TPTP Problem File: SWW892+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW892+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : inferSound__3__tactictoe_prove_2__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : inferSound__3__tactictoe_prove_2__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 70 ( 18 unt; 0 def)
% Number of atoms : 342 ( 129 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 323 ( 51 ~; 38 |; 113 &)
% ( 58 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 23 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 56 ( 56 usr; 13 con; 0-4 aty)
% Number of variables : 307 ( 305 !; 2 ?)
% 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.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.LET_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27x_27] : s__02(V_27B_27,c_27const_2ebool_2eLET_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) ).
fof('thm.bool.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.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.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.EQ_REFL',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.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.RIGHT_OR_OVER_AND',axiom,
! [V_27A_270,V_27B_270,V_27C_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))
| p__01(s__02(cbool__00,V_27A_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.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_FORALL_THM2',axiom,
! [V_27A_27,V_27f_27,V_27v_27] :
( ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27v_27)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27v_27)))) ) ).
fof('thm.bool.bool_case_thm',axiom,
! [V_27A_27] :
( ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.combin.o_DEF',axiom,
! [V_27B_27,V_27C_27,V_27A_27,V_27f_27,V_27g_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2ecombin_2eo_27__02(s__02(cfun__02(V_27C_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,V_27C_27),V_27g_27))),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27C_27,V_27B_27),V_27f_27),s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27A_27,V_27C_27),V_27g_27),s__02(V_27A_27,Vx))))) ).
fof('thm.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27A_27,V_27A_27),c_27const_2ecombin_2eI_27__00),s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.combin.I_o_ID',axiom,
! [V_27A_27,V_27B_27,V_27f_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2ecombin_2eo_27__02(s__02(cfun__02(V_27B_27,V_27B_27),c_27const_2ecombin_2eI_27__00),s__02(cfun__02(V_27A_27,V_27B_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_2ecombin_2eo_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,V_27A_27),c_27const_2ecombin_2eI_27__00))) = s__02(cfun__02(V_27A_27,V_27B_27),V_27f_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.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.pair_CASES',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.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.prim_rec.NOT_LESS_0',axiom,
! [V_27n_27] : ~ p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ).
fof('thm.arithmetic.ADD_0',axiom,
! [V_27m_27] : s__02(c_27type_2enum_2enum_27__00,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) ).
fof('thm.arithmetic.ADD_COMM',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.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.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.ADD_EQ_0',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_2enum_2e0_27__00)
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) ) ) ).
fof('thm.arithmetic.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_LEQ',axiom,
! [V_27m_27,V_27n_27] :
( ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))) ) ).
fof('thm.arithmetic.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.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,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cF__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) )
& ! [V_27n_27,V_27m_27] : s__02(cbool__00,c_27const_2earithmetic_2e_3e_3d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(cbool__00,c_27const_2earithmetic_2e_3c_3d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27n_27] : s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ~ p__01(s__02(cbool__00,c_27const_2earithmetic_2eODD_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))))
& p__01(s__02(cbool__00,c_27const_2earithmetic_2eEVEN_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)))) ) ).
fof('thm.numeral.numeral_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_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_case_def',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27v_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),c_27const_2eoption_2eNONE_27__00),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,V_27v_27)
& ! [V_27x_27,V_27v_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),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_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,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) ) ).
fof('thm.list.EVERY_DEF',axiom,
! [V_27A_27] :
( ! [V_27P_27] : s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(cbool__00,cT__00)
& ! [V_27P_27,V_27h_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))))
<=> ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27h_27))))
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))) ) ) ) ).
fof('thm.finite_map.FLOOKUP_EMPTY',axiom,
! [V_27B_27,V_27A_27,V_27k_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(V_27B_27,V_27A_27),c_27const_2efinite__map_2eFEMPTY_27__00),s__02(V_27B_27,V_27k_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) ).
fof('thm.infer_t.infer_t_induction',axiom,
! [V_27P0_27,V_27P1_27] :
( ( ! [V_27n_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),V_27P0_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& ! [V_27l_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cbool__00),V_27P1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27l_27))))
=> ! [V_27t_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),V_27P0_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27l_27),s__02(c_27type_2east_2etctor_27__00,V_27t_27)))))) )
& ! [V_27n_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),V_27P0_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cbool__00),V_27P1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eNIL_27__00))))
& ! [V_27i_27,V_27l_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),V_27P0_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27i_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cbool__00),V_27P1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27l_27)))) )
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cbool__00),V_27P1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27i_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27l_27)))))) ) )
=> ( ! [V_27i_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),V_27P0_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27i_27))))
& ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cbool__00),V_27P1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27l_27)))) ) ) ).
fof('thm.infer.generalise_def',axiom,
! [V__9] :
( ! [V_27num__gen_27,V_27num__gen_7c39_7c_27,V_27s_7c39_7c_7c39_7c_27,V_27t_7c39_7c_27,V_27ts_7c39_7c_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__9),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_7c39_7c_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_7c39_7c_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2epair_2e_2c_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_27num__gen_27),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_7c39_7c_27)))))))
=> ! [V__8] :
( ! [V_27num__gen_27,V_27num__gen_7c39_7c_27,V_27t_7c39_7c_27,V_27s_7c39_7c_7c39_7c_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__8),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_7c39_7c_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__9),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_7c39_7c_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27)))
=> ! [V__7] :
( ! [V_27num__gen_27,V_27t_7c39_7c_27,V_27num__gen_7c39_7c_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),V__7),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__8),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_7c39_7c_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27)))))
=> ! [V__6] :
( ! [V_27m_27,V_27num__gen_27,V_27n_27,V_27s_7c39_7c_27,V_27ts_27,V_27t_7c39_7c_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))))),V__6),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),V__7),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2einfer_2egeneralise__list_27__04(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_27num__gen_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))))
=> ! [V__5] :
( ! [V_27m_27,V_27num__gen_27,V_27n_27,V_27ts_27,V_27s_7c39_7c_27] : s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))))),V__5),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))) = s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))))),V__6),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))
=> ! [V__4] :
( ! [V_27m_27,V_27n_27,V_27ts_27,V_27num__gen_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__4),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_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))))),V__5),s__02(c_27type_2enum_2enum_27__00,V_27m_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))))
=> ! [V__3] :
( ! [V_27s_27,V_27v_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),chapp__02(s__02(cfun__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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),V__3),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27))),s__02(c_27type_2enum_2enum_27__00,V_27v_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27v_27)))))))
=> ! [V__2] :
( ! [V_27num__gen_27,V_27s_7c39_7c_27,V_27tc_27,V_27ts_7c39_7c_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_7c39_7c_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_7c39_7c_27),s__02(c_27type_2east_2etctor_27__00,V_27tc_27)))))))
=> ! [V__1] :
( ! [V_27num__gen_27,V_27tc_27,V_27s_7c39_7c_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))))),V__2),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27))),s__02(c_27type_2east_2etctor_27__00,V_27tc_27)))
=> ! [V__0] :
( ! [V_27tc_27,V_27num__gen_27] : s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),V__0),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27num__gen_27))),s__02(c_27type_2east_2etctor_27__00,V_27tc_27)))))
=> ( ! [V_27m_27,V_27n_27,V_27s_27,V_27ts_27,V_27tc_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2einfer_2egeneralise_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),chapp__02(s__02(cfun__02(c_27type_2east_2etctor_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))))),V__0),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2einfer_2egeneralise__list_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))))
& ! [V_27m_27,V_27n_27,V_27s_27,V_27uv_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2einfer_2egeneralise_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27uv_27))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFLOOKUP_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2enum_2enum_27__00,V_27uv_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2ebool_2eCOND_27__03(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_27uv_27))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_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_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFUPDATE_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27uv_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))))),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27uv_27))))))))),s__02(cfun__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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00))),chapp__02(s__02(cfun__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)))),V__3),s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27)))))
& ! [V_27m_27,V_27n_27,V_27s_27,V_27k_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2einfer_2egeneralise_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27k_27))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27k_27)))))))
& ! [V_27m_27,V_27n_27,V_27s_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2einfer_2egeneralise__list_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eNIL_27__00)))))
& ! [V_27m_27,V_27n_27,V_27s_27,V_27t_27,V_27ts_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2einfer_2egeneralise__list_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2ebool_2eLET_27__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))))))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)))))))),V__4),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_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))))),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2einfer_2egeneralise_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('thm.infer.check_t_def',axiom,
! [V__0] :
( ! [V_27n_27,V_27uvars_27,V_27a_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27a_27))) = s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27a_27)))
=> ( ! [V_27v_27,V_27uvars_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27v_27))))) = s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2enum_2enum_27__00,V_27v_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27)))
& ! [V_27uvars_27,V_27n_7c39_7c_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_7c39_7c_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& ! [V_27uvars_27,V_27ts_27,V_27tc_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))) = s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27uvars_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))) ) ) ).
fof(conjecture,conjecture,
( ! [V_27t_27,V_27s_7c39_7c_27,V_27t_7c39_7c_27,V_27x_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27x_27))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))))
& s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2einfer_2egeneralise_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFEMPTY_27__00),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2einfer__t_2einfer__t_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_7c39_7c_27))))) )
=> ( s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27) = s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFEMPTY_27__00)
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00))),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27)))) ) )
& ! [V_27ts_27,V_27s_7c39_7c_27,V_27ts_7c39_7c_27,V_27x_27] :
( ( p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),V_27x_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))))
& s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2einfer_2egeneralise__list_27__04(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_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFEMPTY_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00))),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_7c39_7c_27))))) )
=> ( s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27s_7c39_7c_27) = s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2efinite__map_2eFEMPTY_27__00)
& p__01(s__02(cbool__00,c_27const_2elist_2eEVERY_27__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cbool__00),c_27const_2einfer_2echeck__t_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00))),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))) ) ) ) ).
%------------------------------------------------------------------------------