TPTP Problem File: SWW867+1.p
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%------------------------------------------------------------------------------
% File : SWW867+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : typeSysProps__50__tveLookup_bvl__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : typeSysProps__50__tveLookup_bvl__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 85 ( 40 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 64 ( 5 ~; 2 |; 26 &)
% ( 16 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 28 ( 28 usr; 10 con; 0-4 aty)
% Number of variables : 102 ( 98 !; 4 ?)
% 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.EXCLUDED_MIDDLE',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,V_27t_27))
| ~ p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.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.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.COND_CLAUSES',axiom,
! [V_27A_27,V_27t1_27,V_27t2_27] :
( s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.bool.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.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.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.pair.CLOSED_PAIR_EQ',axiom,
! [V_27A_27,V_27B_27,V_27x_27,V_27y_27,V_27a_27,V_27b_27] :
( s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27a_27),s__02(V_27B_27,V_27b_27)))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27)
& s__02(V_27B_27,V_27y_27) = s__02(V_27B_27,V_27b_27) ) ) ).
fof('thm.pair.pair_CASES',axiom,
! [V_27A_27,V_27B_27,V_27x_27] :
? [V_27q_27,V_27r_27] : s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27x_27) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27q_27),s__02(V_27B_27,V_27r_27))) ).
fof('thm.option.option_case_def',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27))) = s__02(V_27B_27,V_27v_27)
& ! [V_27x_27,V_27v_27,V_27f_27] : s__02(V_27B_27,c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eSOME_27__01(s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27v_27),s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) ) ).
fof('thm.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.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.alist.ALOOKUP_def',axiom,
! [V_27A_27,V_27B_27] :
( ! [V_27q_27] : s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),c_27const_2elist_2eNIL_27__00),s__02(V_27B_27,V_27q_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2eoption_2eNONE_27__00)
& ! [V_27y_27,V_27x_27,V_27t_27,V_27q_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(V_27B_27,V_27x_27) = s__02(V_27B_27,V_27q_27) )
& s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,V_27x_27),s__02(V_27A_27,V_27y_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),V_27t_27))),s__02(V_27B_27,V_27q_27))) = s__02(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),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(c_27type_2eoption_2eoption_27__01(V_27A_27),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(V_27B_27,V_27A_27)),V_27t_27),s__02(V_27B_27,V_27q_27))))) ) ) ).
fof('thm.typeSystem.tveLookup_def',axiom,
( ! [V_27n_27,V_27inc_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2eEmpty_27__00))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2eoption_2eNONE_27__00)
& ! [V_27n_27,V_27inc_27,V_27tvs_27,V_27tenvE_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2eBind__tvar_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2e_2b_27__02(s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27))),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27)))
& ! [V_27n_27,V_27inc_27,V_27n_7c39_7c_27,V_27tvs_27,V_27t_27,V_27tenvE_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_7c39_7c_27) = s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27) )
& s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2eBind__name_27__04(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_7c39_7c_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2east_2et_27__00,V_27t_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2east_2et_27__00,c_27const_2etypeSystem_2edeBruijn__inc_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2east_2et_27__00,V_27t_27))))))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27inc_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))))) ) ) ).
fof('thm.typeSystem.bind_var_list_def',axiom,
( ! [V_27tvs_27,V_27tenvE_27] : s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2ebind__var__list_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),c_27const_2elist_2eNIL_27__00),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))) = s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27)
& ! [V_27tvs_27,V_27tenvE_27,V_27t_27,V_27n_27,V_27binds_27] : s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2ebind__var__list_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2east_2et_27__00,V_27t_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),V_27binds_27))),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))) = s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2eBind__name_27__04(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27n_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2east_2et_27__00,V_27t_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2ebind__var__list_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),V_27binds_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))))) ) ).
fof(conjecture,conjecture,
! [V__0] :
( ! [V_27tvs_7c39_7c_27,V_27tvs_27,V_27t_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),chapp__02(s__02(cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00))))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27tvs_7c39_7c_27))),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27))),s__02(c_27type_2east_2et_27__00,V_27t_27))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2eoption_2eSOME_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27tvs_7c39_7c_27),s__02(c_27type_2east_2et_27__00,c_27const_2etypeSystem_2edeBruijn__inc_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_7c39_7c_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2east_2et_27__00,V_27t_27)))))))
=> ! [V_27x_27,V_27tvs_27,V_27tvs_7c39_7c_27,V_27bindings_27,V_27tenvE_27] : s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,c_27const_2etypeSystem_2ebind__var__list_27__03(s__02(c_27type_2enum_2enum_27__00,V_27tvs_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),V_27bindings_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))))) = s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2eoption_2eoption__CASE_27__03(s__02(c_27type_2eoption_2eoption_27__01(c_27type_2east_2et_27__00),c_27const_2ealist_2eALOOKUP_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2epair_2eprod_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),c_27type_2east_2et_27__00)),V_27bindings_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27x_27))),s__02(c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)),c_27const_2etypeSystem_2etveLookup_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00),V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27),s__02(c_27type_2etypeSystem_2etenv__val__exp_27__00,V_27tenvE_27))),s__02(cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00)))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2east_2et_27__00,c_27type_2eoption_2eoption_27__01(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2east_2et_27__00))))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27tvs_7c39_7c_27))),s__02(c_27type_2enum_2enum_27__00,V_27tvs_27))))) ) ).
%------------------------------------------------------------------------------