TPTP Problem File: SWW934+1.p
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%------------------------------------------------------------------------------
% File : SWW934+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : data_to_word_gcProof__118__word_gen_gc_move_loop_thm__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : data_to_word_gcProof__118__word_gen_gc_move_loop_thm__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 138 ( 44 unt; 0 def)
% Number of atoms : 605 ( 310 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 521 ( 54 ~; 44 |; 264 &)
% ( 96 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 38 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 104 ( 104 usr; 14 con; 0-4 aty)
% Number of variables : 527 ( 508 !; 19 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.LET_DEF',axiom,
! [V_27B_27,V_27A_27,Vx,Vx0] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),Vx),s__02(V_27A_27,Vx0))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),Vx),s__02(V_27A_27,Vx0))) ).
fof('thm.bool.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> p__01(s__02(cbool__00,V_27t2_27)) )
=> ( ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.FALSITY',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.EXCLUDED_MIDDLE',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,V_27t_27))
| ~ p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.LET_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) ).
fof('thm.bool.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.CONJ_ASSOC',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27))
& p__01(s__02(cbool__00,V_27t3_27)) )
<=> ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27))
& p__01(s__02(cbool__00,V_27t3_27)) ) ) ).
fof('thm.bool.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.OR_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.IMP_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.NOT_CLAUSES',axiom,
( ! [V_27t_27] :
( ~ ~ p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ~ p__01(s__02(cbool__00,cT__00))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ~ p__01(s__02(cbool__00,cF__00))
<=> p__01(s__02(cbool__00,cT__00)) ) ) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.COND_CLAUSES',axiom,
! [V_27A_27,V_27t1_27,V_27t2_27] :
( s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.bool.DISJ_ASSOC',axiom,
! [V_27A_270,V_27B_270,V_27C_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27C_270)) )
<=> ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27C_270)) ) ) ).
fof('thm.bool.DISJ_COMM',axiom,
! [V_27A_270,V_27B_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
<=> ( p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27A_270)) ) ) ).
fof('thm.bool.DE_MORGAN_THM',axiom,
! [V_27A_270,V_27B_270] :
( ( ~ ( p__01(s__02(cbool__00,V_27A_270))
& p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
| ~ p__01(s__02(cbool__00,V_27B_270)) ) )
& ( ~ ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
& ~ p__01(s__02(cbool__00,V_27B_270)) ) ) ) ).
fof('thm.bool.IMP_DISJ_THM',axiom,
! [V_27A_270,V_27B_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,V_27B_270)) )
<=> ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) ) ) ).
fof('thm.bool.IMP_F_EQ_F',axiom,
! [V_27t_27] :
( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00) ) ).
fof('thm.bool.AND_IMP_INTRO',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t3_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27)) )
=> p__01(s__02(cbool__00,V_27t3_27)) ) ) ).
fof('thm.bool.EQ_EXPAND',axiom,
! [V_27t1_27,V_27t2_27] :
( s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27)
<=> ( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27)) )
| ( ~ p__01(s__02(cbool__00,V_27t1_27))
& ~ p__01(s__02(cbool__00,V_27t2_27)) ) ) ) ).
fof('thm.bool.IMP_CONG',axiom,
! [V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27x_27) = s__02(cbool__00,V_27x_7c39_7c_27)
& ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> s__02(cbool__00,V_27y_27) = s__02(cbool__00,V_27y_7c39_7c_27) ) )
=> ( ( p__01(s__02(cbool__00,V_27x_27))
=> p__01(s__02(cbool__00,V_27y_27)) )
<=> ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> p__01(s__02(cbool__00,V_27y_7c39_7c_27)) ) ) ) ).
fof('thm.bool.COND_CONG',axiom,
! [V_27A_27,V_27P_27,V_27Q_27,V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27P_27) = s__02(cbool__00,V_27Q_27)
& ( p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_7c39_7c_27) )
& ( ~ p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27y_7c39_7c_27) ) )
=> s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(V_27A_27,V_27x_27),s__02(V_27A_27,V_27y_27))) = s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27Q_27),s__02(V_27A_27,V_27x_7c39_7c_27),s__02(V_27A_27,V_27y_7c39_7c_27))) ) ).
fof('thm.bool.EXISTS_REFL',axiom,
! [V_27A_27,V_27a_27] :
? [V_27x_27] : s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27) ).
fof('thm.bool.UNWIND_FORALL_THM2',axiom,
! [V_27A_27,V_27f_27,V_27v_27] :
( ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27v_27)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27v_27)))) ) ).
fof('thm.bool.bool_case_thm',axiom,
! [V_27A_27] :
( ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.bool.BOUNDED_THM',axiom,
! [V_27v_27] : s__02(cbool__00,c_27const_2ebool_2eBOUNDED_27__01(s__02(cbool__00,V_27v_27))) = s__02(cbool__00,cT__00) ).
fof('thm.bool.PULL_FORALL',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ( ( p__01(s__02(cbool__00,V_27Q_27))
=> ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) )
<=> ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27Q_27))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) ) )
& ( ( ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
& p__01(s__02(cbool__00,V_27Q_27)) )
<=> ! [V_27x_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
& p__01(s__02(cbool__00,V_27Q_27)) ) )
& ( ( p__01(s__02(cbool__00,V_27Q_27))
& ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) )
<=> ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27Q_27))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) ) ) ) ).
fof('thm.marker.Abbrev_def',axiom,
! [V_27x_27] : s__02(cbool__00,c_27const_2emarker_2eAbbrev_27__01(s__02(cbool__00,V_27x_27))) = s__02(cbool__00,V_27x_27) ).
fof('thm.combin.K_THM',axiom,
! [V_27B_27,V_27A_27,V_27x_27,V_27y_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27B_27,V_27A_27),c_27const_2ecombin_2eK_27__01(s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27A_27,V_27A_27),c_27const_2ecombin_2eI_27__00),s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.sat.NOT_NOT',axiom,
! [V_27t_27] :
( ~ ~ p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.sat.AND_INV_IMP',axiom,
! [V_27A_270] :
( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.OR_DUAL2',axiom,
! [V_27B_270,V_27A_270] :
( ( ~ ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ~ p__01(s__02(cbool__00,V_27B_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.OR_DUAL3',axiom,
! [V_27B_270,V_27A_270] :
( ( ~ ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27B_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.AND_INV2',axiom,
! [V_27A_270] :
( ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.dc_eq',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> s__02(cbool__00,V_27q_27) = s__02(cbool__00,V_27r_27) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_conj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
& p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_disj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_neg',axiom,
! [V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ~ p__01(s__02(cbool__00,V_27q_27)) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
& ( ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.pair.CLOSED_PAIR_EQ',axiom,
! [V_27A_27,V_27B_27,V_27x_27,V_27y_27,V_27a_27,V_27b_27] :
( s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27a_27),s__02(V_27B_27,V_27b_27)))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27)
& s__02(V_27B_27,V_27y_27) = s__02(V_27B_27,V_27b_27) ) ) ).
fof('thm.pair.UNCURRY_DEF',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27f_27,V_27x_27,V_27y_27] : s__02(V_27C_27,c_27const_2epair_2eUNCURRY_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27B_27,V_27C_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) ).
fof('thm.pair.EXISTS_PROD',axiom,
! [V_27A_27,V_27B_27,V_27P_27] :
( ? [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27p_27))))
<=> ? [V_27p__1_27,V_27p__2_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27p__1_27),s__02(V_27B_27,V_27p__2_27)))))) ) ).
fof('thm.prim_rec.NOT_LESS_0',axiom,
! [V_27n_27] : ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ).
fof('thm.arithmetic.ADD_0',axiom,
! [V_27m_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) ).
fof('thm.arithmetic.ADD_CLAUSES',axiom,
! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.arithmetic.ADD_SYM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.arithmetic.ADD_COMM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.arithmetic.ADD_ASSOC',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) ).
fof('thm.arithmetic.LESS_EQ',axiom,
! [V_27m_27,V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ).
fof('thm.arithmetic.ZERO_LESS_EQ',axiom,
! [V_27n_27] : p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) ).
fof('thm.arithmetic.NOT_LESS',axiom,
! [V_27m_27,V_27n_27] :
( ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ).
fof('thm.arithmetic.SUB_0',axiom,
! [V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) ) ).
fof('thm.arithmetic.MULT_CLAUSES',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.arithmetic.MULT_COMM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ).
fof('thm.arithmetic.RIGHT_ADD_DISTRIB',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) ).
fof('thm.arithmetic.LEFT_ADD_DISTRIB',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27p_27),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27p_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27p_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ).
fof('thm.arithmetic.MULT_ASSOC',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) ).
fof('thm.arithmetic.ADD_EQ_0',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ) ) ).
fof('thm.arithmetic.PRE_SUC_EQ',axiom,
! [V_27m_27,V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
=> ( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27) ) ) ).
fof('thm.arithmetic.EQ_MONO_ADD_EQ',axiom,
! [V_27m_27,V_27n_27,V_27p_27] :
( s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,V_27n_27) ) ).
fof('thm.arithmetic.LESS_EQ_TRANS',axiom,
! [V_27m_27,V_27n_27,V_27p_27] :
( ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) )
=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) ) ).
fof('thm.arithmetic.COMPLETE_INDUCTION',axiom,
! [V_27P_27] :
( ! [V_27n_27] :
( ! [V_27m_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
=> ! [V_27n_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27P_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) ) ).
fof('thm.arithmetic.MULT_EQ_0',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
| s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ) ) ).
fof('thm.arithmetic.EQ_LESS_EQ',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
<=> ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ) ).
fof('thm.arithmetic.ADD_MONO_LESS_EQ',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27p_27))) ).
fof('thm.arithmetic.NOT_LEQ',axiom,
! [V_27m_27,V_27n_27] :
( ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ).
fof('thm.arithmetic.NOT_NUM_EQ',axiom,
! [V_27m_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,V_27m_27) != s__02(c_27type_2enum_2enum_27__00,V_27n_27)
<=> ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
| p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ) ).
fof('thm.arithmetic.SUC_ONE_ADD',axiom,
! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ).
fof('thm.arithmetic.MULT_LESS_EQ_SUC',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27p_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27p_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ).
fof('thm.arithmetic.SUB_RIGHT_LESS',axiom,
! [V_27m_27,V_27n_27,V_27p_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27p_27))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27p_27)))) ) ) ).
fof('thm.arithmetic.DIV_UNIQUE',axiom,
! [V_27n_27,V_27k_27,V_27q_27] :
( ? [V_27r_27] :
( s__02(c_27type_2enum_2enum_27__00,V_27k_27) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27q_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,V_27r_27)))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27r_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
=> s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,V_27q_27) ) ).
fof('thm.arithmetic.LESS_MOD',axiom,
! [V_27n_27,V_27k_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
=> s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eMOD_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,V_27k_27) ) ).
fof('thm.arithmetic.ZERO_MOD',axiom,
! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
=> s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eMOD_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ) ).
fof('thm.numeral.numeral_suc',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ) ).
fof('thm.numeral.numeral_distrib',axiom,
( ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) )
& ! [V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ) ).
fof('thm.numeral.numeral_add',axiom,
! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) ) ).
fof('thm.numeral.numeral_eq',axiom,
! [V_27n_27,V_27m_27] :
( ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) )
& ( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) ) ) ).
fof('thm.numeral.numeral_lt',axiom,
! [V_27n_27,V_27m_27] :
( s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))
<=> ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
& s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ) ).
fof('thm.numeral.numeral_lte',axiom,
! [V_27n_27,V_27m_27] :
( s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))
<=> ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) )
& s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) ) ).
fof('thm.numeral.numeral_pre',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof('thm.numeral.iDUB_removal',axiom,
! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) ) ).
fof('thm.numeral.numeral_mult',axiom,
! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiDUB_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))))) ) ).
fof('thm.numeral.numeral_evenodd',axiom,
! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))) ) ).
fof('thm.numeral.numeral_texp_help',axiom,
! [V_27n_27,V_27acc_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27acc_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27acc_27)))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27acc_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27acc_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27acc_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27acc_27))))) ) ).
fof('thm.numeral.TWO_EXP_THM',axiom,
! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) ) ).
fof('thm.numeral.onecount_def',axiom,
( ! [V_27x_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eonecount_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,V_27x_27)
& ! [V_27n_27,V_27x_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eonecount_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eonecount_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27)))))
& ! [V_27n_27,V_27x_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eonecount_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) ) ).
fof('thm.numeral.exactlog_def',axiom,
! [V__0] :
( ! [V_27x_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2enum_2enum_27__00,V_27x_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V__0),s__02(c_27type_2enum_2enum_27__00,V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))) )
=> ( s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V__0),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eonecount_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))) ) ) ).
fof('thm.numeral.DIV2_BIT1',axiom,
! [V_27x_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))) = s__02(c_27type_2enum_2enum_27__00,V_27x_27) ).
fof('thm.numeral.enumeral_mult',axiom,
! [V__3] :
( ! [V_27m_27,V_27x_27,V_27y_27,V_27n0_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27n0_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2einternal__mult_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))))))
=> ! [V__2] :
( ! [V_27x_27,V_27y_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))))
=> ! [V__1] :
( ! [V_27x_27,V_27y_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2einternal__mult_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))))
=> ! [V__0] :
( ! [V_27x_27,V_27y_27,V_27n0_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27n0_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2etexp__help_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2einternal__mult_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))))
=> ! [V_27y_27,V_27x_27,V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2einternal__mult_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27y_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eexactlog_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))))) ) ) ) ) ) ).
fof('thm.list.list_case_def',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27))) = s__02(V_27B_27,V_27v_27)
& ! [V_27a0_27,V_27a1_27,V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27),s__02(V_27A_27,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) ) ).
fof('thm.list.SUM',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27h_27,V_27t_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2enum_2enum_27__00,V_27h_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27t_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27h_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27t_27))))) ) ).
fof('thm.list.APPEND',axiom,
! [V_27A_27] :
( ! [V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)
& ! [V_27l1_27,V_27l2_27,V_27h_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))) ) ).
fof('thm.list.LENGTH',axiom,
! [V_27A_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27h_27,V_27t_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.MAP',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27f_27,V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.EVERY_DEF',axiom,
! [V_27A_27] :
( ! [V_27P_27] : s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27P_27,V_27h_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))))
<=> ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27h_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))) ) ) ) ).
fof('thm.list.list_nchotomy',axiom,
! [V_27A_27,V_27l_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)
| ? [V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))) ) ).
fof('thm.list.APPEND_NIL',axiom,
! [V_27A_27,V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) ).
fof('thm.list.MAP_APPEND',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27l1_27,V_27l2_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))) ).
fof('thm.list.EVERY_APPEND',axiom,
! [V_27A_27,V_27P_27,V_27l1_27,V_27l2_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))))
<=> ( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27)))) ) ) ).
fof('thm.list.SUM_APPEND',axiom,
! [V_27l1_27,V_27l2_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27l2_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27l1_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),V_27l2_27))))) ).
fof('thm.words.dimword_def',axiom,
! [V_27A_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))) ).
fof('thm.words.ZERO_LT_dimword',axiom,
! [V_27A_27] : p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00)))))) ).
fof('thm.words.n2w_11',axiom,
! [V_27A_27,V_27m_27,V_27n_27] :
( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eMOD_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eMOD_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))) ) ).
fof('thm.words.word_add_n2w',axiom,
! [V_27A_27,V_27m_27,V_27n_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ).
fof('thm.words.word_mul_n2w',axiom,
! [V_27A_27,V_27m_27,V_27n_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) ).
fof('thm.words.WORD_ADD_ASSOC',axiom,
! [V_27A_27,V_27v_27,V_27w_27,V_27x_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27))))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27))) ).
fof('thm.words.WORD_ADD_COMM',axiom,
! [V_27A_27,V_27v_27,V_27w_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))) ).
fof('thm.words.WORD_LEFT_ADD_DISTRIB',axiom,
! [V_27A_27,V_27v_27,V_27w_27,V_27x_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27))))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27))))) ).
fof('thm.words.WORD_EQ_ADD_LCANCEL',axiom,
! [V_27A_27,V_27v_27,V_27w_27,V_27x_27] :
( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) ) ).
fof('thm.words.WORD_EQ_ADD_RCANCEL',axiom,
! [V_27A_27,V_27v_27,V_27w_27,V_27x_27] :
( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) ) ).
fof('thm.misc.LESS_1',axiom,
! [V_27x_27] :
( p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))
<=> s__02(c_27type_2enum_2enum_27__00,V_27x_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ) ).
fof('thm.misc.bytes_in_word_def',axiom,
! [V_27A_27] : s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))) ).
fof('thm.misc.plus_0_I',axiom,
s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2ecombin_2eI_27__00) ).
fof('thm.gc_shared.heap_element_nchotomy',axiom,
! [V_27A_27,V_27B_27,V_27hh_27] :
( ? [V_27n_27] : s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),V_27hh_27) = s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eUnused_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
| ? [V_27n_27,V_27a_27,V_27n0_27] : s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),V_27hh_27) = s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eForwardPointer_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27a_27),s__02(c_27type_2enum_2enum_27__00,V_27n0_27)))
| ? [V_27l_27,V_27n_27,V_27b_27] : s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),V_27hh_27) = s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eDataElement_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__address_27__01(V_27A_27)),V_27l_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27B_27,V_27b_27))) ) ).
fof('thm.gc_shared.el_length_def',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27l_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2egc__shared_2eel__length_27__00),s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eUnused_27__01(s__02(c_27type_2enum_2enum_27__00,V_27l_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27l_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& ! [V_27n_27,V_27d_27,V_27l_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2egc__shared_2eel__length_27__00),s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eForwardPointer_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(V_27A_27,V_27d_27),s__02(c_27type_2enum_2enum_27__00,V_27l_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27l_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& ! [V_27xs_27,V_27l_27,V_27data_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2egc__shared_2eel__length_27__00),s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2eDataElement_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__address_27__01(V_27A_27)),V_27xs_27),s__02(c_27type_2enum_2enum_27__00,V_27l_27),s__02(V_27B_27,V_27data_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,V_27l_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))) ) ).
fof('thm.gc_shared.heap_length_def',axiom,
! [V_27A_27,V_27B_27,V_27heap_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27heap_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2egc__shared_2eel__length_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27heap_27))))) ).
fof('thm.gc_shared.heap_length_NIL',axiom,
! [V_27A_27,V_27B_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ).
fof('thm.gc_shared.heap_length_APPEND',axiom,
! [V_27A_27,V_27B_27,V_27ys_27,V_27xs_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27xs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27ys_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27xs_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27ys_27))))) ).
fof('thm.gen_gc.gc_move_loop_def',axiom,
! [V_27A_27,V_27B_27,V__4] :
( ! [V__2,V_27clock_27,V_27conf_27,V_27state_27,V_27r4_27] : s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),V__4),s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27r4_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egen__gc_2egc__move__refs_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2egc__state__r2__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27))),c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2egc__state__r4__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27))),c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eNIL_27__00))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27)))))))))
=> ! [V__3] :
( ! [V__2,V_27clock_27,V_27conf_27,V_27state_27,V_27h_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))))),V__3),s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),V_27h_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),V__4),s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27)))
=> ! [V__2] :
( ! [V_27conf_27,V_27clock_27,V_27state_7c39_7c_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2enum_2enum_27__00,V_27clock_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_7c39_7c_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egc__shared_2egc__state__ok__fupd_27__02(s__02(cfun__02(cbool__00,cbool__00),c_27const_2ecombin_2eK_27__01(s__02(cbool__00,cF__00))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_7c39_7c_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egen__gc_2egc__move__loop_27__03(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_7c39_7c_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27clock_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))) )
=> ! [V__1] :
( ! [V_27clock_27,V_27conf_27,V_27state_27,V_27h2_27] : s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27h2_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egen__gc_2egc__move__data_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27)))))
=> ! [V__0] :
( ! [V_27clock_27,V_27conf_27,V_27state_27,V_27h_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),V_27h_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27)))
=> ! [V_27state_27,V_27conf_27,V_27clock_27] : s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2egen__gc_2egc__move__loop_27__03(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27),s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))))),s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))),chapp__02(s__02(cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),chapp__02(s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))))),chapp__02(s__02(cfun__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27))))))),V__3),s__02(cfun__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27)))),V__2))),s__02(c_27type_2enum_2enum_27__00,V_27clock_27))),s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27B_27),V_27conf_27))),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27state_27))))) ) ) ) ) ) ).
fof('thm.gen_gc.gc_move_loop_ok',axiom,
! [V_27B_27,V_27A_27,V_27conf_27,V_27s_27,V_27c_27] :
( p__01(s__02(cbool__00,c_27const_2egc__shared_2egc__state__ok_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),c_27const_2egen__gc_2egc__move__loop_27__03(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27A_27),V_27conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27),s__02(c_27type_2enum_2enum_27__00,V_27c_27))))))
=> p__01(s__02(cbool__00,c_27const_2egc__shared_2egc__state__ok_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27)))) ) ).
fof('thm.address.WORD_EQ_ADD_CANCEL',axiom,
! [V_27A_27,V_27v_27,V_27w_27,V_27x_27] :
( ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27x_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) )
& ( s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27))) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27v_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) ) ) ).
fof('thm.labProps.good_dimindex_def',axiom,
! [V_27A_27] :
( p__01(s__02(cbool__00,c_27const_2elabProps_2egood__dimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))
<=> ( s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
| s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))) ) ) ).
fof('thm.data_to_word_gcProof.len_inv_def',axiom,
! [V_27A_27,V_27B_27,V_27s_27] :
( p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))
<=> s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27A_27,V_27B_27),V_27s_27))))))))) ) ).
fof('thm.data_to_word_gcProof.word_heap_parts_def',axiom,
! [V_27A_27,V_27B_27,V_27conf_27,V_27p_27,V_27s_27,V_27xs_27] : s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),V_27xs_27))) = s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2emisc_2eword__list_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),V_27xs_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)),V_27xs_27))))))))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27B_27)))),V_27s_27))))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))) ).
fof('thm.data_to_word_gcProof.gc_move_data_const',axiom,
! [V_27B_27,V_27A_27,V_27gen__conf_27,V_27s_27,V_27s_7c39_7c_27] :
( s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),c_27const_2egen__gc_2egc__move__data_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27A_27),V_27gen__conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27)
=> ( s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27)))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27)))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27))) ) ) ).
fof('thm.data_to_word_gcProof.gc_move_refs_const',axiom,
! [V_27B_27,V_27A_27,V_27gen__conf_27,V_27s_27,V_27s_7c39_7c_27] :
( s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),c_27const_2egen__gc_2egc__move__refs_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(V_27A_27),V_27gen__conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27)
=> s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_7c39_7c_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27B_27,V_27A_27)),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(V_27B_27,V_27A_27),V_27s_27))) ) ).
fof('thm.data_to_word_gcProof.word_gen_gc_move_refs_thm',axiom,
! [V_27A_27,V_27p_27,V_27gen__conf_27,V_27conf_27,V_27k_27,V_27s_27,V_27m_27,V_27dm_27,V_27curr_27,V_27xs_27,V_27s1_27,V_27pb1_27,V_27pa1_27,V_27m1_27,V_27ib1_27,V_27i1_27,V_27frame_27,V_27c1_27,V_27p1_27] :
( ( s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),c_27const_2egen__gc_2egc__move__refs_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)
& p__01(s__02(cbool__00,c_27const_2egc__shared_2egc__state__ok_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2eshift__length_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& ! [V_27t_27,V_27r_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27r_27))))))
<=> s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27) = s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27const_2edata__to__word__memoryProof_2eRefTag_27__00) )
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& 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= s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cbool__00,V_27c1_27)))))))))))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,V_27k_27))))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))
& p__01(s__02(cbool__00,c_27const_2elabProps_2egood__dimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00)))) )
=> ? [V_27xs1_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))))
& p__01(s__02(cbool__00,V_27c1_27))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27)))
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27)))))))))))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))) ) ) ).
fof('thm.data_to_word_gcProof.word_gen_gc_move_data_thm',axiom,
! [V_27A_27,V_27p_27,V_27gen__conf_27,V_27conf_27,V_27k_27,V_27s_27,V_27m_27,V_27dm_27,V_27curr_27,V_27xs_27,V_27s1_27,V_27pb1_27,V_27pa1_27,V_27m1_27,V_27ib1_27,V_27i1_27,V_27frame_27,V_27c1_27] :
( ( s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),c_27const_2egen__gc_2egc__move__data_27__02(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)
& p__01(s__02(cbool__00,c_27const_2egc__shared_2egc__state__ok_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2eshift__length_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& ! [V_27t_27,V_27r_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27r_27))))))
<=> s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27) = s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27const_2edata__to__word__memoryProof_2eRefTag_27__00) )
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& 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= s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cbool__00,V_27c1_27)))))))))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))),s__02(c_27type_2enum_2enum_27__00,V_27k_27))))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))
& p__01(s__02(cbool__00,c_27const_2elabProps_2egood__dimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00)))) )
=> ? [V_27xs1_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))))
& p__01(s__02(cbool__00,V_27c1_27))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27)))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))) = s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))) ) ) ).
fof('thm.data_to_word_gcProof.LENGTH_LESS_EQ_SUM_el_length',axiom,
! [V_27A_27,V_27B_27,V_27t_27] : p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27t_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eSUM_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2egc__shared_2eel__length_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(V_27A_27,V_27B_27)),V_27t_27)))))))) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27gen__conf_27,V_27conf_27,V_27p_27,V_27k_27,V_27s_27,V_27m_27,V_27dm_27,V_27curr_27,V_27xs_27,V_27s1_27,V_27pb1_27,V_27pa1_27,V_27m1_27,V_27ib1_27,V_27i1_27,V_27frame_27,V_27c1_27] :
( ( s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),c_27const_2egen__gc_2egc__move__loop_27__03(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27),s__02(c_27type_2enum_2enum_27__00,V_27k_27))) = s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)
& p__01(s__02(cbool__00,c_27const_2egc__shared_2egc__state__ok_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2eshift__length_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eDIV_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2ewords_2edimword_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& ! [V_27t_27,V_27r_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27r_27))))))
<=> s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,V_27t_27) = s__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27const_2edata__to__word__memoryProof_2eRefTag_27__00) )
& p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2edata__to__word_2econfig__len__size_27__01(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2efcp_2edimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))))
& 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c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))))))))))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cbool__00,V_27c1_27)))))))))))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))
& p__01(s__02(cbool__00,c_27const_2elabProps_2egood__dimindex_27__01(s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00)))) )
=> ? [V_27xs1_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__memoryProof_2eword__heap_27__03(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27curr_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))),s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),c_27const_2edata__to__word__gcProof_2eword__heap__parts_27__04(s__02(c_27type_2edata__to__word_2econfig_27__00,V_27conf_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27))))),s__02(cfun__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),cbool__00),V_27frame_27))),s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cbool__00),c_27const_2eset__sep_2efun2set_27__01(s__02(c_27type_2epair_2eprod_27__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27m1_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),cbool__00),V_27dm_27))))))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r4_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r3_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r2_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2elist_2eNIL_27__00)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__heap_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s_27)))))
& p__01(s__02(cbool__00,V_27c1_27))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27i1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27xs1_27)))
& p__01(s__02(cbool__00,c_27const_2edata__to__word__gcProof_2elen__inv_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pa1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27pb1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__add_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27p_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2eword__mul_27__02(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2emisc_2ebytes__in__word_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2eheap__length_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__h1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))))))
& s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27ib1_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27const_2ewords_2en2w_27__01(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2earithmetic_2e_2b_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__a_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27))))),s__02(c_27type_2enum_2enum_27__00,c_27const_2egc__shared_2egc__state__n_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),cbool__00),c_27const_2edata__to__word__gcProof_2eis__Ref_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))),cbool__00),c_27const_2egen__gc_2egen__gc__conf__isRef_27__01(s__02(c_27type_2egen__gc_2egen__gc__conf_27__01(c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27gen__conf_27))))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egc__shared_2eheap__element_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27))))),c_27const_2egc__shared_2egc__state__r1_27__01(s__02(c_27type_2egc__shared_2egc__state_27__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2edata__to__word__memoryProof_2etag_27__00,c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)))),V_27s1_27)))))) ) ) ).
%------------------------------------------------------------------------------