TPTP Problem File: SWW881+1.p
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%------------------------------------------------------------------------------
% File : SWW881+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : clos_relation__26__get_global_state_rel__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : clos_relation__26__get_global_state_rel__dep [Kum18]
% Status : Theorem
% Rating : 0.97 v8.1.0, 1.00 v7.3.0
% Syntax : Number of formulae : 126 ( 29 unt; 0 def)
% Number of atoms : 541 ( 242 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 481 ( 66 ~; 67 |; 171 &)
% ( 81 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 20 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 113 ( 113 usr; 20 con; 0-8 aty)
% Number of variables : 615 ( 577 !; 38 ?)
% 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.EXISTS_DEF',axiom,
! [V_27A_27,Vx] : s__02(cbool__00,c_24exists__01(s__02(cfun__02(V_27A_27,cbool__00),Vx))) = s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),Vx),s__02(V_27A_27,c_27const_2emin_2e_40_27__01(s__02(cfun__02(V_27A_27,cbool__00),Vx))))) ).
fof('thm.bool.F_DEF',axiom,
( p__01(s__02(cbool__00,cF__00))
<=> ! [V_27t_27] : p__01(s__02(cbool__00,V_27t_27)) ) ).
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.SELECT_AX',axiom,
! [V_27A_27,V_27P_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,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,c_27const_2emin_2e_40_27__01(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27)))))) ) ).
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.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.EXISTS_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.IMP_F',axiom,
! [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)) ) ).
fof('thm.bool.F_IMP',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,cF__00)) ) ) ).
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.FUN_EQ_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27g_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27) = s__02(cfun__02(V_27A_27,V_27B_27),V_27g_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))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27g_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.NOT_EXISTS_THM',axiom,
! [V_27A_27,V_27P_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,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) ) ).
fof('thm.bool.RIGHT_AND_FORALL_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ( p__01(s__02(cbool__00,V_27P_27))
& ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27P_27))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.EXISTS_OR_THM',axiom,
! [V_27A_27,V_27P_27,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,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_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))))
| ? [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.LEFT_OR_EXISTS_THM',axiom,
! [V_27A_27,V_27P_27,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)) )
<=> ? [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)) ) ) ).
fof('thm.bool.RIGHT_OR_EXISTS_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ( p__01(s__02(cbool__00,V_27P_27))
| ? [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ? [V_27x_27] :
( p__01(s__02(cbool__00,V_27P_27))
| p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.LEFT_EXISTS_AND_THM',axiom,
! [V_27A_27,V_27P_27,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)) )
<=> ( ? [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)) ) ) ).
fof('thm.bool.RIGHT_FORALL_OR_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27P_27))
| p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ( p__01(s__02(cbool__00,V_27P_27))
| ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_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.LEFT_OR_OVER_AND',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_27A_270))
| p__01(s__02(cbool__00,V_27C_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.LET_CONG',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27g_27,V_27M_27,V_27N_27] :
( ( s__02(V_27A_27,V_27M_27) = s__02(V_27A_27,V_27N_27)
& ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27N_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))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27g_27),s__02(V_27A_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_27M_27))) = s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27g_27),s__02(V_27A_27,V_27N_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.UNWIND_THM2',axiom,
! [V_27A_27,V_27P_27,V_27a_27] :
( ? [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_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,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_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.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.itself_induction',axiom,
! [V_27A_27,V_27P_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ebool_2eitself_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),c_27const_2ebool_2ethe__value_27__00))))
=> ! [V_27i_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ebool_2eitself_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2ebool_2eitself_27__01(V_27A_27),V_27i_27)))) ) ).
fof('thm.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,c_27const_2ecombin_2eI_27__01(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_imp',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.sat.pth_ni1',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)) ) ).
fof('thm.sat.pth_ni2',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_27q_27)) ) ).
fof('thm.sat.pth_no1',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)) ) ).
fof('thm.sat.pth_no2',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_27q_27)) ) ).
fof('thm.sat.pth_nn',axiom,
! [V_27p_27] :
( ~ ~ p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27p_27)) ) ).
fof('thm.relation.WF_INDUCTION_THM',axiom,
! [V_27A_27,V_27R_27] :
( p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))))
=> ! [V_27P_27] :
( ! [V_27x_27] :
( ! [V_27y_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27y_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_27P_27),s__02(V_27A_27,V_27y_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)))) ) ) ).
fof('thm.relation.inv_image_def',axiom,
! [V_27B_27,V_27A_27,V_27R_27,V_27f_27,Vx,Vx_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),c_27const_2erelation_2einv__image_27__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27))),s__02(V_27A_27,Vx))),s__02(V_27A_27,Vx_27))) = s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R_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,Vx))))),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,Vx_27))))) ).
fof('thm.relation.WF_inv_image',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27f_27] :
( p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))))
=> p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),c_27const_2erelation_2einv__image_27__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27)))))) ) ).
fof('thm.relation.RESTRICT_LEMMA',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27R_27,V_27y_27,V_27z_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27y_27))),s__02(V_27A_27,V_27z_27))))
=> s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2erelation_2eRESTRICT_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27z_27))),s__02(V_27A_27,V_27y_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_27y_27))) ) ).
fof('thm.relation.WFREC_COROLLARY',axiom,
! [V_27B_27,V_27A_27,V_27M_27,V_27R_27,V_27f_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27) = s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2erelation_2eWFREC_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(cfun__02(cfun__02(V_27A_27,V_27B_27),cfun__02(V_27A_27,V_27B_27)),V_27M_27)))
=> ( p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_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))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,V_27B_27),cfun__02(V_27A_27,V_27B_27)),V_27M_27),s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2erelation_2eRESTRICT_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x_27))))),s__02(V_27A_27,V_27x_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.ABS_PAIR_THM',axiom,
! [V_27A_27,V_27B_27,V_27x_27] :
? [V_27q_27,V_27r_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_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_27q_27),s__02(V_27B_27,V_27r_27))) ).
fof('thm.pair.PAIR',axiom,
! [V_27A_27,V_27B_27,V_27x_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,c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27))),s__02(V_27B_27,c_27const_2epair_2eSND_27__01(s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27))))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27) ).
fof('thm.pair.FST',axiom,
! [V_27B_27,V_27A_27,V_27x_27,V_27y_27] : s__02(V_27A_27,c_27const_2epair_2eFST_27__01(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_27A_27,V_27x_27) ).
fof('thm.pair.SND',axiom,
! [V_27A_27,V_27B_27,V_27x_27,V_27y_27] : s__02(V_27B_27,c_27const_2epair_2eSND_27__01(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_27B_27,V_27y_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,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2eUNCURRY_27__01(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.pair_case_thm',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27y_27,V_27x_27,V_27f_27] : s__02(V_27A_27,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,V_27x_27),s__02(V_27C_27,V_27y_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27C_27,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27),s__02(V_27B_27,V_27x_27))),s__02(V_27C_27,V_27y_27))) ).
fof('thm.pair.pair_case_cong',axiom,
! [V_27B_27,V_27C_27,V_27A_27,V_27f_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27f_27] :
( ( s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),V_27M_27) = s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),V_27M_7c39_7c_27)
& ! [V_27x_27,V_27y_27] :
( s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),V_27M_7c39_7c_27) = s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,V_27x_27),s__02(V_27C_27,V_27y_27)))
=> s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27C_27,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27),s__02(V_27B_27,V_27x_27))),s__02(V_27C_27,V_27y_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27C_27,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_7c39_7c_27),s__02(V_27B_27,V_27x_27))),s__02(V_27C_27,V_27y_27))) ) )
=> s__02(V_27A_27,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),V_27M_27),s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27))) = s__02(V_27A_27,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),V_27M_7c39_7c_27),s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_7c39_7c_27))) ) ).
fof('thm.pair.LEX_DEF',axiom,
! [V_27A_27,V_27B_27,V__3] :
( ! [V_27R1_27,V_27s_27,V_27u_27,V_27R2_27,V_27t_27,V_27v_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00))))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)))))),V__3),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(V_27A_27,V_27u_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27B_27,V_27t_27))),s__02(V_27B_27,V_27v_27))))
<=> ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27),s__02(V_27A_27,V_27s_27))),s__02(V_27A_27,V_27u_27))))
| ( s__02(V_27A_27,V_27s_27) = s__02(V_27A_27,V_27u_27)
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27),s__02(V_27B_27,V_27t_27))),s__02(V_27B_27,V_27v_27)))) ) ) )
=> ! [V__2] :
( ! [V_27R1_27,V_27s_27,V_27R2_27,V_27t_27,V_27u_27] : s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00))))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)))))),V__2),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27B_27,V_27t_27))),s__02(V_27A_27,V_27u_27))) = s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00))))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)))))),V__3),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(V_27A_27,V_27u_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27B_27,V_27t_27)))
=> ! [V__1] :
( ! [V_27R1_27,V_27s_27,V_27R2_27,V_27t_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))))),V__1),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27B_27,V_27t_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00))))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)))))),V__2),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27B_27,V_27t_27)))))
=> ! [V__0] :
( ! [V_27R1_27,V_27R2_27,V_27s_27] : s__02(cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))),s__02(V_27A_27,V_27s_27))) = s__02(cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))))),V__1),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(V_27A_27,V_27s_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27)))
=> ! [V_27R1_27,V_27R2_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),c_27const_2epair_2eLEX_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),cfun__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),cfun__02(V_27A_27,cfun__02(V_27B_27,cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00))))),V__0),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R1_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27R2_27))))) ) ) ) ) ).
fof('thm.pair.WF_LEX',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27Q_27] :
( ( p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))))
& p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27Q_27)))) )
=> p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00)),c_27const_2epair_2eLEX_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(cfun__02(V_27B_27,cfun__02(V_27B_27,cbool__00)),V_27Q_27)))))) ) ).
fof('thm.prim_rec.LESS_REFL',axiom,
! [V_27n_27] : ~ p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))) ).
fof('thm.prim_rec.NOT_LESS_0',axiom,
! [V_27n_27] : ~ p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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.prim_rec.WF_LESS',axiom,
p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00)))) ).
fof('thm.arithmetic.ADD_CLAUSES',axiom,
! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,V_27m_27)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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)
& s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_2b_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,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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.ADD_SYM',axiom,
! [V_27m_27,V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_2b_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_ASSOC',axiom,
! [V_27m_27,V_27n_27,V_27p_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_2b_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_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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.LESS_EQ',axiom,
! [V_27m_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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.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,c_27const_2earithmetic_2e_2b_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_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,c_27const_2earithmetic_2e_2b_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_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.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,c_27const_2earithmetic_2e_2b_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_2b_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(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_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,c_27const_2earithmetic_2e_2b_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_27n_27))) ).
fof('thm.sum.sum_CASES',axiom,
! [V_27A_27,V_27B_27,V_27ss_27] :
( ? [V_27x_27] : s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),V_27ss_27) = s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINL_27__01(s__02(V_27A_27,V_27x_27)))
| ? [V_27y_27] : s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),V_27ss_27) = s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINR_27__01(s__02(V_27B_27,V_27y_27))) ) ).
fof('thm.sum.sum_case_def',axiom,
! [V_27A_27,V_27C_27,V_27B_27] :
( ! [V_27x_27,V_27f_27,V_27f1_27] : s__02(V_27C_27,c_27const_2esum_2esum__CASE_27__03(s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINL_27__01(s__02(V_27A_27,V_27x_27))),s__02(cfun__02(V_27A_27,V_27C_27),V_27f_27),s__02(cfun__02(V_27B_27,V_27C_27),V_27f1_27))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27A_27,V_27C_27),V_27f_27),s__02(V_27A_27,V_27x_27)))
& ! [V_27y_27,V_27f_27,V_27f1_27] : s__02(V_27C_27,c_27const_2esum_2esum__CASE_27__03(s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINR_27__01(s__02(V_27B_27,V_27y_27))),s__02(cfun__02(V_27A_27,V_27C_27),V_27f_27),s__02(cfun__02(V_27B_27,V_27C_27),V_27f1_27))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27B_27,V_27C_27),V_27f1_27),s__02(V_27B_27,V_27y_27))) ) ).
fof('thm.numeral.numeral_distrib',axiom,
( ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_2b_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_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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,V_27n_27))))) = s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,c_27const_2earithmetic_2e_2b_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,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,c_27const_2earithmetic_2e_2b_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,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,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2earithmetic_2e_2b_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_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,c_27const_2earithmetic_2e_2b_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_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,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_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,c_27const_2earithmetic_2e_2b_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_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,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_2enumeral_2eiiSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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(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,c_27const_2earithmetic_2e_2b_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_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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(cbool__00,cF__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_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(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,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),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.option.option_nchotomy',axiom,
! [V_27A_27,V_27opt_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27opt_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
| ? [V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27opt_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ) ).
fof('thm.option.SOME_11',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ).
fof('thm.option.NOT_NONE_SOME',axiom,
! [V_27A_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) != s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ).
fof('thm.option.OPTREL_def',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27x_27,V_27y_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27B_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27))))
<=> ( ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eNONE_27__00) )
| ? [V_27x0_27,V_27y0_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27x_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x0_27)))
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),V_27y_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27y0_27)))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x0_27))),s__02(V_27B_27,V_27y0_27)))) ) ) ) ).
fof('thm.option.option_case_cong',axiom,
! [V_27A_27,V_27B_27,V_27v_7c39_7c_27,V_27f_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27v_27,V_27f_27] :
( ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_7c39_7c_27)
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_7c39_7c_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
=> s__02(V_27B_27,V_27v_27) = s__02(V_27B_27,V_27v_7c39_7c_27) )
& ! [V_27x_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_7c39_7c_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(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))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_7c39_7c_27),s__02(V_27A_27,V_27x_27))) ) )
=> s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_27),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27))) = s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27M_7c39_7c_27),s__02(V_27B_27,V_27v_7c39_7c_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_7c39_7c_27))) ) ).
fof('thm.basicSize.pair_size_def',axiom,
! [V_27A_27,V_27B_27,V__1] :
( ! [V_27f_27,V_27x_27,V_27g_27,V_27y_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)))),V__1),s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27))),s__02(V_27A_27,V_27x_27))),s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27))),s__02(V_27B_27,V_27y_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27),s__02(V_27B_27,V_27y_27)))))
=> ! [V__0] :
( ! [V_27f_27,V_27g_27,V_27x_27] : s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)))),V__0),s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27))),s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27))),s__02(V_27A_27,V_27x_27))) = s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)))),V__1),s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27))),s__02(V_27A_27,V_27x_27))),s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27)))
=> ! [V_27f_27,V_27g_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2ebasicSize_2epair__size_27__02(s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27),s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27type_2enum_2enum_27__00),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)),chapp__02(s__02(cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00))),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),cfun__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(V_27A_27,cfun__02(V_27B_27,c_27type_2enum_2enum_27__00)))),V__0),s__02(cfun__02(V_27A_27,c_27type_2enum_2enum_27__00),V_27f_27))),s__02(cfun__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27g_27))))) ) ) ).
fof('thm.list.list_induction',axiom,
! [V_27A_27,V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(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))))
& ! [V_27t_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))
=> ! [V_27h_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(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)))))) ) )
=> ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))) ) ).
fof('thm.list.MEM',axiom,
! [V_27A_27] :
( ! [V_27x_27] : s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))) = s__02(cbool__00,cF__00)
& ! [V_27x_27,V_27h_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_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(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27h_27)
| p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) ) ) ).
fof('thm.list.LIST_REL_EL_EQN',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27l1_27,V_27l2_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_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),V_27l2_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),V_27l1_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27)))
& ! [V_27n_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_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),V_27l1_27))))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))))),s__02(V_27B_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27)))))) ) ) ) ).
fof('thm.list.LIST_REL_LENGTH',axiom,
! [V_27A_27,V_27B_27,V_27R_27,V_27x_27,V_27y_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27R_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27x_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27y_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),V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27y_27))) ) ).
fof('thm.list.EVERY2_cong',axiom,
! [V_27A_27,V_27B_27,V_27l1_27,V_27l1_7c39_7c_27,V_27l2_27,V_27l2_7c39_7c_27,V_27P_27,V_27P_7c39_7c_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_27l1_7c39_7c_27)
& s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_7c39_7c_27)
& ! [V_27x_27,V_27y_27] :
( ( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_7c39_7c_27))))))
& p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27B_27,V_27y_27),s__02(cfun__02(V_27B_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_7c39_7c_27)))))) )
=> s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27P_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) = s__02(cbool__00,chapp__02(s__02(cfun__02(V_27B_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27P_7c39_7c_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) ) )
=> s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27P_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),V_27l2_27))) = s__02(cbool__00,c_27const_2elist_2eLIST__REL_27__03(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,cbool__00)),V_27P_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_7c39_7c_27))) ) ).
fof('thm.quotient_option.OPTION_REL_def',axiom,
! [V_27A_27,V_27y_27,V_27x_27,V_27R_27] :
( s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(cbool__00,cT__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27))))) = s__02(cbool__00,cF__00)
& s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cfun__02(c_27type_2eoption_2eoption_27__01(V_27A_27),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27))))) = s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x_27))),s__02(V_27A_27,V_27y_27))) ) ).
fof('thm.semanticPrimitives.abort_case_cong',axiom,
! [V_27A_27,V_27v1_7c39_7c_27,V_27v0_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27v0_27,V_27v1_27] :
( ( s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_27) = s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_7c39_7c_27)
& ( s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eabort_27__00,c_27const_2esemanticPrimitives_2eRtype__error_27__00)
=> s__02(V_27A_27,V_27v0_27) = s__02(V_27A_27,V_27v0_7c39_7c_27) )
& ( s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eabort_27__00,c_27const_2esemanticPrimitives_2eRtimeout__error_27__00)
=> s__02(V_27A_27,V_27v1_27) = s__02(V_27A_27,V_27v1_7c39_7c_27) ) )
=> s__02(V_27A_27,c_27const_2esemanticPrimitives_2eabort__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_27),s__02(V_27A_27,V_27v0_27),s__02(V_27A_27,V_27v1_27))) = s__02(V_27A_27,c_27const_2esemanticPrimitives_2eabort__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27M_7c39_7c_27),s__02(V_27A_27,V_27v0_7c39_7c_27),s__02(V_27A_27,V_27v1_7c39_7c_27))) ) ).
fof('thm.semanticPrimitives.error_result_case_cong',axiom,
! [V_27A_27,V_27B_27,V_27f1_7c39_7c_27,V_27f_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27f_27,V_27f1_27] :
( ( s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_27) = s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_7c39_7c_27)
& ! [V_27a_27] :
( s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),c_27const_2esemanticPrimitives_2eRraise_27__01(s__02(V_27A_27,V_27a_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_27a_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_7c39_7c_27),s__02(V_27A_27,V_27a_27))) )
& ! [V_27a_27] :
( s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),c_27const_2esemanticPrimitives_2eRabort_27__01(s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27a_27)))
=> s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27B_27),V_27f1_27),s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27a_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27B_27),V_27f1_7c39_7c_27),s__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27a_27))) ) )
=> s__02(V_27B_27,c_27const_2esemanticPrimitives_2eerror__result__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27B_27),V_27f1_27))) = s__02(V_27B_27,c_27const_2esemanticPrimitives_2eerror__result__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27A_27),V_27M_7c39_7c_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_7c39_7c_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2eabort_27__00,V_27B_27),V_27f1_7c39_7c_27))) ) ).
fof('thm.semanticPrimitives.result_case_cong',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27f1_7c39_7c_27,V_27f_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27f_27,V_27f1_27] :
( ( s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_27) = s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_7c39_7c_27)
& ! [V_27a_27] :
( s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),c_27const_2esemanticPrimitives_2eRval_27__01(s__02(V_27A_27,V_27a_27)))
=> s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27A_27,V_27C_27),V_27f_27),s__02(V_27A_27,V_27a_27))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27A_27,V_27C_27),V_27f_7c39_7c_27),s__02(V_27A_27,V_27a_27))) )
& ! [V_27a_27] :
( s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_7c39_7c_27) = s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),c_27const_2esemanticPrimitives_2eRerr_27__01(s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27a_27)))
=> s__02(V_27C_27,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27C_27),V_27f1_27),s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27a_27))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27C_27),V_27f1_7c39_7c_27),s__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27a_27))) ) )
=> s__02(V_27C_27,c_27const_2esemanticPrimitives_2eresult__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_27),s__02(cfun__02(V_27A_27,V_27C_27),V_27f_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27C_27),V_27f1_27))) = s__02(V_27C_27,c_27const_2esemanticPrimitives_2eresult__CASE_27__03(s__02(c_27type_2esemanticPrimitives_2eresult_27__02(V_27A_27,V_27B_27),V_27M_7c39_7c_27),s__02(cfun__02(V_27A_27,V_27C_27),V_27f_7c39_7c_27),s__02(cfun__02(c_27type_2esemanticPrimitives_2eerror__result_27__01(V_27B_27),V_27C_27),V_27f1_7c39_7c_27))) ) ).
fof('thm.closSem.ref_case_def',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27a_27,V_27f_27,V_27f1_27] : s__02(V_27B_27,c_27const_2eclosSem_2eref__CASE_27__03(s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a_27))),s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27),V_27f_27),s__02(cfun__02(cbool__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27B_27)),V_27f1_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a_27)))
& ! [V_27a0_27,V_27a1_27,V_27f_27,V_27f1_27] : s__02(V_27B_27,c_27const_2eclosSem_2eref__CASE_27__03(s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a1_27))),s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27),V_27f_27),s__02(cfun__02(cbool__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27B_27)),V_27f1_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27B_27),chapp__02(s__02(cfun__02(cbool__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27B_27)),V_27f1_27),s__02(cbool__00,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a1_27))) ) ).
fof('thm.closSem.ref_nchotomy',axiom,
! [V_27A_27,V_27rr_27] :
( ? [V_27l_27] : s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),V_27rr_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eValueArray_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))
| ? [V_27b_27,V_27l_27] : s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),V_27rr_27) = s__02(c_27type_2eclosSem_2eref_27__01(V_27A_27),c_27const_2eclosSem_2eByteArray_27__02(s__02(cbool__00,V_27b_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27l_27))) ) ).
fof('thm.closSem.v_case_def',axiom,
! [V_27A_27] :
( ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27a_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(c_27type_2einteger_2eint_27__00,V_27a_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27a_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27a_27)))
& ! [V_27a0_27,V_27a1_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(c_27type_2enum_2enum_27__00,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a_27)))
& ! [V_27a_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(c_27type_2enum_2enum_27__00,V_27a_27)))
& ! [V_27a0_27,V_27a1_27,V_27a2_27,V_27a3_27,V_27a4_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27),s__02(c_27type_2enum_2enum_27__00,V_27a3_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a4_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27)))),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))),s__02(c_27type_2enum_2enum_27__00,V_27a3_27))),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a4_27)))
& ! [V_27a0_27,V_27a1_27,V_27a2_27,V_27a3_27,V_27a4_27,V_27f_27,V_27f1_27,V_27f2_27,V_27f3_27,V_27f4_27,V_27f5_27,V_27f6_27] : s__02(V_27A_27,c_27const_2eclosSem_2ev__CASE_27__08(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27a3_27),s__02(c_27type_2enum_2enum_27__00,V_27a4_27))),s__02(cfun__02(c_27type_2einteger_2eint_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27A_27),V_27f1_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),V_27f2_27),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27A_27),V_27f3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f4_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2eclosLang_2eexp_27__00,V_27A_27))))),V_27f5_27),s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)))),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))))),V_27f6_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27a3_27))),s__02(c_27type_2enum_2enum_27__00,V_27a4_27))) ) ).
fof('thm.closSem.v_size_def',axiom,
! [V__1] :
( ! [V_27x_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),V__1),s__02(c_27type_2enum_2enum_27__00,V_27x_27))) = s__02(c_27type_2enum_2enum_27__00,V_27x_27)
=> ! [V__0] :
( ! [V_27v_27] : s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))),c_27type_2enum_2enum_27__00),V__0),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))),V_27v_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
=> ( ! [V_27a_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27a_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_27a_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27a_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_27a0_27,V_27a1_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a0_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27)))))))
& ! [V_27a_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2elist_2elist__size_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00)))),c_27type_2enum_2enum_27__00),V__0),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27a_27)))))
& ! [V_27a_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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_27a_27)))
& ! [V_27a0_27,V_27a1_27,V_27a2_27,V_27a3_27,V_27a4_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27),s__02(c_27type_2enum_2enum_27__00,V_27a3_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a4_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2ebasicSize_2eoption__size_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V__1),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a3_27),s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,c_27type_2enum_2enum_27__00),c_27const_2eclosLang_2eexp__size_27__00),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a4_27)))))))))))))
& ! [V_27a0_27,V_27a1_27,V_27a2_27,V_27a3_27,V_27a4_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27a3_27),s__02(c_27type_2enum_2enum_27__00,V_27a4_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2ebasicSize_2eoption__size_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V__1),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27a0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2elist__size_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00),c_27type_2enum_2enum_27__00),c_27const_2ebasicSize_2epair__size_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V__1),s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,c_27type_2enum_2enum_27__00),c_27const_2eclosLang_2eexp__size_27__00))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27a3_27))),s__02(c_27type_2enum_2enum_27__00,V_27a4_27)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27a0_27,V_27a1_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_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,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev__size_27__01(s__02(c_27type_2eclosSem_2ev_27__00,V_27a0_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2eclosSem_2ev1__size_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))))))) ) ) ) ).
fof('thm.closSem.v_nchotomy',axiom,
! [V_27vv_27] :
( ? [V_27i_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eNumber_27__01(s__02(c_27type_2einteger_2eint_27__00,V_27i_27)))
| ? [V_27c_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eWord64_27__01(s__02(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))))),V_27c_27)))
| ? [V_27n_27,V_27l_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eBlock_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27l_27)))
| ? [V_27l_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eByteVector_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2efcp_2ebit0_27__01(c_27type_2eone_2eone_27__00))))),V_27l_27)))
| ? [V_27n_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRefPtr_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
| ? [V_27o_7c39_7c_27,V_27l_27,V_27l0_27,V_27n_27,V_27e_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eClosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27o_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27l_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27l0_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27e_27)))
| ? [V_27o_7c39_7c_27,V_27l_27,V_27l0_27,V_27l1_27,V_27n_27] : s__02(c_27type_2eclosSem_2ev_27__00,V_27vv_27) = s__02(c_27type_2eclosSem_2ev_27__00,c_27const_2eclosSem_2eRecclosure_27__05(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),V_27o_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27l_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27l0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2eclosLang_2eexp_27__00)),V_27l1_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof('thm.closSem.get_global_def',axiom,
! [V_27A_27,V_27n_27,V_27globals_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eclosSem_2eget__global_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27globals_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eprim__rec_2e_3c_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_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),V_27globals_27))))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27globals_27))))),s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00))) ).
fof('thm.closSem.app_kind_case_cong',axiom,
! [V_27A_27,V_27f1_7c39_7c_27,V_27f_7c39_7c_27,V_27M_27,V_27M_7c39_7c_27,V_27f_27,V_27f1_27] :
( ( s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_27) = s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_7c39_7c_27)
& ! [V_27a_27] :
( s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_7c39_7c_27) = s__02(c_27type_2eclosSem_2eapp__kind_27__00,c_27const_2eclosSem_2ePartial__app_27__01(s__02(c_27type_2eclosSem_2ev_27__00,V_27a_27)))
=> s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,V_27A_27),V_27f_27),s__02(c_27type_2eclosSem_2ev_27__00,V_27a_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,V_27A_27),V_27f_7c39_7c_27),s__02(c_27type_2eclosSem_2ev_27__00,V_27a_27))) )
& ! [V_27a0_27,V_27a1_27,V_27a2_27] :
( s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_7c39_7c_27) = s__02(c_27type_2eclosSem_2eapp__kind_27__00,c_27const_2eclosSem_2eFull__app_27__03(s__02(c_27type_2eclosLang_2eexp_27__00,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27)))
=> s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27))),V_27f1_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27))),V_27f1_7c39_7c_27),s__02(c_27type_2eclosLang_2eexp_27__00,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a1_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27a2_27))) ) )
=> s__02(V_27A_27,c_27const_2eclosSem_2eapp__kind__CASE_27__03(s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_27),s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,V_27A_27),V_27f_27),s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27))),V_27f1_27))) = s__02(V_27A_27,c_27const_2eclosSem_2eapp__kind__CASE_27__03(s__02(c_27type_2eclosSem_2eapp__kind_27__00,V_27M_7c39_7c_27),s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,V_27A_27),V_27f_7c39_7c_27),s__02(cfun__02(c_27type_2eclosLang_2eexp_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),V_27A_27))),V_27f1_7c39_7c_27))) ) ).
fof('thm.clos_relation.evaluate_ev_clock',axiom,
! [V_27A_27,V_27c_27,V_27x_27,V_27s1_27,V_27vs_27,V_27s2_27] :
( s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2estate_27__01(V_27A_27)),c_27const_2eclos__relation_2eevaluate__ev_27__03(s__02(c_27type_2enum_2enum_27__00,V_27c_27),s__02(c_27type_2eclos__relation_2eval__or__exp_27__00,V_27x_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s1_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2estate_27__01(V_27A_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2elist_2elist_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2ev_27__00),V_27vs_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_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_2eclosSem_2estate__clock_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27A_27),V_27s2_27))),s__02(c_27type_2enum_2enum_27__00,V_27c_27)))) ) ).
fof('thm.clos_relation.val_rel_UNION_extract3_def',axiom,
! [V_27FFI_27,V_27x_27,V_27x1_27,V_27x2_27,V_27x3_27] : s__02(cbool__00,c_27const_2eclos__relation_2estate__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27x2_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27x3_27))) = s__02(cbool__00,c_27const_2eclos__relation_2eval__rel__UNION_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27)))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27x2_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27x3_27))))))))))))))) ).
fof('thm.clos_relation.val_rel_UNION_extract2_def',axiom,
! [V_27FFI_27,V_27x_27,V_27x1_27,V_27x2_27,V_27x3_27,V_27x4_27] : s__02(cbool__00,c_27const_2eclos__relation_2eref__v__rel_27__05(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2enum_2enum_27__00,V_27x2_27),s__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),V_27x3_27),s__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),V_27x4_27))) = s__02(cbool__00,c_27const_2eclos__relation_2eval__rel__UNION_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27)))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27const_2esum_2eINL_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),V_27x_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x2_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),V_27x3_27),s__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),V_27x4_27))))))))))))))))) ).
fof('thm.clos_relation.val_rel_UNION_extract1_def',axiom,
! [V_27FFI_27,V_27x_27,V_27x1_27,V_27x2_27,V_27x3_27] : s__02(cbool__00,c_27const_2eclos__relation_2eexec__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),V_27x2_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),V_27x3_27))) = s__02(cbool__00,c_27const_2eclos__relation_2eval__rel__UNION_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))))),c_27const_2esum_2eINR_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27)))))),c_27const_2esum_2eINL_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),V_27x2_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),V_27x3_27))))))))))))) ).
fof('thm.clos_relation.val_rel_UNION_extract0_def',axiom,
! [V_27FFI_27,V_27x_27,V_27x1_27,V_27x2_27,V_27x3_27,V_27x4_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__relation_2eval__rel_27__03(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2enum_2enum_27__00,V_27x2_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27x3_27))),s__02(c_27type_2eclosSem_2ev_27__00,V_27x4_27))) = s__02(cbool__00,c_27const_2eclos__relation_2eval__rel__UNION_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27)),c_27type_2epair_2eprod_27__02(c_27type_2eclos__relation_2eval__or__exp_27__00,c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))),c_27type_2esum_2esum_27__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00),c_27type_2eclosSem_2eref_27__01(c_27type_2eclosSem_2ev_27__00))))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),c_27type_2eclosSem_2estate_27__01(V_27FFI_27))))))),c_27const_2esum_2eINL_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),V_27x_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x1_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x2_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2eclosSem_2ev_27__00,c_27type_2eclosSem_2ev_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2eclosSem_2ev_27__00,V_27x3_27),s__02(c_27type_2eclosSem_2ev_27__00,V_27x4_27))))))))))))) ).
fof(conjecture,conjecture,
! [V_27FFI_27,V_27n_27,V_27i_27,V_27w_27,V_27s_27,V_27s_7c39_7c_27] :
( p__01(s__02(cbool__00,c_27const_2eclos__relation_2estate__rel_27__04(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27w_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s_27),s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s_7c39_7c_27))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),cbool__00),chapp__02(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),cfun__02(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00),cbool__00)),c_27const_2eoption_2eOPTREL_27__01(s__02(cfun__02(c_27type_2eclosSem_2ev_27__00,cfun__02(c_27type_2eclosSem_2ev_27__00,cbool__00)),c_27const_2eclos__relation_2eval__rel_27__03(s__02(c_27type_2ebool_2eitself_27__01(V_27FFI_27),c_27const_2ebool_2ethe__value_27__00),s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2enum_2enum_27__00,V_27w_27))))))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2eget__global_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__globals_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s_27))))))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2eget__global_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2eoption_2eoption_27__01(c_27type_2eclosSem_2ev_27__00)),c_27const_2eclosSem_2estate__globals_27__01(s__02(c_27type_2eclosSem_2estate_27__01(V_27FFI_27),V_27s_7c39_7c_27)))))))) ) ).
%------------------------------------------------------------------------------