TPTP Problem File: SWW474_1.p
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%------------------------------------------------------------------------------
% File : SWW474_1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 440, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : hoare_100_tff_l440 [Bla11]
% Status : Theorem
% Rating : 0.22 v8.2.0, 0.30 v8.1.0, 0.18 v7.5.0, 0.25 v7.4.0, 0.00 v6.0.0, 0.20 v5.5.0, 0.00 v5.3.0
% Syntax : Number of formulae : 613 ( 120 unt; 238 typ; 0 def)
% Number of atoms : 817 ( 281 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 545 ( 103 ~; 39 |; 36 &)
% ( 53 <=>; 314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 61 ( 60 usr)
% Number of type conns : 227 ( 135 >; 92 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 177 ( 177 usr; 43 con; 0-2 aty)
% Number of variables : 830 ( 823 !; 7 ?; 830 :)
% SPC : TF0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:45:03
%------------------------------------------------------------------------------
%----Should-be-implicit typings (60)
tff(ty_ty_tc__Com__Ocom,type,
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tff(ty_ty_tc__Com__Opname,type,
pname: $tType ).
tff(ty_ty_tc__HOL__Obool,type,
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%----Explicit typings (178)
tff(sy_c_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc,type,
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tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__030,type,
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tff(sy_c_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_000tc__Com__,type,
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tff(sy_c_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool,type,
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tff(sy_c_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t,type,
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tff(sy_c_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostate_J_0_032,type,
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tff(sy_c_COMBK_000tc__Com__Opname_000tc__Com__Opname,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__O,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiem,type,
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tff(sy_c_Com_OWT,type,
wt: com > bool ).
tff(sy_c_Com_OWT__bodies,type,
wT_bodies: bool ).
tff(sy_c_Com_Obody,type,
body: fun_pname_option_com ).
tff(sy_c_Com_Ocom_OBODY,type,
body_1: fun_pname_com ).
tff(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
finite_finite_pname: fun_fu1430349052l_bool ).
tff(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__C,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otrip,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtk,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL_,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle___,type,
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tff(sy_c_Hoare__Mirabelle__yiemogtkbg_OMGT,type,
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tff(sy_c_Hoare__Mirabelle__yiemogtkbg_Ohoare__derivs_000tc__Com__Ostate,type,
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tff(sy_c_Hoare__Mirabelle__yiemogtkbg_Ostate__not__singleton,type,
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tff(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
dom_pname_com: fun_pname_option_com > fun_pname_bool ).
tff(sy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom,type,
dom_fu2081503504ol_com: fun_fu799392094on_com > fun_fu1430349052l_bool ).
tff(sy_c_Map_Odom_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com,type,
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tff(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
some_com: com > option_com ).
tff(sy_c_Option_Othe_000tc__Com__Ocom,type,
the_com: fun_option_com_com ).
tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
bot_bo844097828e_bool: fun_pname_bool ).
tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg,type,
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tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__O,type,
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tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____y,type,
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tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mt,type,
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tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirab,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Hoare____Mirabelle____yiemo,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__H,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opna,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____,type,
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tff(sy_c_Set_OCollect_000tc__Com__Opname,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
tff(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ost,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc_,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HO,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otr,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemog,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg__Otri,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____yiemogt,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL,type,
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tff(sy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle__,type,
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tff(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostat,type,
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tff(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostat_037,type,
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tff(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostat_038,type,
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tff(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostat_039,type,
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tff(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostat_040,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare____Mi,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__C,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__C_041,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__042,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otrip,type,
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tff(sy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otrip_043,type,
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tff(sy_c_Set_Oinsert_000tc__Com__Opname,type,
insert_pname: ( pname * fun_pname_bool ) > fun_pname_bool ).
tff(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Osta,type,
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tff(sy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_Set_Oinsert_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__,type,
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tff(sy_c_Set_Oinsert_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,type,
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tff(sy_c_Set_Oinsert_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otri,type,
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tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fNot,type,
fNot: fun_bool_bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_fconj,type,
fconj: fun_bo1549164019l_bool ).
tff(sy_c_fdisj,type,
fdisj: fun_bo1549164019l_bool ).
tff(sy_c_fequal_000tc__Com__Opname,type,
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tff(sy_c_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostate_J,type,
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tff(sy_c_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__,type,
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tff(sy_c_fimplies,type,
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tff(sy_c_hAPP_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc_,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__Com__Ocom,type,
hAPP_pname_com: ( fun_pname_com * pname ) > com ).
tff(sy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,type,
hAPP_pname_pname: ( fun_pname_pname * pname ) > pname ).
tff(sy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,type,
hAPP_pname_bool: ( fun_pname_bool * pname ) > bool ).
tff(sy_c_hAPP_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__O,type,
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tff(sy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
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tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
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hAPP_f1258983629l_bool: ( fun_fu1259080373l_bool * fun_Ho734851753e_bool ) > fun_fu64031073l_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_057,type,
hAPP_f32027384l_bool: ( fun_fu1171508960l_bool * fun_fu1430349052l_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Obool_058,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_059,type,
hAPP_f510955609l_bool: ( fun_fu1911931399l_bool * fun_fu1430349052l_bool ) > fun_fu399576434l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc,type,
hAPP_f1526158591l_bool: ( fun_fu64031073l_bool * fun_fu1783763359l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc_060,type,
hAPP_f2022158333l_bool: ( fun_fu296636465l_bool * fun_fu1783763359l_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc_061,type,
hAPP_f1360064833l_bool: ( fun_fu1137856163l_bool * fun_fu1783763359l_bool ) > fun_fu1783763359l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc_062,type,
hAPP_f511954751l_bool: ( fun_fu1483785331l_bool * fun_fu1783763359l_bool ) > fun_fu64031073l_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_063,type,
hAPP_f1759205631l_bool: ( fun_fu1086940979l_bool * fun_fu399576434l_bool ) > fun_fu1438281908l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Ot,type,
hAPP_f1359865257l_bool: ( fun_fu1690815831l_bool * fun_fu64031073l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Ot_064,type,
hAPP_f1607907235l_bool: ( fun_fu325884881l_bool * fun_fu64031073l_bool ) > fun_fu1690815831l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,type,
hAPP_f595608956l_bool: ( fun_fu2065874474l_bool * fun_fu1438281908l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemo,type,
hAPP_f844837559l_bool: ( fun_fu867166233l_bool * fun_fu1690815831l_bool ) > bool ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__Com__Opname,type,
member_pname: fun_pn422929397l_bool ).
tff(sy_c_member_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__Ostate_J,type,
member591555156_state: fun_Ho1489168363l_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____yiemogtkbg__Otriple_Itc__Com__,type,
member1948767740e_bool: fun_fu1259080373l_bool ).
tff(sy_v_Fa,type,
fa: fun_Ho734851753e_bool ).
tff(sy_v_pn,type,
pn: pname ).
tff(sy_v_y,type,
y: com ).
%----Relevant facts (300)
tff(fact_0_empty,axiom,
! [G: fun_Ho734851753e_bool] : hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),bot_bo454148287e_bool)) ).
tff(fact_1_asm,axiom,
! [Ts: fun_Ho734851753e_bool,G: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,Ts),G))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts)) ) ).
tff(fact_2_weaken,axiom,
! [Ts: fun_Ho734851753e_bool,G: fun_Ho734851753e_bool,Ts_1: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts_1))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,Ts),Ts_1))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts)) ) ) ).
tff(fact_3_thin,axiom,
! [G: fun_Ho734851753e_bool,G_1: fun_Ho734851753e_bool,Ts: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G_1),Ts))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,G_1),G))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts)) ) ) ).
tff(fact_4_cut,axiom,
! [G: fun_Ho734851753e_bool,G_1: fun_Ho734851753e_bool,Ts: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G_1),Ts))
=> ( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),G_1))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts)) ) ) ).
tff(fact_5_hoare__derivs_Oinsert,axiom,
! [Ts: fun_Ho734851753e_bool,G: fun_Ho734851753e_bool,T: hoare_1848483303_state] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(T,bot_bo454148287e_bool)))
=> ( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(T,Ts))) ) ) ).
tff(fact_6_derivs__insertD,axiom,
! [G: fun_Ho734851753e_bool,T: hoare_1848483303_state,Ts: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(T,Ts)))
=> ( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(T,bot_bo454148287e_bool)))
& hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),Ts)) ) ) ).
tff(fact_7_MGT__BodyN,axiom,
! [Pn_1: pname,G: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),G)),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),bot_bo454148287e_bool)))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),bot_bo454148287e_bool))) ) ).
tff(fact_8_finite__Collect__subsets,axiom,
! [A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))) ) ).
tff(fact_9_finite__Collect__subsets,axiom,
! [A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(hAPP_f15397171l_bool(cOMBC_80545690l_bool(ord_le1119700979e_bool),A)))) ) ).
tff(fact_10_finite__Collect__subsets,axiom,
! [A: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))) ) ).
tff(fact_11_finite__Collect__subsets,axiom,
! [A: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,A))
=> hBOOL(hAPP_f844837559l_bool(finite1393641268l_bool,collec1616186998l_bool(hAPP_f1607907235l_bool(cOMBC_1420373658l_bool(ord_le101734315l_bool),A)))) ) ).
tff(fact_12_finite__Collect__subsets,axiom,
! [A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,collec2020384458l_bool(hAPP_f511954751l_bool(cOMBC_1690116422l_bool(ord_le1819283413l_bool),A)))) ) ).
tff(fact_13_finite__Collect__subsets,axiom,
! [A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))) ) ).
tff(fact_14_finite__imageI,axiom,
! [H: fun_pn447269700_state,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,image_1256224870_state(H,Fa))) ) ).
tff(fact_15_finite__imageI,axiom,
! [H: fun_fu1664106117_pname,Fa: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,Fa))) ) ).
tff(fact_16_finite__imageI,axiom,
! [H: fun_fu1931361878_pname,Fa: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_2036190066_pname(H,Fa))) ) ).
tff(fact_17_finite__imageI,axiom,
! [H: fun_fu891110808_pname,Fa: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1825746272_pname(H,Fa))) ) ).
tff(fact_18_finite__imageI,axiom,
! [H: fun_fu1499449723_pname,Fa: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,Fa))) ) ).
tff(fact_19_finite__imageI,axiom,
! [H: fun_fu230733820_state,Fa: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,image_2078273054_state(H,Fa))) ) ).
tff(fact_20_finite__imageI,axiom,
! [H: fun_fu1538259051_state,Fa: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,Fa))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,image_71018297_state(H,Fa))) ) ).
tff(fact_21_finite__imageI,axiom,
! [H: fun_fu1404623273_state,Fa: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,Fa))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,image_730818763_state(H,Fa))) ) ).
tff(fact_22_finite__imageI,axiom,
! [H: fun_fu1387033222_state,Fa: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,image_1916896084_state(H,Fa))) ) ).
tff(fact_23_finite__imageI,axiom,
! [H: fun_pn422929397l_bool,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,Fa))) ) ).
tff(fact_24_finite__imageI,axiom,
! [H: fun_pn1359388668l_bool,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,image_1820576158l_bool(H,Fa))) ) ).
tff(fact_25_finite__imageI,axiom,
! [H: fun_pn2079317538e_bool,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,image_2051793258e_bool(H,Fa))) ) ).
tff(fact_26_finite__imageI,axiom,
! [H: fun_pn800050071e_bool,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,Fa))) ) ).
tff(fact_27_finite__imageI,axiom,
! [H: fun_Ho872578118l_bool,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_7400930l_bool(H,Fa))) ) ).
tff(fact_28_finite__imageI,axiom,
! [H: fun_Ho1489168363l_bool,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,image_783059513l_bool(H,Fa))) ) ).
tff(fact_29_finite__imageI,axiom,
! [H: fun_Ho1480763635e_bool,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,image_249571983e_bool(H,Fa))) ) ).
tff(fact_30_finite__imageI,axiom,
! [H: fun_Ho585232518e_bool,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_983321428e_bool(H,Fa))) ) ).
tff(fact_31_finite__imageI,axiom,
! [H: fun_Ho862234382_pname,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_2075962154_pname(H,Fa))) ) ).
tff(fact_32_finite__imageI,axiom,
! [H: fun_pname_pname,Fa: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,Fa))) ) ).
tff(fact_33_empty__subsetI,axiom,
! [A: fun_Ho734851753e_bool] : hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,bot_bo454148287e_bool),A)) ).
tff(fact_34_empty__subsetI,axiom,
! [A: fun_fu1430349052l_bool] : hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),A)) ).
tff(fact_35_empty__subsetI,axiom,
! [A: fun_fu1783763359l_bool] : hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,bot_bo2068035593l_bool),A)) ).
tff(fact_36_empty__subsetI,axiom,
! [A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)) ).
tff(fact_37_finite_OinsertI,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,insert668001005_state(A_2,A))) ) ).
tff(fact_38_finite_OinsertI,axiom,
! [A_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A))) ) ).
tff(fact_39_finite_OinsertI,axiom,
! [A_2: fun_fu1430349052l_bool,A: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_2,A))) ) ).
tff(fact_40_finite_OinsertI,axiom,
! [A_2: fun_fu1783763359l_bool,A: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,A))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,insert1735796133l_bool(A_2,A))) ) ).
tff(fact_41_finite_OinsertI,axiom,
! [A_2: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,insert1390540323e_bool(A_2,A))) ) ).
tff(fact_42_finite_OinsertI,axiom,
! [A_2: fun_pname_bool,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A))) ) ).
tff(fact_43_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ).
tff(fact_44_finite_OemptyI,axiom,
hBOOL(hAPP_f355887345l_bool(finite1765195604_state,bot_bo454148287e_bool)) ).
tff(fact_45_finite_OemptyI,axiom,
hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,bot_bo1537088220l_bool)) ).
tff(fact_46_finite_OemptyI,axiom,
hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,bot_bo973295223l_bool)) ).
tff(fact_47_finite_OemptyI,axiom,
hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,bot_bo2068035593l_bool)) ).
tff(fact_48_finite_OemptyI,axiom,
hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)) ).
tff(fact_49_finite__Collect__conjI,axiom,
! [Q_1: fun_pname_bool,P_1: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,P_1),Q_1)))) ) ).
tff(fact_50_finite__Collect__conjI,axiom,
! [Q_1: fun_Ho734851753e_bool,P_1: fun_Ho734851753e_bool] :
( ( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(P_1)))
| hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(Q_1))) )
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fconj,P_1),Q_1)))) ) ).
tff(fact_51_finite__Collect__conjI,axiom,
! [Q_1: fun_fu399576434l_bool,P_1: fun_fu399576434l_bool] :
( ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(P_1)))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(Q_1))) )
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,P_1),Q_1)))) ) ).
tff(fact_52_finite__Collect__conjI,axiom,
! [Q_1: fun_fu64031073l_bool,P_1: fun_fu64031073l_bool] :
( ( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,collec2020384458l_bool(P_1)))
| hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,collec2020384458l_bool(Q_1))) )
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,collec2020384458l_bool(cOMBS_101732372l_bool(cOMBB_1936369445l_bool(fconj,P_1),Q_1)))) ) ).
tff(fact_53_finite__Collect__conjI,axiom,
! [Q_1: fun_fu1783763359l_bool,P_1: fun_fu1783763359l_bool] :
( ( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(P_1)))
| hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(Q_1))) )
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fconj,P_1),Q_1)))) ) ).
tff(fact_54_finite__Collect__conjI,axiom,
! [Q_1: fun_fu1430349052l_bool,P_1: fun_fu1430349052l_bool] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,P_1),Q_1)))) ) ).
tff(fact_55_image__constant__conv,axiom,
! [C_1: hoare_1848483303_state,A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( image_1256224870_state(cOMBK_240819937_pname(C_1),A) = bot_bo454148287e_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ( image_1256224870_state(cOMBK_240819937_pname(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ) ).
tff(fact_56_image__constant__conv,axiom,
! [C_1: pname,A: fun_Ho734851753e_bool] :
( ( ( A = bot_bo454148287e_bool )
=> ( image_2075962154_pname(cOMBK_1568566301_state(C_1),A) = bot_bo844097828e_bool ) )
& ( ( A != bot_bo454148287e_bool )
=> ( image_2075962154_pname(cOMBK_1568566301_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ) ).
tff(fact_57_image__constant__conv,axiom,
! [C_1: fun_pname_bool,A: fun_Ho734851753e_bool] :
( ( ( A = bot_bo454148287e_bool )
=> ( image_983321428e_bool(cOMBK_1288377053_state(C_1),A) = bot_bo1649642514l_bool ) )
& ( ( A != bot_bo454148287e_bool )
=> ( image_983321428e_bool(cOMBK_1288377053_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ) ) ) ).
tff(fact_58_image__constant__conv,axiom,
! [C_1: fun_Ho734851753e_bool,A: fun_Ho734851753e_bool] :
( ( ( A = bot_bo454148287e_bool )
=> ( image_249571983e_bool(cOMBK_1751623554_state(C_1),A) = bot_bo2068035593l_bool ) )
& ( ( A != bot_bo454148287e_bool )
=> ( image_249571983e_bool(cOMBK_1751623554_state(C_1),A) = insert1390540323e_bool(C_1,bot_bo2068035593l_bool) ) ) ) ).
tff(fact_59_image__constant__conv,axiom,
! [C_1: fun_pname_bool,A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = bot_bo1649642514l_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ) ) ) ).
tff(fact_60_image__constant__conv,axiom,
! [C_1: fun_Ho734851753e_bool,A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( image_2051793258e_bool(cOMBK_1197227241_pname(C_1),A) = bot_bo2068035593l_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ( image_2051793258e_bool(cOMBK_1197227241_pname(C_1),A) = insert1390540323e_bool(C_1,bot_bo2068035593l_bool) ) ) ) ).
tff(fact_61_image__constant__conv,axiom,
! [C_1: pname,A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( image_pname_pname(cOMBK_pname_pname(C_1),A) = bot_bo844097828e_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ( image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ) ).
tff(fact_62_image__constant__conv,axiom,
! [C_1: hoare_1848483303_state,A: fun_fu1430349052l_bool] :
( ( ( A = bot_bo1649642514l_bool )
=> ( image_1916896084_state(cOMBK_354802397e_bool(C_1),A) = bot_bo454148287e_bool ) )
& ( ( A != bot_bo1649642514l_bool )
=> ( image_1916896084_state(cOMBK_354802397e_bool(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ) ).
tff(fact_63_image__constant__conv,axiom,
! [C_1: hoare_1848483303_state,A: fun_fu1783763359l_bool] :
( ( ( A = bot_bo2068035593l_bool )
=> ( image_730818763_state(cOMBK_1270376774e_bool(C_1),A) = bot_bo454148287e_bool ) )
& ( ( A != bot_bo2068035593l_bool )
=> ( image_730818763_state(cOMBK_1270376774e_bool(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ) ).
tff(fact_64_image__constant__conv,axiom,
! [C_1: pname,A: fun_fu1430349052l_bool] :
( ( ( A = bot_bo1649642514l_bool )
=> ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = bot_bo844097828e_bool ) )
& ( ( A != bot_bo1649642514l_bool )
=> ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ) ).
tff(fact_65_image__constant__conv,axiom,
! [C_1: pname,A: fun_fu1783763359l_bool] :
( ( ( A = bot_bo2068035593l_bool )
=> ( image_1825746272_pname(cOMBK_1423274227e_bool(C_1),A) = bot_bo844097828e_bool ) )
& ( ( A != bot_bo2068035593l_bool )
=> ( image_1825746272_pname(cOMBK_1423274227e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ) ).
tff(fact_66_image__constant,axiom,
! [C_1: hoare_1848483303_state,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( image_1256224870_state(cOMBK_240819937_pname(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ).
tff(fact_67_image__constant,axiom,
! [C_1: pname,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( image_2075962154_pname(cOMBK_1568566301_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ).
tff(fact_68_image__constant,axiom,
! [C_1: fun_pname_bool,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( image_983321428e_bool(cOMBK_1288377053_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ) ) ).
tff(fact_69_image__constant,axiom,
! [C_1: fun_Ho734851753e_bool,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( image_249571983e_bool(cOMBK_1751623554_state(C_1),A) = insert1390540323e_bool(C_1,bot_bo2068035593l_bool) ) ) ).
tff(fact_70_image__constant,axiom,
! [C_1: fun_pname_bool,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ) ) ).
tff(fact_71_image__constant,axiom,
! [C_1: fun_Ho734851753e_bool,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( image_2051793258e_bool(cOMBK_1197227241_pname(C_1),A) = insert1390540323e_bool(C_1,bot_bo2068035593l_bool) ) ) ).
tff(fact_72_image__constant,axiom,
! [C_1: pname,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ).
tff(fact_73_image__constant,axiom,
! [C_1: hoare_1848483303_state,X_2: fun_pname_bool,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> ( image_1916896084_state(cOMBK_354802397e_bool(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ).
tff(fact_74_image__constant,axiom,
! [C_1: hoare_1848483303_state,X_2: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_2),A))
=> ( image_730818763_state(cOMBK_1270376774e_bool(C_1),A) = insert668001005_state(C_1,bot_bo454148287e_bool) ) ) ).
tff(fact_75_image__constant,axiom,
! [C_1: pname,X_2: fun_pname_bool,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ).
tff(fact_76_image__constant,axiom,
! [C_1: pname,X_2: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_2),A))
=> ( image_1825746272_pname(cOMBK_1423274227e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ) ) ).
tff(fact_77_insert__dom,axiom,
! [F: fun_pname_option_com,X_2: pname,Y_2: com] :
( ( hAPP_p799580910on_com(F,X_2) = some_com(Y_2) )
=> ( insert_pname(X_2,dom_pname_com(F)) = dom_pname_com(F) ) ) ).
tff(fact_78_insert__dom,axiom,
! [F: fun_fu799392094on_com,X_2: fun_pname_bool,Y_2: com] :
( ( hAPP_f2138803836on_com(F,X_2) = some_com(Y_2) )
=> ( insert1325755072e_bool(X_2,dom_fu2081503504ol_com(F)) = dom_fu2081503504ol_com(F) ) ) ).
tff(fact_79_insert__dom,axiom,
! [F: fun_fu549469569on_com,X_2: fun_Ho734851753e_bool,Y_2: com] :
( ( hAPP_f636233299on_com(F,X_2) = some_com(Y_2) )
=> ( insert1390540323e_bool(X_2,dom_fu475558963ol_com(F)) = dom_fu475558963ol_com(F) ) ) ).
tff(fact_80_finite__surj,axiom,
! [B: fun_Ho734851753e_bool,F: fun_pn447269700_state,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_1256224870_state(F,A)))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B)) ) ) ).
tff(fact_81_finite__surj,axiom,
! [B: fun_pname_bool,F: fun_fu1664106117_pname,A: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1705983821_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_82_finite__surj,axiom,
! [B: fun_pname_bool,F: fun_fu1931361878_pname,A: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_2036190066_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_83_finite__surj,axiom,
! [B: fun_pname_bool,F: fun_fu891110808_pname,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1825746272_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_84_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),image_1283814551_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_85_finite__surj,axiom,
! [B: fun_Ho734851753e_bool,F: fun_fu230733820_state,A: fun_fu399576434l_bool] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_2078273054_state(F,A)))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B)) ) ) ).
tff(fact_86_finite__surj,axiom,
! [B: fun_Ho734851753e_bool,F: fun_fu1538259051_state,A: fun_fu64031073l_bool] :
( hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_71018297_state(F,A)))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B)) ) ) ).
tff(fact_87_finite__surj,axiom,
! [B: fun_Ho734851753e_bool,F: fun_fu1404623273_state,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_730818763_state(F,A)))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B)) ) ) ).
tff(fact_88_finite__surj,axiom,
! [B: fun_Ho734851753e_bool,F: fun_fu1387033222_state,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_1916896084_state(F,A)))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B)) ) ) ).
tff(fact_89_finite__surj,axiom,
! [B: fun_fu399576434l_bool,F: fun_pn422929397l_bool,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1642285373l_bool(F,A)))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B)) ) ) ).
tff(fact_90_finite__surj,axiom,
! [B: fun_fu64031073l_bool,F: fun_pn1359388668l_bool,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1359865257l_bool(hAPP_f1607907235l_bool(ord_le101734315l_bool,B),image_1820576158l_bool(F,A)))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,B)) ) ) ).
tff(fact_91_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),image_pname_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_92_finite__surj,axiom,
! [B: fun_fu1783763359l_bool,F: fun_pn2079317538e_bool,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,B),image_2051793258e_bool(F,A)))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,B)) ) ) ).
tff(fact_93_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),image_47868345e_bool(F,A)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
tff(fact_94_finite__surj,axiom,
! [B: fun_fu399576434l_bool,F: fun_Ho872578118l_bool,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> ( hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_7400930l_bool(F,A)))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B)) ) ) ).
tff(fact_95_finite__surj,axiom,
! [B: fun_fu64031073l_bool,F: fun_Ho1489168363l_bool,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> ( hBOOL(hAPP_f1359865257l_bool(hAPP_f1607907235l_bool(ord_le101734315l_bool,B),image_783059513l_bool(F,A)))
=> hBOOL(hAPP_f1359865257l_bool(finite181314444l_bool,B)) ) ) ).
tff(fact_96_finite__surj,axiom,
! [B: fun_pname_bool,F: fun_Ho862234382_pname,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_2075962154_pname(F,A)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ) ).
tff(fact_97_finite__surj,axiom,
! [B: fun_fu1783763359l_bool,F: fun_Ho1480763635e_bool,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,B),image_249571983e_bool(F,A)))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,B)) ) ) ).
tff(fact_98_finite__surj,axiom,
! [B: fun_fu1430349052l_bool,F: fun_Ho585232518e_bool,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_983321428e_bool(F,A)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ) ).
tff(fact_99_subset__singletonD,axiom,
! [A: fun_Ho734851753e_bool,X_2: hoare_1848483303_state] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),insert668001005_state(X_2,bot_bo454148287e_bool)))
=> ( ( A = bot_bo454148287e_bool )
| ( A = insert668001005_state(X_2,bot_bo454148287e_bool) ) ) ) ).
tff(fact_100_subset__singletonD,axiom,
! [A: fun_fu1430349052l_bool,X_2: fun_pname_bool] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),insert1325755072e_bool(X_2,bot_bo1649642514l_bool)))
=> ( ( A = bot_bo1649642514l_bool )
| ( A = insert1325755072e_bool(X_2,bot_bo1649642514l_bool) ) ) ) ).
tff(fact_101_subset__singletonD,axiom,
! [A: fun_fu1783763359l_bool,X_2: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,A),insert1390540323e_bool(X_2,bot_bo2068035593l_bool)))
=> ( ( A = bot_bo2068035593l_bool )
| ( A = insert1390540323e_bool(X_2,bot_bo2068035593l_bool) ) ) ) ).
tff(fact_102_subset__singletonD,axiom,
! [A: fun_pname_bool,X_2: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,bot_bo844097828e_bool)))
=> ( ( A = bot_bo844097828e_bool )
| ( A = insert_pname(X_2,bot_bo844097828e_bool) ) ) ) ).
tff(fact_103_MGF,axiom,
! [C_1: com] :
( hBOOL(hoare_1310879719gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(wt(C_1))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(bot_bo454148287e_bool),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,C_1),bot_bo454148287e_bool))) ) ) ) ).
tff(fact_104_emptyE,axiom,
! [A_2: hoare_1848483303_state] : ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),bot_bo454148287e_bool)) ).
tff(fact_105_emptyE,axiom,
! [A_2: fun_pname_bool] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),bot_bo1649642514l_bool)) ).
tff(fact_106_emptyE,axiom,
! [A_2: fun_Ho734851753e_bool] : ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),bot_bo2068035593l_bool)) ).
tff(fact_107_emptyE,axiom,
! [A_2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)) ).
tff(fact_108_insertCI,axiom,
! [B_1: hoare_1848483303_state,A_2: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),B))
=> ( A_2 = B_1 ) )
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),insert668001005_state(B_1,B))) ) ).
tff(fact_109_insertCI,axiom,
! [B_1: fun_pname_bool,A_2: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),B))
=> ( A_2 = B_1 ) )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,B))) ) ).
tff(fact_110_insertCI,axiom,
! [B_1: fun_Ho734851753e_bool,A_2: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),B))
=> ( A_2 = B_1 ) )
=> hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),insert1390540323e_bool(B_1,B))) ) ).
tff(fact_111_insertCI,axiom,
! [B_1: pname,A_2: pname,B: fun_pname_bool] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
=> ( A_2 = B_1 ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))) ) ).
tff(fact_112_insertE,axiom,
! [A_2: hoare_1848483303_state,B_1: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),insert668001005_state(B_1,A)))
=> ( ( A_2 != B_1 )
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),A)) ) ) ).
tff(fact_113_insertE,axiom,
! [A_2: fun_pname_bool,B_1: fun_pname_bool,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,A)))
=> ( ( A_2 != B_1 )
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)) ) ) ).
tff(fact_114_insertE,axiom,
! [A_2: fun_Ho734851753e_bool,B_1: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),insert1390540323e_bool(B_1,A)))
=> ( ( A_2 != B_1 )
=> hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),A)) ) ) ).
tff(fact_115_insertE,axiom,
! [A_2: pname,B_1: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
=> ( ( A_2 != B_1 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ) ) ).
tff(fact_116_equalityI,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),A))
=> ( A = B ) ) ) ).
tff(fact_117_equalityI,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(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A))
=> ( A = B ) ) ) ).
tff(fact_118_equalityI,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,A),B))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,B),A))
=> ( A = B ) ) ) ).
tff(fact_119_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_120_subsetD,axiom,
! [C_1: hoare_1848483303_state,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,C_1),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,C_1),B)) ) ) ).
tff(fact_121_subsetD,axiom,
! [C_1: fun_pname_bool,A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),A))
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),B)) ) ) ).
tff(fact_122_subsetD,axiom,
! [C_1: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,A),B))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,C_1),A))
=> hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,C_1),B)) ) ) ).
tff(fact_123_subsetD,axiom,
! [C_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,C_1),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B)) ) ) ).
tff(fact_124_image__eqI,axiom,
! [A: fun_Ho734851753e_bool,B_1: fun_pname_bool,F: fun_Ho585232518e_bool,X_2: hoare_1848483303_state] :
( ( B_1 = hAPP_H1355725988e_bool(F,X_2) )
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_983321428e_bool(F,A))) ) ) ).
tff(fact_125_image__eqI,axiom,
! [A: fun_Ho734851753e_bool,B_1: fun_Ho734851753e_bool,F: fun_Ho1480763635e_bool,X_2: hoare_1848483303_state] :
( ( B_1 = hAPP_H1618070847e_bool(F,X_2) )
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,B_1),image_249571983e_bool(F,A))) ) ) ).
tff(fact_126_image__eqI,axiom,
! [A: fun_pname_bool,B_1: fun_pname_bool,F: fun_pn800050071e_bool,X_2: pname] :
( ( B_1 = hAPP_p61793385e_bool(F,X_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_47868345e_bool(F,A))) ) ) ).
tff(fact_127_image__eqI,axiom,
! [A: fun_pname_bool,B_1: fun_Ho734851753e_bool,F: fun_pn2079317538e_bool,X_2: pname] :
( ( B_1 = hAPP_p276714170e_bool(F,X_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,B_1),image_2051793258e_bool(F,A))) ) ) ).
tff(fact_128_image__eqI,axiom,
! [A: fun_fu1430349052l_bool,B_1: hoare_1848483303_state,F: fun_fu1387033222_state,X_2: fun_pname_bool] :
( ( B_1 = hAPP_f141816996_state(F,X_2) )
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),image_1916896084_state(F,A))) ) ) ).
tff(fact_129_image__eqI,axiom,
! [A: fun_fu1783763359l_bool,B_1: hoare_1848483303_state,F: fun_fu1404623273_state,X_2: fun_Ho734851753e_bool] :
( ( B_1 = hAPP_f2099317627_state(F,X_2) )
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),image_730818763_state(F,A))) ) ) ).
tff(fact_130_image__eqI,axiom,
! [A: fun_Ho734851753e_bool,B_1: pname,F: fun_Ho862234382_pname,X_2: hoare_1848483303_state] :
( ( B_1 = hAPP_H1494965722_pname(F,X_2) )
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_2075962154_pname(F,A))) ) ) ).
tff(fact_131_image__eqI,axiom,
! [A: fun_pname_bool,B_1: pname,F: fun_pname_pname,X_2: pname] :
( ( B_1 = hAPP_pname_pname(F,X_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_pname_pname(F,A))) ) ) ).
tff(fact_132_image__eqI,axiom,
! [A: fun_fu1430349052l_bool,B_1: pname,F: fun_fu1499449723_pname,X_2: fun_pname_bool] :
( ( B_1 = hAPP_f1297739591_pname(F,X_2) )
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_1283814551_pname(F,A))) ) ) ).
tff(fact_133_image__eqI,axiom,
! [A: fun_fu1783763359l_bool,B_1: pname,F: fun_fu891110808_pname,X_2: fun_Ho734851753e_bool] :
( ( B_1 = hAPP_f50667184_pname(F,X_2) )
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_1825746272_pname(F,A))) ) ) ).
tff(fact_134_image__eqI,axiom,
! [A: fun_pname_bool,B_1: hoare_1848483303_state,F: fun_pn447269700_state,X_2: pname] :
( ( B_1 = hAPP_p675228438_state(F,X_2) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),image_1256224870_state(F,A))) ) ) ).
tff(fact_135_equals0D,axiom,
! [A_2: fun_pname_bool,A: fun_fu1430349052l_bool] :
( ( A = bot_bo1649642514l_bool )
=> ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)) ) ).
tff(fact_136_equals0D,axiom,
! [A_2: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( ( A = bot_bo2068035593l_bool )
=> ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_2),A)) ) ).
tff(fact_137_equals0D,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( ( A = bot_bo454148287e_bool )
=> ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),A)) ) ).
tff(fact_138_equals0D,axiom,
! [A_2: pname,A: fun_pname_bool] :
( ( A = bot_bo844097828e_bool )
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ) ).
tff(fact_139_Collect__empty__eq,axiom,
! [P_1: fun_fu399576434l_bool] :
( ( collec1613912337l_bool(P_1) = bot_bo1537088220l_bool )
<=> ! [X_1: fun_fu1430349052l_bool] : ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1)) ) ).
tff(fact_140_Collect__empty__eq,axiom,
! [P_1: fun_fu64031073l_bool] :
( ( collec2020384458l_bool(P_1) = bot_bo973295223l_bool )
<=> ! [X_1: fun_fu1783763359l_bool] : ~ hBOOL(hAPP_f1526158591l_bool(P_1,X_1)) ) ).
tff(fact_141_Collect__empty__eq,axiom,
! [P_1: fun_fu1783763359l_bool] :
( ( collec1657840446e_bool(P_1) = bot_bo2068035593l_bool )
<=> ! [X_1: fun_Ho734851753e_bool] : ~ hBOOL(hAPP_f355887345l_bool(P_1,X_1)) ) ).
tff(fact_142_Collect__empty__eq,axiom,
! [P_1: fun_fu1430349052l_bool] :
( ( collec1974731493e_bool(P_1) = bot_bo1649642514l_bool )
<=> ! [X_1: fun_pname_bool] : ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ).
tff(fact_143_Collect__empty__eq,axiom,
! [P_1: fun_Ho734851753e_bool] :
( ( collec1708318610_state(P_1) = bot_bo454148287e_bool )
<=> ! [X_1: hoare_1848483303_state] : ~ hBOOL(hAPP_H2060173127e_bool(P_1,X_1)) ) ).
tff(fact_144_Collect__empty__eq,axiom,
! [P_1: fun_pname_bool] :
( ( collect_pname(P_1) = bot_bo844097828e_bool )
<=> ! [X_1: pname] : ~ hBOOL(hAPP_pname_bool(P_1,X_1)) ) ).
tff(fact_145_empty__iff,axiom,
! [C_1: fun_pname_bool] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),bot_bo1649642514l_bool)) ).
tff(fact_146_empty__iff,axiom,
! [C_1: fun_Ho734851753e_bool] : ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,C_1),bot_bo2068035593l_bool)) ).
tff(fact_147_empty__iff,axiom,
! [C_1: hoare_1848483303_state] : ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,C_1),bot_bo454148287e_bool)) ).
tff(fact_148_empty__iff,axiom,
! [C_1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)) ).
tff(fact_149_empty__Collect__eq,axiom,
! [P_1: fun_fu399576434l_bool] :
( ( bot_bo1537088220l_bool = collec1613912337l_bool(P_1) )
<=> ! [X_1: fun_fu1430349052l_bool] : ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1)) ) ).
tff(fact_150_empty__Collect__eq,axiom,
! [P_1: fun_fu64031073l_bool] :
( ( bot_bo973295223l_bool = collec2020384458l_bool(P_1) )
<=> ! [X_1: fun_fu1783763359l_bool] : ~ hBOOL(hAPP_f1526158591l_bool(P_1,X_1)) ) ).
tff(fact_151_empty__Collect__eq,axiom,
! [P_1: fun_fu1783763359l_bool] :
( ( bot_bo2068035593l_bool = collec1657840446e_bool(P_1) )
<=> ! [X_1: fun_Ho734851753e_bool] : ~ hBOOL(hAPP_f355887345l_bool(P_1,X_1)) ) ).
tff(fact_152_empty__Collect__eq,axiom,
! [P_1: fun_fu1430349052l_bool] :
( ( bot_bo1649642514l_bool = collec1974731493e_bool(P_1) )
<=> ! [X_1: fun_pname_bool] : ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ).
tff(fact_153_empty__Collect__eq,axiom,
! [P_1: fun_Ho734851753e_bool] :
( ( bot_bo454148287e_bool = collec1708318610_state(P_1) )
<=> ! [X_1: hoare_1848483303_state] : ~ hBOOL(hAPP_H2060173127e_bool(P_1,X_1)) ) ).
tff(fact_154_empty__Collect__eq,axiom,
! [P_1: fun_pname_bool] :
( ( bot_bo844097828e_bool = collect_pname(P_1) )
<=> ! [X_1: pname] : ~ hBOOL(hAPP_pname_bool(P_1,X_1)) ) ).
tff(fact_155_ex__in__conv,axiom,
! [A: fun_fu1430349052l_bool] :
( ? [X_1: fun_pname_bool] : hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
<=> ( A != bot_bo1649642514l_bool ) ) ).
tff(fact_156_ex__in__conv,axiom,
! [A: fun_fu1783763359l_bool] :
( ? [X_1: fun_Ho734851753e_bool] : hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_1),A))
<=> ( A != bot_bo2068035593l_bool ) ) ).
tff(fact_157_ex__in__conv,axiom,
! [A: fun_Ho734851753e_bool] :
( ? [X_1: hoare_1848483303_state] : hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_1),A))
<=> ( A != bot_bo454148287e_bool ) ) ).
tff(fact_158_ex__in__conv,axiom,
! [A: fun_pname_bool] :
( ? [X_1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
<=> ( A != bot_bo844097828e_bool ) ) ).
tff(fact_159_all__not__in__conv,axiom,
! [A: fun_fu1430349052l_bool] :
( ! [X_1: fun_pname_bool] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
<=> ( A = bot_bo1649642514l_bool ) ) ).
tff(fact_160_all__not__in__conv,axiom,
! [A: fun_fu1783763359l_bool] :
( ! [X_1: fun_Ho734851753e_bool] : ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,X_1),A))
<=> ( A = bot_bo2068035593l_bool ) ) ).
tff(fact_161_all__not__in__conv,axiom,
! [A: fun_Ho734851753e_bool] :
( ! [X_1: hoare_1848483303_state] : ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_1),A))
<=> ( A = bot_bo454148287e_bool ) ) ).
tff(fact_162_all__not__in__conv,axiom,
! [A: fun_pname_bool] :
( ! [X_1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
<=> ( A = bot_bo844097828e_bool ) ) ).
tff(fact_163_empty__def,axiom,
bot_bo973295223l_bool = collec2020384458l_bool(cOMBK_2014663096l_bool(fFalse)) ).
tff(fact_164_empty__def,axiom,
bot_bo2068035593l_bool = collec1657840446e_bool(cOMBK_2110745040e_bool(fFalse)) ).
tff(fact_165_empty__def,axiom,
bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)) ).
tff(fact_166_empty__def,axiom,
bot_bo454148287e_bool = collec1708318610_state(cOMBK_2059960192_state(fFalse)) ).
tff(fact_167_empty__def,axiom,
bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)) ).
tff(fact_168_insert__absorb,axiom,
! [A_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
=> ( insert_pname(A_2,A) = A ) ) ).
tff(fact_169_insert__absorb,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),A))
=> ( insert668001005_state(A_2,A) = A ) ) ).
tff(fact_170_insertI2,axiom,
! [B_1: pname,A_2: pname,B: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))) ) ).
tff(fact_171_insertI2,axiom,
! [B_1: hoare_1848483303_state,A_2: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),B))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),insert668001005_state(B_1,B))) ) ).
tff(fact_172_insert__ident,axiom,
! [B: fun_pname_bool,X_2: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
=> ( ( insert_pname(X_2,A) = insert_pname(X_2,B) )
<=> ( A = B ) ) ) ) ).
tff(fact_173_insert__ident,axiom,
! [B: fun_Ho734851753e_bool,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),B))
=> ( ( insert668001005_state(X_2,A) = insert668001005_state(X_2,B) )
<=> ( A = B ) ) ) ) ).
tff(fact_174_insert__code,axiom,
! [Y_2: pname,A: fun_pname_bool,X_2: pname] :
( hBOOL(hAPP_pname_bool(insert_pname(Y_2,A),X_2))
<=> ( ( Y_2 = X_2 )
| hBOOL(hAPP_pname_bool(A,X_2)) ) ) ).
tff(fact_175_insert__code,axiom,
! [Y_2: hoare_1848483303_state,A: fun_Ho734851753e_bool,X_2: hoare_1848483303_state] :
( hBOOL(hAPP_H2060173127e_bool(insert668001005_state(Y_2,A),X_2))
<=> ( ( Y_2 = X_2 )
| hBOOL(hAPP_H2060173127e_bool(A,X_2)) ) ) ).
tff(fact_176_insert__iff,axiom,
! [A_2: pname,B_1: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
<=> ( ( A_2 = B_1 )
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ) ) ).
tff(fact_177_insert__iff,axiom,
! [A_2: hoare_1848483303_state,B_1: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),insert668001005_state(B_1,A)))
<=> ( ( A_2 = B_1 )
| hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),A)) ) ) ).
tff(fact_178_insert__commute,axiom,
! [X_2: pname,Y_2: pname,A: fun_pname_bool] : insert_pname(X_2,insert_pname(Y_2,A)) = insert_pname(Y_2,insert_pname(X_2,A)) ).
tff(fact_179_insert__commute,axiom,
! [X_2: hoare_1848483303_state,Y_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] : insert668001005_state(X_2,insert668001005_state(Y_2,A)) = insert668001005_state(Y_2,insert668001005_state(X_2,A)) ).
tff(fact_180_insert__absorb2,axiom,
! [X_2: pname,A: fun_pname_bool] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A) ).
tff(fact_181_insert__absorb2,axiom,
! [X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] : insert668001005_state(X_2,insert668001005_state(X_2,A)) = insert668001005_state(X_2,A) ).
tff(fact_182_insert__Collect,axiom,
! [A_2: pname,P_1: fun_pname_bool] : insert_pname(A_2,collect_pname(P_1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2))),P_1)) ).
tff(fact_183_insert__Collect,axiom,
! [A_2: hoare_1848483303_state,P_1: fun_Ho734851753e_bool] : insert668001005_state(A_2,collec1708318610_state(P_1)) = collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fimplies,cOMBB_1397003211_state(fNot,hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),A_2))),P_1)) ).
tff(fact_184_insert__Collect,axiom,
! [A_2: fun_pname_bool,P_1: fun_fu1430349052l_bool] : insert1325755072e_bool(A_2,collec1974731493e_bool(P_1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2))),P_1)) ).
tff(fact_185_insert__Collect,axiom,
! [A_2: fun_Ho734851753e_bool,P_1: fun_fu1783763359l_bool] : insert1390540323e_bool(A_2,collec1657840446e_bool(P_1)) = collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fimplies,cOMBB_1356070853e_bool(fNot,hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),A_2))),P_1)) ).
tff(fact_186_insert__compr,axiom,
! [A_2: pname,B: fun_pname_bool] : insert_pname(A_2,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))) ).
tff(fact_187_insert__compr,axiom,
! [A_2: hoare_1848483303_state,B: fun_Ho734851753e_bool] : insert668001005_state(A_2,B) = collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fdisj,hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),A_2)),hAPP_f617245717e_bool(cOMBC_1803918242l_bool(member591555156_state),B))) ).
tff(fact_188_insert__compr,axiom,
! [A_2: fun_pname_bool,B: fun_fu1430349052l_bool] : insert1325755072e_bool(A_2,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))) ).
tff(fact_189_insert__compr,axiom,
! [A_2: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] : insert1390540323e_bool(A_2,B) = collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fdisj,hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),A_2)),hAPP_f1360064833l_bool(cOMBC_1100692246l_bool(member1948767740e_bool),B))) ).
tff(fact_190_insertI1,axiom,
! [A_2: pname,B: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(A_2,B))) ).
tff(fact_191_insertI1,axiom,
! [A_2: hoare_1848483303_state,B: fun_Ho734851753e_bool] : hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_2),insert668001005_state(A_2,B))) ).
tff(fact_192_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_193_equalityE,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ~ ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ~ hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),A)) ) ) ).
tff(fact_194_subset__trans,axiom,
! [C_2: 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_2))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_2)) ) ) ).
tff(fact_195_subset__trans,axiom,
! [C_2: fun_Ho734851753e_bool,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),C_2))
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),C_2)) ) ) ).
tff(fact_196_set__mp,axiom,
! [X_2: 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_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
tff(fact_197_set__mp,axiom,
! [X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),B)) ) ) ).
tff(fact_198_set__rev__mp,axiom,
! [B: fun_pname_bool,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
tff(fact_199_set__rev__mp,axiom,
! [B: fun_Ho734851753e_bool,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),B)) ) ) ).
tff(fact_200_in__mono,axiom,
! [X_2: 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_2),A))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
tff(fact_201_in__mono,axiom,
! [X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),B)) ) ) ).
tff(fact_202_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_203_equalityD2,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),A)) ) ).
tff(fact_204_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_205_equalityD1,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B)) ) ).
tff(fact_206_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_207_set__eq__subset,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
<=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
& hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),A)) ) ) ).
tff(fact_208_subset__refl,axiom,
! [A: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)) ).
tff(fact_209_subset__refl,axiom,
! [A: fun_Ho734851753e_bool] : hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),A)) ).
tff(fact_210_rev__image__eqI,axiom,
! [B_1: hoare_1848483303_state,F: fun_pn447269700_state,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( ( B_1 = hAPP_p675228438_state(F,X_2) )
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),image_1256224870_state(F,A))) ) ) ).
tff(fact_211_imageI,axiom,
! [F: fun_pn447269700_state,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,hAPP_p675228438_state(F,X_2)),image_1256224870_state(F,A))) ) ).
tff(fact_212_image__iff,axiom,
! [Z: hoare_1848483303_state,F: fun_pn447269700_state,A: fun_pname_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,Z),image_1256224870_state(F,A)))
<=> ? [X_1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
& ( Z = hAPP_p675228438_state(F,X_1) ) ) ) ).
tff(fact_213_finite__Collect__disjI,axiom,
! [P_1: fun_pname_bool,Q_1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,P_1),Q_1))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) ) ) ).
tff(fact_214_finite__Collect__disjI,axiom,
! [P_1: fun_Ho734851753e_bool,Q_1: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fdisj,P_1),Q_1))))
<=> ( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(P_1)))
& hBOOL(hAPP_f355887345l_bool(finite1765195604_state,collec1708318610_state(Q_1))) ) ) ).
tff(fact_215_finite__Collect__disjI,axiom,
! [P_1: fun_fu1430349052l_bool,Q_1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,P_1),Q_1))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) ) ) ).
tff(fact_216_finite__Collect__disjI,axiom,
! [P_1: fun_fu1783763359l_bool,Q_1: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fdisj,P_1),Q_1))))
<=> ( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(P_1)))
& hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,collec1657840446e_bool(Q_1))) ) ) ).
tff(fact_217_insert__compr__raw,axiom,
! [X_1: pname,Xa: fun_pname_bool] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))) ).
tff(fact_218_insert__compr__raw,axiom,
! [X_1: hoare_1848483303_state,Xa: fun_Ho734851753e_bool] : insert668001005_state(X_1,Xa) = collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fdisj,hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),X_1)),hAPP_f617245717e_bool(cOMBC_1803918242l_bool(member591555156_state),Xa))) ).
tff(fact_219_insert__compr__raw,axiom,
! [X_1: fun_pname_bool,Xa: fun_fu1430349052l_bool] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))) ).
tff(fact_220_insert__compr__raw,axiom,
! [X_1: fun_Ho734851753e_bool,Xa: fun_fu1783763359l_bool] : insert1390540323e_bool(X_1,Xa) = collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fdisj,hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),X_1)),hAPP_f1360064833l_bool(cOMBC_1100692246l_bool(member1948767740e_bool),Xa))) ).
tff(fact_221_singleton__inject,axiom,
! [A_2: pname,B_1: pname] :
( ( insert_pname(A_2,bot_bo844097828e_bool) = insert_pname(B_1,bot_bo844097828e_bool) )
=> ( A_2 = B_1 ) ) ).
tff(fact_222_singleton__inject,axiom,
! [A_2: hoare_1848483303_state,B_1: hoare_1848483303_state] :
( ( insert668001005_state(A_2,bot_bo454148287e_bool) = insert668001005_state(B_1,bot_bo454148287e_bool) )
=> ( A_2 = B_1 ) ) ).
tff(fact_223_singletonE,axiom,
! [B_1: pname,A_2: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
=> ( B_1 = A_2 ) ) ).
tff(fact_224_singletonE,axiom,
! [B_1: hoare_1848483303_state,A_2: hoare_1848483303_state] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),insert668001005_state(A_2,bot_bo454148287e_bool)))
=> ( B_1 = A_2 ) ) ).
tff(fact_225_doubleton__eq__iff,axiom,
! [A_2: pname,B_1: pname,C_1: pname,D_1: pname] :
( ( insert_pname(A_2,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D_1,bot_bo844097828e_bool)) )
<=> ( ( ( A_2 = C_1 )
& ( B_1 = D_1 ) )
| ( ( A_2 = D_1 )
& ( B_1 = C_1 ) ) ) ) ).
tff(fact_226_doubleton__eq__iff,axiom,
! [A_2: hoare_1848483303_state,B_1: hoare_1848483303_state,C_1: hoare_1848483303_state,D_1: hoare_1848483303_state] :
( ( insert668001005_state(A_2,insert668001005_state(B_1,bot_bo454148287e_bool)) = insert668001005_state(C_1,insert668001005_state(D_1,bot_bo454148287e_bool)) )
<=> ( ( ( A_2 = C_1 )
& ( B_1 = D_1 ) )
| ( ( A_2 = D_1 )
& ( B_1 = C_1 ) ) ) ) ).
tff(fact_227_singleton__iff,axiom,
! [B_1: pname,A_2: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
<=> ( B_1 = A_2 ) ) ).
tff(fact_228_singleton__iff,axiom,
! [B_1: hoare_1848483303_state,A_2: hoare_1848483303_state] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),insert668001005_state(A_2,bot_bo454148287e_bool)))
<=> ( B_1 = A_2 ) ) ).
tff(fact_229_insert__not__empty,axiom,
! [A_2: pname,A: fun_pname_bool] : insert_pname(A_2,A) != bot_bo844097828e_bool ).
tff(fact_230_insert__not__empty,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] : insert668001005_state(A_2,A) != bot_bo454148287e_bool ).
tff(fact_231_empty__not__insert,axiom,
! [A_2: pname,A: fun_pname_bool] : bot_bo844097828e_bool != insert_pname(A_2,A) ).
tff(fact_232_empty__not__insert,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] : bot_bo454148287e_bool != insert668001005_state(A_2,A) ).
tff(fact_233_finite__insert,axiom,
! [A_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ).
tff(fact_234_finite__insert,axiom,
! [A_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,insert668001005_state(A_2,A)))
<=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A)) ) ).
tff(fact_235_finite__insert,axiom,
! [A_2: fun_pname_bool,A: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ).
tff(fact_236_finite__insert,axiom,
! [A_2: fun_Ho734851753e_bool,A: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,insert1390540323e_bool(A_2,A)))
<=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A)) ) ).
tff(fact_237_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_238_subset__empty,axiom,
! [A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),bot_bo454148287e_bool))
<=> ( A = bot_bo454148287e_bool ) ) ).
tff(fact_239_image__is__empty,axiom,
! [F: fun_pn447269700_state,A: fun_pname_bool] :
( ( image_1256224870_state(F,A) = bot_bo454148287e_bool )
<=> ( A = bot_bo844097828e_bool ) ) ).
tff(fact_240_image__empty,axiom,
! [F: fun_pn447269700_state] : image_1256224870_state(F,bot_bo844097828e_bool) = bot_bo454148287e_bool ).
tff(fact_241_empty__is__image,axiom,
! [F: fun_pn447269700_state,A: fun_pname_bool] :
( ( bot_bo454148287e_bool = image_1256224870_state(F,A) )
<=> ( A = bot_bo844097828e_bool ) ) ).
tff(fact_242_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_243_finite__subset,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,A),B))
=> ( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,B))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A)) ) ) ).
tff(fact_244_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_245_finite__subset,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> ( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A)) ) ) ).
tff(fact_246_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_247_rev__finite__subset,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,B))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,A),B))
=> hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,A)) ) ) ).
tff(fact_248_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_249_rev__finite__subset,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> hBOOL(hAPP_f355887345l_bool(finite1765195604_state,A)) ) ) ).
tff(fact_250_insert__mono,axiom,
! [A_2: pname,C_2: fun_pname_bool,D: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),D))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_2,C_2)),insert_pname(A_2,D))) ) ).
tff(fact_251_insert__mono,axiom,
! [A_2: hoare_1848483303_state,C_2: fun_Ho734851753e_bool,D: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,C_2),D))
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,insert668001005_state(A_2,C_2)),insert668001005_state(A_2,D))) ) ).
tff(fact_252_mem__def,axiom,
! [X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
<=> hBOOL(hAPP_pname_bool(A,X_2)) ) ).
tff(fact_253_mem__def,axiom,
! [X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
<=> hBOOL(hAPP_H2060173127e_bool(A,X_2)) ) ).
tff(fact_254_Collect__def,axiom,
! [P_1: fun_pname_bool] : collect_pname(P_1) = P_1 ).
tff(fact_255_Collect__def,axiom,
! [P_1: fun_Ho734851753e_bool] : collec1708318610_state(P_1) = P_1 ).
tff(fact_256_Collect__def,axiom,
! [P_1: fun_fu1430349052l_bool] : collec1974731493e_bool(P_1) = P_1 ).
tff(fact_257_Collect__def,axiom,
! [P_1: fun_fu1783763359l_bool] : collec1657840446e_bool(P_1) = P_1 ).
tff(fact_258_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),insert_pname(B_1,B))) ) ).
tff(fact_259_subset__insertI2,axiom,
! [B_1: hoare_1848483303_state,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B))
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),insert668001005_state(B_1,B))) ) ).
tff(fact_260_subset__insert,axiom,
! [B: fun_pname_bool,X_2: pname,A: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).
tff(fact_261_subset__insert,axiom,
! [B: fun_Ho734851753e_bool,X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool] :
( ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),A))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),insert668001005_state(X_2,B)))
<=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B)) ) ) ).
tff(fact_262_insert__subset,axiom,
! [X_2: pname,A: fun_pname_bool,B: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
<=> ( 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_263_insert__subset,axiom,
! [X_2: hoare_1848483303_state,A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,insert668001005_state(X_2,A)),B))
<=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_2),B))
& hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B)) ) ) ).
tff(fact_264_subset__insertI,axiom,
! [B: fun_pname_bool,A_2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_2,B))) ).
tff(fact_265_subset__insertI,axiom,
! [B: fun_Ho734851753e_bool,A_2: hoare_1848483303_state] : hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),insert668001005_state(A_2,B))) ).
tff(fact_266_insert__image,axiom,
! [F: fun_pn447269700_state,X_2: pname,A: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
=> ( insert668001005_state(hAPP_p675228438_state(F,X_2),image_1256224870_state(F,A)) = image_1256224870_state(F,A) ) ) ).
tff(fact_267_image__insert,axiom,
! [F: fun_pn447269700_state,A_2: pname,B: fun_pname_bool] : image_1256224870_state(F,insert_pname(A_2,B)) = insert668001005_state(hAPP_p675228438_state(F,A_2),image_1256224870_state(F,B)) ).
tff(fact_268_image__mono,axiom,
! [F: fun_pn447269700_state,A: fun_pname_bool,B: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,image_1256224870_state(F,A)),image_1256224870_state(F,B))) ) ).
tff(fact_269_subset__image__iff,axiom,
! [B: fun_Ho734851753e_bool,F: fun_pn447269700_state,A: fun_pname_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_1256224870_state(F,A)))
<=> ? [AA: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
& ( B = image_1256224870_state(F,AA) ) ) ) ).
tff(fact_270_domI,axiom,
! [M: fun_pname_option_com,A_2: pname,B_1: com] :
( ( hAPP_p799580910on_com(M,A_2) = some_com(B_1) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),dom_pname_com(M))) ) ).
tff(fact_271_Collect__conv__if,axiom,
! [P_1: fun_pname_bool,A_2: pname] :
( ( hBOOL(hAPP_pname_bool(P_1,A_2))
=> ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool) ) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A_2))
=> ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = bot_bo844097828e_bool ) ) ) ).
tff(fact_272_Collect__conv__if,axiom,
! [P_1: fun_Ho734851753e_bool,A_2: hoare_1848483303_state] :
( ( hBOOL(hAPP_H2060173127e_bool(P_1,A_2))
=> ( collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fconj,hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),A_2)),P_1)) = insert668001005_state(A_2,bot_bo454148287e_bool) ) )
& ( ~ hBOOL(hAPP_H2060173127e_bool(P_1,A_2))
=> ( collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fconj,hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),A_2)),P_1)) = bot_bo454148287e_bool ) ) ) ).
tff(fact_273_Collect__conv__if,axiom,
! [P_1: fun_fu1430349052l_bool,A_2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
=> ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
=> ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = bot_bo1649642514l_bool ) ) ) ).
tff(fact_274_Collect__conv__if,axiom,
! [P_1: fun_fu1783763359l_bool,A_2: fun_Ho734851753e_bool] :
( ( hBOOL(hAPP_f355887345l_bool(P_1,A_2))
=> ( collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fconj,hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),A_2)),P_1)) = insert1390540323e_bool(A_2,bot_bo2068035593l_bool) ) )
& ( ~ hBOOL(hAPP_f355887345l_bool(P_1,A_2))
=> ( collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fconj,hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),A_2)),P_1)) = bot_bo2068035593l_bool ) ) ) ).
tff(fact_275_Collect__conv__if2,axiom,
! [P_1: fun_pname_bool,A_2: pname] :
( ( hBOOL(hAPP_pname_bool(P_1,A_2))
=> ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool) ) )
& ( ~ hBOOL(hAPP_pname_bool(P_1,A_2))
=> ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = bot_bo844097828e_bool ) ) ) ).
tff(fact_276_Collect__conv__if2,axiom,
! [P_1: fun_Ho734851753e_bool,A_2: hoare_1848483303_state] :
( ( hBOOL(hAPP_H2060173127e_bool(P_1,A_2))
=> ( collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fconj,hAPP_H1618070847e_bool(fequal364418600_state,A_2)),P_1)) = insert668001005_state(A_2,bot_bo454148287e_bool) ) )
& ( ~ hBOOL(hAPP_H2060173127e_bool(P_1,A_2))
=> ( collec1708318610_state(cOMBS_1990964188l_bool(cOMBB_215065709_state(fconj,hAPP_H1618070847e_bool(fequal364418600_state,A_2)),P_1)) = bot_bo454148287e_bool ) ) ) ).
tff(fact_277_Collect__conv__if2,axiom,
! [P_1: fun_fu1430349052l_bool,A_2: fun_pname_bool] :
( ( hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
=> ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
=> ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = bot_bo1649642514l_bool ) ) ) ).
tff(fact_278_Collect__conv__if2,axiom,
! [P_1: fun_fu1783763359l_bool,A_2: fun_Ho734851753e_bool] :
( ( hBOOL(hAPP_f355887345l_bool(P_1,A_2))
=> ( collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fconj,hAPP_f15397171l_bool(fequal1145749800e_bool,A_2)),P_1)) = insert1390540323e_bool(A_2,bot_bo2068035593l_bool) ) )
& ( ~ hBOOL(hAPP_f355887345l_bool(P_1,A_2))
=> ( collec1657840446e_bool(cOMBS_1278217668l_bool(cOMBB_1418941603e_bool(fconj,hAPP_f15397171l_bool(fequal1145749800e_bool,A_2)),P_1)) = bot_bo2068035593l_bool ) ) ) ).
tff(fact_279_singleton__conv,axiom,
! [A_2: pname] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)) = insert_pname(A_2,bot_bo844097828e_bool) ).
tff(fact_280_singleton__conv,axiom,
! [A_2: hoare_1848483303_state] : collec1708318610_state(hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(fequal364418600_state),A_2)) = insert668001005_state(A_2,bot_bo454148287e_bool) ).
tff(fact_281_singleton__conv,axiom,
! [A_2: fun_pname_bool] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ).
tff(fact_282_singleton__conv,axiom,
! [A_2: fun_Ho734851753e_bool] : collec1657840446e_bool(hAPP_f15397171l_bool(cOMBC_80545690l_bool(fequal1145749800e_bool),A_2)) = insert1390540323e_bool(A_2,bot_bo2068035593l_bool) ).
tff(fact_283_singleton__conv2,axiom,
! [A_2: pname] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_2)) = insert_pname(A_2,bot_bo844097828e_bool) ).
tff(fact_284_singleton__conv2,axiom,
! [A_2: hoare_1848483303_state] : collec1708318610_state(hAPP_H1618070847e_bool(fequal364418600_state,A_2)) = insert668001005_state(A_2,bot_bo454148287e_bool) ).
tff(fact_285_singleton__conv2,axiom,
! [A_2: fun_pname_bool] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ).
tff(fact_286_singleton__conv2,axiom,
! [A_2: fun_Ho734851753e_bool] : collec1657840446e_bool(hAPP_f15397171l_bool(fequal1145749800e_bool,A_2)) = insert1390540323e_bool(A_2,bot_bo2068035593l_bool) ).
tff(fact_287_MGF__lemma1,axiom,
! [C_1: com,G: fun_Ho734851753e_bool] :
( hBOOL(hoare_1310879719gleton)
=> ( ! [X_1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),dom_pname_com(body)))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_1)),bot_bo454148287e_bool))) )
=> ( hBOOL(wt(C_1))
=> hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(G),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,C_1),bot_bo454148287e_bool))) ) ) ) ).
tff(fact_288_WT__bodiesD,axiom,
! [Pn: pname,B_2: com] :
( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_2) )
=> hBOOL(wt(B_2)) ) ) ).
tff(fact_289_imageE,axiom,
! [B_1: hoare_1848483303_state,F: fun_pn447269700_state,A: fun_pname_bool] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,B_1),image_1256224870_state(F,A)))
=> ~ ! [X_1: pname] :
( ( B_1 = hAPP_p675228438_state(F,X_1) )
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) ) ).
tff(fact_290_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_1: pname,F_1: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),F_1))
=> ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
=> hBOOL(hAPP_f1664156314l_bool(P_1,insert_pname(A_1,F_1))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ) ).
tff(fact_291_finite__subset__induct,axiom,
! [P_1: fun_fu1783763359l_bool,A: fun_Ho734851753e_bool,Fa: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,Fa))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,Fa),A))
=> ( hBOOL(hAPP_f355887345l_bool(P_1,bot_bo454148287e_bool))
=> ( ! [A_1: hoare_1848483303_state,F_1: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,F_1))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_1),A))
=> ( ~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,A_1),F_1))
=> ( hBOOL(hAPP_f355887345l_bool(P_1,F_1))
=> hBOOL(hAPP_f355887345l_bool(P_1,insert668001005_state(A_1,F_1))) ) ) ) )
=> hBOOL(hAPP_f355887345l_bool(P_1,Fa)) ) ) ) ) ).
tff(fact_292_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_1: fun_pname_bool,F_1: fun_fu1430349052l_bool] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),F_1))
=> ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
=> hBOOL(hAPP_f1935102916l_bool(P_1,insert1325755072e_bool(A_1,F_1))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ) ).
tff(fact_293_finite__subset__induct,axiom,
! [P_1: fun_fu64031073l_bool,A: fun_fu1783763359l_bool,Fa: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,Fa))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f511954751l_bool(ord_le1819283413l_bool,Fa),A))
=> ( hBOOL(hAPP_f1526158591l_bool(P_1,bot_bo2068035593l_bool))
=> ( ! [A_1: fun_Ho734851753e_bool,F_1: fun_fu1783763359l_bool] :
( hBOOL(hAPP_f1526158591l_bool(finite297877756e_bool,F_1))
=> ( hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_1),A))
=> ( ~ hBOOL(hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(member1948767740e_bool,A_1),F_1))
=> ( hBOOL(hAPP_f1526158591l_bool(P_1,F_1))
=> hBOOL(hAPP_f1526158591l_bool(P_1,insert1390540323e_bool(A_1,F_1))) ) ) ) )
=> hBOOL(hAPP_f1526158591l_bool(P_1,Fa)) ) ) ) ) ).
tff(fact_294_WTs__elim__cases_I7_J,axiom,
! [P: pname] :
( hBOOL(wt(hAPP_pname_com(body_1,P)))
=> ~ ! [Y_1: com] : hAPP_p799580910on_com(body,P) != some_com(Y_1) ) ).
tff(fact_295_subsetI,axiom,
! [B: fun_pname_bool,A: fun_pname_bool] :
( ! [X_1: pname] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
=> 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_296_subsetI,axiom,
! [B: fun_Ho734851753e_bool,A: fun_Ho734851753e_bool] :
( ! [X_1: hoare_1848483303_state] :
( hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_1),A))
=> hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,X_1),B)) )
=> hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,A),B)) ) ).
tff(fact_297_finite__subset__image,axiom,
! [F: fun_pn447269700_state,A: fun_pname_bool,B: fun_Ho734851753e_bool] :
( hBOOL(hAPP_f355887345l_bool(finite1765195604_state,B))
=> ( hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,B),image_1256224870_state(F,A)))
=> ? [C: fun_pname_bool] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C))
& ( B = image_1256224870_state(F,C) ) ) ) ) ).
tff(fact_298_finite__dom__body,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))) ).
tff(fact_299_com_Osimps_I6_J,axiom,
! [Pname_1: pname,Pname: pname] :
( ( hAPP_pname_com(body_1,Pname_1) = hAPP_pname_com(body_1,Pname) )
<=> ( Pname_1 = Pname ) ) ).
%----Helper facts (67)
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_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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [P: bool,Q: pname] : hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U,axiom,
! [P: pname,Q: pname] : hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P ).
tff(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X: fun_pname_bool,Y: fun_pname_bool] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X: fun_pname_bool,Y: fun_pname_bool] :
( ( X != Y )
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [P: fun_bool_bool,Q: fun_pname_bool,R: pname] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ).
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(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_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(cOMBC_1149511130e_bool(P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [P: bool,Q: fun_pname_bool] : hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [P: pname,Q: fun_pname_bool] : hAPP_f1297739591_pname(cOMBK_948730864e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [P: fun_pname_bool,Q: pname] : hAPP_p61793385e_bool(cOMBK_37193422_pname(P),Q) = P ).
tff(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com,axiom,
! [X: hoare_1848483303_state,Y: hoare_1848483303_state] :
( ~ hBOOL(hAPP_H2060173127e_bool(hAPP_H1618070847e_bool(fequal364418600_state,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com,axiom,
! [X: hoare_1848483303_state,Y: hoare_1848483303_state] :
( ( X != Y )
| hBOOL(hAPP_H2060173127e_bool(hAPP_H1618070847e_bool(fequal364418600_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(cOMBB_923936821_pname(P,Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
! [P: fun_bool_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_pname_bool,R: pname] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_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(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_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(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__,axiom,
! [P: bool,Q: hoare_1848483303_state] : hAPP_H2060173127e_bool(cOMBK_2059960192_state(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg_,axiom,
! [P: pname,Q: hoare_1848483303_state] : hAPP_H1494965722_pname(cOMBK_1568566301_state(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__,axiom,
! [P: hoare_1848483303_state,Q: pname] : hAPP_p675228438_state(cOMBK_240819937_pname(P),Q) = P ).
tff(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple,axiom,
! [X: fun_Ho734851753e_bool,Y: fun_Ho734851753e_bool] :
( ~ hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(fequal1145749800e_bool,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple,axiom,
! [X: fun_Ho734851753e_bool,Y: fun_Ho734851753e_bool] :
( ( X != Y )
| hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(fequal1145749800e_bool,X),Y)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__O,axiom,
! [P: fun_co1814942666_state,Q: fun_pname_com,R: pname] : hAPP_p675228438_state(cOMBB_573322273_pname(P,Q),R) = hAPP_c379084956_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_Ho734851753e_bool,R: hoare_1848483303_state] : hAPP_H2060173127e_bool(cOMBB_1397003211_state(P,Q),R) = hAPP_bool_bool(P,hAPP_H2060173127e_bool(Q,R)) ).
tff(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__,axiom,
! [P: fun_Ho2109050089l_bool,Q: fun_Ho734851753e_bool,R: hoare_1848483303_state] : hAPP_H2060173127e_bool(cOMBS_1990964188l_bool(P,Q),R) = hAPP_bool_bool(hAPP_H590162869l_bool(P,R),hAPP_H2060173127e_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_065,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
! [P: fun_fu1171508960l_bool,Q: fun_fu399576434l_bool,R: fun_fu1430349052l_bool] : hAPP_f1935102916l_bool(cOMBS_811933079l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f32027384l_bool(P,R),hAPP_f1935102916l_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(cOMBC_1284144636l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____yie,axiom,
! [P: bool,Q: fun_Ho734851753e_bool] : hAPP_f355887345l_bool(cOMBK_2110745040e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____yi,axiom,
! [P: pname,Q: fun_Ho734851753e_bool] : hAPP_f50667184_pname(cOMBK_1423274227e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___066,axiom,
! [P: hoare_1848483303_state,Q: fun_pname_bool] : hAPP_f141816996_state(cOMBK_354802397e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,axiom,
! [P: fun_pname_bool,Q: hoare_1848483303_state] : hAPP_H1355725988e_bool(cOMBK_1288377053_state(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I,axiom,
! [P: fun_Ho734851753e_bool,Q: pname] : hAPP_p276714170e_bool(cOMBK_1197227241_pname(P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
! [P: fun_bool_bool,Q: fun_fu1783763359l_bool,R: fun_Ho734851753e_bool] : hAPP_f355887345l_bool(cOMBB_1356070853e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f355887345l_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_067,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_Ho734851753e_bool,R: hoare_1848483303_state] : hAPP_H590162869l_bool(cOMBB_215065709_state(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_H2060173127e_bool(Q,R)) ).
tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I,axiom,
! [P: fun_fu947309171l_bool,Q: fun_fu1783763359l_bool,R: fun_Ho734851753e_bool] : hAPP_f355887345l_bool(cOMBS_1278217668l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f170941835l_bool(P,R),hAPP_f355887345l_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_068,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_fu399576434l_bool,R: fun_fu1430349052l_bool] : hAPP_f32027384l_bool(cOMBB_689948150l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1935102916l_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_069,axiom,
! [P: fun_fu931343505l_bool,Q: fun_fu1430349052l_bool,R: fun_pname_bool] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel,axiom,
! [P: bool,Q: fun_fu1783763359l_bool] : hAPP_f1526158591l_bool(cOMBK_2014663096l_bool(P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__,axiom,
! [P: fun_Ho1480763635e_bool,Q: hoare_1848483303_state,R: hoare_1848483303_state] : hAPP_H2060173127e_bool(hAPP_H1618070847e_bool(cOMBC_1947058646e_bool(P),Q),R) = hAPP_H2060173127e_bool(hAPP_H1618070847e_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_070,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_fu1783763359l_bool,R: fun_Ho734851753e_bool] : hAPP_f170941835l_bool(cOMBB_1418941603e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f355887345l_bool(Q,R)) ).
tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__,axiom,
! [P: fun_fu296636465l_bool,Q: fun_fu64031073l_bool,R: fun_fu1783763359l_bool] : hAPP_f1526158591l_bool(cOMBS_101732372l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f2022158333l_bool(P,R),hAPP_f1526158591l_bool(Q,R)) ).
tff(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___071,axiom,
! [P: hoare_1848483303_state,Q: fun_Ho734851753e_bool] : hAPP_f2099317627_state(cOMBK_1270376774e_bool(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_072,axiom,
! [P: fun_Ho734851753e_bool,Q: hoare_1848483303_state] : hAPP_H1618070847e_bool(cOMBK_1751623554_state(P),Q) = P ).
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(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___073,axiom,
! [P: fun_Ho1489168363l_bool,Q: fun_Ho734851753e_bool,R: hoare_1848483303_state] : hAPP_H2060173127e_bool(hAPP_f617245717e_bool(cOMBC_1803918242l_bool(P),Q),R) = hAPP_f355887345l_bool(hAPP_H1199573897l_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_074,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_fu64031073l_bool,R: fun_fu1783763359l_bool] : hAPP_f2022158333l_bool(cOMBB_1936369445l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1526158591l_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I,axiom,
! [P: fun_fu1478462177l_bool,Q: fun_Ho734851753e_bool,R: fun_Ho734851753e_bool] : hAPP_f355887345l_bool(hAPP_f15397171l_bool(cOMBC_80545690l_bool(P),Q),R) = hAPP_f355887345l_bool(hAPP_f15397171l_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [P: fun_fu1086940979l_bool,Q: fun_fu399576434l_bool,R: fun_fu399576434l_bool] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_075,axiom,
! [P: fun_fu1259080373l_bool,Q: fun_fu1783763359l_bool,R: fun_Ho734851753e_bool] : hAPP_f355887345l_bool(hAPP_f1360064833l_bool(cOMBC_1100692246l_bool(P),Q),R) = hAPP_f1526158591l_bool(hAPP_f1258983629l_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__,axiom,
! [P: fun_fu1483785331l_bool,Q: fun_fu1783763359l_bool,R: fun_fu1783763359l_bool] : hAPP_f1526158591l_bool(hAPP_f511954751l_bool(cOMBC_1690116422l_bool(P),Q),R) = hAPP_f1526158591l_bool(hAPP_f511954751l_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yie,axiom,
! [P: fun_fu325884881l_bool,Q: fun_fu64031073l_bool,R: fun_fu64031073l_bool] : hAPP_f1359865257l_bool(hAPP_f1607907235l_bool(cOMBC_1420373658l_bool(P),Q),R) = hAPP_f1359865257l_bool(hAPP_f1607907235l_bool(P,R),Q) ).
%----Conjectures (8)
tff(conj_0,hypothesis,
hBOOL(hoare_1310879719gleton) ).
tff(conj_1,hypothesis,
hBOOL(wT_bodies) ).
tff(conj_2,hypothesis,
hBOOL(hAPP_f355887345l_bool(finite1765195604_state,fa)) ).
tff(conj_3,hypothesis,
~ hBOOL(hAPP_f355887345l_bool(hAPP_H1199573897l_bool(member591555156_state,hAPP_c379084956_state(hoare_Mirabelle_MGT,y)),fa)) ).
tff(conj_4,hypothesis,
hBOOL(hAPP_f355887345l_bool(hAPP_f15397171l_bool(ord_le1119700979e_bool,fa),image_1256224870_state(cOMBB_573322273_pname(hoare_Mirabelle_MGT,cOMBB_923936821_pname(the_com,body)),dom_pname_com(body)))) ).
tff(conj_5,hypothesis,
hAPP_p799580910on_com(body,pn) = some_com(y) ).
tff(conj_6,hypothesis,
hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(image_1256224870_state(cOMBB_573322273_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),fa)) ).
tff(conj_7,conjecture,
hBOOL(hAPP_f355887345l_bool(hoare_1193527299_state(image_1256224870_state(cOMBB_573322273_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert668001005_state(hAPP_c379084956_state(hoare_Mirabelle_MGT,y),bot_bo454148287e_bool))) ).
%------------------------------------------------------------------------------