TPTP Problem File: SWW470_1.p
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%------------------------------------------------------------------------------
% File : SWW470_1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Hoare's Logic with Procedures line 200, 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_l200 [Bla11]
% Status : Theorem
% Rating : 0.11 v8.2.0, 0.20 v8.1.0, 0.27 v7.5.0, 0.38 v7.4.0, 0.20 v7.3.0, 0.17 v7.1.0, 0.00 v6.1.0, 0.33 v6.0.0, 0.40 v5.5.0, 0.25 v5.4.0, 0.67 v5.3.0
% Syntax : Number of formulae : 271 ( 50 unt; 136 typ; 0 def)
% Number of atoms : 310 ( 119 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 235 ( 60 ~; 27 |; 22 &)
% ( 22 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 46 ( 45 usr)
% Number of type conns : 109 ( 61 >; 48 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 90 ( 90 usr; 30 con; 0-3 aty)
% Number of variables : 371 ( 353 !; 18 ?; 371 :)
% SPC : TF0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:21:39
%------------------------------------------------------------------------------
%----Should-be-implicit typings (45)
tff(ty_ty_t__a,type,
x_a: $tType ).
tff(ty_ty_tc__Com__Ocom,type,
com: $tType ).
tff(ty_ty_tc__Com__Ostate,type,
state: $tType ).
tff(ty_ty_tc__HOL__Obool,type,
bool: $tType ).
tff(ty_ty_tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
hoare_1927711152iple_a: $tType ).
tff(ty_ty_tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_J,type,
fun_a_fun_state_bool: $tType ).
tff(ty_ty_tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL_,type,
fun_a_1632297036l_bool: $tType ).
tff(ty_ty_tc__fun_It__a_Mtc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Com__Ostate_Mtc__HOL_,type,
fun_a_998512028e_bool: $tType ).
tff(ty_ty_tc__fun_It__a_Mtc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_Mtc__fu,type,
fun_a_2117018159e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J,type,
fun_state_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_J,type,
fun_st1506752259e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_J,type,
fun_st2063251938l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
fun_bool_bool: $tType ).
tff(ty_ty_tc__fun_Itc__HOL__Obool_Mtc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL_,type,
fun_bo675861616e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_J,type,
fun_bo1936561970e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_J,type,
fun_bo1549164019l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__HOL__O,type,
fun_Ho1877127206a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__Hoare_,type,
fun_Ho843200573iple_a: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__fun_It,type,
fun_Ho957066028l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__fun_It_001,type,
fun_Ho440810351a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__fun_It_002,type,
fun_Ho333840202iple_a: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__fun_It_003,type,
fun_Ho525994229l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__fun_It_004,type,
fun_Ho1630563774a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_J_Mtc__,type,
fun_fu2118559873l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_,type,
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tff(ty_ty_tc__fun_Itc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool__005,type,
fun_fu2008829792e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_It__a_Mtc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Com__Ostate_,type,
fun_fu222103665e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_It__a_Mtc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_,type,
fun_fu734682033e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_Mtc__fun_It__a_Mtc__fu,type,
fun_fu281355805e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_Mtc__fun_Itc__Com__Ost,type,
fun_fu373216837e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_Mtc__fun_Itc__Com__Ost_006,type,
fun_fu1658206819l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Oboo,type,
fun_fu402792811e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool,type,
fun_fu1219323149e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_007,type,
fun_fu1047394976e_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt,type,
fun_fu832487784l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_008,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_009,type,
fun_fu1585556401a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_010,type,
fun_fu269925879l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_011,type,
fun_fu276214394a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_012,type,
fun_fu1644852787l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_013,type,
fun_fu1249172034a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_014,type,
fun_fu1563903738a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_015,type,
fun_fu893561155a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_016,type,
fun_fu1192765369a_bool: $tType ).
tff(ty_ty_tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt_017,type,
fun_fu1905604217a_bool: $tType ).
%----Explicit typings (91)
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate,type,
cOMBB_160679318_state: fun_bool_bool > fun_fu373216837e_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiem,type,
cOMBB_213049548iple_a: fun_bool_bool > fun_fu1585556401a_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
cOMBB_188601460_state: fun_bo1549164019l_bool > fun_fu1658206819l_bool ).
tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__018,type,
cOMBB_196465322iple_a: fun_bo1549164019l_bool > fun_fu269925879l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Os,type,
cOMBB_1355796797bool_a: fun_fu1658206819l_bool > fun_fu2118559873l_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
cOMBB_1348041619bool_a: fun_fu1219323149e_bool > fun_fu1591723597e_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool__019,type,
cOMBB_145932198bool_a: fun_fu1047394976e_bool > fun_fu2008829792e_bool ).
tff(sy_c_COMBB_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc,type,
cOMBB_1083611331iple_a: fun_fu832487784l_bool > fun_fu1563903738a_bool ).
tff(sy_c_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool,type,
cOMBC_41962815e_bool: fun_fu222103665e_bool ).
tff(sy_c_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc_,type,
cOMBC_892787026e_bool: fun_fu734682033e_bool ).
tff(sy_c_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool,type,
cOMBC_2027030106e_bool: fun_fu402792811e_bool ).
tff(sy_c_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool,type,
cOMBC_231445413l_bool: fun_fu1219323149e_bool ).
tff(sy_c_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__Hoare,type,
cOMBC_671859290a_bool: fun_fu893561155a_bool ).
tff(sy_c_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_I,type,
cOMBC_862840740l_bool: fun_fu1192765369a_bool ).
tff(sy_c_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_I_020,type,
cOMBC_825881325a_bool: fun_fu1905604217a_bool ).
tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Com__Ostate,type,
cOMBK_bool_state: bool > fun_state_bool ).
tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It,type,
cOMBK_712844119iple_a: bool > fun_Ho1877127206a_bool ).
tff(sy_c_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a,type,
cOMBK_1458035955bool_a: fun_state_bool > fun_a_fun_state_bool ).
tff(sy_c_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool,type,
cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).
tff(sy_c_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__HOL__,type,
cOMBS_2061548107l_bool: fun_fu1249172034a_bool ).
tff(sy_c_Com_Ocom_OSKIP,type,
skip: com ).
tff(sy_c_Com_Ocom_OSemi,type,
semi: ( com * com ) > com ).
tff(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_,type,
finite68738179iple_a: fun_fu832487784l_bool ).
tff(sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__,type,
finite2098837632iple_a: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
finite1943414032iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a ).
tff(sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_I,type,
finite148164294iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_,type,
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tff(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____yiemogtkbg__Ot,type,
finite1511031594iple_a: ( fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > bool ).
tff(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
the_Ho1307659873iple_a: fun_fu1033095803iple_a ).
tff(sy_c_Hoare__Mirabelle__yiemogtkbg_Ohoare__derivs_000t__a,type,
hoare_1617968510rivs_a: fun_Ho1877127206a_bool > fun_fu832487784l_bool ).
tff(sy_c_Hoare__Mirabelle__yiemogtkbg_Otriple_Otriple_000t__a,type,
hoare_1652181356iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_1927711152iple_a ).
tff(sy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,type,
bot_bot_bool: bool ).
tff(sy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg,type,
bot_bo1208640912a_bool: fun_Ho1877127206a_bool ).
tff(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
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tff(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
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the_el1997360207iple_a: fun_fu1033095803iple_a ).
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__Ostate,type,
fequal_state: fun_st1506752259e_bool ).
tff(sy_c_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
fequal1440857775iple_a: fun_Ho440810351a_bool ).
tff(sy_c_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mt,type,
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tff(sy_c_fimplies,type,
fimplies: fun_bo1549164019l_bool ).
tff(sy_c_hAPP_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool,type,
hAPP_state_bool: ( fun_state_bool * state ) > bool ).
tff(sy_c_hAPP_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__Com__Ostate_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
hAPP_s58564346l_bool: ( fun_st2063251938l_bool * state ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL_,type,
hAPP_b540892988e_bool: ( fun_bo675861616e_bool * bool ) > fun_a_fun_state_bool ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J,type,
hAPP_b2019457360e_bool: ( fun_bo1936561970e_bool * bool ) > fun_state_bool ).
tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__HOL__O,type,
hAPP_H1448631928a_bool: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > bool ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__Hoare_,type,
hAPP_H963118037iple_a: ( fun_Ho843200573iple_a * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_It,type,
hAPP_H1487873860l_bool: ( fun_Ho957066028l_bool * hoare_1927711152iple_a ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_It_021,type,
hAPP_H1027145665a_bool: ( fun_Ho440810351a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_It_022,type,
hAPP_H1700437986iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a ) > fun_Ho843200573iple_a ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_It_023,type,
hAPP_H694056973l_bool: ( fun_Ho525994229l_bool * hoare_1927711152iple_a ) > fun_fu832487784l_bool ).
tff(sy_c_hAPP_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_000tc__fun_It_024,type,
hAPP_H1975128022a_bool: ( fun_Ho1630563774a_bool * hoare_1927711152iple_a ) > fun_fu1585556401a_bool ).
tff(sy_c_hAPP_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_J_000tc__,type,
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hAPP_f340725611e_bool: ( fun_fu1591723597e_bool * fun_a_1632297036l_bool ) > fun_a_998512028e_bool ).
tff(sy_c_hAPP_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mt_025,type,
hAPP_f963367678e_bool: ( fun_fu2008829792e_bool * fun_a_1632297036l_bool ) > fun_a_2117018159e_bool ).
tff(sy_c_hAPP_000tc__fun_It__a_Mtc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Com__Ostate_Mt,type,
hAPP_f1824947087e_bool: ( fun_fu222103665e_bool * fun_a_998512028e_bool ) > fun_bo675861616e_bool ).
tff(sy_c_hAPP_000tc__fun_It__a_Mtc__fun_Itc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_,type,
hAPP_f1261923407e_bool: ( fun_fu734682033e_bool * fun_a_2117018159e_bool ) > fun_fu281355805e_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__fu,type,
hAPP_f762886889e_bool: ( fun_fu281355805e_bool * fun_state_bool ) > fun_a_fun_state_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Ost,type,
hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Ost_026,type,
hAPP_f1259673775l_bool: ( fun_fu1658206819l_bool * fun_state_bool ) > fun_st2063251938l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_,type,
hAPP_f817621513e_bool: ( fun_fu402792811e_bool * fun_st1506752259e_bool ) > fun_st1506752259e_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
hAPP_f167292325e_bool: ( fun_fu1219323149e_bool * fun_st2063251938l_bool ) > fun_bo1936561970e_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_027,type,
hAPP_f644196280e_bool: ( fun_fu1047394976e_bool * fun_st2063251938l_bool ) > fun_fu373216837e_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc_,type,
hAPP_f1454306822l_bool: ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__028,type,
hAPP_f490779847iple_a: ( fun_fu1033095803iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__029,type,
hAPP_f16502863a_bool: ( fun_fu1585556401a_bool * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__030,type,
hAPP_f749678531l_bool: ( fun_fu269925879l_bool * fun_Ho1877127206a_bool ) > fun_Ho957066028l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__031,type,
hAPP_f993216280a_bool: ( fun_fu276214394a_bool * fun_Ho1877127206a_bool ) > fun_Ho440810351a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__032,type,
hAPP_f625100287l_bool: ( fun_fu1644852787l_bool * fun_Ho1877127206a_bool ) > fun_fu832487784l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__033,type,
hAPP_f2112551770a_bool: ( fun_fu1249172034a_bool * fun_Ho957066028l_bool ) > fun_fu1585556401a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__034,type,
hAPP_f909473944a_bool: ( fun_fu1563903738a_bool * fun_Ho440810351a_bool ) > fun_Ho1877127206a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__035,type,
hAPP_f1216137953a_bool: ( fun_fu893561155a_bool * fun_Ho440810351a_bool ) > fun_Ho440810351a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__036,type,
hAPP_f684479953a_bool: ( fun_fu1192765369a_bool * fun_Ho525994229l_bool ) > fun_fu1585556401a_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_Mtc__037,type,
hAPP_f1022403729a_bool: ( fun_fu1905604217a_bool * fun_Ho1630563774a_bool ) > fun_fu276214394a_bool ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J,type,
member127332739iple_a: fun_Ho525994229l_bool ).
tff(sy_v_G,type,
g: fun_Ho1877127206a_bool ).
tff(sy_v_P,type,
p: fun_a_fun_state_bool ).
tff(sy_v_b,type,
b: fun_state_bool ).
tff(sy_v_c,type,
c: com ).
%----Relevant facts (95)
tff(fact_0_empty,axiom,
! [Ga: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),bot_bo1208640912a_bool)) ).
tff(fact_1_triple_Oinject,axiom,
! [Fun1_2: fun_a_fun_state_bool,Com_2: com,Fun2_2: fun_a_fun_state_bool,Fun1_1: fun_a_fun_state_bool,Com_1: com,Fun2_1: fun_a_fun_state_bool] :
( ( hoare_1652181356iple_a(Fun1_2,Com_2,Fun2_2) = hoare_1652181356iple_a(Fun1_1,Com_1,Fun2_1) )
<=> ( ( Fun1_2 = Fun1_1 )
& ( Com_2 = Com_1 )
& ( Fun2_2 = Fun2_1 ) ) ) ).
tff(fact_2_cut,axiom,
! [Ga: fun_Ho1877127206a_bool,G_1: fun_Ho1877127206a_bool,Ts: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(G_1),Ts))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),G_1))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),Ts)) ) ) ).
tff(fact_3_hoare__derivs_Oinsert,axiom,
! [Ts: fun_Ho1877127206a_bool,Ga: fun_Ho1877127206a_bool,T: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,T),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),Ts))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,T),Ts))) ) ) ).
tff(fact_4_constant,axiom,
! [Ga: fun_Ho1877127206a_bool,Pa: fun_a_fun_state_bool,Ca: com,Q_1: fun_a_fun_state_bool,C: bool] :
( ( hBOOL(C)
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),C),Ca,Q_1)),bot_bo1208640912a_bool))) ) ).
tff(fact_5_escape,axiom,
! [Ga: fun_Ho1877127206a_bool,Ca: com,Q_1: fun_a_fun_state_bool,Pa: fun_a_fun_state_bool] :
( ! [Z_1: x_a,S: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S)),Ca,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(Q_1,Z_1)))),bot_bo1208640912a_bool))) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ) ).
tff(fact_6_conseq2,axiom,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,Pa: fun_a_fun_state_bool,Ca: com,Q_3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_3)),bot_bo1208640912a_bool)))
=> ( ! [Z_1: x_a,S: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_1),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ) ) ).
tff(fact_7_conseq1,axiom,
! [Pa: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,P_2: fun_a_fun_state_bool,Ca: com,Q_1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(P_2,Ca,Q_1)),bot_bo1208640912a_bool)))
=> ( ! [Z_1: x_a,S: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_1),S)) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ) ) ).
tff(fact_8_conseq12,axiom,
! [Q_1: fun_a_fun_state_bool,Pa: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,P_2: fun_a_fun_state_bool,Ca: com,Q_3: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(P_2,Ca,Q_3)),bot_bo1208640912a_bool)))
=> ( ! [Z_1: x_a,S: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ! [S_1: state] :
( ! [Z_2: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ) ) ).
tff(fact_9_insertE,axiom,
! [A_3: hoare_1927711152iple_a,Ba: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),A)))
=> ( ( A_3 != Ba )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A)) ) ) ).
tff(fact_10_insertCI,axiom,
! [Ba: hoare_1927711152iple_a,A_3: hoare_1927711152iple_a,B_1: fun_Ho1877127206a_bool] :
( ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),B_1))
=> ( A_3 = Ba ) )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),B_1))) ) ).
tff(fact_11_emptyE,axiom,
! [A_3: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),bot_bo1208640912a_bool)) ).
tff(fact_12_singleton__conv2,axiom,
! [A_3: hoare_1927711152iple_a] : collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ).
tff(fact_13_singleton__conv,axiom,
! [A_3: hoare_1927711152iple_a] : collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ).
tff(fact_14_Collect__conv__if2,axiom,
! [Pa: fun_Ho1877127206a_bool,A_3: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3))),Pa)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ) )
& ( ~ hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3))),Pa)) = bot_bo1208640912a_bool ) ) ) ).
tff(fact_15_Collect__conv__if,axiom,
! [Pa: fun_Ho1877127206a_bool,A_3: hoare_1927711152iple_a] :
( ( hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3))),Pa)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ) )
& ( ~ hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3))),Pa)) = bot_bo1208640912a_bool ) ) ) ).
tff(fact_16_equals0D,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( ( A = bot_bo1208640912a_bool )
=> ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A)) ) ).
tff(fact_17_Collect__empty__eq,axiom,
! [Pa: fun_Ho1877127206a_bool] :
( ( collec829051333iple_a(Pa) = bot_bo1208640912a_bool )
<=> ! [X_2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(Pa,X_2)) ) ).
tff(fact_18_empty__iff,axiom,
! [Ca: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,Ca),bot_bo1208640912a_bool)) ).
tff(fact_19_empty__Collect__eq,axiom,
! [Pa: fun_Ho1877127206a_bool] :
( ( bot_bo1208640912a_bool = collec829051333iple_a(Pa) )
<=> ! [X_2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(Pa,X_2)) ) ).
tff(fact_20_ex__in__conv,axiom,
! [A: fun_Ho1877127206a_bool] :
( ? [X_2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),A))
<=> ( A != bot_bo1208640912a_bool ) ) ).
tff(fact_21_all__not__in__conv,axiom,
! [A: fun_Ho1877127206a_bool] :
( ! [X_2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),A))
<=> ( A = bot_bo1208640912a_bool ) ) ).
tff(fact_22_empty__def,axiom,
bot_bo1208640912a_bool = collec829051333iple_a(cOMBK_712844119iple_a(fFalse)) ).
tff(fact_23_insert__absorb,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A))
=> ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A) = A ) ) ).
tff(fact_24_insertI2,axiom,
! [Ba: hoare_1927711152iple_a,A_3: hoare_1927711152iple_a,B_1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),B_1))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),B_1))) ) ).
tff(fact_25_insert__ident,axiom,
! [B_1: fun_Ho1877127206a_bool,X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),B_1))
=> ( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),B_1) )
<=> ( A = B_1 ) ) ) ) ).
tff(fact_26_insert__code,axiom,
! [Y_2: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool,X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Y_2),A),X_1))
<=> ( ( Y_2 = X_1 )
| hBOOL(hAPP_H1448631928a_bool(A,X_1)) ) ) ).
tff(fact_27_insert__iff,axiom,
! [A_3: hoare_1927711152iple_a,Ba: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),A)))
<=> ( ( A_3 = Ba )
| hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A)) ) ) ).
tff(fact_28_insert__commute,axiom,
! [X_1: hoare_1927711152iple_a,Y_2: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Y_2),A)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Y_2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A)) ).
tff(fact_29_insert__absorb2,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A) ).
tff(fact_30_insert__Collect,axiom,
! [A_3: hoare_1927711152iple_a,Pa: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),collec829051333iple_a(Pa)) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fimplies),hAPP_f16502863a_bool(cOMBB_213049548iple_a(fNot),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3)))),Pa)) ).
tff(fact_31_insert__compr,axiom,
! [A_3: hoare_1927711152iple_a,B_1: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),B_1) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),B_1))) ).
tff(fact_32_insertI1,axiom,
! [A_3: hoare_1927711152iple_a,B_1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),B_1))) ).
tff(fact_33_insert__compr__raw,axiom,
! [X_2: hoare_1927711152iple_a,Xa: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),Xa) = collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X_2))),hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,member127332739iple_a),Xa))) ).
tff(fact_34_singleton__inject,axiom,
! [A_3: hoare_1927711152iple_a,Ba: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),bot_bo1208640912a_bool) )
=> ( A_3 = Ba ) ) ).
tff(fact_35_singletonE,axiom,
! [Ba: hoare_1927711152iple_a,A_3: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,Ba),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool)))
=> ( Ba = A_3 ) ) ).
tff(fact_36_doubleton__eq__iff,axiom,
! [A_3: hoare_1927711152iple_a,Ba: hoare_1927711152iple_a,Ca: hoare_1927711152iple_a,D: hoare_1927711152iple_a] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ba),bot_bo1208640912a_bool)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Ca),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,D),bot_bo1208640912a_bool)) )
<=> ( ( ( A_3 = Ca )
& ( Ba = D ) )
| ( ( A_3 = D )
& ( Ba = Ca ) ) ) ) ).
tff(fact_37_singleton__iff,axiom,
! [Ba: hoare_1927711152iple_a,A_3: hoare_1927711152iple_a] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,Ba),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool)))
<=> ( Ba = A_3 ) ) ).
tff(fact_38_insert__not__empty,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] : hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A) != bot_bo1208640912a_bool ).
tff(fact_39_empty__not__insert,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] : bot_bo1208640912a_bool != hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A) ).
tff(fact_40_the__elem__eq,axiom,
! [X_1: hoare_1927711152iple_a] : hAPP_f490779847iple_a(the_el1997360207iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),bot_bo1208640912a_bool)) = X_1 ).
tff(fact_41_bot__apply,axiom,
! [X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_1))
<=> hBOOL(bot_bot_bool) ) ).
tff(fact_42_bot__fun__def,axiom,
! [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_2))
<=> hBOOL(bot_bot_bool) ) ).
tff(fact_43_hoare__derivs_OSkip,axiom,
! [Ga: fun_Ho1877127206a_bool,Pa: fun_a_fun_state_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,skip,Pa)),bot_bo1208640912a_bool))) ).
tff(fact_44_Comp,axiom,
! [D: com,R_1: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,Pa: fun_a_fun_state_bool,Ca: com,Q_1: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool)))
=> ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Q_1,D,R_1)),bot_bo1208640912a_bool)))
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,semi(Ca,D),R_1)),bot_bo1208640912a_bool))) ) ) ).
tff(fact_45_triple_Oexhaust,axiom,
! [Y_2: hoare_1927711152iple_a] :
~ ! [Fun1: fun_a_fun_state_bool,Com: com,Fun2: fun_a_fun_state_bool] : Y_2 != hoare_1652181356iple_a(Fun1,Com,Fun2) ).
tff(fact_46_Set_Oset__insert,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
=> ~ ! [B: fun_Ho1877127206a_bool] :
( ( A = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),B) )
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),B)) ) ) ).
tff(fact_47_com_Osimps_I13_J,axiom,
! [Com1_2: com,Com2_2: com] : semi(Com1_2,Com2_2) != skip ).
tff(fact_48_com_Osimps_I12_J,axiom,
! [Com1_2: com,Com2_2: com] : skip != semi(Com1_2,Com2_2) ).
tff(fact_49_the__elem__def,axiom,
! [X_3: fun_Ho1877127206a_bool] : hAPP_f490779847iple_a(the_el1997360207iple_a,X_3) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f909473944a_bool(cOMBB_1083611331iple_a(hAPP_f625100287l_bool(fequal1285825639a_bool,X_3)),hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,insert1434104874iple_a),bot_bo1208640912a_bool))) ).
tff(fact_50_mk__disjoint__insert,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A))
=> ? [B: fun_Ho1877127206a_bool] :
( ( A = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),B) )
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),B)) ) ) ).
tff(fact_51_com_Osimps_I3_J,axiom,
! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
( ( semi(Com1_1,Com2_1) = semi(Com1,Com2) )
<=> ( ( Com1_1 = Com1 )
& ( Com2_1 = Com2 ) ) ) ).
tff(fact_52_the__sym__eq__trivial,axiom,
! [X_1: hoare_1927711152iple_a] : hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(fequal1440857775iple_a,X_1)) = X_1 ).
tff(fact_53_the__eq__trivial,axiom,
! [A_3: hoare_1927711152iple_a] : hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3)) = A_3 ).
tff(fact_54_If__def,axiom,
! [X_1: hoare_1927711152iple_a,Y_2: hoare_1927711152iple_a,Pa: bool] :
( ( hBOOL(Pa)
=> ( X_1 = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X_1)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),Y_2)))) ) )
& ( ~ hBOOL(Pa)
=> ( Y_2 = hAPP_f490779847iple_a(the_Ho1307659873iple_a,hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),X_1)))),hAPP_f16502863a_bool(cOMBB_213049548iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),Y_2)))) ) ) ) ).
tff(fact_55_equals0I,axiom,
! [A: fun_Ho1877127206a_bool] :
( ! [Y_1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,Y_1),A))
=> ( A = bot_bo1208640912a_bool ) ) ).
tff(fact_56_the__equality,axiom,
! [Pa: fun_Ho1877127206a_bool,A_3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( ! [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,X_2))
=> ( X_2 = A_3 ) )
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,Pa) = A_3 ) ) ) ).
tff(fact_57_theI,axiom,
! [Pa: fun_Ho1877127206a_bool,A_3: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( ! [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,X_2))
=> ( X_2 = A_3 ) )
=> hBOOL(hAPP_H1448631928a_bool(Pa,hAPP_f490779847iple_a(the_Ho1307659873iple_a,Pa))) ) ) ).
tff(fact_58_the1__equality,axiom,
! [A_3: hoare_1927711152iple_a,Pa: fun_Ho1877127206a_bool] :
( ? [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,X_2))
& ! [Y_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,Y_1))
=> ( Y_1 = X_2 ) ) )
=> ( hBOOL(hAPP_H1448631928a_bool(Pa,A_3))
=> ( hAPP_f490779847iple_a(the_Ho1307659873iple_a,Pa) = A_3 ) ) ) ).
tff(fact_59_theI_H,axiom,
! [Pa: fun_Ho1877127206a_bool] :
( ? [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,X_2))
& ! [Y_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(Pa,Y_1))
=> ( Y_1 = X_2 ) ) )
=> hBOOL(hAPP_H1448631928a_bool(Pa,hAPP_f490779847iple_a(the_Ho1307659873iple_a,Pa))) ) ).
tff(fact_60_conseq,axiom,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( ! [Z_1: x_a,S: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(P_1,Ca,Q_2)),bot_bo1208640912a_bool)))
& ! [S_1: state] :
( ! [Z_2: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ) ).
tff(fact_61_nonempty__iff,axiom,
! [A: fun_Ho1877127206a_bool] :
( ( A != bot_bo1208640912a_bool )
<=> ? [X_2: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
( ( A = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),B) )
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),B)) ) ) ).
tff(fact_62_fold1Set__sing,axiom,
! [F_1: fun_Ho333840202iple_a,A_3: hoare_1927711152iple_a,Ba: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool)),Ba))
<=> ( A_3 = Ba ) ) ).
tff(fact_63_folding__one_Osingleton,axiom,
! [X_1: hoare_1927711152iple_a,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(F_1,F))
=> ( hAPP_f490779847iple_a(F,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),bot_bo1208640912a_bool)) = X_1 ) ) ).
tff(fact_64_bot__empty__eq,axiom,
! [X_2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_2))
<=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),bot_bo1208640912a_bool)) ) ).
tff(fact_65_empty__fold1SetE,axiom,
! [F_1: fun_Ho333840202iple_a,X_1: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,bot_bo1208640912a_bool),X_1)) ).
tff(fact_66_fold1Set__nonempty,axiom,
! [F_1: fun_Ho333840202iple_a,A: fun_Ho1877127206a_bool,X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,A),X_1))
=> ( A != bot_bo1208640912a_bool ) ) ).
tff(fact_67_fold1Set_Ointros,axiom,
! [F_1: fun_Ho333840202iple_a,A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool,X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,A_3,A),X_1))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_3),A))
=> hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A)),X_1)) ) ) ).
tff(fact_68_folding__one_Oinsert,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(F_1,F))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
=> ( ( A != bot_bo1208640912a_bool )
=> ( hAPP_f490779847iple_a(F,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_1),hAPP_f490779847iple_a(F,A)) ) ) ) ) ) ).
tff(fact_69_fold1__def,axiom,
! [F_1: fun_Ho333840202iple_a,A: fun_Ho1877127206a_bool] : hAPP_f490779847iple_a(finite1943414032iple_a(F_1),A) = hAPP_f490779847iple_a(the_Ho1307659873iple_a,finite2098837632iple_a(F_1,A)) ).
tff(fact_70_finite__Collect__conjI,axiom,
! [Q_1: fun_Ho1877127206a_bool,Pa: fun_Ho1877127206a_bool] :
( ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(Pa)))
| hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(Q_1))) )
=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fconj),Pa)),Q_1)))) ) ).
tff(fact_71_finite_OemptyI,axiom,
hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)) ).
tff(fact_72_finite_OinsertI,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A))) ) ).
tff(fact_73_mem__def,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
<=> hBOOL(hAPP_H1448631928a_bool(A,X_1)) ) ).
tff(fact_74_Collect__def,axiom,
! [Pa: fun_Ho1877127206a_bool] : collec829051333iple_a(Pa) = Pa ).
tff(fact_75_folding__one_Oeq__fold,axiom,
! [A: fun_Ho1877127206a_bool,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(F_1,F))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( hAPP_f490779847iple_a(F,A) = hAPP_f490779847iple_a(finite1943414032iple_a(F_1),A) ) ) ) ).
tff(fact_76_fold__graph_OemptyI,axiom,
! [F_1: fun_Ho333840202iple_a,Z: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,bot_bo1208640912a_bool),Z)) ).
tff(fact_77_empty__fold__graphE,axiom,
! [F_1: fun_Ho333840202iple_a,Z: hoare_1927711152iple_a,X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,bot_bo1208640912a_bool),X_1))
=> ( X_1 = Z ) ) ).
tff(fact_78_fold__graph_OinsertI,axiom,
! [F_1: fun_Ho333840202iple_a,Z: hoare_1927711152iple_a,Y_2: hoare_1927711152iple_a,X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,A),Y_2))
=> hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A)),hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_1),Y_2))) ) ) ).
tff(fact_79_finite__Collect__disjI,axiom,
! [Pa: fun_Ho1877127206a_bool,Q_1: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,hAPP_f749678531l_bool(cOMBB_196465322iple_a(fdisj),Pa)),Q_1))))
<=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(Pa)))
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,collec829051333iple_a(Q_1))) ) ) ).
tff(fact_80_finite__insert,axiom,
! [A_3: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),A)))
<=> hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A)) ) ).
tff(fact_81_fold1__singleton__def,axiom,
! [A_3: hoare_1927711152iple_a,G: fun_fu1033095803iple_a,F_1: fun_Ho333840202iple_a] :
( ( G = finite1943414032iple_a(F_1) )
=> ( hAPP_f490779847iple_a(G,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool)) = A_3 ) ) ).
tff(fact_82_fold1__singleton,axiom,
! [F_1: fun_Ho333840202iple_a,A_3: hoare_1927711152iple_a] : hAPP_f490779847iple_a(finite1943414032iple_a(F_1),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool)) = A_3 ).
tff(fact_83_folding__one_Oclosed,axiom,
! [A: fun_Ho1877127206a_bool,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite83514413iple_a(F_1,F))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( ( A != bot_bo1208640912a_bool )
=> ( ! [X_2: hoare_1927711152iple_a,Y_1: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_2),Y_1)),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,Y_1),bot_bo1208640912a_bool))))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,hAPP_f490779847iple_a(F,A)),A)) ) ) ) ) ).
tff(fact_84_insert__fold1SetE,axiom,
! [F_1: fun_Ho333840202iple_a,A_3: hoare_1927711152iple_a,X_3: fun_Ho1877127206a_bool,X_1: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),X_3)),X_1))
=> ~ ! [A_2: hoare_1927711152iple_a,A_1: fun_Ho1877127206a_bool] :
( ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),X_3) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_2),A_1) )
=> ( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,A_2,A_1),X_1))
=> hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_2),A_1)) ) ) ) ).
tff(fact_85_finite__nonempty__imp__fold1Set,axiom,
! [F_1: fun_Ho333840202iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( ( A != bot_bo1208640912a_bool )
=> ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,A),X1)) ) ) ).
tff(fact_86_finite__induct,axiom,
! [Pa: fun_fu832487784l_bool,F: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,F))
=> ( hBOOL(hAPP_f1454306822l_bool(Pa,bot_bo1208640912a_bool))
=> ( ! [X_2: hoare_1927711152iple_a,F_2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,F_2))
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),F_2))
=> ( hBOOL(hAPP_f1454306822l_bool(Pa,F_2))
=> hBOOL(hAPP_f1454306822l_bool(Pa,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),F_2))) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(Pa,F)) ) ) ) ).
tff(fact_87_finite_Osimps,axiom,
! [A_3: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A_3))
<=> ( ( A_3 = bot_bo1208640912a_bool )
| ? [A_1: fun_Ho1877127206a_bool,A_2: hoare_1927711152iple_a] :
( ( A_3 = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_2),A_1) )
& hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A_1)) ) ) ) ).
tff(fact_88_finite__imp__fold__graph,axiom,
! [F_1: fun_Ho333840202iple_a,Z: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ? [X1: hoare_1927711152iple_a] : hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,A),X1)) ) ).
tff(fact_89_fold1Set_Osimps,axiom,
! [F_1: fun_Ho333840202iple_a,A1: fun_Ho1877127206a_bool,A2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite2098837632iple_a(F_1,A1),A2))
<=> ? [A_2: hoare_1927711152iple_a,A_1: fun_Ho1877127206a_bool,X_2: hoare_1927711152iple_a] :
( ( A1 = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_2),A_1) )
& ( A2 = X_2 )
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,A_2,A_1),X_2))
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,A_2),A_1)) ) ) ).
tff(fact_90_fold__graph_Osimps,axiom,
! [F_1: fun_Ho333840202iple_a,Z: hoare_1927711152iple_a,A1: fun_Ho1877127206a_bool,A2: hoare_1927711152iple_a] :
( hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,A1),A2))
<=> ( ( ( A1 = bot_bo1208640912a_bool )
& ( A2 = Z ) )
| ? [X_2: hoare_1927711152iple_a,A_1: fun_Ho1877127206a_bool,Y_1: hoare_1927711152iple_a] :
( ( A1 = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),A_1) )
& ( A2 = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_2),Y_1) )
& ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),A_1))
& hBOOL(hAPP_H1448631928a_bool(finite148164294iple_a(F_1,Z,A_1),Y_1)) ) ) ) ).
tff(fact_91_folding__one__idem_Oinsert__idem,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(F_1,F))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( ( A != bot_bo1208640912a_bool )
=> ( hAPP_f490779847iple_a(F,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_1),A)) = hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_1),hAPP_f490779847iple_a(F,A)) ) ) ) ) ).
tff(fact_92_finite__ne__induct,axiom,
! [Pa: fun_fu832487784l_bool,F: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,F))
=> ( ( F != bot_bo1208640912a_bool )
=> ( ! [X_2: hoare_1927711152iple_a] : hBOOL(hAPP_f1454306822l_bool(Pa,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),bot_bo1208640912a_bool)))
=> ( ! [X_2: hoare_1927711152iple_a,F_2: fun_Ho1877127206a_bool] :
( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,F_2))
=> ( ( F_2 != bot_bo1208640912a_bool )
=> ( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_2),F_2))
=> ( hBOOL(hAPP_f1454306822l_bool(Pa,F_2))
=> hBOOL(hAPP_f1454306822l_bool(Pa,hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,X_2),F_2))) ) ) ) )
=> hBOOL(hAPP_f1454306822l_bool(Pa,F)) ) ) ) ) ).
tff(fact_93_folding__one__idem_Oidem,axiom,
! [X_1: hoare_1927711152iple_a,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(F_1,F))
=> ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_1),X_1) = X_1 ) ) ).
tff(fact_94_folding__one__idem_Oin__idem,axiom,
! [X_1: hoare_1927711152iple_a,A: fun_Ho1877127206a_bool,F_1: fun_Ho333840202iple_a,F: fun_fu1033095803iple_a] :
( hBOOL(finite1511031594iple_a(F_1,F))
=> ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A))
=> ( hBOOL(hAPP_f1454306822l_bool(hAPP_H694056973l_bool(member127332739iple_a,X_1),A))
=> ( hAPP_H963118037iple_a(hAPP_H1700437986iple_a(F_1,X_1),hAPP_f490779847iple_a(F,A)) = hAPP_f490779847iple_a(F,A) ) ) ) ) ).
%----Helper facts (39)
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__Ostate_T,axiom,
! [X: state,Y: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
! [X: state,Y: state] :
( ( X != Y )
| hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) ) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
! [P: bool,Q: state] : hAPP_state_bool(cOMBK_bool_state(P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U,axiom,
! [P: fun_state_bool,Q: x_a] : hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
! [P: fun_bool_bool,Q: fun_state_bool,R: state] : hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P: fun_st2063251938l_bool,Q: bool,R: state] : hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q) ).
tff(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P: fun_st2063251938l_bool,Q: fun_state_bool,R: state] : hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U,axiom,
! [P: fun_st1506752259e_bool,Q: state,R: state] : hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q) ).
tff(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_,axiom,
! [X: hoare_1927711152iple_a,Y: hoare_1927711152iple_a] :
( ~ hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_,axiom,
! [X: hoare_1927711152iple_a,Y: hoare_1927711152iple_a] :
( ( X != Y )
| hBOOL(hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(fequal1440857775iple_a,X),Y)) ) ).
tff(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__,axiom,
! [P: fun_a_998512028e_bool,Q: bool,R: x_a] : hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__,axiom,
! [P: bool,Q: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(cOMBK_712844119iple_a(P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_state_bool,R: state] : hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_bool(Q,R)) ).
tff(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple,axiom,
! [X: fun_Ho1877127206a_bool,Y: fun_Ho1877127206a_bool] :
( ~ hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple,axiom,
! [X: fun_Ho1877127206a_bool,Y: fun_Ho1877127206a_bool] :
( ( X != Y )
| hBOOL(hAPP_f1454306822l_bool(hAPP_f625100287l_bool(fequal1285825639a_bool,X),Y)) ) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
! [P: fun_bool_bool,Q: fun_Ho1877127206a_bool,R: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(hAPP_f16502863a_bool(cOMBB_213049548iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1448631928a_bool(Q,R)) ).
tff(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00,axiom,
! [P: fun_Ho957066028l_bool,Q: fun_Ho1877127206a_bool,R: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f2112551770a_bool(cOMBS_2061548107l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1487873860l_bool(P,R),hAPP_H1448631928a_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc,axiom,
! [P: fun_a_2117018159e_bool,Q: fun_state_bool,R: x_a] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038,axiom,
! [P: fun_bo1549164019l_bool,Q: fun_Ho1877127206a_bool,R: hoare_1927711152iple_a] : hAPP_H1487873860l_bool(hAPP_f749678531l_bool(cOMBB_196465322iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1448631928a_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [P: fun_fu1658206819l_bool,Q: fun_a_fun_state_bool,R: x_a] : hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00,axiom,
! [P: fun_Ho440810351a_bool,Q: hoare_1927711152iple_a,R: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,P),Q),R) = hAPP_H1448631928a_bool(hAPP_H1027145665a_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H,axiom,
! [P: fun_fu1219323149e_bool,Q: fun_a_1632297036l_bool,R: x_a] : hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I,axiom,
! [P: fun_fu832487784l_bool,Q: fun_Ho440810351a_bool,R: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(hAPP_f909473944a_bool(cOMBB_1083611331iple_a(P),Q),R) = hAPP_f1454306822l_bool(P,hAPP_H1027145665a_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_039,axiom,
! [P: fun_Ho525994229l_bool,Q: fun_Ho1877127206a_bool,R: hoare_1927711152iple_a] : hAPP_H1448631928a_bool(hAPP_f16502863a_bool(hAPP_f684479953a_bool(cOMBC_862840740l_bool,P),Q),R) = hAPP_f1454306822l_bool(hAPP_H694056973l_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_040,axiom,
! [P: fun_fu1047394976e_bool,Q: fun_a_1632297036l_bool,R: x_a] : hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_041,axiom,
! [P: fun_Ho1630563774a_bool,Q: fun_Ho1877127206a_bool,R: hoare_1927711152iple_a] : hAPP_H1027145665a_bool(hAPP_f993216280a_bool(hAPP_f1022403729a_bool(cOMBC_825881325a_bool,P),Q),R) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(P,R),Q) ).
%----Conjectures (1)
tff(conj_0,conjecture,
hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1208640912a_bool))) ).
%------------------------------------------------------------------------------