X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FLAMBDA-TYPES%2FLevel-1%2FLambdaDelta%2Fcsub3%2Fgetl.ma;h=acb352ea3db74f8c8e0eb9e513cea0e9727154a9;hb=94873bb61a663b4fca3dc6d07b7bb9f42122003e;hp=68f1d825e330b6b0e2a153eebc63bde1347254a0;hpb=884ac867259b5303a8f6c64faaf1591bd96a264e;p=helm.git

diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/csub3/getl.ma b/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/csub3/getl.ma
index 68f1d825e..acb352ea3 100644
--- a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/csub3/getl.ma
+++ b/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/csub3/getl.ma
@@ -37,105 +37,108 @@ C).(drop n O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abbr) u)))
 (\forall (c2: C).((csub3 g c1 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 
 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u)))))) (\lambda (x: 
 C).(\lambda (H1: (drop n O c1 x)).(\lambda (H2: (clear x (CHead d1 (Bind 
-Abbr) u))).((match x in C return (\lambda (c: C).((drop n O c1 c) \to ((clear 
-c (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csub3 g c1 c2) \to (ex2 C 
+Abbr) u))).(C_ind (\lambda (c: C).((drop n O c1 c) \to ((clear c (CHead d1 
+(Bind Abbr) u)) \to (\forall (c2: C).((csub3 g c1 c2) \to (ex2 C (\lambda 
+(d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) 
+u))))))))) (\lambda (n0: nat).(\lambda (_: (drop n O c1 (CSort n0))).(\lambda 
+(H4: (clear (CSort n0) (CHead d1 (Bind Abbr) u))).(clear_gen_sort (CHead d1 
+(Bind Abbr) u) n0 H4 (\forall (c2: C).((csub3 g c1 c2) \to (ex2 C (\lambda 
+(d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) 
+u)))))))))) (\lambda (x0: C).(\lambda (_: (((drop n O c1 x0) \to ((clear x0 
+(CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csub3 g c1 c2) \to (ex2 C 
 (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind 
-Abbr) u))))))))) with [(CSort n0) \Rightarrow (\lambda (_: (drop n O c1 
-(CSort n0))).(\lambda (H4: (clear (CSort n0) (CHead d1 (Bind Abbr) 
-u))).(clear_gen_sort (CHead d1 (Bind Abbr) u) n0 H4 (\forall (c2: C).((csub3 
-g c1 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl 
-n c2 (CHead d2 (Bind Abbr) u))))))))) | (CHead c k t) \Rightarrow (\lambda 
-(H3: (drop n O c1 (CHead c k t))).(\lambda (H4: (clear (CHead c k t) (CHead 
-d1 (Bind Abbr) u))).((match k in K return (\lambda (k0: K).((drop n O c1 
-(CHead c k0 t)) \to ((clear (CHead c k0 t) (CHead d1 (Bind Abbr) u)) \to 
-(\forall (c2: C).((csub3 g c1 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))))))))) with [(Bind 
-b) \Rightarrow (\lambda (H5: (drop n O c1 (CHead c (Bind b) t))).(\lambda 
-(H6: (clear (CHead c (Bind b) t) (CHead d1 (Bind Abbr) u))).(let H7 \def 
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with 
-[(CSort _) \Rightarrow d1 | (CHead c0 _ _) \Rightarrow c0])) (CHead d1 (Bind 
-Abbr) u) (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind Abbr) u) t 
-H6)) in ((let H8 \def (f_equal C B (\lambda (e: C).(match e in C return 
-(\lambda (_: C).B) with [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) 
-\Rightarrow (match k0 in K return (\lambda (_: K).B) with [(Bind b0) 
-\Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u) 
-(CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind Abbr) u) t H6)) in 
-((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: 
-C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead 
-d1 (Bind Abbr) u) (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind 
-Abbr) u) t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 
-c)).(\lambda (c2: C).(\lambda (H12: (csub3 g c1 c2)).(let H13 \def (eq_ind_r 
-T t (\lambda (t0: T).(drop n O c1 (CHead c (Bind b) t0))) H5 u H9) in (let 
-H14 \def (eq_ind_r B b (\lambda (b0: B).(drop n O c1 (CHead c (Bind b0) u))) 
-H13 Abbr H10) in (let H15 \def (eq_ind_r C c (\lambda (c0: C).(drop n O c1 
-(CHead c0 (Bind Abbr) u))) H14 d1 H11) in (ex2_ind C (\lambda (d2: C).(csub3 
-g d1 d2)) (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abbr) u))) (ex2 C 
-(\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind 
-Abbr) u)))) (\lambda (x0: C).(\lambda (H16: (csub3 g d1 x0)).(\lambda (H17: 
-(drop n O c2 (CHead x0 (Bind Abbr) u))).(ex_intro2 C (\lambda (d2: C).(csub3 
-g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))) x0 H16 
-(getl_intro n c2 (CHead x0 (Bind Abbr) u) (CHead x0 (Bind Abbr) u) H17 
-(clear_bind Abbr x0 u)))))) (csub3_drop_abbr g n c1 c2 H12 d1 u H15)))))))))) 
-H8)) H7)))) | (Flat f) \Rightarrow (\lambda (H5: (drop n O c1 (CHead c (Flat 
-f) t))).(\lambda (H6: (clear (CHead c (Flat f) t) (CHead d1 (Bind Abbr) 
-u))).(let H7 \def H5 in (unintro C c1 (\lambda (c0: C).((drop n O c0 (CHead c 
-(Flat f) t)) \to (\forall (c2: C).((csub3 g c0 c2) \to (ex2 C (\lambda (d2: 
-C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) 
-u)))))))) (nat_ind (\lambda (n0: nat).(\forall (x0: C).((drop n0 O x0 (CHead 
-c (Flat f) t)) \to (\forall (c2: C).((csub3 g x0 c2) \to (ex2 C (\lambda (d2: 
-C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n0 c2 (CHead d2 (Bind Abbr) 
-u))))))))) (\lambda (x0: C).(\lambda (H8: (drop O O x0 (CHead c (Flat f) 
-t))).(\lambda (c2: C).(\lambda (H9: (csub3 g x0 c2)).(let H10 \def (eq_ind C 
-x0 (\lambda (c0: C).(csub3 g c0 c2)) H9 (CHead c (Flat f) t) (drop_gen_refl 
-x0 (CHead c (Flat f) t) H8)) in (let H_y \def (clear_flat c (CHead d1 (Bind 
-Abbr) u) (clear_gen_flat f c (CHead d1 (Bind Abbr) u) t H6) f t) in (let H11 
-\def (csub3_clear_conf g (CHead c (Flat f) t) c2 H10 (CHead d1 (Bind Abbr) u) 
+Abbr) u)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (H3: (drop n O c1 
+(CHead x0 k t))).(\lambda (H4: (clear (CHead x0 k t) (CHead d1 (Bind Abbr) 
+u))).(K_ind (\lambda (k0: K).((drop n O c1 (CHead x0 k0 t)) \to ((clear 
+(CHead x0 k0 t) (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csub3 g c1 
+c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 
+(CHead d2 (Bind Abbr) u))))))))) (\lambda (b: B).(\lambda (H5: (drop n O c1 
+(CHead x0 (Bind b) t))).(\lambda (H6: (clear (CHead x0 (Bind b) t) (CHead d1 
+(Bind Abbr) u))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C 
+return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) 
+\Rightarrow c])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t) 
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H8 \def 
+(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with 
+[(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 in K 
+return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) 
+\Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t) 
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H9 \def 
+(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with 
+[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind 
+Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) 
+t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda 
+(c2: C).(\lambda (H12: (csub3 g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda 
+(t0: T).(drop n O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def 
+(eq_ind_r B b (\lambda (b0: B).(drop n O c1 (CHead x0 (Bind b0) u))) H13 Abbr 
+H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop n O c1 (CHead c 
+(Bind Abbr) u))) H14 d1 H11) in (ex2_ind C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abbr) u))) (ex2 C (\lambda (d2: 
+C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u)))) 
+(\lambda (x1: C).(\lambda (H16: (csub3 g d1 x1)).(\lambda (H17: (drop n O c2 
+(CHead x1 (Bind Abbr) u))).(ex_intro2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))) x1 H16 (getl_intro n 
+c2 (CHead x1 (Bind Abbr) u) (CHead x1 (Bind Abbr) u) H17 (clear_bind Abbr x1 
+u)))))) (csub3_drop_abbr g n c1 c2 H12 d1 u H15)))))))))) H8)) H7))))) 
+(\lambda (f: F).(\lambda (H5: (drop n O c1 (CHead x0 (Flat f) t))).(\lambda 
+(H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abbr) u))).(let H7 \def H5 
+in (unintro C c1 (\lambda (c: C).((drop n O c (CHead x0 (Flat f) t)) \to 
+(\forall (c2: C).((csub3 g c c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u)))))))) (nat_ind (\lambda 
+(n0: nat).(\forall (x1: C).((drop n0 O x1 (CHead x0 (Flat f) t)) \to (\forall 
+(c2: C).((csub3 g x1 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n0 c2 (CHead d2 (Bind Abbr) u))))))))) (\lambda (x1: 
+C).(\lambda (H8: (drop O O x1 (CHead x0 (Flat f) t))).(\lambda (c2: 
+C).(\lambda (H9: (csub3 g x1 c2)).(let H10 \def (eq_ind C x1 (\lambda (c: 
+C).(csub3 g c c2)) H9 (CHead x0 (Flat f) t) (drop_gen_refl x1 (CHead x0 (Flat 
+f) t) H8)) in (let H_y \def (clear_flat x0 (CHead d1 (Bind Abbr) u) 
+(clear_gen_flat f x0 (CHead d1 (Bind Abbr) u) t H6) f t) in (let H11 \def 
+(csub3_clear_conf g (CHead x0 (Flat f) t) c2 H10 (CHead d1 (Bind Abbr) u) 
 H_y) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead d1 (Bind Abbr) u) e2)) 
 (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
-(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (x1: 
-C).(\lambda (H12: (csub3 g (CHead d1 (Bind Abbr) u) x1)).(\lambda (H13: 
-(clear c2 x1)).(let H14 \def (csub3_gen_abbr g d1 x1 u H12) in (ex2_ind C 
-(\lambda (e2: C).(eq C x1 (CHead e2 (Bind Abbr) u))) (\lambda (e2: C).(csub3 
+(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (x2: 
+C).(\lambda (H12: (csub3 g (CHead d1 (Bind Abbr) u) x2)).(\lambda (H13: 
+(clear c2 x2)).(let H14 \def (csub3_gen_abbr g d1 x2 u H12) in (ex2_ind C 
+(\lambda (e2: C).(eq C x2 (CHead e2 (Bind Abbr) u))) (\lambda (e2: C).(csub3 
 g d1 e2)) (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl O 
-c2 (CHead d2 (Bind Abbr) u)))) (\lambda (x2: C).(\lambda (H15: (eq C x1 
-(CHead x2 (Bind Abbr) u))).(\lambda (H16: (csub3 g d1 x2)).(let H17 \def 
-(eq_ind C x1 (\lambda (c0: C).(clear c2 c0)) H13 (CHead x2 (Bind Abbr) u) 
-H15) in (ex_intro2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl 
-O c2 (CHead d2 (Bind Abbr) u))) x2 H16 (getl_intro O c2 (CHead x2 (Bind Abbr) 
-u) c2 (drop_refl c2) H17)))))) H14))))) H11)))))))) (\lambda (n0: 
-nat).(\lambda (H8: ((\forall (x0: C).((drop n0 O x0 (CHead c (Flat f) t)) \to 
-(\forall (c2: C).((csub3 g x0 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(getl n0 c2 (CHead d2 (Bind Abbr) u)))))))))).(\lambda 
-(x0: C).(\lambda (H9: (drop (S n0) O x0 (CHead c (Flat f) t))).(\lambda (c2: 
-C).(\lambda (H10: (csub3 g x0 c2)).(let H11 \def (drop_clear x0 (CHead c 
+c2 (CHead d2 (Bind Abbr) u)))) (\lambda (x3: C).(\lambda (H15: (eq C x2 
+(CHead x3 (Bind Abbr) u))).(\lambda (H16: (csub3 g d1 x3)).(let H17 \def 
+(eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Abbr) u) H15) 
+in (ex_intro2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl O c2 
+(CHead d2 (Bind Abbr) u))) x3 H16 (getl_intro O c2 (CHead x3 (Bind Abbr) u) 
+c2 (drop_refl c2) H17)))))) H14))))) H11)))))))) (\lambda (n0: nat).(\lambda 
+(H8: ((\forall (x1: C).((drop n0 O x1 (CHead x0 (Flat f) t)) \to (\forall 
+(c2: C).((csub3 g x1 c2) \to (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n0 c2 (CHead d2 (Bind Abbr) u)))))))))).(\lambda (x1: 
+C).(\lambda (H9: (drop (S n0) O x1 (CHead x0 (Flat f) t))).(\lambda (c2: 
+C).(\lambda (H10: (csub3 g x1 c2)).(let H11 \def (drop_clear x1 (CHead x0 
 (Flat f) t) n0 H9) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e: 
-C).(\lambda (v: T).(clear x0 (CHead e (Bind b) v))))) (\lambda (_: 
-B).(\lambda (e: C).(\lambda (_: T).(drop n0 O e (CHead c (Flat f) t))))) (ex2 
-C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead 
-d2 (Bind Abbr) u)))) (\lambda (x1: B).(\lambda (x2: C).(\lambda (x3: 
-T).(\lambda (H12: (clear x0 (CHead x2 (Bind x1) x3))).(\lambda (H13: (drop n0 
-O x2 (CHead c (Flat f) t))).(let H14 \def (csub3_clear_conf g x0 c2 H10 
-(CHead x2 (Bind x1) x3) H12) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead 
-x2 (Bind x1) x3) e2)) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2: 
+C).(\lambda (v: T).(clear x1 (CHead e (Bind b) v))))) (\lambda (_: 
+B).(\lambda (e: C).(\lambda (_: T).(drop n0 O e (CHead x0 (Flat f) t))))) 
+(ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 
+(CHead d2 (Bind Abbr) u)))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: 
+T).(\lambda (H12: (clear x1 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n0 
+O x3 (CHead x0 (Flat f) t))).(let H14 \def (csub3_clear_conf g x1 c2 H10 
+(CHead x3 (Bind x2) x4) H12) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead 
+x3 (Bind x2) x4) e2)) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2: 
 C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abbr) 
-u)))) (\lambda (x4: C).(\lambda (H15: (csub3 g (CHead x2 (Bind x1) x3) 
-x4)).(\lambda (H16: (clear c2 x4)).(let H17 \def (csub3_gen_bind g x1 x2 x4 
-x3 H15) in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: 
-T).(eq C x4 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: 
-C).(\lambda (_: T).(csub3 g x2 e2)))) (ex2 C (\lambda (d2: C).(csub3 g d1 
+u)))) (\lambda (x5: C).(\lambda (H15: (csub3 g (CHead x3 (Bind x2) x4) 
+x5)).(\lambda (H16: (clear c2 x5)).(let H17 \def (csub3_gen_bind g x2 x3 x5 
+x4 H15) in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: 
+T).(eq C x5 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: 
+C).(\lambda (_: T).(csub3 g x3 e2)))) (ex2 C (\lambda (d2: C).(csub3 g d1 
 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda 
-(x5: B).(\lambda (x6: C).(\lambda (x7: T).(\lambda (H18: (eq C x4 (CHead x6 
-(Bind x5) x7))).(\lambda (H19: (csub3 g x2 x6)).(let H20 \def (eq_ind C x4 
-(\lambda (c0: C).(clear c2 c0)) H16 (CHead x6 (Bind x5) x7) H18) in (let H21 
-\def (H8 x2 H13 x6 H19) in (ex2_ind C (\lambda (d2: C).(csub3 g d1 d2)) 
-(\lambda (d2: C).(getl n0 x6 (CHead d2 (Bind Abbr) u))) (ex2 C (\lambda (d2: 
+(x6: B).(\lambda (x7: C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 
+(Bind x6) x8))).(\lambda (H19: (csub3 g x3 x7)).(let H20 \def (eq_ind C x5 
+(\lambda (c: C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 
+\def (H8 x3 H13 x7 H19) in (ex2_ind C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n0 x7 (CHead d2 (Bind Abbr) u))) (ex2 C (\lambda (d2: 
 C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abbr) 
-u)))) (\lambda (x8: C).(\lambda (H22: (csub3 g d1 x8)).(\lambda (H23: (getl 
-n0 x6 (CHead x8 (Bind Abbr) u))).(ex_intro2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abbr) u))) x8 H22 
-(getl_clear_bind x5 c2 x6 x7 H20 (CHead x8 (Bind Abbr) u) n0 H23))))) 
-H21)))))))) H17))))) H14))))))) H11)))))))) n) H7))))]) H3 H4)))]) H1 H2)))) 
-H0))))))).
+u)))) (\lambda (x9: C).(\lambda (H22: (csub3 g d1 x9)).(\lambda (H23: (getl 
+n0 x7 (CHead x9 (Bind Abbr) u))).(ex_intro2 C (\lambda (d2: C).(csub3 g d1 
+d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abbr) u))) x9 H22 
+(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abbr) u) n0 H23))))) 
+H21)))))))) H17))))) H14))))))) H11)))))))) n) H7))))) k H3 H4))))))) x H1 
+H2)))) H0))))))).
 
 theorem csub3_getl_abst:
  \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (t: T).(\forall 
@@ -155,69 +158,74 @@ d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T
 (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
 (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
 T).(ty3 g d2 u t))))))) (\lambda (x: C).(\lambda (H1: (drop n O c1 
-x)).(\lambda (H2: (clear x (CHead d1 (Bind Abst) t))).((match x in C return 
-(\lambda (c: C).((drop n O c1 c) \to ((clear c (CHead d1 (Bind Abst) t)) \to 
-(\forall (c2: C).((csub3 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
-(\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
-(u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
-T).(ty3 g d2 u t)))))))))) with [(CSort n0) \Rightarrow (\lambda (_: (drop n 
-O c1 (CSort n0))).(\lambda (H4: (clear (CSort n0) (CHead d1 (Bind Abst) 
+x)).(\lambda (H2: (clear x (CHead d1 (Bind Abst) t))).(C_ind (\lambda (c: 
+C).((drop n O c1 c) \to ((clear c (CHead d1 (Bind Abst) t)) \to (\forall (c2: 
+C).((csub3 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
+(d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
+C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
+c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
+t)))))))))) (\lambda (n0: nat).(\lambda (_: (drop n O c1 (CSort 
+n0))).(\lambda (H4: (clear (CSort n0) (CHead d1 (Bind Abst) 
 t))).(clear_gen_sort (CHead d1 (Bind Abst) t) n0 H4 (\forall (c2: C).((csub3 
 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
 C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t)))))))))) | (CHead c k t0) \Rightarrow (\lambda (H3: (drop n O c1 (CHead c 
-k t0))).(\lambda (H4: (clear (CHead c k t0) (CHead d1 (Bind Abst) 
-t))).((match k in K return (\lambda (k0: K).((drop n O c1 (CHead c k0 t0)) 
-\to ((clear (CHead c k0 t0) (CHead d1 (Bind Abst) t)) \to (\forall (c2: 
-C).((csub3 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
-c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t)))))))))) with [(Bind b) \Rightarrow (\lambda (H5: (drop n O c1 (CHead c 
-(Bind b) t0))).(\lambda (H6: (clear (CHead c (Bind b) t0) (CHead d1 (Bind 
-Abst) t))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return 
-(\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c0 _ _) 
-\Rightarrow c0])) (CHead d1 (Bind Abst) t) (CHead c (Bind b) t0) 
-(clear_gen_bind b c (CHead d1 (Bind Abst) t) t0 H6)) in ((let H8 \def 
+t))))))))))) (\lambda (x0: C).(\lambda (_: (((drop n O c1 x0) \to ((clear x0 
+(CHead d1 (Bind Abst) t)) \to (\forall (c2: C).((csub3 g c1 c2) \to (or (ex2 
+C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 
+(Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 
+d2))) (\lambda (d2: C).(\lambda (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) 
+(\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))))))))).(\lambda (k: 
+K).(\lambda (t0: T).(\lambda (H3: (drop n O c1 (CHead x0 k t0))).(\lambda 
+(H4: (clear (CHead x0 k t0) (CHead d1 (Bind Abst) t))).(K_ind (\lambda (k0: 
+K).((drop n O c1 (CHead x0 k0 t0)) \to ((clear (CHead x0 k0 t0) (CHead d1 
+(Bind Abst) t)) \to (\forall (c2: C).((csub3 g c1 c2) \to (or (ex2 C (\lambda 
+(d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) 
+t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda 
+(d2: C).(\lambda (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: 
+C).(\lambda (u: T).(ty3 g d2 u t)))))))))) (\lambda (b: B).(\lambda (H5: 
+(drop n O c1 (CHead x0 (Bind b) t0))).(\lambda (H6: (clear (CHead x0 (Bind b) 
+t0) (CHead d1 (Bind Abst) t))).(let H7 \def (f_equal C C (\lambda (e: 
+C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | 
+(CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) t) (CHead x0 (Bind b) 
+t0) (clear_gen_bind b x0 (CHead d1 (Bind Abst) t) t0 H6)) in ((let H8 \def 
 (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with 
 [(CSort _) \Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0 in K 
 return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) 
-\Rightarrow Abst])])) (CHead d1 (Bind Abst) t) (CHead c (Bind b) t0) 
-(clear_gen_bind b c (CHead d1 (Bind Abst) t) t0 H6)) in ((let H9 \def 
+\Rightarrow Abst])])) (CHead d1 (Bind Abst) t) (CHead x0 (Bind b) t0) 
+(clear_gen_bind b x0 (CHead d1 (Bind Abst) t) t0 H6)) in ((let H9 \def 
 (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with 
 [(CSort _) \Rightarrow t | (CHead _ _ t1) \Rightarrow t1])) (CHead d1 (Bind 
-Abst) t) (CHead c (Bind b) t0) (clear_gen_bind b c (CHead d1 (Bind Abst) t) 
-t0 H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 c)).(\lambda 
-(c2: C).(\lambda (H12: (csub3 g c1 c2)).(let H13 \def (eq_ind_r T t0 (\lambda 
-(t1: T).(drop n O c1 (CHead c (Bind b) t1))) H5 t H9) in (let H14 \def 
-(eq_ind_r B b (\lambda (b0: B).(drop n O c1 (CHead c (Bind b0) t))) H13 Abst 
-H10) in (let H15 \def (eq_ind_r C c (\lambda (c0: C).(drop n O c1 (CHead c0 
-(Bind Abst) t))) H14 d1 H11) in (or_ind (ex2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
+Abst) t) (CHead x0 (Bind b) t0) (clear_gen_bind b x0 (CHead d1 (Bind Abst) t) 
+t0 H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 
+x0)).(\lambda (c2: C).(\lambda (H12: (csub3 g c1 c2)).(let H13 \def (eq_ind_r 
+T t0 (\lambda (t1: T).(drop n O c1 (CHead x0 (Bind b) t1))) H5 t H9) in (let 
+H14 \def (eq_ind_r B b (\lambda (b0: B).(drop n O c1 (CHead x0 (Bind b0) t))) 
+H13 Abst H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop n O c1 
+(CHead c (Bind Abst) t))) H14 d1 H11) in (or_ind (ex2 C (\lambda (d2: 
+C).(csub3 g d1 d2)) (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) t)))) 
+(ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: 
+C).(\lambda (u: T).(drop n O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: 
+C).(\lambda (u: T).(ty3 g d2 u t)))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 
+d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
-(u: T).(drop n O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
-T).(ty3 g d2 u t)))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
+(u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
+T).(ty3 g d2 u t))))) (\lambda (H16: (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) t))))).(ex2_ind C 
+(\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(drop n O c2 (CHead d2 
+(Bind Abst) t))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
+C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t))))) (\lambda (H16: (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
-C).(drop n O c2 (CHead d2 (Bind Abst) t))))).(ex2_ind C (\lambda (d2: 
-C).(csub3 g d1 d2)) (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) t))) 
-(or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 
-(CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: 
-T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n c2 (CHead d2 
-(Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) 
-(\lambda (x0: C).(\lambda (H17: (csub3 g d1 x0)).(\lambda (H18: (drop n O c2 
-(CHead x0 (Bind Abst) t))).(or_introl (ex2 C (\lambda (d2: C).(csub3 g d1 
-d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
+t))))) (\lambda (x1: C).(\lambda (H17: (csub3 g d1 x1)).(\lambda (H18: (drop 
+n O c2 (CHead x1 (Bind Abst) t))).(or_introl (ex2 C (\lambda (d2: C).(csub3 g 
+d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
 (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
 T).(ty3 g d2 u t)))) (ex_intro2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl n c2 (CHead d2 (Bind Abst) t))) x0 H17 (getl_intro n c2 (CHead 
-x0 (Bind Abst) t) (CHead x0 (Bind Abst) t) H18 (clear_bind Abst x0 t))))))) 
+(d2: C).(getl n c2 (CHead d2 (Bind Abst) t))) x1 H17 (getl_intro n c2 (CHead 
+x1 (Bind Abst) t) (CHead x1 (Bind Abst) t) H18 (clear_bind Abst x1 t))))))) 
 H16)) (\lambda (H16: (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 
 d2))) (\lambda (d2: C).(\lambda (u: T).(drop n O c2 (CHead d2 (Bind Abbr) 
 u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))).(ex3_2_ind C T 
@@ -227,164 +235,164 @@ T).(ty3 g d2 u t))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda
 (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H17: (csub3 g d1 
-x0)).(\lambda (H18: (drop n O c2 (CHead x0 (Bind Abbr) x1))).(\lambda (H19: 
-(ty3 g x0 x1 t)).(or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
+t))))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (H17: (csub3 g d1 
+x1)).(\lambda (H18: (drop n O c2 (CHead x1 (Bind Abbr) x2))).(\lambda (H19: 
+(ty3 g x1 x2 t)).(or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
 (d2: C).(getl n c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n 
 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
 t)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) 
 (\lambda (d2: C).(\lambda (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) 
-(\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x0 x1 H17 (getl_intro n c2 
-(CHead x0 (Bind Abbr) x1) (CHead x0 (Bind Abbr) x1) H18 (clear_bind Abbr x0 
-x1)) H19))))))) H16)) (csub3_drop_abst g n c1 c2 H12 d1 t H15)))))))))) H8)) 
-H7)))) | (Flat f) \Rightarrow (\lambda (H5: (drop n O c1 (CHead c (Flat f) 
-t0))).(\lambda (H6: (clear (CHead c (Flat f) t0) (CHead d1 (Bind Abst) 
-t))).(let H7 \def H5 in (unintro C c1 (\lambda (c0: C).((drop n O c0 (CHead c 
-(Flat f) t0)) \to (\forall (c2: C).((csub3 g c0 c2) \to (or (ex2 C (\lambda 
+(\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x1 x2 H17 (getl_intro n c2 
+(CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2) H18 (clear_bind Abbr x1 
+x2)) H19))))))) H16)) (csub3_drop_abst g n c1 c2 H12 d1 t H15)))))))))) H8)) 
+H7))))) (\lambda (f: F).(\lambda (H5: (drop n O c1 (CHead x0 (Flat f) 
+t0))).(\lambda (H6: (clear (CHead x0 (Flat f) t0) (CHead d1 (Bind Abst) 
+t))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop n O c (CHead x0 
+(Flat f) t0)) \to (\forall (c2: C).((csub3 g c c2) \to (or (ex2 C (\lambda 
 (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) 
 t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda 
 (d2: C).(\lambda (u: T).(getl n c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: 
 C).(\lambda (u: T).(ty3 g d2 u t))))))))) (nat_ind (\lambda (n0: 
-nat).(\forall (x0: C).((drop n0 O x0 (CHead c (Flat f) t0)) \to (\forall (c2: 
-C).((csub3 g x0 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl n0 c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl 
-n0 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 
-u t)))))))))) (\lambda (x0: C).(\lambda (H8: (drop O O x0 (CHead c (Flat f) 
-t0))).(\lambda (c2: C).(\lambda (H9: (csub3 g x0 c2)).(let H10 \def (eq_ind C 
-x0 (\lambda (c0: C).(csub3 g c0 c2)) H9 (CHead c (Flat f) t0) (drop_gen_refl 
-x0 (CHead c (Flat f) t0) H8)) in (let H_y \def (clear_flat c (CHead d1 (Bind 
-Abst) t) (clear_gen_flat f c (CHead d1 (Bind Abst) t) t0 H6) f t0) in (let 
-H11 \def (csub3_clear_conf g (CHead c (Flat f) t0) c2 H10 (CHead d1 (Bind 
-Abst) t) H_y) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead d1 (Bind Abst) 
-t) e2)) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(csub3 g 
-d1 d2)) (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
-(\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
-(u: T).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
-T).(ty3 g d2 u t))))) (\lambda (x1: C).(\lambda (H12: (csub3 g (CHead d1 
-(Bind Abst) t) x1)).(\lambda (H13: (clear c2 x1)).(let H14 \def 
-(csub3_gen_abst g d1 x1 t H12) in (or_ind (ex2 C (\lambda (e2: C).(eq C x1 
+nat).(\forall (x1: C).((drop n0 O x1 (CHead x0 (Flat f) t0)) \to (\forall 
+(c2: C).((csub3 g x1 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl n0 c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda 
+(d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: 
+T).(getl n0 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
+T).(ty3 g d2 u t)))))))))) (\lambda (x1: C).(\lambda (H8: (drop O O x1 (CHead 
+x0 (Flat f) t0))).(\lambda (c2: C).(\lambda (H9: (csub3 g x1 c2)).(let H10 
+\def (eq_ind C x1 (\lambda (c: C).(csub3 g c c2)) H9 (CHead x0 (Flat f) t0) 
+(drop_gen_refl x1 (CHead x0 (Flat f) t0) H8)) in (let H_y \def (clear_flat x0 
+(CHead d1 (Bind Abst) t) (clear_gen_flat f x0 (CHead d1 (Bind Abst) t) t0 H6) 
+f t0) in (let H11 \def (csub3_clear_conf g (CHead x0 (Flat f) t0) c2 H10 
+(CHead d1 (Bind Abst) t) H_y) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead 
+d1 (Bind Abst) t) e2)) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda 
+(d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) 
+t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda 
+(d2: C).(\lambda (u: T).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: 
+C).(\lambda (u: T).(ty3 g d2 u t))))) (\lambda (x2: C).(\lambda (H12: (csub3 
+g (CHead d1 (Bind Abst) t) x2)).(\lambda (H13: (clear c2 x2)).(let H14 \def 
+(csub3_gen_abst g d1 x2 t H12) in (or_ind (ex2 C (\lambda (e2: C).(eq C x2 
 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csub3 g d1 e2))) (ex3_2 C T 
-(\lambda (e2: C).(\lambda (v2: T).(eq C x1 (CHead e2 (Bind Abbr) v2)))) 
+(\lambda (e2: C).(\lambda (v2: T).(eq C x2 (CHead e2 (Bind Abbr) v2)))) 
 (\lambda (e2: C).(\lambda (_: T).(csub3 g d1 e2))) (\lambda (e2: C).(\lambda 
 (v2: T).(ty3 g e2 v2 t)))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
 (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda 
 (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: 
 T).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
-T).(ty3 g d2 u t))))) (\lambda (H15: (ex2 C (\lambda (e2: C).(eq C x1 (CHead 
+T).(ty3 g d2 u t))))) (\lambda (H15: (ex2 C (\lambda (e2: C).(eq C x2 (CHead 
 e2 (Bind Abst) t))) (\lambda (e2: C).(csub3 g d1 e2)))).(ex2_ind C (\lambda 
-(e2: C).(eq C x1 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csub3 g d1 e2)) 
+(e2: C).(eq C x2 (CHead e2 (Bind Abst) t))) (\lambda (e2: C).(csub3 g d1 e2)) 
 (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl O c2 
 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: 
 T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl O c2 (CHead d2 
 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) 
-(\lambda (x2: C).(\lambda (H16: (eq C x1 (CHead x2 (Bind Abst) t))).(\lambda 
-(H17: (csub3 g d1 x2)).(let H18 \def (eq_ind C x1 (\lambda (c0: C).(clear c2 
-c0)) H13 (CHead x2 (Bind Abst) t) H16) in (or_introl (ex2 C (\lambda (d2: 
+(\lambda (x3: C).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abst) t))).(\lambda 
+(H17: (csub3 g d1 x3)).(let H18 \def (eq_ind C x2 (\lambda (c: C).(clear c2 
+c)) H13 (CHead x3 (Bind Abst) t) H16) in (or_introl (ex2 C (\lambda (d2: 
 C).(csub3 g d1 d2)) (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t)))) 
 (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: 
 C).(\lambda (u: T).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: 
 C).(\lambda (u: T).(ty3 g d2 u t)))) (ex_intro2 C (\lambda (d2: C).(csub3 g 
-d1 d2)) (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t))) x2 H17 
-(getl_intro O c2 (CHead x2 (Bind Abst) t) c2 (drop_refl c2) H18))))))) H15)) 
-(\lambda (H15: (ex3_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C x1 (CHead 
+d1 d2)) (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t))) x3 H17 
+(getl_intro O c2 (CHead x3 (Bind Abst) t) c2 (drop_refl c2) H18))))))) H15)) 
+(\lambda (H15: (ex3_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C x2 (CHead 
 e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csub3 g d1 e2))) 
 (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 t))))).(ex3_2_ind C T (\lambda 
-(e2: C).(\lambda (v2: T).(eq C x1 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: 
+(e2: C).(\lambda (v2: T).(eq C x2 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: 
 C).(\lambda (_: T).(csub3 g d1 e2))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g 
 e2 v2 t))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
 C).(getl O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl O 
 c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (H16: (eq C x1 (CHead x2 
-(Bind Abbr) x3))).(\lambda (H17: (csub3 g d1 x2)).(\lambda (H18: (ty3 g x2 x3 
-t)).(let H19 \def (eq_ind C x1 (\lambda (c0: C).(clear c2 c0)) H13 (CHead x2 
-(Bind Abbr) x3) H16) in (or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+t))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (H16: (eq C x2 (CHead x3 
+(Bind Abbr) x4))).(\lambda (H17: (csub3 g d1 x3)).(\lambda (H18: (ty3 g x3 x4 
+t)).(let H19 \def (eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 
+(Bind Abbr) x4) H16) in (or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
 (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda 
 (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: 
 T).(getl O c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
 T).(ty3 g d2 u t)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csub3 
 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl O c2 (CHead d2 (Bind Abbr) 
-u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x2 x3 H17 (getl_intro 
-O c2 (CHead x2 (Bind Abbr) x3) c2 (drop_refl c2) H19) H18)))))))) H15)) 
-H14))))) H11)))))))) (\lambda (n0: nat).(\lambda (H8: ((\forall (x0: 
-C).((drop n0 O x0 (CHead c (Flat f) t0)) \to (\forall (c2: C).((csub3 g x0 
+u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x3 x4 H17 (getl_intro 
+O c2 (CHead x3 (Bind Abbr) x4) c2 (drop_refl c2) H19) H18)))))))) H15)) 
+H14))))) H11)))))))) (\lambda (n0: nat).(\lambda (H8: ((\forall (x1: 
+C).((drop n0 O x1 (CHead x0 (Flat f) t0)) \to (\forall (c2: C).((csub3 g x1 
 c2) \to (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl 
 n0 c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: 
 T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl n0 c2 (CHead d2 
 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t))))))))))).(\lambda (x0: C).(\lambda (H9: (drop (S n0) O x0 (CHead c (Flat 
-f) t0))).(\lambda (c2: C).(\lambda (H10: (csub3 g x0 c2)).(let H11 \def 
-(drop_clear x0 (CHead c (Flat f) t0) n0 H9) in (ex2_3_ind B C T (\lambda (b: 
-B).(\lambda (e: C).(\lambda (v: T).(clear x0 (CHead e (Bind b) v))))) 
-(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n0 O e (CHead c (Flat 
+t))))))))))).(\lambda (x1: C).(\lambda (H9: (drop (S n0) O x1 (CHead x0 (Flat 
+f) t0))).(\lambda (c2: C).(\lambda (H10: (csub3 g x1 c2)).(let H11 \def 
+(drop_clear x1 (CHead x0 (Flat f) t0) n0 H9) in (ex2_3_ind B C T (\lambda (b: 
+B).(\lambda (e: C).(\lambda (v: T).(clear x1 (CHead e (Bind b) v))))) 
+(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n0 O e (CHead x0 (Flat 
 f) t0))))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
 C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl 
 (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g 
-d2 u t))))) (\lambda (x1: B).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H12: 
-(clear x0 (CHead x2 (Bind x1) x3))).(\lambda (H13: (drop n0 O x2 (CHead c 
-(Flat f) t0))).(let H14 \def (csub3_clear_conf g x0 c2 H10 (CHead x2 (Bind 
-x1) x3) H12) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead x2 (Bind x1) x3) 
+d2 u t))))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H12: 
+(clear x1 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n0 O x3 (CHead x0 
+(Flat f) t0))).(let H14 \def (csub3_clear_conf g x1 c2 H10 (CHead x3 (Bind 
+x2) x4) H12) in (ex2_ind C (\lambda (e2: C).(csub3 g (CHead x3 (Bind x2) x4) 
 e2)) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(csub3 g d1 
 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
 (u: T).(getl (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda 
-(u: T).(ty3 g d2 u t))))) (\lambda (x4: C).(\lambda (H15: (csub3 g (CHead x2 
-(Bind x1) x3) x4)).(\lambda (H16: (clear c2 x4)).(let H17 \def 
-(csub3_gen_bind g x1 x2 x4 x3 H15) in (ex2_3_ind B C T (\lambda (b2: 
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C x4 (CHead e2 (Bind b2) v2))))) 
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csub3 g x2 e2)))) (or (ex2 
+(u: T).(ty3 g d2 u t))))) (\lambda (x5: C).(\lambda (H15: (csub3 g (CHead x3 
+(Bind x2) x4) x5)).(\lambda (H16: (clear c2 x5)).(let H17 \def 
+(csub3_gen_bind g x2 x3 x5 x4 H15) in (ex2_3_ind B C T (\lambda (b2: 
+B).(\lambda (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2 (Bind b2) v2))))) 
+(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csub3 g x3 e2)))) (or (ex2 
 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead 
 d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 
 d2))) (\lambda (d2: C).(\lambda (u: T).(getl (S n0) c2 (CHead d2 (Bind Abbr) 
-u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) (\lambda (x5: 
-B).(\lambda (x6: C).(\lambda (x7: T).(\lambda (H18: (eq C x4 (CHead x6 (Bind 
-x5) x7))).(\lambda (H19: (csub3 g x2 x6)).(let H20 \def (eq_ind C x4 (\lambda 
-(c0: C).(clear c2 c0)) H16 (CHead x6 (Bind x5) x7) H18) in (let H21 \def (H8 
-x2 H13 x6 H19) in (or_ind (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl n0 x6 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
+u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) (\lambda (x6: 
+B).(\lambda (x7: C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind 
+x6) x8))).(\lambda (H19: (csub3 g x3 x7)).(let H20 \def (eq_ind C x5 (\lambda 
+(c: C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 
+H13 x7 H19) in (or_ind (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
+C).(getl n0 x7 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl 
-n0 x6 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 
+n0 x7 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 
 u t)))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl 
 (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda 
 (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl (S n0) c2 
 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
 t))))) (\lambda (H22: (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: 
-C).(getl n0 x6 (CHead d2 (Bind Abst) t))))).(ex2_ind C (\lambda (d2: 
-C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n0 x6 (CHead d2 (Bind Abst) t))) 
+C).(getl n0 x7 (CHead d2 (Bind Abst) t))))).(ex2_ind C (\lambda (d2: 
+C).(csub3 g d1 d2)) (\lambda (d2: C).(getl n0 x7 (CHead d2 (Bind Abst) t))) 
 (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda (d2: C).(getl (S n0) c2 
 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: C).(\lambda (_: 
 T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl (S n0) c2 (CHead 
 d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))) 
-(\lambda (x8: C).(\lambda (H23: (csub3 g d1 x8)).(\lambda (H24: (getl n0 x6 
-(CHead x8 (Bind Abst) t))).(or_introl (ex2 C (\lambda (d2: C).(csub3 g d1 
+(\lambda (x9: C).(\lambda (H23: (csub3 g d1 x9)).(\lambda (H24: (getl n0 x7 
+(CHead x9 (Bind Abst) t))).(or_introl (ex2 C (\lambda (d2: C).(csub3 g d1 
 d2)) (\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
 (u: T).(getl (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda 
 (u: T).(ty3 g d2 u t)))) (ex_intro2 C (\lambda (d2: C).(csub3 g d1 d2)) 
-(\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t))) x8 H23 
-(getl_clear_bind x5 c2 x6 x7 H20 (CHead x8 (Bind Abst) t) n0 H24)))))) H22)) 
+(\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t))) x9 H23 
+(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abst) t) n0 H24)))))) H22)) 
 (\lambda (H22: (ex3_2 C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) 
-(\lambda (d2: C).(\lambda (u: T).(getl n0 x6 (CHead d2 (Bind Abbr) u)))) 
+(\lambda (d2: C).(\lambda (u: T).(getl n0 x7 (CHead d2 (Bind Abbr) u)))) 
 (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))))).(ex3_2_ind C T (\lambda 
 (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: 
-T).(getl n0 x6 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
+T).(getl n0 x7 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: 
 T).(ty3 g d2 u t))) (or (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
 (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl 
 (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g 
-d2 u t))))) (\lambda (x8: C).(\lambda (x9: T).(\lambda (H23: (csub3 g d1 
-x8)).(\lambda (H24: (getl n0 x6 (CHead x8 (Bind Abbr) x9))).(\lambda (H25: 
-(ty3 g x8 x9 t)).(or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) (\lambda 
-(d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl 
-(S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g 
-d2 u t)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_: T).(csub3 g d1 
-d2))) (\lambda (d2: C).(\lambda (u: T).(getl (S n0) c2 (CHead d2 (Bind Abbr) 
-u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x8 x9 H23 
-(getl_clear_bind x5 c2 x6 x7 H20 (CHead x8 (Bind Abbr) x9) n0 H24) H25))))))) 
-H22)) H21)))))))) H17))))) H14))))))) H11)))))))) n) H7))))]) H3 H4)))]) H1 
-H2)))) H0))))))).
+d2 u t))))) (\lambda (x9: C).(\lambda (x10: T).(\lambda (H23: (csub3 g d1 
+x9)).(\lambda (H24: (getl n0 x7 (CHead x9 (Bind Abbr) x10))).(\lambda (H25: 
+(ty3 g x9 x10 t)).(or_intror (ex2 C (\lambda (d2: C).(csub3 g d1 d2)) 
+(\lambda (d2: C).(getl (S n0) c2 (CHead d2 (Bind Abst) t)))) (ex3_2 C T 
+(\lambda (d2: C).(\lambda (_: T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda 
+(u: T).(getl (S n0) c2 (CHead d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda 
+(u: T).(ty3 g d2 u t)))) (ex3_2_intro C T (\lambda (d2: C).(\lambda (_: 
+T).(csub3 g d1 d2))) (\lambda (d2: C).(\lambda (u: T).(getl (S n0) c2 (CHead 
+d2 (Bind Abbr) u)))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u t))) x9 x10 
+H23 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abbr) x10) n0 H24) 
+H25))))))) H22)) H21)))))))) H17))))) H14))))))) H11)))))))) n) H7))))) k H3 
+H4))))))) x H1 H2)))) H0))))))).