TPTP Problem File: SWW869+1.p
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%------------------------------------------------------------------------------
% File : SWW869+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : cmlPtreeConversionProps__33__SpecLineList_OK__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : cmlPtreeConversionProps__33__SpecLineList_OK__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 88 ( 15 unt; 0 def)
% Number of atoms : 454 ( 241 equ)
% Maximal formula atoms : 75 ( 5 avg)
% Number of connectives : 409 ( 43 ~; 35 |; 186 &)
% ( 78 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 8 avg)
% Maximal term depth : 154 ( 4 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 149 ( 149 usr; 94 con; 0-3 aty)
% Number of variables : 376 ( 353 !; 23 ?)
% 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.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> p__01(s__02(cbool__00,V_27t2_27)) )
=> ( ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.FALSITY',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.EXISTS_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ? [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.OR_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
| p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.IMP_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.NOT_CLAUSES',axiom,
( ! [V_27t_27] :
( ~ ~ p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ~ p__01(s__02(cbool__00,cT__00))
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ~ p__01(s__02(cbool__00,cF__00))
<=> p__01(s__02(cbool__00,cT__00)) ) ) ).
fof('thm.bool.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.FORALL_AND_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ! [V_27x_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ( ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
& ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.LEFT_FORALL_IMP_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ! [V_27x_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
=> p__01(s__02(cbool__00,V_27Q_27)) )
<=> ( ? [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27))))
=> p__01(s__02(cbool__00,V_27Q_27)) ) ) ).
fof('thm.bool.RIGHT_FORALL_IMP_THM',axiom,
! [V_27A_27,V_27P_27,V_27Q_27] :
( ! [V_27x_27] :
( p__01(s__02(cbool__00,V_27P_27))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) )
<=> ( p__01(s__02(cbool__00,V_27P_27))
=> ! [V_27x_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27Q_27),s__02(V_27A_27,V_27x_27)))) ) ) ).
fof('thm.bool.DISJ_ASSOC',axiom,
! [V_27A_270,V_27B_270,V_27C_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27C_270)) )
<=> ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27C_270)) ) ) ).
fof('thm.bool.DISJ_COMM',axiom,
! [V_27A_270,V_27B_270] :
( ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_270)) )
<=> ( p__01(s__02(cbool__00,V_27B_270))
| p__01(s__02(cbool__00,V_27A_270)) ) ) ).
fof('thm.bool.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.DISJ_IMP_THM',axiom,
! [V_27P_27,V_27Q_27,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_27R_27)) ) ) ) ).
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.EXISTS_REFL',axiom,
! [V_27A_27,V_27a_27] :
? [V_27x_27] : s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27) ).
fof('thm.bool.UNWIND_THM2',axiom,
! [V_27A_27,V_27P_27,V_27a_27] :
( ? [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27)
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27a_27)))) ) ).
fof('thm.bool.UNWIND_FORALL_THM2',axiom,
! [V_27A_27,V_27f_27,V_27v_27] :
( ! [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27v_27)
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27f_27),s__02(V_27A_27,V_27v_27)))) ) ).
fof('thm.bool.bool_case_thm',axiom,
! [V_27A_27] :
( ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& ! [V_27t1_27,V_27t2_27] : s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.bool.BOUNDED_THM',axiom,
! [V_27v_27] : s__02(cbool__00,c_27const_2ebool_2eBOUNDED_27__01(s__02(cbool__00,V_27v_27))) = s__02(cbool__00,cT__00) ).
fof('thm.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_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.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.ABS_PAIR_THM',axiom,
! [V_27A_27,V_27B_27,V_27x_27] :
? [V_27q_27,V_27r_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27q_27),s__02(V_27B_27,V_27r_27))) ).
fof('thm.pair.FST',axiom,
! [V_27B_27,V_27A_27,V_27x_27,V_27y_27] : s__02(V_27A_27,c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.pair.FORALL_PROD',axiom,
! [V_27A_27,V_27B_27,V_27P_27] :
( ! [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27p_27))))
<=> ! [V_27p__1_27,V_27p__2_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27p__1_27),s__02(V_27B_27,V_27p__2_27)))))) ) ).
fof('thm.sum.INR_INL_11',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27y_27,V_27x_27] :
( s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINL_27__01(s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINL_27__01(s__02(V_27A_27,V_27y_27)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) )
& ! [V_27y_27,V_27x_27] :
( s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINR_27__01(s__02(V_27B_27,V_27x_27))) = s__02(c_27type_2esum_2esum_27__02(V_27A_27,V_27B_27),c_27const_2esum_2eINR_27__01(s__02(V_27B_27,V_27y_27)))
<=> s__02(V_27B_27,V_27x_27) = s__02(V_27B_27,V_27y_27) ) ) ).
fof('thm.numeral.numeral_distrib',axiom,
( ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enumeral_2eiZ_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2a_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,V_27n_27)
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2d_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27,V_27m_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eEXP_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27m_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
& ! [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2eprim__rec_2ePRE_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00) )
& ! [V_27n_27,V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,V_27m_27)))
<=> s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27) )
& ! [V_27n_27] : s__02(cbool__00,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.option.SOME_11',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27y_27)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ).
fof('thm.option.NOT_NONE_SOME',axiom,
! [V_27A_27,V_27x_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) != s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))) ).
fof('thm.option.OPTION_BIND_def',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27f_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eNONE_27__00),s__02(cfun__02(V_27B_27,c_27type_2eoption_2eoption_27__01(V_27A_27)),V_27f_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
& ! [V_27x_27,V_27f_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27x_27))),s__02(cfun__02(V_27B_27,c_27type_2eoption_2eoption_27__01(V_27A_27)),V_27f_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,c_27type_2eoption_2eoption_27__01(V_27A_27)),V_27f_27),s__02(V_27B_27,V_27x_27))) ) ).
fof('thm.option.OPTION_BIND_EQUALS_OPTION',axiom,
! [V_27A_27,V_27B_27,V_27y_27,V_27p_27,V_27f_27] :
( ( s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27p_27),s__02(cfun__02(V_27A_27,c_27type_2eoption_2eoption_27__01(V_27B_27)),V_27f_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eNONE_27__00)
<=> ( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27p_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
| ? [V_27x_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27p_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27)))
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2eoption_2eoption_27__01(V_27B_27)),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eNONE_27__00) ) ) )
& ( s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27p_27),s__02(cfun__02(V_27A_27,c_27type_2eoption_2eoption_27__01(V_27B_27)),V_27f_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27y_27)))
<=> ? [V_27x_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),V_27p_27) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27)))
& s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2eoption_2eoption_27__01(V_27B_27)),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27B_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27B_27,V_27y_27))) ) ) ) ).
fof('thm.pred_set.NOT_IN_EMPTY',axiom,
! [V_27A_27,V_27x_27] : ~ p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)))) ).
fof('thm.pred_set.IN_INSERT',axiom,
! [V_27A_27,V_27x_27,V_27y_27,V_27s_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(V_27A_27,V_27y_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
| p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)))) ) ) ).
fof('thm.list.list_case_def',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27))) = s__02(V_27B_27,V_27v_27)
& ! [V_27a0_27,V_27a1_27,V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27B_27)),V_27f_27),s__02(V_27A_27,V_27a0_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) ) ).
fof('thm.list.APPEND',axiom,
! [V_27A_27] :
( ! [V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)
& ! [V_27l1_27,V_27l2_27,V_27h_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l2_27))))) ) ).
fof('thm.list.FLAT',axiom,
! [V_27A_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eFLAT_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eFLAT_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27h_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(V_27A_27)),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eFLAT_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(V_27A_27)),V_27t_27))))) ) ).
fof('thm.list.MAP',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27f_27,V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.list_induction',axiom,
! [V_27A_27,V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))
& ! [V_27t_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))
=> ! [V_27h_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) )
=> ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))) ) ).
fof('thm.list.list_nchotomy',axiom,
! [V_27A_27,V_27l_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)
| ? [V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))) ) ).
fof('thm.list.CONS_11',axiom,
! [V_27A_27,V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27)))
<=> ( s__02(V_27A_27,V_27a0_27) = s__02(V_27A_27,V_27a0_7c39_7c_27)
& s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27) ) ) ).
fof('thm.list.NOT_NIL_CONS',axiom,
! [V_27A_27,V_27a1_27,V_27a0_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00) != s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) ).
fof('thm.list.APPEND_NIL',axiom,
! [V_27A_27,V_27l_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) ).
fof('thm.list.MAP_EQ_NIL',axiom,
! [V_27B_27,V_27A_27,V_27l_27,V_27f_27] :
( ( s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
<=> s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00) )
& ( s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))
<=> s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00) ) ) ).
fof('thm.list.MAP_EQ_CONS',axiom,
! [V_27B_27,V_27A_27,V_27t_27,V_27l_27,V_27h_27,V_27f_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27t_27)))
<=> ? [V_27x0_27,V_27t0_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27x0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t0_27)))
& s__02(V_27B_27,V_27h_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_27x0_27)))
& s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27t_27) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t0_27))) ) ) ).
fof('thm.list.MAP_EQ_SING',axiom,
! [V_27B_27,V_27A_27,V_27x_27,V_27l_27,V_27f_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,V_27x_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)))
<=> ? [V_27x0_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27x0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00)))
& s__02(V_27B_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_27x0_27))) ) ) ).
fof('thm.list.MAP_EQ_APPEND',axiom,
! [V_27B_27,V_27A_27,V_27l2_27,V_27l1_27,V_27l_27,V_27f_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l1_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27)))
<=> ? [V_27l10_27,V_27l20_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l10_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l20_27)))
& s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l1_27) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l10_27)))
& s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27l2_27) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l20_27))) ) ) ).
fof('thm.list.MEM',axiom,
! [V_27A_27] :
( ! [V_27x_27] : s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))) = s__02(cbool__00,cF__00)
& ! [V_27x_27,V_27h_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))))))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27h_27)
| p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) ) ) ).
fof('thm.grammar.symbol_11',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27a_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27a_7c39_7c_27)))
<=> s__02(V_27A_27,V_27a_27) = s__02(V_27A_27,V_27a_7c39_7c_27) )
& ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27a_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27a_7c39_7c_27)))
<=> s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27a_27) = s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27a_7c39_7c_27) ) ) ).
fof('thm.grammar.symbol_distinct',axiom,
! [V_27A_27,V_27B_27,V_27a_7c39_7c_27,V_27a_27] : s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27a_27))) != s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27a_7c39_7c_27))) ).
fof('thm.grammar.parsetree_nchotomy',axiom,
! [V_27A_27,V_27B_27,V_27LOCS_27,V_27pp_27] :
( ? [V_27p_27] : s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),V_27pp_27) = s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27LOCS_27),V_27p_27)))
| ? [V_27p_27,V_27l_27] : s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),V_27pp_27) = s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27LOCS_27),V_27p_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27)),V_27l_27))) ) ).
fof('thm.grammar.ptree_head_def',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27tok_27,V_27nt_27,V_27l_27,V_27children_27] :
( s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27tok_27),s__02(V_27C_27,V_27l_27))))))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27tok_27)
& s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27nt_27),s__02(V_27C_27,V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27nt_27))) ) ).
fof('thm.grammar.valid_ptree_def',axiom,
! [V_27A_27,V_27B_27,V_27C_27] :
( ! [V_27v0_27,V_27G_27] : s__02(cbool__00,c_27const_2egrammar_2evalid__ptree_27__02(s__02(c_27type_2egrammar_2egrammar_27__02(V_27A_27,V_27B_27),V_27G_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),V_27v0_27))))) = s__02(cbool__00,cT__00)
& ! [V_27nt_27,V_27l_27,V_27children_27,V_27G_27] :
( p__01(s__02(cbool__00,c_27const_2egrammar_2evalid__ptree_27__02(s__02(c_27type_2egrammar_2egrammar_27__02(V_27A_27,V_27B_27),V_27G_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27nt_27),s__02(V_27C_27,V_27l_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))))))
<=> ( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27nt_27),s__02(cfun__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),cbool__00),c_27const_2efinite__map_2eFDOM_27__01(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),cbool__00)),c_27const_2egrammar_2egrammar__rules_27__01(s__02(c_27type_2egrammar_2egrammar_27__02(V_27A_27,V_27B_27),V_27G_27))))))))
& p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),cbool__00),c_27const_2efinite__map_2eFAPPLY_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),cbool__00)),c_27const_2egrammar_2egrammar__rules_27__01(s__02(c_27type_2egrammar_2egrammar_27__02(V_27A_27,V_27B_27),V_27G_27))),s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27nt_27))))))
& ! [V_27pt_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27),s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))))))
=> p__01(s__02(cbool__00,c_27const_2egrammar_2evalid__ptree_27__02(s__02(c_27type_2egrammar_2egrammar_27__02(V_27A_27,V_27B_27),V_27G_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27)))) ) ) ) ) ).
fof('thm.grammar.ptree_fringe_def',axiom,
! [V_27A_27,V_27B_27,V_27C_27] :
( ! [V_27v0_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27))),c_27const_2egrammar_2eptree__fringe_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27C_27,V_27v0_27))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eNIL_27__00)))
& ! [V_27v1_27,V_27children_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27))),c_27const_2egrammar_2eptree__fringe_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27C_27),V_27v1_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2elist_2eFLAT_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27))),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27))),c_27const_2egrammar_2eptree__fringe_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27children_27))))) ) ).
fof('thm.grammar.ptree_ind',axiom,
! [V_27A_27,V_27B_27,V_27LOCS_27,V_27P_27] :
( ( ! [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),cbool__00),V_27P_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27LOCS_27),V_27p_27))))))
& ! [V_27l_27] :
( ! [V_27pt_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),V_27pt_27),s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27)),V_27l_27))))))
=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),cbool__00),V_27P_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),V_27pt_27)))) )
=> ! [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),cbool__00),V_27P_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27LOCS_27),V_27p_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27)),V_27l_27)))))) ) )
=> ! [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),cbool__00),V_27P_27),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27LOCS_27),V_27p_27)))) ) ).
fof('thm.tokenUtils.destLf_def',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27x_27,V_27v3_27,V_27v2_27,V_27v0_27] :
( s__02(c_27type_2eoption_2eoption_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2etokenUtils_2edestLf_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27x_27),s__02(V_27C_27,V_27v0_27))))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27x_27)))
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2etokenUtils_2edestLf_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27C_27),V_27v2_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27)),V_27v3_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2eoption_2eNONE_27__00) ) ).
fof('thm.tokenUtils.destTOK_def',axiom,
! [V_27B_27,V_27A_27,V_27v1_27,V_27t_27] :
( s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27type_2eoption_2eoption_27__01(V_27A_27)),c_27const_2etokenUtils_2edestTOK_27__00),s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27t_27))))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27t_27)))
& s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27type_2eoption_2eoption_27__01(V_27A_27)),c_27const_2etokenUtils_2edestTOK_27__00),s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(V_27B_27,c_27type_2enum_2enum_27__00),V_27v1_27))))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00) ) ).
fof('thm.gram.MMLnonT2num_thm',axiom,
( s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enV_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_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enUQTyOp_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enUQConstructorName_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTyvarN_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTypeName_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTypeList2_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTypeList1_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTypeDec_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTypeAbbrevDec_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enType_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTyVarList_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTyOp_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTopLevelDecs_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTopLevelDec_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTbaseList_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enTbase_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enStructure_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enStructName_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSpecLineList_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSpecLine_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSignatureValue_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enRelOps_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPtuple_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPcons_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPbaseList1_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPbase_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPatternList_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPattern_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPapp_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPType_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPTbase_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPEs_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPE_7c39_7c_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPE_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enPConApp_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enOptionalSignatureAscription_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enOptTypEqn_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enOpID_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enNonETopLevelDecs_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enMultOps_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enListOps_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enLetDecs_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enLetDec_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enFQV_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enFDecl_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEtyped_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEtuple_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEseq_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enErel_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEmult_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enElogicOR_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enElogicAND_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEliteral_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enElistop_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enElist2_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enElist1_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEhandle_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEcomp_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEbefore_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEbase_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEapp_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enEadd_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enE_7c39_7c_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enE_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDtypeDecls_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDtypeDecl_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDtypeCons_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDecls_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDecl_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDconstructor_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enDType_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enConstructorName_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_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enCompOps_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enAndFDecls_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_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00)))))))))))))))
& s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enAddOps_27__00))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT2_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))))))))))) ) ).
fof('thm.gram.MMLnonT_EQ_MMLnonT',axiom,
! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2egram_2eMMLnonT_27__00,V_27a_27) = s__02(c_27type_2egram_2eMMLnonT_27__00,V_27a_7c39_7c_27)
<=> s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,V_27a_27))) = s__02(c_27type_2enum_2enum_27__00,c_27const_2egram_2eMMLnonT2num_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,V_27a_7c39_7c_27))) ) ).
fof('thm.cmlPtreeConversion.tokcheck_def',axiom,
! [V_27C_27,V_27B_27,V_27A_27,V_27pt_27,V_27tok_27] :
( p__01(s__02(cbool__00,c_27const_2ecmlPtreeConversion_2etokcheck_27__02(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27),s__02(V_27A_27,V_27tok_27))))
<=> s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2etokenUtils_2edestLf_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27))),s__02(cfun__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),c_27type_2eoption_2eoption_27__01(V_27A_27)),c_27const_2etokenUtils_2edestTOK_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27tok_27))) ) ).
fof('thm.cmlPtreeConversion.ptree_SpeclineList_def',axiom,
! [V__7] :
( ! [V_27v11_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),V__7),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27v11_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eNONE_27__00)
=> ! [V__6] :
( ! [V_27v10_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__6),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27v10_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),V__7)
=> ! [V__5] :
( ! [V_27sl_27,V_27sll_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2east_2espec_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__5),s__02(c_27type_2east_2espec_27__00,V_27sl_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),V_27sll_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2east_2espec_27__00,V_27sl_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),V_27sll_27)))))
=> ! [V__4] :
( ! [V_27sll__pt_27,V_27sl_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),chapp__02(s__02(cfun__02(c_27type_2east_2espec_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2east_2espec_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__4),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))),s__02(c_27type_2east_2espec_27__00,V_27sl_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ecmlPtreeConversion_2eptree__SpeclineList_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))),s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2east_2espec_27__00,cfun__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__5),s__02(c_27type_2east_2espec_27__00,V_27sl_27)))))
=> ! [V__3] :
( ! [V_27sl__pt_27,V_27sll__pt_27,V_27v7_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))))),V__3),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27v7_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27v7_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2ecmlPtreeConversion_2etokcheck_27__02(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27),s__02(c_27type_2etokens_2etoken_27__00,c_27const_2etokens_2eSemicolonT_27__00))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ecmlPtreeConversion_2eptree__SpeclineList_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eOPTION__BIND_27__02(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2east_2espec_27__00),c_27const_2ecmlPtreeConversion_2eptree__SpecLine_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))),s__02(cfun__02(c_27type_2east_2espec_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2east_2espec_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__4),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))))))),s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__6)))
=> ! [V__2] :
( ! [V_27sl__pt_27,V_27sll__pt_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))))),V__2),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))))),V__3),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sll__pt_27)))
=> ! [V__1] :
( ! [V_27sl__pt_27,V_27v3_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__1),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27v3_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27v3_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eNONE_27__00),s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))))),V__2),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27)))))
=> ! [V__0] :
( ! [V_27sl__pt_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__0),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00))),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__1),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27sl__pt_27)))
=> ( ! [V_27v0_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ecmlPtreeConversion_2eptree__SpeclineList_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27type_2elocation_2elocs_27__00),V_27v0_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27nt_27,V_27args_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27type_2elocation_2elocs_27__00),V_27nt_27))) != s__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27const_2esum_2eINL_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSpecLineList_27__00))) )
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ecmlPtreeConversion_2eptree__SpeclineList_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27const_2egrammar_2eNd_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27type_2elocation_2elocs_27__00),V_27nt_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27args_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eNONE_27__00),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2elist_2elist__CASE_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),V_27args_27),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),c_27const_2elist_2eNIL_27__00))),s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00)),c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)))),V__0))))) ) ) ) ) ) ) ) ) ) ) ).
fof('thm.gramProps.cmlG_FDOM',axiom,
s__02(cfun__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),cbool__00),c_27const_2efinite__map_2eFDOM_27__01(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),cbool__00)),c_27const_2egrammar_2egrammar__rules_27__01(s__02(c_27type_2egrammar_2egrammar_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27const_2egram_2ecmlG_27__00))))) = 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).
fof('thm.cmlPtreeConversionProps.ptree_head_TOK',axiom,
! [V_27B_27,V_27A_27,V_27C_27,V_27sym_27,V_27pt_27] :
( ( s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27sym_27)))
<=> ? [V_27l_27] : s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27) = s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27sym_27))),s__02(V_27C_27,V_27l_27))))) )
& ( s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27sym_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27)))
<=> ? [V_27l_27] : s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),V_27pt_27) = s__02(c_27type_2egrammar_2eparsetree_27__03(V_27A_27,V_27B_27,V_27C_27),c_27const_2egrammar_2eLf_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27),chapp__02(s__02(cfun__02(V_27A_27,c_27type_2egrammar_2esymbol_27__02(V_27A_27,V_27B_27)),c_27const_2egrammar_2eTOK_27__00),s__02(V_27A_27,V_27sym_27))),s__02(V_27C_27,V_27l_27))))) ) ) ).
fof('thm.cmlPtreeConversionProps.SpecLine_OK',axiom,
! [V_27toks_27,V_27pt_27] :
( ( p__01(s__02(cbool__00,c_27const_2egrammar_2evalid__ptree_27__02(s__02(c_27type_2egrammar_2egrammar_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27const_2egram_2ecmlG_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))))
& s__02(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27const_2esum_2eINL_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSpecLine_27__00)))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2etokens_2etoken_27__00,c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2egrammar_2eTOK_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2etokens_2etoken_27__00),V_27toks_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00))),c_27const_2egrammar_2eptree__fringe_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) )
=> ? [V_27sl_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2east_2espec_27__00),c_27const_2ecmlPtreeConversion_2eptree__SpecLine_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2east_2espec_27__00),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2east_2espec_27__00,V_27sl_27))) ) ).
fof(conjecture,conjecture,
! [V_27pt_27,V_27toks_27] :
( ( p__01(s__02(cbool__00,c_27const_2egrammar_2evalid__ptree_27__02(s__02(c_27type_2egrammar_2egrammar_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27const_2egram_2ecmlG_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))))
& s__02(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2egrammar_2eptree__head_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) = s__02(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00),c_27const_2egrammar_2eNT_27__01(s__02(c_27type_2esum_2esum_27__02(c_27type_2egram_2eMMLnonT_27__00,c_27type_2enum_2enum_27__00),c_27const_2esum_2eINL_27__01(s__02(c_27type_2egram_2eMMLnonT_27__00,c_27const_2egram_2enSpecLineList_27__00)))))
& s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2etokens_2etoken_27__00,c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),c_27const_2egrammar_2eTOK_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2etokens_2etoken_27__00),V_27toks_27))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00)),chapp__02(s__02(cfun__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),c_27type_2elist_2elist_27__01(c_27type_2egrammar_2esymbol_27__02(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00))),c_27const_2egrammar_2eptree__fringe_27__00),s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) )
=> ? [V_27sl_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2ecmlPtreeConversion_2eptree__SpeclineList_27__01(s__02(c_27type_2egrammar_2eparsetree_27__03(c_27type_2etokens_2etoken_27__00,c_27type_2egram_2eMMLnonT_27__00,c_27type_2elocation_2elocs_27__00),V_27pt_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2east_2espec_27__00),V_27sl_27))) ) ).
%------------------------------------------------------------------------------