X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fcsubst1%2Fgetl.ma;h=9724dd2601e134ae2006be0b902ab8d9c0321bca;hb=639e798161afea770f41d78673c0fe3be4125beb;hp=8c737fc0332044847ee6d6eeb2b555cf121b1416;hpb=15455aa487e001c643b4f46daf82612b8409f1ae;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma b/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma
index 8c737fc03..9724dd260 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma
@@ -28,12 +28,11 @@ theorem csubst1_getl_ge:
 e) \to (getl n c2 e)))))))))
 \def
  \lambda (i: nat).(\lambda (n: nat).(\lambda (H: (le i n)).(\lambda (c1: 
-C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 c2)).(let 
-TMP_1 \def (\lambda (c: C).(\forall (e: C).((getl n c1 e) \to (getl n c e)))) 
-in (let TMP_2 \def (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) in (let 
-TMP_3 \def (\lambda (c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: 
-C).(\lambda (H2: (getl n c1 e)).(csubst0_getl_ge i n H c1 c3 v H1 e H2))))) 
-in (csubst1_ind i v c1 TMP_1 TMP_2 TMP_3 c2 H0)))))))))).
+C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 
+c2)).(csubst1_ind i v c1 (\lambda (c: C).(\forall (e: C).((getl n c1 e) \to 
+(getl n c e)))) (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) (\lambda 
+(c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: C).(\lambda (H2: 
+(getl n c1 e)).(csubst0_getl_ge i n H c1 c3 v H1 e H2))))) c2 H0))))))).
 
 theorem csubst1_getl_lt:
  \forall (i: nat).(\forall (n: nat).((lt n i) \to (\forall (c1: C).(\forall 
@@ -42,189 +41,101 @@ e1) \to (ex2 C (\lambda (e2: C).(csubst1 (minus i n) v e1 e2)) (\lambda (e2:
 C).(getl n c2 e2)))))))))))
 \def
  \lambda (i: nat).(\lambda (n: nat).(\lambda (H: (lt n i)).(\lambda (c1: 
-C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 c2)).(let 
-TMP_4 \def (\lambda (c: C).(\forall (e1: C).((getl n c1 e1) \to (let TMP_2 
-\def (\lambda (e2: C).(let TMP_1 \def (minus i n) in (csubst1 TMP_1 v e1 
-e2))) in (let TMP_3 \def (\lambda (e2: C).(getl n c e2)) in (ex2 C TMP_2 
-TMP_3)))))) in (let TMP_23 \def (\lambda (e1: C).(\lambda (H1: (getl n c1 
-e1)).(let TMP_5 \def (S n) in (let TMP_6 \def (minus i TMP_5) in (let TMP_7 
-\def (S TMP_6) in (let TMP_10 \def (\lambda (n0: nat).(let TMP_8 \def 
-(\lambda (e2: C).(csubst1 n0 v e1 e2)) in (let TMP_9 \def (\lambda (e2: 
-C).(getl n c1 e2)) in (ex2 C TMP_8 TMP_9)))) in (let TMP_14 \def (\lambda 
-(e2: C).(let TMP_11 \def (S n) in (let TMP_12 \def (minus i TMP_11) in (let 
-TMP_13 \def (S TMP_12) in (csubst1 TMP_13 v e1 e2))))) in (let TMP_15 \def 
-(\lambda (e2: C).(getl n c1 e2)) in (let TMP_16 \def (S n) in (let TMP_17 
-\def (minus i TMP_16) in (let TMP_18 \def (S TMP_17) in (let TMP_19 \def 
-(csubst1_refl TMP_18 v e1) in (let TMP_20 \def (ex_intro2 C TMP_14 TMP_15 e1 
-TMP_19 H1) in (let TMP_21 \def (minus i n) in (let TMP_22 \def (minus_x_Sy i 
-n H) in (eq_ind_r nat TMP_7 TMP_10 TMP_20 TMP_21 TMP_22)))))))))))))))) in 
-(let TMP_224 \def (\lambda (c3: C).(\lambda (H1: (csubst0 i v c1 
-c3)).(\lambda (e1: C).(\lambda (H2: (getl n c1 e1)).(let TMP_24 \def (S n) in 
-(let TMP_25 \def (minus i TMP_24) in (let TMP_26 \def (S TMP_25) in (let 
-TMP_29 \def (\lambda (n0: nat).(let TMP_27 \def (\lambda (e2: C).(csubst1 n0 
-v e1 e2)) in (let TMP_28 \def (\lambda (e2: C).(getl n c3 e2)) in (ex2 C 
-TMP_27 TMP_28)))) in (let H3 \def (csubst0_getl_lt i n H c1 c3 v H1 e1 H2) in 
-(let TMP_30 \def (getl n c3 e1) in (let TMP_33 \def (\lambda (b: B).(\lambda 
-(e0: C).(\lambda (u: T).(\lambda (_: T).(let TMP_31 \def (Bind b) in (let 
-TMP_32 \def (CHead e0 TMP_31 u) in (eq C e1 TMP_32))))))) in (let TMP_36 \def 
-(\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(let TMP_34 
-\def (Bind b) in (let TMP_35 \def (CHead e0 TMP_34 w) in (getl n c3 
-TMP_35))))))) in (let TMP_39 \def (\lambda (_: B).(\lambda (_: C).(\lambda 
-(u: T).(\lambda (w: T).(let TMP_37 \def (S n) in (let TMP_38 \def (minus i 
-TMP_37) in (subst0 TMP_38 v u w))))))) in (let TMP_40 \def (ex3_4 B C T T 
-TMP_33 TMP_36 TMP_39) in (let TMP_43 \def (\lambda (b: B).(\lambda (e2: 
-C).(\lambda (_: C).(\lambda (u: T).(let TMP_41 \def (Bind b) in (let TMP_42 
-\def (CHead e2 TMP_41 u) in (eq C e1 TMP_42))))))) in (let TMP_46 \def 
-(\lambda (b: B).(\lambda (_: C).(\lambda (e3: C).(\lambda (u: T).(let TMP_44 
-\def (Bind b) in (let TMP_45 \def (CHead e3 TMP_44 u) in (getl n c3 
-TMP_45))))))) in (let TMP_49 \def (\lambda (_: B).(\lambda (e2: C).(\lambda 
-(e3: C).(\lambda (_: T).(let TMP_47 \def (S n) in (let TMP_48 \def (minus i 
-TMP_47) in (csubst0 TMP_48 v e2 e3))))))) in (let TMP_50 \def (ex3_4 B C C T 
-TMP_43 TMP_46 TMP_49) in (let TMP_53 \def (\lambda (b: B).(\lambda (e2: 
-C).(\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(let TMP_51 \def (Bind b) 
-in (let TMP_52 \def (CHead e2 TMP_51 u) in (eq C e1 TMP_52)))))))) in (let 
-TMP_56 \def (\lambda (b: B).(\lambda (_: C).(\lambda (e3: C).(\lambda (_: 
-T).(\lambda (w: T).(let TMP_54 \def (Bind b) in (let TMP_55 \def (CHead e3 
-TMP_54 w) in (getl n c3 TMP_55)))))))) in (let TMP_59 \def (\lambda (_: 
-B).(\lambda (_: C).(\lambda (_: C).(\lambda (u: T).(\lambda (w: T).(let 
-TMP_57 \def (S n) in (let TMP_58 \def (minus i TMP_57) in (subst0 TMP_58 v u 
-w)))))))) in (let TMP_62 \def (\lambda (_: B).(\lambda (e2: C).(\lambda (e3: 
-C).(\lambda (_: T).(\lambda (_: T).(let TMP_60 \def (S n) in (let TMP_61 \def 
-(minus i TMP_60) in (csubst0 TMP_61 v e2 e3)))))))) in (let TMP_63 \def 
-(ex4_5 B C C T T TMP_53 TMP_56 TMP_59 TMP_62) in (let TMP_67 \def (\lambda 
-(e2: C).(let TMP_64 \def (S n) in (let TMP_65 \def (minus i TMP_64) in (let 
-TMP_66 \def (S TMP_65) in (csubst1 TMP_66 v e1 e2))))) in (let TMP_68 \def 
-(\lambda (e2: C).(getl n c3 e2)) in (let TMP_69 \def (ex2 C TMP_67 TMP_68) in 
-(let TMP_79 \def (\lambda (H4: (getl n c3 e1)).(let TMP_73 \def (\lambda (e2: 
-C).(let TMP_70 \def (S n) in (let TMP_71 \def (minus i TMP_70) in (let TMP_72 
-\def (S TMP_71) in (csubst1 TMP_72 v e1 e2))))) in (let TMP_74 \def (\lambda 
-(e2: C).(getl n c3 e2)) in (let TMP_75 \def (S n) in (let TMP_76 \def (minus 
-i TMP_75) in (let TMP_77 \def (S TMP_76) in (let TMP_78 \def (csubst1_refl 
-TMP_77 v e1) in (ex_intro2 C TMP_73 TMP_74 e1 TMP_78 H4)))))))) in (let 
-TMP_125 \def (\lambda (H4: (ex3_4 B C T T (\lambda (b: B).(\lambda (e0: 
-C).(\lambda (u: T).(\lambda (_: T).(eq C e1 (CHead e0 (Bind b) u)))))) 
-(\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 
-(CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u: 
-T).(\lambda (w: T).(subst0 (minus i (S n)) v u w))))))).(let TMP_82 \def 
-(\lambda (b: B).(\lambda (e0: C).(\lambda (u: T).(\lambda (_: T).(let TMP_80 
-\def (Bind b) in (let TMP_81 \def (CHead e0 TMP_80 u) in (eq C e1 
-TMP_81))))))) in (let TMP_85 \def (\lambda (b: B).(\lambda (e0: C).(\lambda 
-(_: T).(\lambda (w: T).(let TMP_83 \def (Bind b) in (let TMP_84 \def (CHead 
-e0 TMP_83 w) in (getl n c3 TMP_84))))))) in (let TMP_88 \def (\lambda (_: 
-B).(\lambda (_: C).(\lambda (u: T).(\lambda (w: T).(let TMP_86 \def (S n) in 
-(let TMP_87 \def (minus i TMP_86) in (subst0 TMP_87 v u w))))))) in (let 
-TMP_92 \def (\lambda (e2: C).(let TMP_89 \def (S n) in (let TMP_90 \def 
-(minus i TMP_89) in (let TMP_91 \def (S TMP_90) in (csubst1 TMP_91 v e1 
-e2))))) in (let TMP_93 \def (\lambda (e2: C).(getl n c3 e2)) in (let TMP_94 
-\def (ex2 C TMP_92 TMP_93) in (let TMP_124 \def (\lambda (x0: B).(\lambda 
-(x1: C).(\lambda (x2: T).(\lambda (x3: T).(\lambda (H5: (eq C e1 (CHead x1 
-(Bind x0) x2))).(\lambda (H6: (getl n c3 (CHead x1 (Bind x0) x3))).(\lambda 
-(H7: (subst0 (minus i (S n)) v x2 x3)).(let TMP_95 \def (Bind x0) in (let 
-TMP_96 \def (CHead x1 TMP_95 x2) in (let TMP_102 \def (\lambda (c: C).(let 
-TMP_100 \def (\lambda (e2: C).(let TMP_97 \def (S n) in (let TMP_98 \def 
-(minus i TMP_97) in (let TMP_99 \def (S TMP_98) in (csubst1 TMP_99 v c 
-e2))))) in (let TMP_101 \def (\lambda (e2: C).(getl n c3 e2)) in (ex2 C 
-TMP_100 TMP_101)))) in (let TMP_108 \def (\lambda (e2: C).(let TMP_103 \def 
-(S n) in (let TMP_104 \def (minus i TMP_103) in (let TMP_105 \def (S TMP_104) 
-in (let TMP_106 \def (Bind x0) in (let TMP_107 \def (CHead x1 TMP_106 x2) in 
-(csubst1 TMP_105 v TMP_107 e2))))))) in (let TMP_109 \def (\lambda (e2: 
-C).(getl n c3 e2)) in (let TMP_110 \def (Bind x0) in (let TMP_111 \def (CHead 
-x1 TMP_110 x3) in (let TMP_112 \def (S n) in (let TMP_113 \def (minus i 
-TMP_112) in (let TMP_114 \def (S TMP_113) in (let TMP_115 \def (Bind x0) in 
-(let TMP_116 \def (CHead x1 TMP_115 x2) in (let TMP_117 \def (Bind x0) in 
-(let TMP_118 \def (CHead x1 TMP_117 x3) in (let TMP_119 \def (S n) in (let 
-TMP_120 \def (minus i TMP_119) in (let TMP_121 \def (csubst0_snd_bind x0 
-TMP_120 v x2 x3 H7 x1) in (let TMP_122 \def (csubst1_sing TMP_114 v TMP_116 
-TMP_118 TMP_121) in (let TMP_123 \def (ex_intro2 C TMP_108 TMP_109 TMP_111 
-TMP_122 H6) in (eq_ind_r C TMP_96 TMP_102 TMP_123 e1 
-H5))))))))))))))))))))))))))) in (ex3_4_ind B C T T TMP_82 TMP_85 TMP_88 
-TMP_94 TMP_124 H4))))))))) in (let TMP_171 \def (\lambda (H4: (ex3_4 B C C T 
+C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 
+c2)).(csubst1_ind i v c1 (\lambda (c: C).(\forall (e1: C).((getl n c1 e1) \to 
+(ex2 C (\lambda (e2: C).(csubst1 (minus i n) v e1 e2)) (\lambda (e2: C).(getl 
+n c e2)))))) (\lambda (e1: C).(\lambda (H1: (getl n c1 e1)).(eq_ind_r nat (S 
+(minus i (S n))) (\lambda (n0: nat).(ex2 C (\lambda (e2: C).(csubst1 n0 v e1 
+e2)) (\lambda (e2: C).(getl n c1 e2)))) (ex_intro2 C (\lambda (e2: 
+C).(csubst1 (S (minus i (S n))) v e1 e2)) (\lambda (e2: C).(getl n c1 e2)) e1 
+(csubst1_refl (S (minus i (S n))) v e1) H1) (minus i n) (minus_x_Sy i n H)))) 
+(\lambda (c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e1: C).(\lambda 
+(H2: (getl n c1 e1)).(eq_ind_r nat (S (minus i (S n))) (\lambda (n0: 
+nat).(ex2 C (\lambda (e2: C).(csubst1 n0 v e1 e2)) (\lambda (e2: C).(getl n 
+c3 e2)))) (let H3 \def (csubst0_getl_lt i n H c1 c3 v H1 e1 H2) in (or4_ind 
+(getl n c3 e1) (ex3_4 B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u: 
+T).(\lambda (_: T).(eq C e1 (CHead e0 (Bind b) u)))))) (\lambda (b: 
+B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e0 
+(Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u: T).(\lambda (w: 
+T).(subst0 (minus i (S n)) v u w)))))) (ex3_4 B C C T (\lambda (b: 
+B).(\lambda (e2: C).(\lambda (_: C).(\lambda (u: T).(eq C e1 (CHead e2 (Bind 
+b) u)))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e3: C).(\lambda (u: 
+T).(getl n c3 (CHead e3 (Bind b) u)))))) (\lambda (_: B).(\lambda (e2: 
+C).(\lambda (e3: C).(\lambda (_: T).(csubst0 (minus i (S n)) v e2 e3)))))) 
+(ex4_5 B C C T T (\lambda (b: B).(\lambda (e2: C).(\lambda (_: C).(\lambda 
+(u: T).(\lambda (_: T).(eq C e1 (CHead e2 (Bind b) u))))))) (\lambda (b: 
+B).(\lambda (_: C).(\lambda (e3: C).(\lambda (_: T).(\lambda (w: T).(getl n 
+c3 (CHead e3 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: 
+C).(\lambda (u: T).(\lambda (w: T).(subst0 (minus i (S n)) v u w)))))) 
+(\lambda (_: B).(\lambda (e2: C).(\lambda (e3: C).(\lambda (_: T).(\lambda 
+(_: T).(csubst0 (minus i (S n)) v e2 e3))))))) (ex2 C (\lambda (e2: 
+C).(csubst1 (S (minus i (S n))) v e1 e2)) (\lambda (e2: C).(getl n c3 e2))) 
+(\lambda (H4: (getl n c3 e1)).(ex_intro2 C (\lambda (e2: C).(csubst1 (S 
+(minus i (S n))) v e1 e2)) (\lambda (e2: C).(getl n c3 e2)) e1 (csubst1_refl 
+(S (minus i (S n))) v e1) H4)) (\lambda (H4: (ex3_4 B C T T (\lambda (b: 
+B).(\lambda (e0: C).(\lambda (u: T).(\lambda (_: T).(eq C e1 (CHead e0 (Bind 
+b) u)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: 
+T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_: 
+C).(\lambda (u: T).(\lambda (w: T).(subst0 (minus i (S n)) v u 
+w))))))).(ex3_4_ind B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u: 
+T).(\lambda (_: T).(eq C e1 (CHead e0 (Bind b) u)))))) (\lambda (b: 
+B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e0 
+(Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u: T).(\lambda (w: 
+T).(subst0 (minus i (S n)) v u w))))) (ex2 C (\lambda (e2: C).(csubst1 (S 
+(minus i (S n))) v e1 e2)) (\lambda (e2: C).(getl n c3 e2))) (\lambda (x0: 
+B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (x3: T).(\lambda (H5: (eq C e1 
+(CHead x1 (Bind x0) x2))).(\lambda (H6: (getl n c3 (CHead x1 (Bind x0) 
+x3))).(\lambda (H7: (subst0 (minus i (S n)) v x2 x3)).(eq_ind_r C (CHead x1 
+(Bind x0) x2) (\lambda (c: C).(ex2 C (\lambda (e2: C).(csubst1 (S (minus i (S 
+n))) v c e2)) (\lambda (e2: C).(getl n c3 e2)))) (ex_intro2 C (\lambda (e2: 
+C).(csubst1 (S (minus i (S n))) v (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: 
+C).(getl n c3 e2)) (CHead x1 (Bind x0) x3) (csubst1_sing (S (minus i (S n))) 
+v (CHead x1 (Bind x0) x2) (CHead x1 (Bind x0) x3) (csubst0_snd_bind x0 (minus 
+i (S n)) v x2 x3 H7 x1)) H6) e1 H5)))))))) H4)) (\lambda (H4: (ex3_4 B C C T 
 (\lambda (b: B).(\lambda (e2: C).(\lambda (_: C).(\lambda (u: T).(eq C e1 
 (CHead e2 (Bind b) u)))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e3: 
 C).(\lambda (u: T).(getl n c3 (CHead e3 (Bind b) u)))))) (\lambda (_: 
 B).(\lambda (e2: C).(\lambda (e3: C).(\lambda (_: T).(csubst0 (minus i (S n)) 
-v e2 e3))))))).(let TMP_128 \def (\lambda (b: B).(\lambda (e2: C).(\lambda 
-(_: C).(\lambda (u: T).(let TMP_126 \def (Bind b) in (let TMP_127 \def (CHead 
-e2 TMP_126 u) in (eq C e1 TMP_127))))))) in (let TMP_131 \def (\lambda (b: 
-B).(\lambda (_: C).(\lambda (e3: C).(\lambda (u: T).(let TMP_129 \def (Bind 
-b) in (let TMP_130 \def (CHead e3 TMP_129 u) in (getl n c3 TMP_130))))))) in 
-(let TMP_134 \def (\lambda (_: B).(\lambda (e2: C).(\lambda (e3: C).(\lambda 
-(_: T).(let TMP_132 \def (S n) in (let TMP_133 \def (minus i TMP_132) in 
-(csubst0 TMP_133 v e2 e3))))))) in (let TMP_138 \def (\lambda (e2: C).(let 
-TMP_135 \def (S n) in (let TMP_136 \def (minus i TMP_135) in (let TMP_137 
-\def (S TMP_136) in (csubst1 TMP_137 v e1 e2))))) in (let TMP_139 \def 
-(\lambda (e2: C).(getl n c3 e2)) in (let TMP_140 \def (ex2 C TMP_138 TMP_139) 
-in (let TMP_170 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
-C).(\lambda (x3: T).(\lambda (H5: (eq C e1 (CHead x1 (Bind x0) x3))).(\lambda 
-(H6: (getl n c3 (CHead x2 (Bind x0) x3))).(\lambda (H7: (csubst0 (minus i (S 
-n)) v x1 x2)).(let TMP_141 \def (Bind x0) in (let TMP_142 \def (CHead x1 
-TMP_141 x3) in (let TMP_148 \def (\lambda (c: C).(let TMP_146 \def (\lambda 
-(e2: C).(let TMP_143 \def (S n) in (let TMP_144 \def (minus i TMP_143) in 
-(let TMP_145 \def (S TMP_144) in (csubst1 TMP_145 v c e2))))) in (let TMP_147 
-\def (\lambda (e2: C).(getl n c3 e2)) in (ex2 C TMP_146 TMP_147)))) in (let 
-TMP_154 \def (\lambda (e2: C).(let TMP_149 \def (S n) in (let TMP_150 \def 
-(minus i TMP_149) in (let TMP_151 \def (S TMP_150) in (let TMP_152 \def (Bind 
-x0) in (let TMP_153 \def (CHead x1 TMP_152 x3) in (csubst1 TMP_151 v TMP_153 
-e2))))))) in (let TMP_155 \def (\lambda (e2: C).(getl n c3 e2)) in (let 
-TMP_156 \def (Bind x0) in (let TMP_157 \def (CHead x2 TMP_156 x3) in (let 
-TMP_158 \def (S n) in (let TMP_159 \def (minus i TMP_158) in (let TMP_160 
-\def (S TMP_159) in (let TMP_161 \def (Bind x0) in (let TMP_162 \def (CHead 
-x1 TMP_161 x3) in (let TMP_163 \def (Bind x0) in (let TMP_164 \def (CHead x2 
-TMP_163 x3) in (let TMP_165 \def (S n) in (let TMP_166 \def (minus i TMP_165) 
-in (let TMP_167 \def (csubst0_fst_bind x0 TMP_166 x1 x2 v H7 x3) in (let 
-TMP_168 \def (csubst1_sing TMP_160 v TMP_162 TMP_164 TMP_167) in (let TMP_169 
-\def (ex_intro2 C TMP_154 TMP_155 TMP_157 TMP_168 H6) in (eq_ind_r C TMP_142 
-TMP_148 TMP_169 e1 H5))))))))))))))))))))))))))) in (ex3_4_ind B C C T 
-TMP_128 TMP_131 TMP_134 TMP_140 TMP_170 H4))))))))) in (let TMP_220 \def 
-(\lambda (H4: (ex4_5 B C C T T (\lambda (b: B).(\lambda (e2: C).(\lambda (_: 
-C).(\lambda (u: T).(\lambda (_: T).(eq C e1 (CHead e2 (Bind b) u))))))) 
-(\lambda (b: B).(\lambda (_: C).(\lambda (e3: C).(\lambda (_: T).(\lambda (w: 
-T).(getl n c3 (CHead e3 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: 
-C).(\lambda (_: C).(\lambda (u: T).(\lambda (w: T).(subst0 (minus i (S n)) v 
-u w)))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (e3: C).(\lambda (_: 
-T).(\lambda (_: T).(csubst0 (minus i (S n)) v e2 e3)))))))).(let TMP_174 \def 
-(\lambda (b: B).(\lambda (e2: C).(\lambda (_: C).(\lambda (u: T).(\lambda (_: 
-T).(let TMP_172 \def (Bind b) in (let TMP_173 \def (CHead e2 TMP_172 u) in 
-(eq C e1 TMP_173)))))))) in (let TMP_177 \def (\lambda (b: B).(\lambda (_: 
-C).(\lambda (e3: C).(\lambda (_: T).(\lambda (w: T).(let TMP_175 \def (Bind 
-b) in (let TMP_176 \def (CHead e3 TMP_175 w) in (getl n c3 TMP_176)))))))) in 
-(let TMP_180 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda 
-(u: T).(\lambda (w: T).(let TMP_178 \def (S n) in (let TMP_179 \def (minus i 
-TMP_178) in (subst0 TMP_179 v u w)))))))) in (let TMP_183 \def (\lambda (_: 
-B).(\lambda (e2: C).(\lambda (e3: C).(\lambda (_: T).(\lambda (_: T).(let 
-TMP_181 \def (S n) in (let TMP_182 \def (minus i TMP_181) in (csubst0 TMP_182 
-v e2 e3)))))))) in (let TMP_187 \def (\lambda (e2: C).(let TMP_184 \def (S n) 
-in (let TMP_185 \def (minus i TMP_184) in (let TMP_186 \def (S TMP_185) in 
-(csubst1 TMP_186 v e1 e2))))) in (let TMP_188 \def (\lambda (e2: C).(getl n 
-c3 e2)) in (let TMP_189 \def (ex2 C TMP_187 TMP_188) in (let TMP_219 \def 
-(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: C).(\lambda (x3: T).(\lambda 
-(x4: T).(\lambda (H5: (eq C e1 (CHead x1 (Bind x0) x3))).(\lambda (H6: (getl 
-n c3 (CHead x2 (Bind x0) x4))).(\lambda (H7: (subst0 (minus i (S n)) v x3 
-x4)).(\lambda (H8: (csubst0 (minus i (S n)) v x1 x2)).(let TMP_190 \def (Bind 
-x0) in (let TMP_191 \def (CHead x1 TMP_190 x3) in (let TMP_197 \def (\lambda 
-(c: C).(let TMP_195 \def (\lambda (e2: C).(let TMP_192 \def (S n) in (let 
-TMP_193 \def (minus i TMP_192) in (let TMP_194 \def (S TMP_193) in (csubst1 
-TMP_194 v c e2))))) in (let TMP_196 \def (\lambda (e2: C).(getl n c3 e2)) in 
-(ex2 C TMP_195 TMP_196)))) in (let TMP_203 \def (\lambda (e2: C).(let TMP_198 
-\def (S n) in (let TMP_199 \def (minus i TMP_198) in (let TMP_200 \def (S 
-TMP_199) in (let TMP_201 \def (Bind x0) in (let TMP_202 \def (CHead x1 
-TMP_201 x3) in (csubst1 TMP_200 v TMP_202 e2))))))) in (let TMP_204 \def 
-(\lambda (e2: C).(getl n c3 e2)) in (let TMP_205 \def (Bind x0) in (let 
-TMP_206 \def (CHead x2 TMP_205 x4) in (let TMP_207 \def (S n) in (let TMP_208 
-\def (minus i TMP_207) in (let TMP_209 \def (S TMP_208) in (let TMP_210 \def 
-(Bind x0) in (let TMP_211 \def (CHead x1 TMP_210 x3) in (let TMP_212 \def 
-(Bind x0) in (let TMP_213 \def (CHead x2 TMP_212 x4) in (let TMP_214 \def (S 
-n) in (let TMP_215 \def (minus i TMP_214) in (let TMP_216 \def 
-(csubst0_both_bind x0 TMP_215 v x3 x4 H7 x1 x2 H8) in (let TMP_217 \def 
-(csubst1_sing TMP_209 v TMP_211 TMP_213 TMP_216) in (let TMP_218 \def 
-(ex_intro2 C TMP_203 TMP_204 TMP_206 TMP_217 H6) in (eq_ind_r C TMP_191 
-TMP_197 TMP_218 e1 H5))))))))))))))))))))))))))))) in (ex4_5_ind B C C T T 
-TMP_174 TMP_177 TMP_180 TMP_183 TMP_189 TMP_219 H4)))))))))) in (let TMP_221 
-\def (or4_ind TMP_30 TMP_40 TMP_50 TMP_63 TMP_69 TMP_79 TMP_125 TMP_171 
-TMP_220 H3) in (let TMP_222 \def (minus i n) in (let TMP_223 \def (minus_x_Sy 
-i n H) in (eq_ind_r nat TMP_26 TMP_29 TMP_221 TMP_222 
-TMP_223)))))))))))))))))))))))))))))))))) in (csubst1_ind i v c1 TMP_4 TMP_23 
-TMP_224 c2 H0)))))))))).
+v e2 e3))))))).(ex3_4_ind B C C T (\lambda (b: B).(\lambda (e2: C).(\lambda 
+(_: C).(\lambda (u: T).(eq C e1 (CHead e2 (Bind b) u)))))) (\lambda (b: 
+B).(\lambda (_: C).(\lambda (e3: C).(\lambda (u: T).(getl n c3 (CHead e3 
+(Bind b) u)))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (e3: C).(\lambda 
+(_: T).(csubst0 (minus i (S n)) v e2 e3))))) (ex2 C (\lambda (e2: C).(csubst1 
+(S (minus i (S n))) v e1 e2)) (\lambda (e2: C).(getl n c3 e2))) (\lambda (x0: 
+B).(\lambda (x1: C).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H5: (eq C e1 
+(CHead x1 (Bind x0) x3))).(\lambda (H6: (getl n c3 (CHead x2 (Bind x0) 
+x3))).(\lambda (H7: (csubst0 (minus i (S n)) v x1 x2)).(eq_ind_r C (CHead x1 
+(Bind x0) x3) (\lambda (c: C).(ex2 C (\lambda (e2: C).(csubst1 (S (minus i (S 
+n))) v c e2)) (\lambda (e2: C).(getl n c3 e2)))) (ex_intro2 C (\lambda (e2: 
+C).(csubst1 (S (minus i (S n))) v (CHead x1 (Bind x0) x3) e2)) (\lambda (e2: 
+C).(getl n c3 e2)) (CHead x2 (Bind x0) x3) (csubst1_sing (S (minus i (S n))) 
+v (CHead x1 (Bind x0) x3) (CHead x2 (Bind x0) x3) (csubst0_fst_bind x0 (minus 
+i (S n)) x1 x2 v H7 x3)) H6) e1 H5)))))))) H4)) (\lambda (H4: (ex4_5 B C C T 
+T (\lambda (b: B).(\lambda (e2: C).(\lambda (_: C).(\lambda (u: T).(\lambda 
+(_: T).(eq C e1 (CHead e2 (Bind b) u))))))) (\lambda (b: B).(\lambda (_: 
+C).(\lambda (e3: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e3 
+(Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda 
+(u: T).(\lambda (w: T).(subst0 (minus i (S n)) v u w)))))) (\lambda (_: 
+B).(\lambda (e2: C).(\lambda (e3: C).(\lambda (_: T).(\lambda (_: T).(csubst0 
+(minus i (S n)) v e2 e3)))))))).(ex4_5_ind B C C T T (\lambda (b: B).(\lambda 
+(e2: C).(\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(eq C e1 (CHead e2 
+(Bind b) u))))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e3: C).(\lambda 
+(_: T).(\lambda (w: T).(getl n c3 (CHead e3 (Bind b) w))))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: C).(\lambda (u: T).(\lambda (w: T).(subst0 
+(minus i (S n)) v u w)))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (e3: 
+C).(\lambda (_: T).(\lambda (_: T).(csubst0 (minus i (S n)) v e2 e3)))))) 
+(ex2 C (\lambda (e2: C).(csubst1 (S (minus i (S n))) v e1 e2)) (\lambda (e2: 
+C).(getl n c3 e2))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
+C).(\lambda (x3: T).(\lambda (x4: T).(\lambda (H5: (eq C e1 (CHead x1 (Bind 
+x0) x3))).(\lambda (H6: (getl n c3 (CHead x2 (Bind x0) x4))).(\lambda (H7: 
+(subst0 (minus i (S n)) v x3 x4)).(\lambda (H8: (csubst0 (minus i (S n)) v x1 
+x2)).(eq_ind_r C (CHead x1 (Bind x0) x3) (\lambda (c: C).(ex2 C (\lambda (e2: 
+C).(csubst1 (S (minus i (S n))) v c e2)) (\lambda (e2: C).(getl n c3 e2)))) 
+(ex_intro2 C (\lambda (e2: C).(csubst1 (S (minus i (S n))) v (CHead x1 (Bind 
+x0) x3) e2)) (\lambda (e2: C).(getl n c3 e2)) (CHead x2 (Bind x0) x4) 
+(csubst1_sing (S (minus i (S n))) v (CHead x1 (Bind x0) x3) (CHead x2 (Bind 
+x0) x4) (csubst0_both_bind x0 (minus i (S n)) v x3 x4 H7 x1 x2 H8)) H6) e1 
+H5)))))))))) H4)) H3)) (minus i n) (minus_x_Sy i n H)))))) c2 H0))))))).
 
 theorem csubst1_getl_ge_back:
  \forall (i: nat).(\forall (n: nat).((le i n) \to (\forall (c1: C).(\forall 
@@ -232,12 +143,11 @@ theorem csubst1_getl_ge_back:
 e) \to (getl n c1 e)))))))))
 \def
  \lambda (i: nat).(\lambda (n: nat).(\lambda (H: (le i n)).(\lambda (c1: 
-C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 c2)).(let 
-TMP_1 \def (\lambda (c: C).(\forall (e: C).((getl n c e) \to (getl n c1 e)))) 
-in (let TMP_2 \def (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) in (let 
-TMP_3 \def (\lambda (c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: 
-C).(\lambda (H2: (getl n c3 e)).(csubst0_getl_ge_back i n H c1 c3 v H1 e 
-H2))))) in (csubst1_ind i v c1 TMP_1 TMP_2 TMP_3 c2 H0)))))))))).
+C).(\lambda (c2: C).(\lambda (v: T).(\lambda (H0: (csubst1 i v c1 
+c2)).(csubst1_ind i v c1 (\lambda (c: C).(\forall (e: C).((getl n c e) \to 
+(getl n c1 e)))) (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) (\lambda 
+(c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: C).(\lambda (H2: 
+(getl n c3 e)).(csubst0_getl_ge_back i n H c1 c3 v H1 e H2))))) c2 H0))))))).
 
 theorem getl_csubst1:
  \forall (d: nat).(\forall (c: C).(\forall (e: C).(\forall (u: T).((getl d c 
@@ -245,219 +155,115 @@ theorem getl_csubst1:
 C).(csubst1 d u c a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) d a0 
 a))))))))
 \def
- \lambda (d: nat).(let TMP_4 \def (\lambda (n: nat).(\forall (c: C).(\forall 
-(e: C).(\forall (u: T).((getl n c (CHead e (Bind Abbr) u)) \to (let TMP_1 
-\def (\lambda (a0: C).(\lambda (_: C).(csubst1 n u c a0))) in (let TMP_3 \def 
-(\lambda (a0: C).(\lambda (a: C).(let TMP_2 \def (S O) in (drop TMP_2 n a0 
-a)))) in (ex2_2 C C TMP_1 TMP_3)))))))) in (let TMP_141 \def (\lambda (c: 
-C).(let TMP_8 \def (\lambda (c0: C).(\forall (e: C).(\forall (u: T).((getl O 
-c0 (CHead e (Bind Abbr) u)) \to (let TMP_5 \def (\lambda (a0: C).(\lambda (_: 
-C).(csubst1 O u c0 a0))) in (let TMP_7 \def (\lambda (a0: C).(\lambda (a: 
-C).(let TMP_6 \def (S O) in (drop TMP_6 O a0 a)))) in (ex2_2 C C TMP_5 
-TMP_7))))))) in (let TMP_16 \def (\lambda (n: nat).(\lambda (e: C).(\lambda 
-(u: T).(\lambda (H: (getl O (CSort n) (CHead e (Bind Abbr) u))).(let TMP_9 
-\def (Bind Abbr) in (let TMP_10 \def (CHead e TMP_9 u) in (let TMP_12 \def 
-(\lambda (a0: C).(\lambda (_: C).(let TMP_11 \def (CSort n) in (csubst1 O u 
-TMP_11 a0)))) in (let TMP_14 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_13 \def (S O) in (drop TMP_13 O a0 a)))) in (let TMP_15 \def (ex2_2 C C 
-TMP_12 TMP_14) in (getl_gen_sort n O TMP_10 H TMP_15)))))))))) in (let 
-TMP_140 \def (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u: 
-T).((getl O c0 (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: 
-C).(\lambda (_: C).(csubst1 O u c0 a0))) (\lambda (a0: C).(\lambda (a: 
-C).(drop (S O) O a0 a))))))))).(\lambda (k: K).(let TMP_21 \def (\lambda (k0: 
-K).(\forall (t: T).(\forall (e: C).(\forall (u: T).((getl O (CHead c0 k0 t) 
-(CHead e (Bind Abbr) u)) \to (let TMP_18 \def (\lambda (a0: C).(\lambda (_: 
-C).(let TMP_17 \def (CHead c0 k0 t) in (csubst1 O u TMP_17 a0)))) in (let 
-TMP_20 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_19 \def (S O) in (drop 
-TMP_19 O a0 a)))) in (ex2_2 C C TMP_18 TMP_20)))))))) in (let TMP_90 \def 
-(\lambda (b: B).(\lambda (t: T).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: 
-(getl O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u))).(let TMP_22 \def 
-(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow e | (CHead c1 _ _) 
-\Rightarrow c1])) in (let TMP_23 \def (Bind Abbr) in (let TMP_24 \def (CHead 
-e TMP_23 u) in (let TMP_25 \def (Bind b) in (let TMP_26 \def (CHead c0 TMP_25 
-t) in (let TMP_27 \def (Bind Abbr) in (let TMP_28 \def (CHead e TMP_27 u) in 
-(let TMP_29 \def (Bind b) in (let TMP_30 \def (CHead c0 TMP_29 t) in (let 
-TMP_31 \def (Bind Abbr) in (let TMP_32 \def (CHead e TMP_31 u) in (let TMP_33 
-\def (getl_gen_O TMP_30 TMP_32 H0) in (let TMP_34 \def (clear_gen_bind b c0 
-TMP_28 t TMP_33) in (let H1 \def (f_equal C C TMP_22 TMP_24 TMP_26 TMP_34) in 
-(let TMP_35 \def (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow Abbr 
-| (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) \Rightarrow b0 | (Flat 
-_) \Rightarrow Abbr])])) in (let TMP_36 \def (Bind Abbr) in (let TMP_37 \def 
-(CHead e TMP_36 u) in (let TMP_38 \def (Bind b) in (let TMP_39 \def (CHead c0 
-TMP_38 t) in (let TMP_40 \def (Bind Abbr) in (let TMP_41 \def (CHead e TMP_40 
-u) in (let TMP_42 \def (Bind b) in (let TMP_43 \def (CHead c0 TMP_42 t) in 
-(let TMP_44 \def (Bind Abbr) in (let TMP_45 \def (CHead e TMP_44 u) in (let 
-TMP_46 \def (getl_gen_O TMP_43 TMP_45 H0) in (let TMP_47 \def (clear_gen_bind 
-b c0 TMP_41 t TMP_46) in (let H2 \def (f_equal C B TMP_35 TMP_37 TMP_39 
-TMP_47) in (let TMP_48 \def (\lambda (e0: C).(match e0 with [(CSort _) 
-\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_49 \def (Bind 
-Abbr) in (let TMP_50 \def (CHead e TMP_49 u) in (let TMP_51 \def (Bind b) in 
-(let TMP_52 \def (CHead c0 TMP_51 t) in (let TMP_53 \def (Bind Abbr) in (let 
-TMP_54 \def (CHead e TMP_53 u) in (let TMP_55 \def (Bind b) in (let TMP_56 
-\def (CHead c0 TMP_55 t) in (let TMP_57 \def (Bind Abbr) in (let TMP_58 \def 
-(CHead e TMP_57 u) in (let TMP_59 \def (getl_gen_O TMP_56 TMP_58 H0) in (let 
-TMP_60 \def (clear_gen_bind b c0 TMP_54 t TMP_59) in (let H3 \def (f_equal C 
-T TMP_48 TMP_50 TMP_52 TMP_60) in (let TMP_88 \def (\lambda (H4: (eq B Abbr 
-b)).(\lambda (_: (eq C e c0)).(let TMP_66 \def (\lambda (t0: T).(let TMP_63 
-\def (\lambda (a0: C).(\lambda (_: C).(let TMP_61 \def (Bind b) in (let 
-TMP_62 \def (CHead c0 TMP_61 t) in (csubst1 O t0 TMP_62 a0))))) in (let 
-TMP_65 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_64 \def (S O) in (drop 
-TMP_64 O a0 a)))) in (ex2_2 C C TMP_63 TMP_65)))) in (let TMP_72 \def 
-(\lambda (b0: B).(let TMP_69 \def (\lambda (a0: C).(\lambda (_: C).(let 
-TMP_67 \def (Bind b0) in (let TMP_68 \def (CHead c0 TMP_67 t) in (csubst1 O t 
-TMP_68 a0))))) in (let TMP_71 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_70 \def (S O) in (drop TMP_70 O a0 a)))) in (ex2_2 C C TMP_69 TMP_71)))) 
-in (let TMP_75 \def (\lambda (a0: C).(\lambda (_: C).(let TMP_73 \def (Bind 
-Abbr) in (let TMP_74 \def (CHead c0 TMP_73 t) in (csubst1 O t TMP_74 a0))))) 
-in (let TMP_77 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_76 \def (S O) 
-in (drop TMP_76 O a0 a)))) in (let TMP_78 \def (Bind Abbr) in (let TMP_79 
-\def (CHead c0 TMP_78 t) in (let TMP_80 \def (Bind Abbr) in (let TMP_81 \def 
-(CHead c0 TMP_80 t) in (let TMP_82 \def (csubst1_refl O t TMP_81) in (let 
-TMP_83 \def (Bind Abbr) in (let TMP_84 \def (drop_refl c0) in (let TMP_85 
-\def (drop_drop TMP_83 O c0 c0 TMP_84 t) in (let TMP_86 \def (ex2_2_intro C C 
-TMP_75 TMP_77 TMP_79 c0 TMP_82 TMP_85) in (let TMP_87 \def (eq_ind B Abbr 
-TMP_72 TMP_86 b H4) in (eq_ind_r T t TMP_66 TMP_87 u H3))))))))))))))))) in 
-(let TMP_89 \def (TMP_88 H2) in (TMP_89 
-H1)))))))))))))))))))))))))))))))))))))))))))))))))) in (let TMP_139 \def 
-(\lambda (f: F).(\lambda (t: T).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: 
-(getl O (CHead c0 (Flat f) t) (CHead e (Bind Abbr) u))).(let H_x \def 
-(subst1_ex u t O) in (let H1 \def H_x in (let TMP_93 \def (\lambda (t2: 
-T).(let TMP_91 \def (S O) in (let TMP_92 \def (lift TMP_91 O t2) in (subst1 O 
-u t TMP_92)))) in (let TMP_96 \def (\lambda (a0: C).(\lambda (_: C).(let 
-TMP_94 \def (Flat f) in (let TMP_95 \def (CHead c0 TMP_94 t) in (csubst1 O u 
-TMP_95 a0))))) in (let TMP_98 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_97 \def (S O) in (drop TMP_97 O a0 a)))) in (let TMP_99 \def (ex2_2 C C 
-TMP_96 TMP_98) in (let TMP_138 \def (\lambda (x: T).(\lambda (H2: (subst1 O u 
-t (lift (S O) O x))).(let TMP_100 \def (Bind Abbr) in (let TMP_101 \def 
-(CHead e TMP_100 u) in (let TMP_102 \def (drop_refl c0) in (let TMP_103 \def 
-(Bind Abbr) in (let TMP_104 \def (CHead e TMP_103 u) in (let TMP_105 \def 
-(Flat f) in (let TMP_106 \def (CHead c0 TMP_105 t) in (let TMP_107 \def (Bind 
-Abbr) in (let TMP_108 \def (CHead e TMP_107 u) in (let TMP_109 \def 
-(getl_gen_O TMP_106 TMP_108 H0) in (let TMP_110 \def (clear_gen_flat f c0 
-TMP_104 t TMP_109) in (let TMP_111 \def (getl_intro O c0 TMP_101 c0 TMP_102 
-TMP_110) in (let H3 \def (H e u TMP_111) in (let TMP_112 \def (\lambda (a0: 
-C).(\lambda (_: C).(csubst1 O u c0 a0))) in (let TMP_114 \def (\lambda (a0: 
-C).(\lambda (a: C).(let TMP_113 \def (S O) in (drop TMP_113 O a0 a)))) in 
-(let TMP_117 \def (\lambda (a0: C).(\lambda (_: C).(let TMP_115 \def (Flat f) 
-in (let TMP_116 \def (CHead c0 TMP_115 t) in (csubst1 O u TMP_116 a0))))) in 
-(let TMP_119 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_118 \def (S O) in 
-(drop TMP_118 O a0 a)))) in (let TMP_120 \def (ex2_2 C C TMP_117 TMP_119) in 
-(let TMP_137 \def (\lambda (x0: C).(\lambda (x1: C).(\lambda (H4: (csubst1 O 
-u c0 x0)).(\lambda (H5: (drop (S O) O x0 x1)).(let TMP_123 \def (\lambda (a0: 
-C).(\lambda (_: C).(let TMP_121 \def (Flat f) in (let TMP_122 \def (CHead c0 
-TMP_121 t) in (csubst1 O u TMP_122 a0))))) in (let TMP_125 \def (\lambda (a0: 
-C).(\lambda (a: C).(let TMP_124 \def (S O) in (drop TMP_124 O a0 a)))) in 
-(let TMP_126 \def (Flat f) in (let TMP_127 \def (S O) in (let TMP_128 \def 
-(lift TMP_127 O x) in (let TMP_129 \def (CHead x0 TMP_126 TMP_128) in (let 
-TMP_130 \def (S O) in (let TMP_131 \def (lift TMP_130 O x) in (let TMP_132 
-\def (csubst1_flat f O u t TMP_131 H2 c0 x0 H4) in (let TMP_133 \def (Flat f) 
-in (let TMP_134 \def (S O) in (let TMP_135 \def (lift TMP_134 O x) in (let 
-TMP_136 \def (drop_drop TMP_133 O x0 x1 H5 TMP_135) in (ex2_2_intro C C 
-TMP_123 TMP_125 TMP_129 x1 TMP_132 TMP_136)))))))))))))))))) in (ex2_2_ind C 
-C TMP_112 TMP_114 TMP_120 TMP_137 H3)))))))))))))))))))))) in (ex_ind T 
-TMP_93 TMP_99 TMP_138 H1))))))))))))) in (K_ind TMP_21 TMP_90 TMP_139 
-k))))))) in (C_ind TMP_8 TMP_16 TMP_140 c))))) in (let TMP_269 \def (\lambda 
-(n: nat).(\lambda (H: ((\forall (c: C).(\forall (e: C).(\forall (u: T).((getl 
-n c (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: 
-C).(csubst1 n u c a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) n a0 
-a)))))))))).(\lambda (c: C).(let TMP_147 \def (\lambda (c0: C).(\forall (e: 
-C).(\forall (u: T).((getl (S n) c0 (CHead e (Bind Abbr) u)) \to (let TMP_143 
-\def (\lambda (a0: C).(\lambda (_: C).(let TMP_142 \def (S n) in (csubst1 
-TMP_142 u c0 a0)))) in (let TMP_146 \def (\lambda (a0: C).(\lambda (a: 
-C).(let TMP_144 \def (S O) in (let TMP_145 \def (S n) in (drop TMP_144 
-TMP_145 a0 a))))) in (ex2_2 C C TMP_143 TMP_146))))))) in (let TMP_158 \def 
-(\lambda (n0: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl (S n) 
-(CSort n0) (CHead e (Bind Abbr) u))).(let TMP_148 \def (S n) in (let TMP_149 
-\def (Bind Abbr) in (let TMP_150 \def (CHead e TMP_149 u) in (let TMP_153 
-\def (\lambda (a0: C).(\lambda (_: C).(let TMP_151 \def (S n) in (let TMP_152 
-\def (CSort n0) in (csubst1 TMP_151 u TMP_152 a0))))) in (let TMP_156 \def 
-(\lambda (a0: C).(\lambda (a: C).(let TMP_154 \def (S O) in (let TMP_155 \def 
-(S n) in (drop TMP_154 TMP_155 a0 a))))) in (let TMP_157 \def (ex2_2 C C 
-TMP_153 TMP_156) in (getl_gen_sort n0 TMP_148 TMP_150 H0 TMP_157))))))))))) 
-in (let TMP_268 \def (\lambda (c0: C).(\lambda (H0: ((\forall (e: C).(\forall 
-(u: T).((getl (S n) c0 (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: 
-C).(\lambda (_: C).(csubst1 (S n) u c0 a0))) (\lambda (a0: C).(\lambda (a: 
-C).(drop (S O) (S n) a0 a))))))))).(\lambda (k: K).(let TMP_165 \def (\lambda 
-(k0: K).(\forall (t: T).(\forall (e: C).(\forall (u: T).((getl (S n) (CHead 
-c0 k0 t) (CHead e (Bind Abbr) u)) \to (let TMP_161 \def (\lambda (a0: 
-C).(\lambda (_: C).(let TMP_159 \def (S n) in (let TMP_160 \def (CHead c0 k0 
-t) in (csubst1 TMP_159 u TMP_160 a0))))) in (let TMP_164 \def (\lambda (a0: 
-C).(\lambda (a: C).(let TMP_162 \def (S O) in (let TMP_163 \def (S n) in 
-(drop TMP_162 TMP_163 a0 a))))) in (ex2_2 C C TMP_161 TMP_164)))))))) in (let 
-TMP_212 \def (\lambda (b: B).(\lambda (t: T).(\lambda (e: C).(\lambda (u: 
-T).(\lambda (H1: (getl (S n) (CHead c0 (Bind b) t) (CHead e (Bind Abbr) 
-u))).(let H_x \def (subst1_ex u t n) in (let H2 \def H_x in (let TMP_168 \def 
-(\lambda (t2: T).(let TMP_166 \def (S O) in (let TMP_167 \def (lift TMP_166 n 
-t2) in (subst1 n u t TMP_167)))) in (let TMP_172 \def (\lambda (a0: 
-C).(\lambda (_: C).(let TMP_169 \def (S n) in (let TMP_170 \def (Bind b) in 
-(let TMP_171 \def (CHead c0 TMP_170 t) in (csubst1 TMP_169 u TMP_171 a0)))))) 
-in (let TMP_175 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_173 \def (S O) 
-in (let TMP_174 \def (S n) in (drop TMP_173 TMP_174 a0 a))))) in (let TMP_176 
-\def (ex2_2 C C TMP_172 TMP_175) in (let TMP_211 \def (\lambda (x: 
-T).(\lambda (H3: (subst1 n u t (lift (S O) n x))).(let TMP_177 \def (Bind b) 
-in (let TMP_178 \def (Bind Abbr) in (let TMP_179 \def (CHead e TMP_178 u) in 
-(let TMP_180 \def (getl_gen_S TMP_177 c0 TMP_179 t n H1) in (let H4 \def (H 
-c0 e u TMP_180) in (let TMP_181 \def (\lambda (a0: C).(\lambda (_: 
-C).(csubst1 n u c0 a0))) in (let TMP_183 \def (\lambda (a0: C).(\lambda (a: 
-C).(let TMP_182 \def (S O) in (drop TMP_182 n a0 a)))) in (let TMP_187 \def 
-(\lambda (a0: C).(\lambda (_: C).(let TMP_184 \def (S n) in (let TMP_185 \def 
-(Bind b) in (let TMP_186 \def (CHead c0 TMP_185 t) in (csubst1 TMP_184 u 
-TMP_186 a0)))))) in (let TMP_190 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_188 \def (S O) in (let TMP_189 \def (S n) in (drop TMP_188 TMP_189 a0 
-a))))) in (let TMP_191 \def (ex2_2 C C TMP_187 TMP_190) in (let TMP_210 \def 
-(\lambda (x0: C).(\lambda (x1: C).(\lambda (H5: (csubst1 n u c0 x0)).(\lambda 
-(H6: (drop (S O) n x0 x1)).(let TMP_195 \def (\lambda (a0: C).(\lambda (_: 
-C).(let TMP_192 \def (S n) in (let TMP_193 \def (Bind b) in (let TMP_194 \def 
-(CHead c0 TMP_193 t) in (csubst1 TMP_192 u TMP_194 a0)))))) in (let TMP_198 
-\def (\lambda (a0: C).(\lambda (a: C).(let TMP_196 \def (S O) in (let TMP_197 
-\def (S n) in (drop TMP_196 TMP_197 a0 a))))) in (let TMP_199 \def (Bind b) 
-in (let TMP_200 \def (S O) in (let TMP_201 \def (lift TMP_200 n x) in (let 
-TMP_202 \def (CHead x0 TMP_199 TMP_201) in (let TMP_203 \def (Bind b) in (let 
-TMP_204 \def (CHead x1 TMP_203 x) in (let TMP_205 \def (S O) in (let TMP_206 
-\def (lift TMP_205 n x) in (let TMP_207 \def (csubst1_bind b n u t TMP_206 H3 
-c0 x0 H5) in (let TMP_208 \def (S O) in (let TMP_209 \def (drop_skip_bind 
-TMP_208 n x0 x1 H6 b x) in (ex2_2_intro C C TMP_195 TMP_198 TMP_202 TMP_204 
-TMP_207 TMP_209)))))))))))))))))) in (ex2_2_ind C C TMP_181 TMP_183 TMP_191 
-TMP_210 H4)))))))))))))) in (ex_ind T TMP_168 TMP_176 TMP_211 H2))))))))))))) 
-in (let TMP_267 \def (\lambda (f: F).(\lambda (t: T).(\lambda (e: C).(\lambda 
-(u: T).(\lambda (H1: (getl (S n) (CHead c0 (Flat f) t) (CHead e (Bind Abbr) 
-u))).(let TMP_213 \def (S n) in (let H_x \def (subst1_ex u t TMP_213) in (let 
-H2 \def H_x in (let TMP_218 \def (\lambda (t2: T).(let TMP_214 \def (S n) in 
-(let TMP_215 \def (S O) in (let TMP_216 \def (S n) in (let TMP_217 \def (lift 
-TMP_215 TMP_216 t2) in (subst1 TMP_214 u t TMP_217)))))) in (let TMP_222 \def 
-(\lambda (a0: C).(\lambda (_: C).(let TMP_219 \def (S n) in (let TMP_220 \def 
-(Flat f) in (let TMP_221 \def (CHead c0 TMP_220 t) in (csubst1 TMP_219 u 
-TMP_221 a0)))))) in (let TMP_225 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_223 \def (S O) in (let TMP_224 \def (S n) in (drop TMP_223 TMP_224 a0 
-a))))) in (let TMP_226 \def (ex2_2 C C TMP_222 TMP_225) in (let TMP_266 \def 
-(\lambda (x: T).(\lambda (H3: (subst1 (S n) u t (lift (S O) (S n) x))).(let 
-TMP_227 \def (Flat f) in (let TMP_228 \def (Bind Abbr) in (let TMP_229 \def 
-(CHead e TMP_228 u) in (let TMP_230 \def (getl_gen_S TMP_227 c0 TMP_229 t n 
-H1) in (let H4 \def (H0 e u TMP_230) in (let TMP_232 \def (\lambda (a0: 
-C).(\lambda (_: C).(let TMP_231 \def (S n) in (csubst1 TMP_231 u c0 a0)))) in 
-(let TMP_235 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_233 \def (S O) in 
-(let TMP_234 \def (S n) in (drop TMP_233 TMP_234 a0 a))))) in (let TMP_239 
-\def (\lambda (a0: C).(\lambda (_: C).(let TMP_236 \def (S n) in (let TMP_237 
-\def (Flat f) in (let TMP_238 \def (CHead c0 TMP_237 t) in (csubst1 TMP_236 u 
-TMP_238 a0)))))) in (let TMP_242 \def (\lambda (a0: C).(\lambda (a: C).(let 
-TMP_240 \def (S O) in (let TMP_241 \def (S n) in (drop TMP_240 TMP_241 a0 
-a))))) in (let TMP_243 \def (ex2_2 C C TMP_239 TMP_242) in (let TMP_265 \def 
-(\lambda (x0: C).(\lambda (x1: C).(\lambda (H5: (csubst1 (S n) u c0 
-x0)).(\lambda (H6: (drop (S O) (S n) x0 x1)).(let TMP_247 \def (\lambda (a0: 
-C).(\lambda (_: C).(let TMP_244 \def (S n) in (let TMP_245 \def (Flat f) in 
-(let TMP_246 \def (CHead c0 TMP_245 t) in (csubst1 TMP_244 u TMP_246 a0)))))) 
-in (let TMP_250 \def (\lambda (a0: C).(\lambda (a: C).(let TMP_248 \def (S O) 
-in (let TMP_249 \def (S n) in (drop TMP_248 TMP_249 a0 a))))) in (let TMP_251 
-\def (Flat f) in (let TMP_252 \def (S O) in (let TMP_253 \def (S n) in (let 
-TMP_254 \def (lift TMP_252 TMP_253 x) in (let TMP_255 \def (CHead x0 TMP_251 
-TMP_254) in (let TMP_256 \def (Flat f) in (let TMP_257 \def (CHead x1 TMP_256 
-x) in (let TMP_258 \def (S n) in (let TMP_259 \def (S O) in (let TMP_260 \def 
-(S n) in (let TMP_261 \def (lift TMP_259 TMP_260 x) in (let TMP_262 \def 
-(csubst1_flat f TMP_258 u t TMP_261 H3 c0 x0 H5) in (let TMP_263 \def (S O) 
-in (let TMP_264 \def (drop_skip_flat TMP_263 n x0 x1 H6 f x) in (ex2_2_intro 
-C C TMP_247 TMP_250 TMP_255 TMP_257 TMP_262 TMP_264))))))))))))))))))))) in 
-(ex2_2_ind C C TMP_232 TMP_235 TMP_243 TMP_265 H4)))))))))))))) in (ex_ind T 
-TMP_218 TMP_226 TMP_266 H2)))))))))))))) in (K_ind TMP_165 TMP_212 TMP_267 
-k))))))) in (C_ind TMP_147 TMP_158 TMP_268 c))))))) in (nat_ind TMP_4 TMP_141 
-TMP_269 d)))).
+ \lambda (d: nat).(nat_ind (\lambda (n: nat).(\forall (c: C).(\forall (e: 
+C).(\forall (u: T).((getl n c (CHead e (Bind Abbr) u)) \to (ex2_2 C C 
+(\lambda (a0: C).(\lambda (_: C).(csubst1 n u c a0))) (\lambda (a0: 
+C).(\lambda (a: C).(drop (S O) n a0 a))))))))) (\lambda (c: C).(C_ind 
+(\lambda (c0: C).(\forall (e: C).(\forall (u: T).((getl O c0 (CHead e (Bind 
+Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O u c0 
+a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a)))))))) (\lambda 
+(n: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (H: (getl O (CSort n) 
+(CHead e (Bind Abbr) u))).(getl_gen_sort n O (CHead e (Bind Abbr) u) H (ex2_2 
+C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O u (CSort n) a0))) (\lambda 
+(a0: C).(\lambda (a: C).(drop (S O) O a0 a))))))))) (\lambda (c0: C).(\lambda 
+(H: ((\forall (e: C).(\forall (u: T).((getl O c0 (CHead e (Bind Abbr) u)) \to 
+(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O u c0 a0))) (\lambda 
+(a0: C).(\lambda (a: C).(drop (S O) O a0 a))))))))).(\lambda (k: K).(K_ind 
+(\lambda (k0: K).(\forall (t: T).(\forall (e: C).(\forall (u: T).((getl O 
+(CHead c0 k0 t) (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: 
+C).(\lambda (_: C).(csubst1 O u (CHead c0 k0 t) a0))) (\lambda (a0: 
+C).(\lambda (a: C).(drop (S O) O a0 a))))))))) (\lambda (b: B).(\lambda (t: 
+T).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl O (CHead c0 (Bind b) 
+t) (CHead e (Bind Abbr) u))).(let H1 \def (f_equal C C (\lambda (e0: 
+C).(match e0 with [(CSort _) \Rightarrow e | (CHead c1 _ _) \Rightarrow c1])) 
+(CHead e (Bind Abbr) u) (CHead c0 (Bind b) t) (clear_gen_bind b c0 (CHead e 
+(Bind Abbr) u) t (getl_gen_O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u) 
+H0))) in ((let H2 \def (f_equal C B (\lambda (e0: C).(match e0 with [(CSort 
+_) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) 
+\Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead e (Bind Abbr) u) 
+(CHead c0 (Bind b) t) (clear_gen_bind b c0 (CHead e (Bind Abbr) u) t 
+(getl_gen_O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u) H0))) in ((let H3 
+\def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | 
+(CHead _ _ t0) \Rightarrow t0])) (CHead e (Bind Abbr) u) (CHead c0 (Bind b) 
+t) (clear_gen_bind b c0 (CHead e (Bind Abbr) u) t (getl_gen_O (CHead c0 (Bind 
+b) t) (CHead e (Bind Abbr) u) H0))) in (\lambda (H4: (eq B Abbr b)).(\lambda 
+(_: (eq C e c0)).(eq_ind_r T t (\lambda (t0: T).(ex2_2 C C (\lambda (a0: 
+C).(\lambda (_: C).(csubst1 O t0 (CHead c0 (Bind b) t) a0))) (\lambda (a0: 
+C).(\lambda (a: C).(drop (S O) O a0 a))))) (eq_ind B Abbr (\lambda (b0: 
+B).(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O t (CHead c0 (Bind 
+b0) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a))))) 
+(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O t (CHead c0 
+(Bind Abbr) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a))) 
+(CHead c0 (Bind Abbr) t) c0 (csubst1_refl O t (CHead c0 (Bind Abbr) t)) 
+(drop_drop (Bind Abbr) O c0 c0 (drop_refl c0) t)) b H4) u H3)))) H2)) 
+H1))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (e: C).(\lambda (u: 
+T).(\lambda (H0: (getl O (CHead c0 (Flat f) t) (CHead e (Bind Abbr) u))).(let 
+H_x \def (subst1_ex u t O) in (let H1 \def H_x in (ex_ind T (\lambda (t2: 
+T).(subst1 O u t (lift (S O) O t2))) (ex2_2 C C (\lambda (a0: C).(\lambda (_: 
+C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: 
+C).(drop (S O) O a0 a)))) (\lambda (x: T).(\lambda (H2: (subst1 O u t (lift 
+(S O) O x))).(let H3 \def (H e u (getl_intro O c0 (CHead e (Bind Abbr) u) c0 
+(drop_refl c0) (clear_gen_flat f c0 (CHead e (Bind Abbr) u) t (getl_gen_O 
+(CHead c0 (Flat f) t) (CHead e (Bind Abbr) u) H0)))) in (ex2_2_ind C C 
+(\lambda (a0: C).(\lambda (_: C).(csubst1 O u c0 a0))) (\lambda (a0: 
+C).(\lambda (a: C).(drop (S O) O a0 a))) (ex2_2 C C (\lambda (a0: C).(\lambda 
+(_: C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: 
+C).(drop (S O) O a0 a)))) (\lambda (x0: C).(\lambda (x1: C).(\lambda (H4: 
+(csubst1 O u c0 x0)).(\lambda (H5: (drop (S O) O x0 x1)).(ex2_2_intro C C 
+(\lambda (a0: C).(\lambda (_: C).(csubst1 O u (CHead c0 (Flat f) t) a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a))) (CHead x0 (Flat f) 
+(lift (S O) O x)) x1 (csubst1_flat f O u t (lift (S O) O x) H2 c0 x0 H4) 
+(drop_drop (Flat f) O x0 x1 H5 (lift (S O) O x))))))) H3)))) H1)))))))) k)))) 
+c)) (\lambda (n: nat).(\lambda (H: ((\forall (c: C).(\forall (e: C).(\forall 
+(u: T).((getl n c (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: 
+C).(\lambda (_: C).(csubst1 n u c a0))) (\lambda (a0: C).(\lambda (a: 
+C).(drop (S O) n a0 a)))))))))).(\lambda (c: C).(C_ind (\lambda (c0: 
+C).(\forall (e: C).(\forall (u: T).((getl (S n) c0 (CHead e (Bind Abbr) u)) 
+\to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u c0 a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))))))) (\lambda (n0: 
+nat).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl (S n) (CSort n0) 
+(CHead e (Bind Abbr) u))).(getl_gen_sort n0 (S n) (CHead e (Bind Abbr) u) H0 
+(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CSort n0) a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))))))))) (\lambda 
+(c0: C).(\lambda (H0: ((\forall (e: C).(\forall (u: T).((getl (S n) c0 (CHead 
+e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S 
+n) u c0 a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 
+a))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t: T).(\forall 
+(e: C).(\forall (u: T).((getl (S n) (CHead c0 k0 t) (CHead e (Bind Abbr) u)) 
+\to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 k0 
+t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))))))))) 
+(\lambda (b: B).(\lambda (t: T).(\lambda (e: C).(\lambda (u: T).(\lambda (H1: 
+(getl (S n) (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u))).(let H_x \def 
+(subst1_ex u t n) in (let H2 \def H_x in (ex_ind T (\lambda (t2: T).(subst1 n 
+u t (lift (S O) n t2))) (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 
+(S n) u (CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S 
+O) (S n) a0 a)))) (\lambda (x: T).(\lambda (H3: (subst1 n u t (lift (S O) n 
+x))).(let H4 \def (H c0 e u (getl_gen_S (Bind b) c0 (CHead e (Bind Abbr) u) t 
+n H1)) in (ex2_2_ind C C (\lambda (a0: C).(\lambda (_: C).(csubst1 n u c0 
+a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) n a0 a))) (ex2_2 C C 
+(\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Bind b) t) a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0: 
+C).(\lambda (x1: C).(\lambda (H5: (csubst1 n u c0 x0)).(\lambda (H6: (drop (S 
+O) n x0 x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) 
+u (CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S 
+n) a0 a))) (CHead x0 (Bind b) (lift (S O) n x)) (CHead x1 (Bind b) x) 
+(csubst1_bind b n u t (lift (S O) n x) H3 c0 x0 H5) (drop_skip_bind (S O) n 
+x0 x1 H6 b x)))))) H4)))) H2)))))))) (\lambda (f: F).(\lambda (t: T).(\lambda 
+(e: C).(\lambda (u: T).(\lambda (H1: (getl (S n) (CHead c0 (Flat f) t) (CHead 
+e (Bind Abbr) u))).(let H_x \def (subst1_ex u t (S n)) in (let H2 \def H_x in 
+(ex_ind T (\lambda (t2: T).(subst1 (S n) u t (lift (S O) (S n) t2))) (ex2_2 C 
+C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Flat f) t) 
+a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda 
+(x: T).(\lambda (H3: (subst1 (S n) u t (lift (S O) (S n) x))).(let H4 \def 
+(H0 e u (getl_gen_S (Flat f) c0 (CHead e (Bind Abbr) u) t n H1)) in 
+(ex2_2_ind C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u c0 a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))) (ex2_2 C C 
+(\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Flat f) t) a0))) 
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0: 
+C).(\lambda (x1: C).(\lambda (H5: (csubst1 (S n) u c0 x0)).(\lambda (H6: 
+(drop (S O) (S n) x0 x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: 
+C).(csubst1 (S n) u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: 
+C).(drop (S O) (S n) a0 a))) (CHead x0 (Flat f) (lift (S O) (S n) x)) (CHead 
+x1 (Flat f) x) (csubst1_flat f (S n) u t (lift (S O) (S n) x) H3 c0 x0 H5) 
+(drop_skip_flat (S O) n x0 x1 H6 f x)))))) H4)))) H2)))))))) k)))) c)))) d).