X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fcsubst1%2Fgetl.ma;h=1d37fd761ffcfa29ea21ebd7078a82d6cf2f9f5d;hb=57ae1762497a5f3ea75740e2908e04adb8642cc2;hp=e24ba95339b0cc80f9506682a566a525ca067855;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;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 e24ba9533..1d37fd761 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubst1/getl.ma
@@ -14,15 +14,15 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/csubst1/props.ma".
+include "basic_1/csubst1/props.ma".
 
-include "Basic-1/csubst0/getl.ma".
+include "basic_1/csubst0/getl.ma".
 
-include "Basic-1/subst1/props.ma".
+include "basic_1/subst1/props.ma".
 
-include "Basic-1/drop/props.ma".
+include "basic_1/drop/props.ma".
 
-theorem csubst1_getl_ge:
+lemma csubst1_getl_ge:
  \forall (i: nat).(\forall (n: nat).((le i n) \to (\forall (c1: C).(\forall 
 (c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e: C).((getl n c1 
 e) \to (getl n c2 e)))))))))
@@ -33,11 +33,8 @@ 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))))))).
-(* COMMENTS
-Initial nodes: 111
-END *)
 
-theorem csubst1_getl_lt:
+lemma csubst1_getl_lt:
  \forall (i: nat).(\forall (n: nat).((lt n i) \to (\forall (c1: C).(\forall 
 (c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e1: C).((getl n c1 
 e1) \to (ex2 C (\lambda (e2: C).(csubst1 (minus i n) v e1 e2)) (\lambda (e2: 
@@ -139,11 +136,8 @@ 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))))))).
-(* COMMENTS
-Initial nodes: 2035
-END *)
 
-theorem csubst1_getl_ge_back:
+lemma csubst1_getl_ge_back:
  \forall (i: nat).(\forall (n: nat).((le i n) \to (\forall (c1: C).(\forall 
 (c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e: C).((getl n c2 
 e) \to (getl n c1 e)))))))))
@@ -154,11 +148,8 @@ 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))))))).
-(* COMMENTS
-Initial nodes: 111
-END *)
 
-theorem getl_csubst1:
+lemma getl_csubst1:
  \forall (d: nat).(\forall (c: C).(\forall (e: C).(\forall (u: T).((getl d c 
 (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: 
 C).(csubst1 d u c a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) d a0 
@@ -184,100 +175,95 @@ 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 in C return (\lambda (_: C).C) 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 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 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 in C return (\lambda 
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) 
+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 (\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 
+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 (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 (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 (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 
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-(CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S 
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-(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).
-(* COMMENTS
-Initial nodes: 2467
-END *)
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+(drop (S O) (S n) x0 x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: 
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+(drop_skip_flat (S O) n x0 x1 H6 f x)))))) H4)))) H2)))))))) k)))) c)))) d).