include "basic_1/iso/props.ma".
-theorem nf2_iso_appls_lref:
+lemma nf2_iso_appls_lref:
\forall (c: C).(\forall (i: nat).((nf2 c (TLRef i)) \to (\forall (vs:
TList).(\forall (u: T).((pr3 c (THeads (Flat Appl) vs (TLRef i)) u) \to (iso
(THeads (Flat Appl) vs (TLRef i)) u))))))
\def
\lambda (c: C).(\lambda (i: nat).(\lambda (H: (nf2 c (TLRef i))).(\lambda
-(vs: TList).(let TMP_4 \def (\lambda (t: TList).(\forall (u: T).((pr3 c
-(THeads (Flat Appl) t (TLRef i)) u) \to (let TMP_1 \def (Flat Appl) in (let
-TMP_2 \def (TLRef i) in (let TMP_3 \def (THeads TMP_1 t TMP_2) in (iso TMP_3
-u))))))) in (let TMP_14 \def (\lambda (u: T).(\lambda (H0: (pr3 c (TLRef i)
-u)).(let TMP_5 \def (TLRef i) in (let H_y \def (nf2_pr3_unfold c TMP_5 u H0
-H) in (let TMP_7 \def (\lambda (t: T).(let TMP_6 \def (TLRef i) in (pr3 c
-TMP_6 t))) in (let TMP_8 \def (TLRef i) in (let H1 \def (eq_ind_r T u TMP_7
-H0 TMP_8 H_y) in (let TMP_9 \def (TLRef i) in (let TMP_11 \def (\lambda (t:
-T).(let TMP_10 \def (TLRef i) in (iso TMP_10 t))) in (let TMP_12 \def (TLRef
-i) in (let TMP_13 \def (iso_refl TMP_12) in (eq_ind T TMP_9 TMP_11 TMP_13 u
-H_y)))))))))))) in (let TMP_162 \def (\lambda (t: T).(\lambda (t0:
-TList).(\lambda (H0: ((\forall (u: T).((pr3 c (THeads (Flat Appl) t0 (TLRef
-i)) u) \to (iso (THeads (Flat Appl) t0 (TLRef i)) u))))).(\lambda (u:
-T).(\lambda (H1: (pr3 c (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef
-i))) u)).(let TMP_15 \def (Flat Appl) in (let TMP_16 \def (TLRef i) in (let
-TMP_17 \def (THeads TMP_15 t0 TMP_16) in (let H2 \def (pr3_gen_appl c t
-TMP_17 u H1) in (let TMP_20 \def (\lambda (u2: T).(\lambda (t2: T).(let
-TMP_18 \def (Flat Appl) in (let TMP_19 \def (THead TMP_18 u2 t2) in (eq T u
-TMP_19))))) in (let TMP_21 \def (\lambda (u2: T).(\lambda (_: T).(pr3 c t
-u2))) in (let TMP_25 \def (\lambda (_: T).(\lambda (t2: T).(let TMP_22 \def
-(Flat Appl) in (let TMP_23 \def (TLRef i) in (let TMP_24 \def (THeads TMP_22
-t0 TMP_23) in (pr3 c TMP_24 t2)))))) in (let TMP_26 \def (ex3_2 T T TMP_20
-TMP_21 TMP_25) in (let TMP_29 \def (\lambda (_: T).(\lambda (_: T).(\lambda
-(u2: T).(\lambda (t2: T).(let TMP_27 \def (Bind Abbr) in (let TMP_28 \def
-(THead TMP_27 u2 t2) in (pr3 c TMP_28 u))))))) in (let TMP_30 \def (\lambda
-(_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) in
-(let TMP_36 \def (\lambda (y1: T).(\lambda (z1: T).(\lambda (_: T).(\lambda
-(_: T).(let TMP_31 \def (Flat Appl) in (let TMP_32 \def (TLRef i) in (let
-TMP_33 \def (THeads TMP_31 t0 TMP_32) in (let TMP_34 \def (Bind Abst) in (let
-TMP_35 \def (THead TMP_34 y1 z1) in (pr3 c TMP_33 TMP_35)))))))))) in (let
-TMP_39 \def (\lambda (_: T).(\lambda (z1: T).(\lambda (_: T).(\lambda (t2:
-T).(\forall (b: B).(\forall (u0: T).(let TMP_37 \def (Bind b) in (let TMP_38
-\def (CHead c TMP_37 u0) in (pr3 TMP_38 z1 t2))))))))) in (let TMP_40 \def
-(ex4_4 T T T T TMP_29 TMP_30 TMP_36 TMP_39) in (let TMP_42 \def (\lambda (b:
+(vs: TList).(TList_ind (\lambda (t: TList).(\forall (u: T).((pr3 c (THeads
+(Flat Appl) t (TLRef i)) u) \to (iso (THeads (Flat Appl) t (TLRef i)) u))))
+(\lambda (u: T).(\lambda (H0: (pr3 c (TLRef i) u)).(let H_y \def
+(nf2_pr3_unfold c (TLRef i) u H0 H) in (let H1 \def (eq_ind_r T u (\lambda
+(t: T).(pr3 c (TLRef i) t)) H0 (TLRef i) H_y) in (eq_ind T (TLRef i) (\lambda
+(t: T).(iso (TLRef i) t)) (iso_refl (TLRef i)) u H_y))))) (\lambda (t:
+T).(\lambda (t0: TList).(\lambda (H0: ((\forall (u: T).((pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) u) \to (iso (THeads (Flat Appl) t0 (TLRef i))
+u))))).(\lambda (u: T).(\lambda (H1: (pr3 c (THead (Flat Appl) t (THeads
+(Flat Appl) t0 (TLRef i))) u)).(let H2 \def (pr3_gen_appl c t (THeads (Flat
+Appl) t0 (TLRef i)) u H1) in (or3_ind (ex3_2 T T (\lambda (u2: T).(\lambda
+(t2: T).(eq T u (THead (Flat Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_:
+T).(pr3 c t u2))) (\lambda (_: T).(\lambda (t2: T).(pr3 c (THeads (Flat Appl)
+t0 (TLRef i)) t2)))) (ex4_4 T T T T (\lambda (_: T).(\lambda (_: T).(\lambda
+(u2: T).(\lambda (t2: T).(pr3 c (THead (Bind Abbr) u2 t2) u))))) (\lambda (_:
+T).(\lambda (_: T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) (\lambda
+(y1: T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_: T).(pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) (THead (Bind Abst) y1 z1)))))) (\lambda (_: T).(\lambda
+(z1: T).(\lambda (_: T).(\lambda (t2: T).(\forall (b: B).(\forall (u0:
+T).(pr3 (CHead c (Bind b) u0) z1 t2)))))))) (ex6_6 B T T T T T (\lambda (b:
B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda
-(_: T).(let TMP_41 \def (eq B b Abst) in (not TMP_41)))))))) in (let TMP_48
-\def (\lambda (b: B).(\lambda (y1: T).(\lambda (z1: T).(\lambda (_:
-T).(\lambda (_: T).(\lambda (_: T).(let TMP_43 \def (Flat Appl) in (let
-TMP_44 \def (TLRef i) in (let TMP_45 \def (THeads TMP_43 t0 TMP_44) in (let
-TMP_46 \def (Bind b) in (let TMP_47 \def (THead TMP_46 y1 z1) in (pr3 c
-TMP_45 TMP_47)))))))))))) in (let TMP_55 \def (\lambda (b: B).(\lambda (_:
-T).(\lambda (_: T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2: T).(let
-TMP_49 \def (Bind b) in (let TMP_50 \def (Flat Appl) in (let TMP_51 \def (S
-O) in (let TMP_52 \def (lift TMP_51 O u2) in (let TMP_53 \def (THead TMP_50
-TMP_52 z2) in (let TMP_54 \def (THead TMP_49 y2 TMP_53) in (pr3 c TMP_54
-u))))))))))))) in (let TMP_56 \def (\lambda (_: B).(\lambda (_: T).(\lambda
-(_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))))) in
-(let TMP_57 \def (\lambda (_: B).(\lambda (y1: T).(\lambda (_: T).(\lambda
-(_: T).(\lambda (_: T).(\lambda (y2: T).(pr3 c y1 y2))))))) in (let TMP_60
-\def (\lambda (b: B).(\lambda (_: T).(\lambda (z1: T).(\lambda (z2:
-T).(\lambda (_: T).(\lambda (y2: T).(let TMP_58 \def (Bind b) in (let TMP_59
-\def (CHead c TMP_58 y2) in (pr3 TMP_59 z1 z2))))))))) in (let TMP_61 \def
-(ex6_6 B T T T T T TMP_42 TMP_48 TMP_55 TMP_56 TMP_57 TMP_60) in (let TMP_62
-\def (Flat Appl) in (let TMP_63 \def (Flat Appl) in (let TMP_64 \def (TLRef
-i) in (let TMP_65 \def (THeads TMP_63 t0 TMP_64) in (let TMP_66 \def (THead
-TMP_62 t TMP_65) in (let TMP_67 \def (iso TMP_66 u) in (let TMP_96 \def
-(\lambda (H3: (ex3_2 T T (\lambda (u2: T).(\lambda (t2: T).(eq T u (THead
-(Flat Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_: T).(pr3 c t u2)))
+(_: T).(not (eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: T).(\lambda
+(z1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) (THead (Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda
+(_: T).(\lambda (_: T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2:
+T).(pr3 c (THead (Bind b) y2 (THead (Flat Appl) (lift (S O) O u2) z2))
+u))))))) (\lambda (_: B).(\lambda (_: T).(\lambda (_: T).(\lambda (_:
+T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))))) (\lambda (_:
+B).(\lambda (y1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda
+(y2: T).(pr3 c y1 y2))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (z1:
+T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(pr3 (CHead c (Bind b)
+y2) z1 z2)))))))) (iso (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef
+i))) u) (\lambda (H3: (ex3_2 T T (\lambda (u2: T).(\lambda (t2: T).(eq T u
+(THead (Flat Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_: T).(pr3 c t u2)))
(\lambda (_: T).(\lambda (t2: T).(pr3 c (THeads (Flat Appl) t0 (TLRef i))
-t2))))).(let TMP_70 \def (\lambda (u2: T).(\lambda (t2: T).(let TMP_68 \def
-(Flat Appl) in (let TMP_69 \def (THead TMP_68 u2 t2) in (eq T u TMP_69)))))
-in (let TMP_71 \def (\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))) in (let
-TMP_75 \def (\lambda (_: T).(\lambda (t2: T).(let TMP_72 \def (Flat Appl) in
-(let TMP_73 \def (TLRef i) in (let TMP_74 \def (THeads TMP_72 t0 TMP_73) in
-(pr3 c TMP_74 t2)))))) in (let TMP_76 \def (Flat Appl) in (let TMP_77 \def
-(Flat Appl) in (let TMP_78 \def (TLRef i) in (let TMP_79 \def (THeads TMP_77
-t0 TMP_78) in (let TMP_80 \def (THead TMP_76 t TMP_79) in (let TMP_81 \def
-(iso TMP_80 u) in (let TMP_95 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda
-(H4: (eq T u (THead (Flat Appl) x0 x1))).(\lambda (_: (pr3 c t x0)).(\lambda
-(_: (pr3 c (THeads (Flat Appl) t0 (TLRef i)) x1)).(let TMP_82 \def (Flat
-Appl) in (let TMP_83 \def (THead TMP_82 x0 x1) in (let TMP_89 \def (\lambda
-(t1: T).(let TMP_84 \def (Flat Appl) in (let TMP_85 \def (Flat Appl) in (let
-TMP_86 \def (TLRef i) in (let TMP_87 \def (THeads TMP_85 t0 TMP_86) in (let
-TMP_88 \def (THead TMP_84 t TMP_87) in (iso TMP_88 t1))))))) in (let TMP_90
-\def (Flat Appl) in (let TMP_91 \def (TLRef i) in (let TMP_92 \def (THeads
-TMP_90 t0 TMP_91) in (let TMP_93 \def (Flat Appl) in (let TMP_94 \def
-(iso_head t x0 TMP_92 x1 TMP_93) in (eq_ind_r T TMP_83 TMP_89 TMP_94 u
-H4)))))))))))))) in (ex3_2_ind T T TMP_70 TMP_71 TMP_75 TMP_81 TMP_95
-H3)))))))))))) in (let TMP_125 \def (\lambda (H3: (ex4_4 T T T T (\lambda (_:
+t2))))).(ex3_2_ind T T (\lambda (u2: T).(\lambda (t2: T).(eq T u (THead (Flat
+Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))) (\lambda (_:
+T).(\lambda (t2: T).(pr3 c (THeads (Flat Appl) t0 (TLRef i)) t2))) (iso
+(THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) u) (\lambda (x0:
+T).(\lambda (x1: T).(\lambda (H4: (eq T u (THead (Flat Appl) x0
+x1))).(\lambda (_: (pr3 c t x0)).(\lambda (_: (pr3 c (THeads (Flat Appl) t0
+(TLRef i)) x1)).(eq_ind_r T (THead (Flat Appl) x0 x1) (\lambda (t1: T).(iso
+(THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) t1)) (iso_head t x0
+(THeads (Flat Appl) t0 (TLRef i)) x1 (Flat Appl)) u H4)))))) H3)) (\lambda
+(H3: (ex4_4 T T T T (\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda
+(t2: T).(pr3 c (THead (Bind Abbr) u2 t2) u))))) (\lambda (_: T).(\lambda (_:
+T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) (\lambda (y1:
+T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_: T).(pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) (THead (Bind Abst) y1 z1)))))) (\lambda (_: T).(\lambda
+(z1: T).(\lambda (_: T).(\lambda (t2: T).(\forall (b: B).(\forall (u0:
+T).(pr3 (CHead c (Bind b) u0) z1 t2))))))))).(ex4_4_ind T T T T (\lambda (_:
T).(\lambda (_: T).(\lambda (u2: T).(\lambda (t2: T).(pr3 c (THead (Bind
Abbr) u2 t2) u))))) (\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda
(_: T).(pr3 c t u2))))) (\lambda (y1: T).(\lambda (z1: T).(\lambda (_:
T).(\lambda (_: T).(pr3 c (THeads (Flat Appl) t0 (TLRef i)) (THead (Bind
Abst) y1 z1)))))) (\lambda (_: T).(\lambda (z1: T).(\lambda (_: T).(\lambda
(t2: T).(\forall (b: B).(\forall (u0: T).(pr3 (CHead c (Bind b) u0) z1
-t2))))))))).(let TMP_99 \def (\lambda (_: T).(\lambda (_: T).(\lambda (u2:
-T).(\lambda (t2: T).(let TMP_97 \def (Bind Abbr) in (let TMP_98 \def (THead
-TMP_97 u2 t2) in (pr3 c TMP_98 u))))))) in (let TMP_100 \def (\lambda (_:
-T).(\lambda (_: T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) in (let
-TMP_106 \def (\lambda (y1: T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_:
-T).(let TMP_101 \def (Flat Appl) in (let TMP_102 \def (TLRef i) in (let
-TMP_103 \def (THeads TMP_101 t0 TMP_102) in (let TMP_104 \def (Bind Abst) in
-(let TMP_105 \def (THead TMP_104 y1 z1) in (pr3 c TMP_103 TMP_105))))))))))
-in (let TMP_109 \def (\lambda (_: T).(\lambda (z1: T).(\lambda (_:
-T).(\lambda (t2: T).(\forall (b: B).(\forall (u0: T).(let TMP_107 \def (Bind
-b) in (let TMP_108 \def (CHead c TMP_107 u0) in (pr3 TMP_108 z1 t2)))))))))
-in (let TMP_110 \def (Flat Appl) in (let TMP_111 \def (Flat Appl) in (let
-TMP_112 \def (TLRef i) in (let TMP_113 \def (THeads TMP_111 t0 TMP_112) in
-(let TMP_114 \def (THead TMP_110 t TMP_113) in (let TMP_115 \def (iso TMP_114
-u) in (let TMP_124 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (x2:
-T).(\lambda (x3: T).(\lambda (_: (pr3 c (THead (Bind Abbr) x2 x3)
-u)).(\lambda (_: (pr3 c t x2)).(\lambda (H6: (pr3 c (THeads (Flat Appl) t0
-(TLRef i)) (THead (Bind Abst) x0 x1))).(\lambda (_: ((\forall (b: B).(\forall
-(u0: T).(pr3 (CHead c (Bind b) u0) x1 x3))))).(let TMP_116 \def (Bind Abst)
-in (let TMP_117 \def (THead TMP_116 x0 x1) in (let H_y \def (H0 TMP_117 H6)
-in (let TMP_118 \def (Flat Appl) in (let TMP_119 \def (Flat Appl) in (let
-TMP_120 \def (TLRef i) in (let TMP_121 \def (THeads TMP_119 t0 TMP_120) in
-(let TMP_122 \def (THead TMP_118 t TMP_121) in (let TMP_123 \def (iso TMP_122
-u) in (iso_flats_lref_bind_false Appl Abst i x0 x1 t0 H_y
-TMP_123)))))))))))))))))) in (ex4_4_ind T T T T TMP_99 TMP_100 TMP_106
-TMP_109 TMP_115 TMP_124 H3))))))))))))) in (let TMP_161 \def (\lambda (H3:
-(ex6_6 B T T T T T (\lambda (b: B).(\lambda (_: T).(\lambda (_: T).(\lambda
-(_: T).(\lambda (_: T).(\lambda (_: T).(not (eq B b Abst)))))))) (\lambda (b:
+t2))))))) (iso (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) u)
+(\lambda (x0: T).(\lambda (x1: T).(\lambda (x2: T).(\lambda (x3: T).(\lambda
+(_: (pr3 c (THead (Bind Abbr) x2 x3) u)).(\lambda (_: (pr3 c t x2)).(\lambda
+(H6: (pr3 c (THeads (Flat Appl) t0 (TLRef i)) (THead (Bind Abst) x0
+x1))).(\lambda (_: ((\forall (b: B).(\forall (u0: T).(pr3 (CHead c (Bind b)
+u0) x1 x3))))).(let H_y \def (H0 (THead (Bind Abst) x0 x1) H6) in
+(iso_flats_lref_bind_false Appl Abst i x0 x1 t0 H_y (iso (THead (Flat Appl) t
+(THeads (Flat Appl) t0 (TLRef i))) u))))))))))) H3)) (\lambda (H3: (ex6_6 B T
+T T T T (\lambda (b: B).(\lambda (_: T).(\lambda (_: T).(\lambda (_:
+T).(\lambda (_: T).(\lambda (_: T).(not (eq B b Abst)))))))) (\lambda (b:
B).(\lambda (y1: T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_: T).(\lambda
(_: T).(pr3 c (THeads (Flat Appl) t0 (TLRef i)) (THead (Bind b) y1 z1))))))))
(\lambda (b: B).(\lambda (_: T).(\lambda (_: T).(\lambda (z2: T).(\lambda
(\lambda (_: B).(\lambda (y1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_:
T).(\lambda (y2: T).(pr3 c y1 y2))))))) (\lambda (b: B).(\lambda (_:
T).(\lambda (z1: T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(pr3
-(CHead c (Bind b) y2) z1 z2))))))))).(let TMP_127 \def (\lambda (b:
+(CHead c (Bind b) y2) z1 z2))))))))).(ex6_6_ind B T T T T T (\lambda (b:
B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda
-(_: T).(let TMP_126 \def (eq B b Abst) in (not TMP_126)))))))) in (let
-TMP_133 \def (\lambda (b: B).(\lambda (y1: T).(\lambda (z1: T).(\lambda (_:
-T).(\lambda (_: T).(\lambda (_: T).(let TMP_128 \def (Flat Appl) in (let
-TMP_129 \def (TLRef i) in (let TMP_130 \def (THeads TMP_128 t0 TMP_129) in
-(let TMP_131 \def (Bind b) in (let TMP_132 \def (THead TMP_131 y1 z1) in (pr3
-c TMP_130 TMP_132)))))))))))) in (let TMP_140 \def (\lambda (b: B).(\lambda
+(_: T).(not (eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: T).(\lambda
+(z1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) (THead (Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda
(_: T).(\lambda (_: T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2:
-T).(let TMP_134 \def (Bind b) in (let TMP_135 \def (Flat Appl) in (let
-TMP_136 \def (S O) in (let TMP_137 \def (lift TMP_136 O u2) in (let TMP_138
-\def (THead TMP_135 TMP_137 z2) in (let TMP_139 \def (THead TMP_134 y2
-TMP_138) in (pr3 c TMP_139 u))))))))))))) in (let TMP_141 \def (\lambda (_:
-B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda
-(_: T).(pr3 c t u2))))))) in (let TMP_142 \def (\lambda (_: B).(\lambda (y1:
-T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (y2: T).(pr3 c y1
-y2))))))) in (let TMP_145 \def (\lambda (b: B).(\lambda (_: T).(\lambda (z1:
-T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(let TMP_143 \def (Bind
-b) in (let TMP_144 \def (CHead c TMP_143 y2) in (pr3 TMP_144 z1 z2)))))))))
-in (let TMP_146 \def (Flat Appl) in (let TMP_147 \def (Flat Appl) in (let
-TMP_148 \def (TLRef i) in (let TMP_149 \def (THeads TMP_147 t0 TMP_148) in
-(let TMP_150 \def (THead TMP_146 t TMP_149) in (let TMP_151 \def (iso TMP_150
-u) in (let TMP_160 \def (\lambda (x0: B).(\lambda (x1: T).(\lambda (x2:
-T).(\lambda (x3: T).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (not (eq B
-x0 Abst))).(\lambda (H5: (pr3 c (THeads (Flat Appl) t0 (TLRef i)) (THead
-(Bind x0) x1 x2))).(\lambda (_: (pr3 c (THead (Bind x0) x5 (THead (Flat Appl)
-(lift (S O) O x4) x3)) u)).(\lambda (_: (pr3 c t x4)).(\lambda (_: (pr3 c x1
-x5)).(\lambda (_: (pr3 (CHead c (Bind x0) x5) x2 x3)).(let TMP_152 \def (Bind
-x0) in (let TMP_153 \def (THead TMP_152 x1 x2) in (let H_y \def (H0 TMP_153
-H5) in (let TMP_154 \def (Flat Appl) in (let TMP_155 \def (Flat Appl) in (let
-TMP_156 \def (TLRef i) in (let TMP_157 \def (THeads TMP_155 t0 TMP_156) in
-(let TMP_158 \def (THead TMP_154 t TMP_157) in (let TMP_159 \def (iso TMP_158
-u) in (iso_flats_lref_bind_false Appl x0 i x1 x2 t0 H_y
-TMP_159)))))))))))))))))))))) in (ex6_6_ind B T T T T T TMP_127 TMP_133
-TMP_140 TMP_141 TMP_142 TMP_145 TMP_151 TMP_160 H3))))))))))))))) in (or3_ind
-TMP_26 TMP_40 TMP_61 TMP_67 TMP_96 TMP_125 TMP_161
-H2))))))))))))))))))))))))))))))))))) in (TList_ind TMP_4 TMP_14 TMP_162
-vs))))))).
+T).(pr3 c (THead (Bind b) y2 (THead (Flat Appl) (lift (S O) O u2) z2))
+u))))))) (\lambda (_: B).(\lambda (_: T).(\lambda (_: T).(\lambda (_:
+T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))))) (\lambda (_:
+B).(\lambda (y1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda
+(y2: T).(pr3 c y1 y2))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (z1:
+T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(pr3 (CHead c (Bind b)
+y2) z1 z2))))))) (iso (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i)))
+u) (\lambda (x0: B).(\lambda (x1: T).(\lambda (x2: T).(\lambda (x3:
+T).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (not (eq B x0
+Abst))).(\lambda (H5: (pr3 c (THeads (Flat Appl) t0 (TLRef i)) (THead (Bind
+x0) x1 x2))).(\lambda (_: (pr3 c (THead (Bind x0) x5 (THead (Flat Appl) (lift
+(S O) O x4) x3)) u)).(\lambda (_: (pr3 c t x4)).(\lambda (_: (pr3 c x1
+x5)).(\lambda (_: (pr3 (CHead c (Bind x0) x5) x2 x3)).(let H_y \def (H0
+(THead (Bind x0) x1 x2) H5) in (iso_flats_lref_bind_false Appl x0 i x1 x2 t0
+H_y (iso (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i)))
+u))))))))))))))) H3)) H2))))))) vs)))).
projects / helm.git / blobdiff