)),hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila1635148844e_bool),C),A))) ) ) ).

tff(fact_1177_inf__le__fold__inf,axiom,
    ! [C: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( ! [X_2: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),A))
           => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,B_1),X_2)) )
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,B_1),C)),hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1129477150e_bool),C),A))) ) ) ).

tff(fact_1178_inf__le__fold__inf,axiom,
    ! [C: bool,B_1: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
     => ( ! [X_2: bool] :
            ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
           => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),X_2)) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(hAPP_b589554111l_bool(semila310582991f_bool,B_1),C)),hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila310582991f_bool),C),A))) ) ) ).

tff(fact_1179_fold__sup__le__sup,axiom,
    ! [C: fun_pname_bool,B_1: fun_pname_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ! [X_2: fun_pname_bool] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),B_1)) )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f674760225e_bool(hAPP_f246190092e_bool(finite446335722e_bool(semila278973382e_bool),C),A)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila278973382e_bool,B_1),C))) ) ) ).

tff(fact_1180_fold__sup__le__sup,axiom,
    ! [C: fun_Ho320143120e_bool,B_1: fun_Ho320143120e_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( ! [X_2: fun_Ho320143120e_bool] :
            ( hBOOL(hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(member1534059107e_bool,X_2),A))
           => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,X_2),B_1)) )
       => hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1180969799e_bool(hAPP_f644061942e_bool(finite1334634696e_bool(semila1579166468e_bool),C),A)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1579166468e_bool,B_1),C))) ) ) ).

tff(fact_1181_fold__sup__le__sup,axiom,
    ! [C: bool,B_1: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,A))
     => ( ! [X_2: bool] :
            ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
           => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),B_1)) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f387058535l_bool(hAPP_b1787118453l_bool(finite1909292976l_bool(semila1168014441p_bool),C),A)),hAPP_bool_bool(hAPP_b589554111l_bool(semila1168014441p_bool,B_1),C))) ) ) ).

tff(fact_1182_inj__on__iff__surj,axiom,
    ! [A_3: fun_pname_bool,A: fun_Ho320143120e_bool] :
      ( ( A != bot_bo39439654e_bool )
     => ( ? [F_1: fun_Ho713471079_pname] :
            ( hBOOL(hAPP_f568432088l_bool(inj_on216215575_pname(F_1),A))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f773602357e_bool(image_1927198851_pname(F_1),A)),A_3)) )
      <=> ? [G_1: fun_pn1262351275_state] : hAPP_f1763243027e_bool(image_1918575693_state(G_1),A_3) = A ) ) ).

tff(fact_1183_inj__on__iff__surj,axiom,
    ! [A_3: fun_Ho320143120e_bool,A: fun_pname_bool] :
      ( ( A != bot_bo844097828e_bool )
     => ( ? [F_1: fun_pn1262351275_state] :
            ( hBOOL(hAPP_f1664156314l_bool(inj_on207592417_state(F_1),A))
            & hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F_1),A)),A_3)) )
      <=> ? [G_1: fun_Ho713471079_pname] : hAPP_f773602357e_bool(image_1927198851_pname(G_1),A_3) = A ) ) ).

tff(fact_1184_option_Oexhaust,axiom,
    ! [Y_1: option_com] :
      ( ( Y_1 != none_com )
     => ~ ! [A_2: com] : Y_1 != hAPP_com_option_com(some_com,A_2) ) ).

tff(fact_1185_option_Oexhaust,axiom,
    ! [Y_1: option_pname] :
      ( ( Y_1 != none_pname )
     => ~ ! [A_2: pname] : Y_1 != hAPP_p1252095976_pname(some_pname,A_2) ) ).

tff(fact_1186_option_Oexhaust,axiom,
    ! [Y_1: option131732143_state] :
      ( ( Y_1 != none_H1908530691_state )
     => ~ ! [A_2: hoare_363350478_state] : Y_1 != hAPP_H1942146718_state(some_H629028223_state,A_2) ) ).

tff(fact_1187_Cantor__Bernstein__aux,axiom,
    ! [G: fun_Ho713471079_pname,B: fun_Ho320143120e_bool,F: fun_pn1262351275_state,A: fun_pname_bool] :
    ? [A_1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A))
      & ! [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),hAPP_f773602357e_bool(image_1927198851_pname(G),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),hAPP_f1763243027e_bool(image_1918575693_state(F),A_1))))) )
      & ? [H: fun_pn1262351275_state] :
          ( ! [X_2: pname] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A_1))
             => ( hAPP_p1337579261_state(H,X_2) = hAPP_p1337579261_state(F,X_2) ) )
          & ! [X_2: pname] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),A_1)))
             => ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_p1337579261_state(H,X_2)),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,B),hAPP_f1763243027e_bool(image_1918575693_state(F),A_1))))
                & ( X_2 = hAPP_H1346202419_pname(G,hAPP_p1337579261_state(H,X_2)) ) ) ) ) ) ).

tff(fact_1188_Cantor__Bernstein__aux,axiom,
    ! [G: fun_pn1262351275_state,B: fun_pname_bool,F: fun_Ho713471079_pname,A: fun_Ho320143120e_bool] :
    ? [A_1: fun_Ho320143120e_bool] :
      ( hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,A_1),A))
      & ! [X_2: hoare_363350478_state] :
          ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A_1))
         => ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1763243027e_bool(image_1918575693_state(G),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f773602357e_bool(image_1927198851_pname(F),A_1))))) )
      & ? [H: fun_Ho713471079_pname] :
          ( ! [X_2: hoare_363350478_state] :
              ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),A_1))
             => ( hAPP_H1346202419_pname(H,X_2) = hAPP_H1346202419_pname(F,X_2) ) )
          & ! [X_2: hoare_363350478_state] :
              ( hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_2),hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(minus_1060678561e_bool,A),A_1)))
             => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H1346202419_pname(H,X_2)),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,B),hAPP_f773602357e_bool(image_1927198851_pname(F),A_1))))
                & ( X_2 = hAPP_p1337579261_state(G,hAPP_H1346202419_pname(H,X_2)) ) ) ) ) ) ).

tff(fact_1189_image__vimage__subset,axiom,
    ! [F: fun_pn1262351275_state,A: fun_Ho320143120e_bool] : hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,hAPP_f1763243027e_bool(image_1918575693_state(F),vimage597774871_state(F,A))),A)) ).

tff(fact_1190_dom__restrict,axiom,
    ! [M: fun_pname_option_com,A: fun_pname_bool] : dom_pname_com(restri1382200118me_com(M,A)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,dom_pname_com(M)),A) ).

tff(fact_1191_Inf__fin_Ounion__disjoint,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ( A != bot_bo1649642514l_bool )
       => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
         => ( ( B != bot_bo1649642514l_bool )
           => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) = bot_bo1649642514l_bool )
             => ( hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B)) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B)) ) ) ) ) ) ) ).

tff(fact_1192_Inf__fin_Ounion__disjoint,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( ( A != bot_bo133096688l_bool )
       => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
         => ( ( B != bot_bo133096688l_bool )
           => ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B) = bot_bo133096688l_bool )
             => ( hAPP_f1180969799e_bool(big_la1639670082e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B)) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1180969799e_bool(big_la1639670082e_bool,A)),hAPP_f1180969799e_bool(big_la1639670082e_bool,B)) ) ) ) ) ) ) ).

tff(fact_1193_Inf__fin_Ounion__inter,axiom,
    ! [B: fun_fu1430349052l_bool,A: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( ( hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B) != bot_bo1649642514l_bool )
         => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1782091504l_bool,A),B))),hAPP_f674760225e_bool(big_la28065288e_bool,hAPP_f559147733l_bool(hAPP_f230953622l_bool(semila1130628874l_bool,A),B))) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(semila1635148844e_bool,hAPP_f674760225e_bool(big_la28065288e_bool,A)),hAPP_f674760225e_bool(big_la28065288e_bool,B)) ) ) ) ) ).

tff(fact_1194_Inf__fin_Ounion__inter,axiom,
    ! [B: fun_fu1996308102l_bool,A: fun_fu1996308102l_bool] :
      ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,A))
     => ( hBOOL(hAPP_f1287348838l_bool(finite2030652771e_bool,B))
       => ( ( hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B) != bot_bo133096688l_bool )
         => ( hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1180969799e_bool(big_la1639670082e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila862847378l_bool,A),B))),hAPP_f1180969799e_bool(big_la1639670082e_bool,hAPP_f85652879l_bool(hAPP_f1175211816l_bool(semila218417144l_bool,A),B))) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(semila1129477150e_bool,hAPP_f1180969799e_bool(big_la1639670082e_bool,A)),hAPP_f1180969799e_bool(big_la1639670082e_bool,B)) ) ) ) ) ).

tff(fact_1195_UNIV__I,axiom,
    ! [X_1: com] : hBOOL(hAPP_f990396704l_bool(hAPP_c667411853l_bool(member_com,X_1),top_top_fun_com_bool)) ).

tff(fact_1196_UNIV__I,axiom,
    ! [X_1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),top_to2127735616e_bool)) ).

tff(fact_1197_UNIV__I,axiom,
    ! [X_1: hoare_363350478_state] : hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,X_1),top_to1618141706e_bool)) ).

tff(fact_1198_rangeI,axiom,
    ! [F: fun_pn1262351275_state,X_1: pname] : hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_p1337579261_state(F,X_1)),hAPP_f1763243027e_bool(image_1918575693_state(F),top_to2127735616e_bool))) ).

%----Helper facts (152)
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__Ocom_T,axiom,
    ! [X: com,Y: com] :
      ( ~ hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Com__Ocom_T,axiom,
    ! [X: com,Y: com] :
      ( ( X != Y )
      | hBOOL(hAPP_com_bool(hAPP_c1396316405m_bool(fequal_com,X),Y)) ) ).

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__Ocom_U,axiom,
    ! [P: bool,Q: com] : hAPP_com_bool(hAPP_b1153789088m_bool(cOMBK_bool_com,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__Com__Ocom_000tc__Com__Opname_U,axiom,
    ! [P: com,Q: pname] : hAPP_pname_com(hAPP_c1494068046me_com(cOMBK_com_pname,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
    ! [P: bool,Q: pname] : hAPP_pname_bool(hAPP_b76515610e_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_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U,axiom,
    ! [P: pname,Q: pname] : hAPP_pname_pname(hAPP_p1170154830_pname(cOMBK_pname_pname,P),Q) = P ).

tff(help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
    ! [X: option_com,Y: option_com] :
      ( ~ hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
    ! [X: option_com,Y: option_com] :
      ( ( X != Y )
      | hBOOL(hAPP_option_com_bool(hAPP_o1684370239m_bool(fequal_option_com,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T,axiom,
    ! [X: fun_com_bool,Y: fun_com_bool] :
      ( ~ hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_T,axiom,
    ! [X: fun_com_bool,Y: fun_com_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f990396704l_bool(hAPP_f273696895l_bool(fequal_fun_com_bool,X),Y)) ) ).

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_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Ocom_000tc__HOL__Obool_U,axiom,
    ! [P: fun_com_fun_com_bool,Q: com,R: com] : hAPP_com_bool(hAPP_c1396316405m_bool(hAPP_f908845385m_bool(cOMBC_com_com_bool,P),Q),R) = hAPP_com_bool(hAPP_c1396316405m_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ocom_U,axiom,
    ! [P: fun_bool_bool,Q: fun_com_bool,R: com] : hAPP_com_bool(hAPP_f1682609283m_bool(cOMBB_bool_bool_com(P),Q),R) = hAPP_bool_bool(P,hAPP_com_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Ocom_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_co2042843794l_bool,Q: fun_com_bool,R: com] : hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f328772264m_bool(cOMBS_com_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_c1580157610l_bool(P,R),hAPP_com_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
    ! [P: fun_co1877906717e_bool,Q: pname,R: com] : hAPP_com_bool(hAPP_p1639923567m_bool(hAPP_f734198589m_bool(cOMBC_com_pname_bool,P),Q),R) = hAPP_pname_bool(hAPP_c1967741679e_bool(P,R),Q) ).

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__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Opname_,axiom,
    ! [P: option_com,Q: pname] : hAPP_p799580910on_com(hAPP_o129566686on_com(cOMBK_413306633_pname,P),Q) = P ).

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(hAPP_b357632156l_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(hAPP_f1863945078e_bool(cOMBK_631994958_state,P),Q) = P ).

tff(help_If_1_1_If_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Ostate,axiom,
    ! [X: hoare_363350478_state,Y: hoare_363350478_state] : hAPP_H1982017439_state(hAPP_H230141040_state(hAPP_b594649092_state(if_Hoa29189214_state,fTrue),X),Y) = X ).

tff(help_If_2_1_If_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Ostate,axiom,
    ! [X: hoare_363350478_state,Y: hoare_363350478_state] : hAPP_H1982017439_state(hAPP_H230141040_state(hAPP_b594649092_state(if_Hoa29189214_state,fFalse),X),Y) = Y ).

tff(help_If_3_1_If_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__Ostate,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com,axiom,
    ! [X: hoare_363350478_state,Y: hoare_363350478_state] :
      ( ~ hBOOL(hAPP_H1645464494e_bool(hAPP_H705653759e_bool(fequal1026769423_state,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com,axiom,
    ! [X: hoare_363350478_state,Y: hoare_363350478_state] :
      ( ( X != Y )
      | hBOOL(hAPP_H1645464494e_bool(hAPP_H705653759e_bool(fequal1026769423_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_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_,axiom,
    ! [P: fun_pn1824415994m_bool,Q: option_com,R: pname] : hAPP_pname_bool(hAPP_o1092643708e_bool(hAPP_f837293113e_bool(cOMBC_1381995473m_bool,P),Q),R) = hAPP_option_com_bool(hAPP_p558118546m_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P: fun_fu1362071682l_bool,Q: fun_com_fun_com_bool,R: com] : hAPP_com_bool(hAPP_f1998868198m_bool(cOMBB_298914627ol_com(P),Q),R) = hAPP_f990396704l_bool(P,hAPP_c1396316405m_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_,axiom,
    ! [P: fun_co1633267573l_bool,Q: fun_com_bool,R: com] : hAPP_com_bool(hAPP_f1682609283m_bool(hAPP_f578650245m_bool(cOMBC_1904837336l_bool,P),Q),R) = hAPP_f990396704l_bool(hAPP_c667411853l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_com_bool,R: com] : hAPP_c1580157610l_bool(hAPP_f954469007l_bool(cOMBB_886968260ol_com(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_com_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_com_pname,R: com] : hAPP_c1967741679e_bool(hAPP_f835719487e_bool(cOMBB_1083901850ol_com(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_com_pname(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_359,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_360,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_361,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__Com__Ocom_000tc__Hoare____Mirabelle____wdcyoqcnvy__O,axiom,
    ! [P: com,Q: hoare_363350478_state] : hAPP_H2142737465te_com(hAPP_c6662434te_com(cOMBK_1864507658_state,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__,axiom,
    ! [P: hoare_363350478_state,Q: com] : hAPP_c1041435779_state(hAPP_H154362754_state(cOMBK_818325696te_com,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____wdcyoqcnvy__,axiom,
    ! [P: bool,Q: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_b230077104e_bool(cOMBK_574827367_state,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____wdcyoqcnvy_,axiom,
    ! [P: pname,Q: hoare_363350478_state] : hAPP_H1346202419_pname(hAPP_p1379817622_pname(cOMBK_83433476_state,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___362,axiom,
    ! [P: hoare_363350478_state,Q: pname] : hAPP_p1337579261_state(hAPP_H1607320188_state(cOMBK_92056634_pname,P),Q) = P ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple,axiom,
    ! [X: fun_Ho320143120e_bool,Y: fun_Ho320143120e_bool] :
      ( ~ hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(fequal731041167e_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple,axiom,
    ! [X: fun_Ho320143120e_bool,Y: fun_Ho320143120e_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(fequal731041167e_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_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__Hoare____Mirabelle____wdcyoqcnvy__O,axiom,
    ! [P: fun_co1098712835e_bool,Q: hoare_363350478_state,R: com] : hAPP_com_bool(hAPP_H176808977m_bool(hAPP_f1375689733m_bool(cOMBC_1517337958e_bool,P),Q),R) = hAPP_H1645464494e_bool(hAPP_c566546971e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____wdcyoqcnvy__O,axiom,
    ! [P: fun_co482540593_state,Q: fun_pname_com,R: pname] : hAPP_p1337579261_state(hAPP_f481860441_state(cOMBB_424558970_pname(P),Q),R) = hAPP_c1041435779_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_Ho320143120e_bool,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(cOMBB_2059354034_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H1645464494e_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho544647106l_bool,Q: fun_Ho320143120e_bool,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1612626488e_bool(cOMBS_56025283l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1173243534l_bool(P,R),hAPP_H1645464494e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Ocom_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool__363,axiom,
    ! [P: fun_co2038576728m_bool,Q: fun_com_bool,R: com] : hAPP_c1396316405m_bool(hAPP_f721468006m_bool(hAPP_f947797701m_bool(cOMBC_1977231931m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_c566651504m_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____wdcyoqcnvy_,axiom,
    ! [P: fun_pn1521100553e_bool,Q: hoare_363350478_state,R: pname] : hAPP_pname_bool(hAPP_H2033014795e_bool(hAPP_f443781369e_bool(cOMBC_1422551904e_bool,P),Q),R) = hAPP_H1645464494e_bool(hAPP_p2009489185e_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho1262521325e_bool,Q: pname,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_p2009489185e_bool(hAPP_f626747953e_bool(cOMBC_1026256022e_bool,P),Q),R) = hAPP_pname_bool(hAPP_H2033014795e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_364,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_365,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_366,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____wdc,axiom,
    ! [P: bool,Q: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_b1504838374l_bool(cOMBK_1696036407e_bool,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__fun_Itc__Opt,axiom,
    ! [P: fun_op2091355123m_bool,Q: fun_pname_option_com,R: pname] : hAPP_p558118546m_bool(hAPP_f919496731m_bool(cOMBB_418828222_pname(P),Q),R) = hAPP_o1684370239m_bool(P,hAPP_p799580910on_com(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1996308102l_bool,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_f85652879l_bool(cOMBB_941362220e_bool(P),Q),R) = hAPP_bool_bool(P,hAPP_f568432088l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_367,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Ho320143120e_bool,R: hoare_363350478_state] : hAPP_H1173243534l_bool(hAPP_f1422032445l_bool(cOMBB_877416532_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1645464494e_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I,axiom,
    ! [P: fun_fu24650956l_bool,Q: fun_fu1996308102l_bool,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_f85652879l_bool(hAPP_f927797370l_bool(cOMBS_1039407915l_bool,P),Q),R) = hAPP_bool_bool(hAPP_f1395767268l_bool(P,R),hAPP_f568432088l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____wd,axiom,
    ! [P: fun_pn1419495779l_bool,Q: fun_Ho320143120e_bool,R: pname] : hAPP_pname_bool(hAPP_f773602357e_bool(hAPP_f1863577801e_bool(cOMBC_947783590l_bool,P),Q),R) = hAPP_f568432088l_bool(hAPP_p425615669l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___368,axiom,
    ! [P: fun_Ho769804319l_bool,Q: fun_pname_bool,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_f1763243027e_bool(hAPP_f1421439337e_bool(cOMBC_1674478480l_bool,P),Q),R) = hAPP_f1664156314l_bool(hAPP_H444605547l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P: fun_fu1107293590m_bool,Q: fun_com_bool,R: fun_com_bool] : hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(hAPP_f1898485935m_bool(cOMBC_788185579m_bool,P),Q),R) = hAPP_f1682609283m_bool(hAPP_f1120618594m_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,axiom,
    ! [P: fun_fu1937087815e_bool,Q: hoare_363350478_state,R: fun_pname_bool] : hAPP_f1664156314l_bool(hAPP_H444605547l_bool(hAPP_f1075942761l_bool(cOMBC_1091669008e_bool,P),Q),R) = hAPP_H1645464494e_bool(hAPP_f1763243027e_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I,axiom,
    ! [P: fun_fu665342307e_bool,Q: pname,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_p425615669l_bool(hAPP_f883421385l_bool(cOMBC_1845395470e_bool,P),Q),R) = hAPP_pname_bool(hAPP_f773602357e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_369,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_Ho713471079_pname,R: hoare_363350478_state] : hAPP_H2033014795e_bool(hAPP_f875047427e_bool(cOMBB_951329022_state(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_H1346202419_pname(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_370,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_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_371,axiom,
    ! [P: fun_fu2101097872e_bool,Q: fun_pname_bool,R: fun_pname_bool] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(hAPP_f182188835e_bool(cOMBC_1880008793e_bool,P),Q),R) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_372,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__373,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____wdcyoqcnvy__Otriple_Itc__Com___374,axiom,
    ! [P: fun_Ho424838195e_bool,Q: hoare_363350478_state,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_H705653759e_bool(hAPP_f114072425e_bool(cOMBC_13083556e_bool,P),Q),R) = hAPP_H1645464494e_bool(hAPP_H705653759e_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____wdcyoqcnvy_,axiom,
    ! [P: fun_pn983485306_state,Q: fun_pn1262351275_state,R: pname] : hAPP_p1337579261_state(hAPP_f901668953_state(hAPP_f1521026326_state(cOMBS_113846849_state,P),Q),R) = hAPP_H1982017439_state(hAPP_p726046354_state(P,R),hAPP_p1337579261_state(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_375,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_fu1996308102l_bool,R: fun_Ho320143120e_bool] : hAPP_f1395767268l_bool(hAPP_f945781379l_bool(cOMBB_1004232970e_bool(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f568432088l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ocom_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P: fun_fu1107293590m_bool,Q: fun_com_fun_com_bool,R: com] : hAPP_c566651504m_bool(hAPP_f57617970m_bool(cOMBB_2112550369ol_com(P),Q),R) = hAPP_f1120618594m_bool(P,hAPP_c1396316405m_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_376,axiom,
    ! [P: fun_pn800050071e_bool,Q: fun_fu2380401_pname,R: fun_Ho320143120e_bool] : hAPP_f773602357e_bool(hAPP_f1544555711e_bool(cOMBB_655928288e_bool(P),Q),R) = hAPP_p61793385e_bool(P,hAPP_f1309420425_pname(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc,axiom,
    ! [P: fun_pn640817967_state,Q: fun_pn12888928e_bool,R: pname] : hAPP_p1337579261_state(hAPP_f19336718_state(hAPP_f720869462_state(cOMBS_1110920566_state,P),Q),R) = hAPP_f83715540_state(hAPP_p435788871_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__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_377,axiom,
    ! [P: fun_fu2101097872e_bool,Q: fun_pn800050071e_bool,R: pname] : hAPP_p905327722e_bool(hAPP_f647826488e_bool(cOMBB_1919352417_pname(P),Q),R) = hAPP_f1388330588e_bool(P,hAPP_p61793385e_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__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com__,axiom,
    ! [P: fun_Ho424838195e_bool,Q: fun_co482540593_state,R: com] : hAPP_c566546971e_bool(hAPP_f1813061839e_bool(cOMBB_147383684ol_com(P),Q),R) = hAPP_H705653759e_bool(P,hAPP_c1041435779_state(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I,axiom,
    ! [P: fun_fu1996308102l_bool,Q: fun_Ho424838195e_bool,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_f265222234e_bool(cOMBB_1356223341_state(P),Q),R) = hAPP_f568432088l_bool(P,hAPP_H705653759e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___378,axiom,
    ! [P: fun_Ho177530809l_bool,Q: fun_Ho320143120e_bool,R: hoare_363350478_state] : hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(hAPP_f1072682137e_bool(cOMBC_1415895650l_bool,P),Q),R) = hAPP_f568432088l_bool(hAPP_H40373975l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_379,axiom,
    ! [P: fun_fu1066574909e_bool,Q: hoare_363350478_state,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_H40373975l_bool(hAPP_f1585300113l_bool(cOMBC_497487404e_bool,P),Q),R) = hAPP_H1645464494e_bool(hAPP_f1749453397e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___380,axiom,
    ! [P: fun_Ho424838195e_bool,Q: fun_pn1262351275_state,R: pname] : hAPP_p2009489185e_bool(hAPP_f1284518107e_bool(cOMBB_1755629310_pname(P),Q),R) = hAPP_H705653759e_bool(P,hAPP_p1337579261_state(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_381,axiom,
    ! [P: fun_fu802393907l_bool,Q: fun_Ho1262521325e_bool,R: hoare_363350478_state] : hAPP_H444605547l_bool(hAPP_f399561463l_bool(cOMBB_1217374484_state(P),Q),R) = hAPP_f434788991l_bool(P,hAPP_H2033014795e_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc,axiom,
    ! [P: fun_pn203430818_state,Q: fun_pname_com,R: pname] : hAPP_p435788871_state(hAPP_f1146170881_state(hAPP_f1311198492_state(cOMBS_124505571_state,P),Q),R) = hAPP_c1279058753_state(hAPP_p1042965178_state(P,R),hAPP_pname_com(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P: fun_fu1476767085_state,Q: fun_fu1022316450e_bool,R: fun_pname_bool] : hAPP_f804167819_state(hAPP_f2070959648_state(hAPP_f820078872_state(cOMBS_444947014_state,P),Q),R) = hAPP_f83715540_state(hAPP_f972256569_state(P,R),hAPP_f887530048e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_382,axiom,
    ! [P: fun_fu1232732404l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : hAPP_f434788991l_bool(hAPP_f417341722l_bool(hAPP_f836143551l_bool(cOMBC_772615479l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f1320879424l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_383,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____wdcyoqcnvy__Otriple_I_384,axiom,
    ! [P: fun_fu2036837167l_bool,Q: fun_Ho320143120e_bool,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_f726209793l_bool(hAPP_f205303905l_bool(cOMBC_1250231770l_bool,P),Q),R) = hAPP_f568432088l_bool(hAPP_f726209793l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___385,axiom,
    ! [P: fun_Ho424838195e_bool,Q: fun_fu54631149_state,R: fun_pname_bool] : hAPP_f1763243027e_bool(hAPP_f272807711e_bool(cOMBB_543245952e_bool(P),Q),R) = hAPP_H705653759e_bool(P,hAPP_f804167819_state(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____wd_386,axiom,
    ! [P: fun_pn73701814e_bool,Q: fun_Ho320143120e_bool,R: pname] : hAPP_p2009489185e_bool(hAPP_f265219918e_bool(hAPP_f1853922773e_bool(cOMBC_1001821703e_bool,P),Q),R) = hAPP_f1749453397e_bool(hAPP_p678758990e_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
    ! [P: fun_fu121404128_state,Q: fun_fu78728705ol_com,R: fun_pname_bool] : hAPP_f972256569_state(hAPP_f926121585_state(hAPP_f907647536_state(cOMBS_1636274867_state,P),Q),R) = hAPP_c1279058753_state(hAPP_f637646508_state(P,R),hAPP_f792846925ol_com(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__387,axiom,
    ! [P: fun_fu1759027710l_bool,Q: fun_fu1430349052l_bool,R: fun_fu1430349052l_bool] : hAPP_f559147733l_bool(hAPP_f230953622l_bool(hAPP_f1477350485l_bool(cOMBC_694979519l_bool,P),Q),R) = hAPP_f559147733l_bool(hAPP_f230953622l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___388,axiom,
    ! [P: fun_Ho424838195e_bool,Q: fun_Ho901937921_state,R: hoare_363350478_state] : hAPP_H705653759e_bool(hAPP_f355123231e_bool(cOMBB_496159380_state(P),Q),R) = hAPP_H705653759e_bool(P,hAPP_H1982017439_state(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____wdcyoqcnvy__389,axiom,
    ! [P: fun_pn1681257857_state,Q: fun_pn1262351275_state,R: pname] : hAPP_p726046354_state(hAPP_f1180972108_state(hAPP_f1993951364_state(cOMBS_89825358_state,P),Q),R) = hAPP_H230141040_state(hAPP_p760538963_state(P,R),hAPP_p1337579261_state(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_390,axiom,
    ! [P: fun_fu1467933941l_bool,Q: fun_fu1996308102l_bool,R: fun_Ho320143120e_bool] : hAPP_f568432088l_bool(hAPP_f85652879l_bool(hAPP_f1854331281l_bool(cOMBC_1522409444l_bool,P),Q),R) = hAPP_f1287348838l_bool(hAPP_f1610329741l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_391,axiom,
    ! [P: fun_fu2036837167l_bool,Q: fun_pn1521100553e_bool,R: pname] : hAPP_p425615669l_bool(hAPP_f1841796439l_bool(cOMBB_343228284_pname(P),Q),R) = hAPP_f726209793l_bool(P,hAPP_p2009489185e_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_392,axiom,
    ! [P: fun_fu422494307_state,Q: fun_fu1232608556e_bool,R: fun_Ho320143120e_bool] : hAPP_f1242401993_state(hAPP_f605405862_state(hAPP_f1593397690_state(cOMBS_1452472386_state,P),Q),R) = hAPP_f83715540_state(hAPP_f680128379_state(P,R),hAPP_f877220222e_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___393,axiom,
    ! [P: fun_Ho424838195e_bool,Q: fun_fu700438391_state,R: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f440040771e_bool(cOMBB_238163658e_bool(P),Q),R) = hAPP_H705653759e_bool(P,hAPP_f1242401993_state(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___394,axiom,
    ! [P: fun_Ho1500656352e_bool,Q: fun_Ho320143120e_bool,R: hoare_363350478_state] : hAPP_H705653759e_bool(hAPP_f596150574e_bool(hAPP_f961492031e_bool(cOMBC_1774708299e_bool,P),Q),R) = hAPP_f1749453397e_bool(hAPP_H122293036e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____wdc,axiom,
    ! [P: fun_bo1278783462_state,Q: fun_pname_bool,R: pname] : hAPP_p760538963_state(hAPP_f1418159294_state(cOMBB_1777678681_pname(P),Q),R) = hAPP_b594649092_state(P,hAPP_pname_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__,axiom,
    ! [P: fun_fu1575689779l_bool,Q: fun_fu1996308102l_bool,R: fun_fu1996308102l_bool] : hAPP_f1287348838l_bool(hAPP_f746351743l_bool(hAPP_f992844137l_bool(cOMBC_736208532l_bool,P),Q),R) = hAPP_f1287348838l_bool(hAPP_f746351743l_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_395,axiom,
    ! [P: fun_fu47394518_state,Q: fun_fu1203007991ol_com,R: fun_Ho320143120e_bool] : hAPP_f680128379_state(hAPP_f153770241_state(hAPP_f2014973160_state(cOMBS_319359663_state,P),Q),R) = hAPP_c1279058753_state(hAPP_f1659249646_state(P,R),hAPP_f1577230223ol_com(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___396,axiom,
    ! [P: fun_fu515363031_state,Q: fun_pn12888928e_bool,R: pname] : hAPP_p1042965178_state(hAPP_f387017471_state(cOMBB_1212270426_pname(P),Q),R) = hAPP_f960042659_state(P,hAPP_p1637813682e_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
    ! [P: fun_fu1759027710l_bool,Q: fun_fu802393907l_bool,R: fun_pname_bool] : hAPP_f1320879424l_bool(hAPP_f1149191722l_bool(cOMBB_631815671e_bool(P),Q),R) = hAPP_f230953622l_bool(P,hAPP_f434788991l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_397,axiom,
    ! [P: fun_fu2036837167l_bool,Q: fun_Ho424838195e_bool,R: hoare_363350478_state] : hAPP_H40373975l_bool(hAPP_f565239043l_bool(cOMBB_867654038_state(P),Q),R) = hAPP_f726209793l_bool(P,hAPP_H705653759e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_398,axiom,
    ! [P: fun_fu531943146e_bool,Q: fun_Ho320143120e_bool,R: fun_Ho320143120e_bool] : hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(hAPP_f1873524693e_bool(cOMBC_1626046675e_bool,P),Q),R) = hAPP_f1749453397e_bool(hAPP_f1043393922e_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_Itc__Com___399,axiom,
    ! [P: fun_Ho1500656352e_bool,Q: fun_pn1262351275_state,R: pname] : hAPP_p678758990e_bool(hAPP_f43306888e_bool(cOMBB_1717464465_pname(P),Q),R) = hAPP_H122293036e_bool(P,hAPP_p1337579261_state(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___400,axiom,
    ! [P: fun_fu515363031_state,Q: fun_fu1022316450e_bool,R: fun_pname_bool] : hAPP_f637646508_state(hAPP_f1215319405_state(cOMBB_151548708e_bool(P),Q),R) = hAPP_f960042659_state(P,hAPP_f887530048e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_401,axiom,
    ! [P: fun_fu1997055262l_bool,Q: fun_fu1996308102l_bool,R: fun_Ho320143120e_bool] : hAPP_f726209793l_bool(hAPP_f434845752l_bool(hAPP_f1793815761l_bool(cOMBC_2079418125l_bool,P),Q),R) = hAPP_f85652879l_bool(hAPP_f1941218614l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___402,axiom,
    ! [P: fun_fu515363031_state,Q: fun_fu1232608556e_bool,R: fun_Ho320143120e_bool] : hAPP_f1659249646_state(hAPP_f1323754599_state(cOMBB_188465958e_bool(P),Q),R) = hAPP_f960042659_state(P,hAPP_f877220222e_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__Otriple_I_403,axiom,
    ! [P: fun_fu531943146e_bool,Q: fun_Ho424838195e_bool,R: hoare_363350478_state] : hAPP_H122293036e_bool(hAPP_f306007574e_bool(cOMBB_1253415543_state(P),Q),R) = hAPP_f1043393922e_bool(P,hAPP_H705653759e_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy___404,axiom,
    ! [P: fun_fu1392972380l_bool,Q: fun_fu1996308102l_bool,R: fun_fu1996308102l_bool] : hAPP_f85652879l_bool(hAPP_f1175211816l_bool(hAPP_f103280059l_bool(cOMBC_646647229l_bool,P),Q),R) = hAPP_f85652879l_bool(hAPP_f1175211816l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____wdcyoqcnvy__,axiom,
    ! [P: fun_fu1392972380l_bool,Q: fun_fu2036837167l_bool,R: fun_Ho320143120e_bool] : hAPP_f1941218614l_bool(hAPP_f471491948l_bool(cOMBB_460931425e_bool(P),Q),R) = hAPP_f1175211816l_bool(P,hAPP_f726209793l_bool(Q,R)) ).

%----Conjectures (8)
tff(conj_0,hypothesis,
    hBOOL(hoare_265376576gleton) ).

tff(conj_1,hypothesis,
    hBOOL(wT_bodies) ).

tff(conj_2,hypothesis,
    hBOOL(hAPP_f568432088l_bool(finite280062779_state,fa)) ).

tff(conj_3,hypothesis,
    ~ hBOOL(hAPP_f568432088l_bool(hAPP_H40373975l_bool(member1253905979_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,y)),fa)) ).

tff(conj_4,hypothesis,
    hBOOL(hAPP_f568432088l_bool(hAPP_f726209793l_bool(ord_le704992346e_bool,fa),hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_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) = hAPP_com_option_com(some_com,y) ).

tff(conj_6,hypothesis,
    hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),fa)) ).

tff(conj_7,conjecture,
    hBOOL(hAPP_f568432088l_bool(hoare_95103338_state(hAPP_f1763243027e_bool(image_1918575693_state(hAPP_f481860441_state(cOMBB_424558970_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f1749453397e_bool(hAPP_H122293036e_bool(insert1330351828_state,hAPP_c1041435779_state(hoare_Mirabelle_MGT,y)),bot_bo39439654e_bool))) ).

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