update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubt / drop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubt/drop.ma b/matita/matita/contribs/lambdadelta/basic_1/csubt/drop.ma
index adaedcc9aab011844924b66714ec918eb63cd4b5..8d05e4b1491cda699093be8ca651c444e5a89ee3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubt/drop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubt/drop.ma
@@ -14,11 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/csubt/fwd.ma".
+include "basic_1/csubt/fwd.ma".
 
-include "Basic-1/drop/fwd.ma".
+include "basic_1/drop/fwd.ma".
 
-theorem csubt_drop_flat:
+lemma csubt_drop_flat:
  \forall (g: G).(\forall (f: F).(\forall (n: nat).(\forall (c1: C).(\forall 
 (c2: C).((csubt g c1 c2) \to (\forall (d1: C).(\forall (u: T).((drop n O c1 
 (CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda 
@@ -54,28 +54,28 @@ T).(\lambda (H1: (drop (S n0) O (CSort n1) (CHead d1 (Flat f) u))).(and3_ind
 (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) 
 (CHead d2 (Flat f) u)))) (\lambda (_: (eq C (CHead d1 (Flat f) u) (CSort 
 n1))).(\lambda (H3: (eq nat (S n0) O)).(\lambda (_: (eq nat O O)).(let H5 
-\def (eq_ind nat (S n0) (\lambda (ee: nat).(match ee in nat return (\lambda 
-(_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H3) 
-in (False_ind (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop 
-(S n0) O (CSort n1) (CHead d2 (Flat f) u)))) H5))))) (drop_gen_sort n1 (S n0) 
-O (CHead d1 (Flat f) u) H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda 
-(H1: (csubt g c0 c3)).(\lambda (H2: ((\forall (d1: C).(\forall (u: T).((drop 
-(S n0) O c0 (CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 
-d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Flat f) 
-u))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall 
-(d1: C).(\forall (u0: T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 (Flat f) 
-u0)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S 
-n0) O (CHead c3 k0 u) (CHead d2 (Flat f) u0))))))))) (\lambda (b: B).(\lambda 
-(u: T).(\lambda (d1: C).(\lambda (u0: T).(\lambda (H3: (drop (S n0) O (CHead 
-c0 (Bind b) u) (CHead d1 (Flat f) u0))).(ex2_ind C (\lambda (d2: C).(csubt g 
-d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 (Flat f) u0))) (ex2 C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
-(Bind b) u) (CHead d2 (Flat f) u0)))) (\lambda (x: C).(\lambda (H4: (csubt g 
-d1 x)).(\lambda (H5: (drop n0 O c3 (CHead x (Flat f) u0))).(ex_intro2 C 
+\def (eq_ind nat (S n0) (\lambda (ee: nat).(match ee with [O \Rightarrow 
+False | (S _) \Rightarrow True])) I O H3) in (False_ind (ex2 C (\lambda (d2: 
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 
+(Flat f) u)))) H5))))) (drop_gen_sort n1 (S n0) O (CHead d1 (Flat f) u) 
+H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g c0 
+c3)).(\lambda (H2: ((\forall (d1: C).(\forall (u: T).((drop (S n0) O c0 
+(CHead d1 (Flat f) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda 
+(d2: C).(drop (S n0) O c3 (CHead d2 (Flat f) u))))))))).(\lambda (k: 
+K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall (d1: C).(\forall (u0: 
+T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 (Flat f) u0)) \to (ex2 C 
 (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
-(Bind b) u) (CHead d2 (Flat f) u0))) x H4 (drop_drop (Bind b) n0 c3 (CHead x 
-(Flat f) u0) H5 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind b) c0 (CHead d1 
-(Flat f) u0) u n0 H3)))))))) (\lambda (f0: F).(\lambda (u: T).(\lambda (d1: 
+k0 u) (CHead d2 (Flat f) u0))))))))) (\lambda (b: B).(\lambda (u: T).(\lambda 
+(d1: C).(\lambda (u0: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Bind b) u) 
+(CHead d1 (Flat f) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) 
+(\lambda (d2: C).(drop n0 O c3 (CHead d2 (Flat f) u0))) (ex2 C (\lambda (d2: 
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind b) u) 
+(CHead d2 (Flat f) u0)))) (\lambda (x: C).(\lambda (H4: (csubt g d1 
+x)).(\lambda (H5: (drop n0 O c3 (CHead x (Flat f) u0))).(ex_intro2 C (\lambda 
+(d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind b) 
+u) (CHead d2 (Flat f) u0))) x H4 (drop_drop (Bind b) n0 c3 (CHead x (Flat f) 
+u0) H5 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind b) c0 (CHead d1 (Flat f) 
+u0) u n0 H3)))))))) (\lambda (f0: F).(\lambda (u: T).(\lambda (d1: 
 C).(\lambda (u0: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Flat f0) u) 
 (CHead d1 (Flat f) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) 
 (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Flat f) u0))) (ex2 C (\lambda 
@@ -115,11 +115,8 @@ c3 (CHead x (Flat f) u0))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2))
 u0))) x H6 (drop_drop (Bind Abbr) n0 c3 (CHead x (Flat f) u0) H7 u))))) (H c0 
 c3 H1 d1 u0 (drop_gen_drop (Bind Abst) c0 (CHead d1 (Flat f) u0) t n0 
 H5)))))))))))))) c1 c2 H0)))))) n))).
-(* COMMENTS
-Initial nodes: 2090
-END *)
 
-theorem csubt_drop_abbr:
+lemma csubt_drop_abbr:
  \forall (g: G).(\forall (n: nat).(\forall (c1: C).(\forall (c2: C).((csubt g 
 c1 c2) \to (\forall (d1: C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind 
 Abbr) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop 
@@ -156,73 +153,69 @@ u) (CSort n1)) (eq nat (S n0) O) (eq nat O O) (ex2 C (\lambda (d2: C).(csubt
 g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) 
 u)))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u) (CSort n1))).(\lambda (H3: 
 (eq nat (S n0) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n0) 
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O 
-\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (ex2 C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) 
-(CHead d2 (Bind Abbr) u)))) H5))))) (drop_gen_sort n1 (S n0) O (CHead d1 
-(Bind Abbr) u) H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: 
-(csubt g c0 c3)).(\lambda (H2: ((\forall (d1: C).(\forall (u: T).((drop (S 
-n0) O c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 
-d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abbr) 
-u))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall 
-(d1: C).(\forall (u0: T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 (Bind 
-Abbr) u0)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
-C).(drop (S n0) O (CHead c3 k0 u) (CHead d2 (Bind Abbr) u0))))))))) (\lambda 
-(b: B).(\lambda (u: T).(\lambda (d1: C).(\lambda (u0: T).(\lambda (H3: (drop 
-(S n0) O (CHead c0 (Bind b) u) (CHead d1 (Bind Abbr) u0))).(ex2_ind C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 
-(Bind Abbr) u0))) (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
-C).(drop (S n0) O (CHead c3 (Bind b) u) (CHead d2 (Bind Abbr) u0)))) (\lambda 
-(x: C).(\lambda (H4: (csubt g d1 x)).(\lambda (H5: (drop n0 O c3 (CHead x 
-(Bind Abbr) u0))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda 
-(d2: C).(drop (S n0) O (CHead c3 (Bind b) u) (CHead d2 (Bind Abbr) u0))) x H4 
-(drop_drop (Bind b) n0 c3 (CHead x (Bind Abbr) u0) H5 u))))) (H c0 c3 H1 d1 
-u0 (drop_gen_drop (Bind b) c0 (CHead d1 (Bind Abbr) u0) u n0 H3)))))))) 
-(\lambda (f: F).(\lambda (u: T).(\lambda (d1: C).(\lambda (u0: T).(\lambda 
-(H3: (drop (S n0) O (CHead c0 (Flat f) u) (CHead d1 (Bind Abbr) 
-u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S 
-n0) O c3 (CHead d2 (Bind Abbr) u0))) (ex2 C (\lambda (d2: C).(csubt g d1 d2)) 
-(\lambda (d2: C).(drop (S n0) O (CHead c3 (Flat f) u) (CHead d2 (Bind Abbr) 
-u0)))) (\lambda (x: C).(\lambda (H4: (csubt g d1 x)).(\lambda (H5: (drop (S 
-n0) O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 
-d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Flat f) u) (CHead d2 (Bind 
-Abbr) u0))) x H4 (drop_drop (Flat f) n0 c3 (CHead x (Bind Abbr) u0) H5 u))))) 
-(H2 d1 u0 (drop_gen_drop (Flat f) c0 (CHead d1 (Bind Abbr) u0) u n0 
-H3)))))))) k)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g 
-c0 c3)).(\lambda (_: ((\forall (d1: C).(\forall (u: T).((drop (S n0) O c0 
-(CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) 
-(\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abbr) u))))))))).(\lambda 
-(b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2: 
-T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H4: (drop (S n0) O (CHead c0 
-(Bind Void) u1) (CHead d1 (Bind Abbr) u))).(ex2_ind C (\lambda (d2: C).(csubt 
-g d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 (Bind Abbr) u))) (ex2 C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
-(Bind b) u2) (CHead d2 (Bind Abbr) u)))) (\lambda (x: C).(\lambda (H5: (csubt 
-g d1 x)).(\lambda (H6: (drop n0 O c3 (CHead x (Bind Abbr) u))).(ex_intro2 C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
-(Bind b) u2) (CHead d2 (Bind Abbr) u))) x H5 (drop_drop (Bind b) n0 c3 (CHead 
-x (Bind Abbr) u) H6 u2))))) (H c0 c3 H1 d1 u (drop_gen_drop (Bind Void) c0 
-(CHead d1 (Bind Abbr) u) u1 n0 H4)))))))))))))) (\lambda (c0: C).(\lambda 
-(c3: C).(\lambda (H1: (csubt g c0 c3)).(\lambda (_: ((\forall (d1: 
-C).(\forall (u: T).((drop (S n0) O c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C 
-(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead 
-d2 (Bind Abbr) u))))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g 
-c0 u t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (d1: C).(\lambda (u0: 
-T).(\lambda (H5: (drop (S n0) O (CHead c0 (Bind Abst) t) (CHead d1 (Bind 
+(\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) \Rightarrow 
+True])) I O H3) in (False_ind (ex2 C (\lambda (d2: C).(csubt g d1 d2)) 
+(\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) u)))) 
+H5))))) (drop_gen_sort n1 (S n0) O (CHead d1 (Bind Abbr) u) H1)))))) (\lambda 
+(c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g c0 c3)).(\lambda (H2: 
+((\forall (d1: C).(\forall (u: T).((drop (S n0) O c0 (CHead d1 (Bind Abbr) 
+u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S 
+n0) O c3 (CHead d2 (Bind Abbr) u))))))))).(\lambda (k: K).(K_ind (\lambda 
+(k0: K).(\forall (u: T).(\forall (d1: C).(\forall (u0: T).((drop (S n0) O 
+(CHead c0 k0 u) (CHead d1 (Bind Abbr) u0)) \to (ex2 C (\lambda (d2: C).(csubt 
+g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 k0 u) (CHead d2 (Bind 
+Abbr) u0))))))))) (\lambda (b: B).(\lambda (u: T).(\lambda (d1: C).(\lambda 
+(u0: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Bind b) u) (CHead d1 (Bind 
 Abbr) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
 C).(drop n0 O c3 (CHead d2 (Bind Abbr) u0))) (ex2 C (\lambda (d2: C).(csubt g 
-d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u) (CHead d2 
-(Bind Abbr) u0)))) (\lambda (x: C).(\lambda (H6: (csubt g d1 x)).(\lambda 
-(H7: (drop n0 O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C (\lambda (d2: 
-C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind Abbr) u) 
-(CHead d2 (Bind Abbr) u0))) x H6 (drop_drop (Bind Abbr) n0 c3 (CHead x (Bind 
-Abbr) u0) H7 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind Abst) c0 (CHead d1 
-(Bind Abbr) u0) t n0 H5)))))))))))))) c1 c2 H0)))))) n)).
-(* COMMENTS
-Initial nodes: 2084
-END *)
+d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind b) u) (CHead d2 (Bind 
+Abbr) u0)))) (\lambda (x: C).(\lambda (H4: (csubt g d1 x)).(\lambda (H5: 
+(drop n0 O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C (\lambda (d2: C).(csubt 
+g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind b) u) (CHead d2 
+(Bind Abbr) u0))) x H4 (drop_drop (Bind b) n0 c3 (CHead x (Bind Abbr) u0) H5 
+u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind b) c0 (CHead d1 (Bind Abbr) u0) 
+u n0 H3)))))))) (\lambda (f: F).(\lambda (u: T).(\lambda (d1: C).(\lambda 
+(u0: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Flat f) u) (CHead d1 (Bind 
+Abbr) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
+C).(drop (S n0) O c3 (CHead d2 (Bind Abbr) u0))) (ex2 C (\lambda (d2: 
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Flat f) u) 
+(CHead d2 (Bind Abbr) u0)))) (\lambda (x: C).(\lambda (H4: (csubt g d1 
+x)).(\lambda (H5: (drop (S n0) O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C 
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
+(Flat f) u) (CHead d2 (Bind Abbr) u0))) x H4 (drop_drop (Flat f) n0 c3 (CHead 
+x (Bind Abbr) u0) H5 u))))) (H2 d1 u0 (drop_gen_drop (Flat f) c0 (CHead d1 
+(Bind Abbr) u0) u n0 H3)))))))) k)))))) (\lambda (c0: C).(\lambda (c3: 
+C).(\lambda (H1: (csubt g c0 c3)).(\lambda (_: ((\forall (d1: C).(\forall (u: 
+T).((drop (S n0) O c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: 
+C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abbr) 
+u))))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1: 
+T).(\lambda (u2: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H4: (drop (S 
+n0) O (CHead c0 (Bind Void) u1) (CHead d1 (Bind Abbr) u))).(ex2_ind C 
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop n0 O c3 (CHead d2 
+(Bind Abbr) u))) (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
+C).(drop (S n0) O (CHead c3 (Bind b) u2) (CHead d2 (Bind Abbr) u)))) (\lambda 
+(x: C).(\lambda (H5: (csubt g d1 x)).(\lambda (H6: (drop n0 O c3 (CHead x 
+(Bind Abbr) u))).(ex_intro2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
+C).(drop (S n0) O (CHead c3 (Bind b) u2) (CHead d2 (Bind Abbr) u))) x H5 
+(drop_drop (Bind b) n0 c3 (CHead x (Bind Abbr) u) H6 u2))))) (H c0 c3 H1 d1 u 
+(drop_gen_drop (Bind Void) c0 (CHead d1 (Bind Abbr) u) u1 n0 H4)))))))))))))) 
+(\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g c0 c3)).(\lambda (_: 
+((\forall (d1: C).(\forall (u: T).((drop (S n0) O c0 (CHead d1 (Bind Abbr) 
+u)) \to (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S 
+n0) O c3 (CHead d2 (Bind Abbr) u))))))))).(\lambda (u: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c0 u t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (d1: 
+C).(\lambda (u0: T).(\lambda (H5: (drop (S n0) O (CHead c0 (Bind Abst) t) 
+(CHead d1 (Bind Abbr) u0))).(ex2_ind C (\lambda (d2: C).(csubt g d1 d2)) 
+(\lambda (d2: C).(drop n0 O c3 (CHead d2 (Bind Abbr) u0))) (ex2 C (\lambda 
+(d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 (Bind 
+Abbr) u) (CHead d2 (Bind Abbr) u0)))) (\lambda (x: C).(\lambda (H6: (csubt g 
+d1 x)).(\lambda (H7: (drop n0 O c3 (CHead x (Bind Abbr) u0))).(ex_intro2 C 
+(\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CHead c3 
+(Bind Abbr) u) (CHead d2 (Bind Abbr) u0))) x H6 (drop_drop (Bind Abbr) n0 c3 
+(CHead x (Bind Abbr) u0) H7 u))))) (H c0 c3 H1 d1 u0 (drop_gen_drop (Bind 
+Abst) c0 (CHead d1 (Bind Abbr) u0) t n0 H5)))))))))))))) c1 c2 H0)))))) n)).
 
-theorem csubt_drop_abst:
+lemma csubt_drop_abst:
  \forall (g: G).(\forall (n: nat).(\forall (c1: C).(\forall (c2: C).((csubt g 
 c1 c2) \to (\forall (d1: C).(\forall (t: T).((drop n O c1 (CHead d1 (Bind 
 Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
@@ -325,32 +318,31 @@ C).(\lambda (u: T).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) u))))
 (\lambda (_: C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda 
 (u: T).(ty3 g d2 u t))))) (\lambda (_: (eq C (CHead d1 (Bind Abst) t) (CSort 
 n1))).(\lambda (H3: (eq nat (S n0) O)).(\lambda (_: (eq nat O O)).(let H5 
-\def (eq_ind nat (S n0) (\lambda (ee: nat).(match ee in nat return (\lambda 
-(_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H3) 
-in (False_ind (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
-C).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda 
-(d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u: 
-T).(drop (S n0) O (CSort n1) (CHead d2 (Bind Abbr) u)))) (\lambda (_: 
+\def (eq_ind nat (S n0) (\lambda (ee: nat).(match ee with [O \Rightarrow 
+False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2 C (\lambda 
+(d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop (S n0) O (CSort n1) (CHead d2 
+(Bind Abst) t)))) (ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 
+d2))) (\lambda (d2: C).(\lambda (u: T).(drop (S n0) O (CSort n1) (CHead d2 
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+(CHead d1 (Bind Abst) t) H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda 
+(H1: (csubt g c0 c3)).(\lambda (H2: ((\forall (d1: C).(\forall (t: T).((drop 
+(S n0) O c0 (CHead d1 (Bind Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt 
+g d1 d2)) (\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abst) t)))) 
+(ex4_2 C T (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: 
+C).(\lambda (u: T).(drop (S n0) O c3 (CHead d2 (Bind Abbr) u)))) (\lambda (_: 
 C).(\lambda (u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g 
-d2 u t))))) H5))))) (drop_gen_sort n1 (S n0) O (CHead d1 (Bind Abst) t) 
-H1)))))) (\lambda (c0: C).(\lambda (c3: C).(\lambda (H1: (csubt g c0 
-c3)).(\lambda (H2: ((\forall (d1: C).(\forall (t: T).((drop (S n0) O c0 
-(CHead d1 (Bind Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) 
-(\lambda (d2: C).(drop (S n0) O c3 (CHead d2 (Bind Abst) t)))) (ex4_2 C T 
+d2 u t)))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: 
+T).(\forall (d1: C).(\forall (t: T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 
+(Bind Abst) t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda 
+(d2: C).(drop (S n0) O (CHead c3 k0 u) (CHead d2 (Bind Abst) t)))) (ex4_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda 
-(u: T).(drop (S n0) O c3 (CHead d2 (Bind Abbr) u)))) (\lambda (_: C).(\lambda 
-(u: T).(ty3 g d1 u t))) (\lambda (d2: C).(\lambda (u: T).(ty3 g d2 u 
-t)))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall 
-(d1: C).(\forall (t: T).((drop (S n0) O (CHead c0 k0 u) (CHead d1 (Bind Abst) 
-t)) \to (or (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: C).(drop 
-(S n0) O (CHead c3 k0 u) (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop 
-(S n0) O (CHead c3 k0 u) (CHead d2 (Bind Abbr) u0)))) (\lambda (_: 
-C).(\lambda (u0: T).(ty3 g d1 u0 t))) (\lambda (d2: C).(\lambda (u0: T).(ty3 
-g d2 u0 t)))))))))) (\lambda (b: B).(\lambda (u: T).(\lambda (d1: C).(\lambda 
-(t: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Bind b) u) (CHead d1 (Bind 
-Abst) t))).(or_ind (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda (d2: 
-C).(drop n0 O c3 (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: 
+(u0: T).(drop (S n0) O (CHead c3 k0 u) (CHead d2 (Bind Abbr) u0)))) (\lambda 
+(_: C).(\lambda (u0: T).(ty3 g d1 u0 t))) (\lambda (d2: C).(\lambda (u0: 
+T).(ty3 g d2 u0 t)))))))))) (\lambda (b: B).(\lambda (u: T).(\lambda (d1: 
+C).(\lambda (t: T).(\lambda (H3: (drop (S n0) O (CHead c0 (Bind b) u) (CHead 
+d1 (Bind Abst) t))).(or_ind (ex2 C (\lambda (d2: C).(csubt g d1 d2)) (\lambda 
+(d2: C).(drop n0 O c3 (CHead d2 (Bind Abst) t)))) (ex4_2 C T (\lambda (d2: 
 C).(\lambda (_: T).(csubt g d1 d2))) (\lambda (d2: C).(\lambda (u0: T).(drop 
 n0 O c3 (CHead d2 (Bind Abbr) u0)))) (\lambda (_: C).(\lambda (u0: T).(ty3 g 
 d1 u0 t))) (\lambda (d2: C).(\lambda (u0: T).(ty3 g d2 u0 t)))) (or (ex2 C 
@@ -584,7 +576,4 @@ C).(\lambda (u0: T).(ty3 g d1 u0 t0))) (\lambda (d2: C).(\lambda (u0: T).(ty3
 g d2 u0 t0))) x0 x1 H7 (drop_drop (Bind Abbr) n0 c3 (CHead x0 (Bind Abbr) x1) 
 H8 u) H9 H10)))))))) H6)) (H c0 c3 H1 d1 t0 (drop_gen_drop (Bind Abst) c0 
 (CHead d1 (Bind Abst) t0) t n0 H5)))))))))))))) c1 c2 H0)))))) n)).
-(* COMMENTS
-Initial nodes: 7940
-END *)