X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fclear%2Fdrop.ma;h=4383e2650f73143c4a73514cf9dd34e304574994;hb=83cf6c88d2d0bd2c8af86ab7f95bf94c1ae59bc9;hp=aae3fedc025032c819c6d995b55fc69c280ca7a6;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma
index aae3fedc0..4383e2650 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/clear/drop.ma
@@ -14,11 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/clear/fwd.ma".
+include "basic_1/clear/fwd.ma".
 
-include "Basic-1/drop/fwd.ma".
+include "basic_1/drop/fwd.ma".
 
-theorem drop_clear:
+lemma drop_clear:
  \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((drop (S i) O c1 c2) \to 
 (ex2_3 B C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear c1 (CHead 
 e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e 
@@ -33,40 +33,37 @@ C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda
 B).(\lambda (e: C).(\lambda (v: T).(clear (CSort n) (CHead e (Bind b) v))))) 
 (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) (\lambda 
 (_: (eq C c2 (CSort n))).(\lambda (H1: (eq nat (S i) O)).(\lambda (_: (eq nat 
-O O)).(let H3 \def (eq_ind nat (S i) (\lambda (ee: nat).(match ee in nat 
-return (\lambda (_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow 
-True])) I O H1) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (e: 
-C).(\lambda (v: T).(clear (CSort n) (CHead e (Bind b) v))))) (\lambda (_: 
-B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) H3))))) (drop_gen_sort 
-n (S i) O c2 H)))))) (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall 
-(i: nat).((drop (S i) O c c2) \to (ex2_3 B C T (\lambda (b: B).(\lambda (e: 
-C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda 
-(e: C).(\lambda (_: T).(drop i O e c2)))))))))).(\lambda (k: K).(\lambda (t: 
-T).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H0: (drop (S i) O (CHead c k 
-t) c2)).(K_ind (\lambda (k0: K).((drop (r k0 i) O c c2) \to (ex2_3 B C T 
-(\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c k0 t) (CHead 
-e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e 
-c2))))))) (\lambda (b: B).(\lambda (H1: (drop (r (Bind b) i) O c 
-c2)).(ex2_3_intro B C T (\lambda (b0: B).(\lambda (e: C).(\lambda (v: 
-T).(clear (CHead c (Bind b) t) (CHead e (Bind b0) v))))) (\lambda (_: 
-B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2)))) b c t (clear_bind b c 
-t) H1))) (\lambda (f: F).(\lambda (H1: (drop (r (Flat f) i) O c c2)).(let H2 
-\def (H c2 i H1) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda 
-(v: T).(clear c (CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: 
-C).(\lambda (_: T).(drop i O e c2)))) (ex2_3 B C T (\lambda (b: B).(\lambda 
-(e: C).(\lambda (v: T).(clear (CHead c (Flat f) t) (CHead e (Bind b) v))))) 
-(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))) (\lambda 
-(x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H3: (clear c (CHead x1 
-(Bind x0) x2))).(\lambda (H4: (drop i O x1 c2)).(ex2_3_intro B C T (\lambda 
-(b: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c (Flat f) t) (CHead e 
+O O)).(let H3 \def (eq_ind nat (S i) (\lambda (ee: nat).(match ee with [O 
+\Rightarrow False | (S _) \Rightarrow True])) I O H1) in (False_ind (ex2_3 B 
+C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear (CSort n) (CHead e 
 (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e 
-c2)))) x0 x1 x2 (clear_flat c (CHead x1 (Bind x0) x2) H3 f t) H4)))))) H2)))) 
-k (drop_gen_drop k c c2 t i H0))))))))) c1).
-(* COMMENTS
-Initial nodes: 770
-END *)
+c2))))) H3))))) (drop_gen_sort n (S i) O c2 H)))))) (\lambda (c: C).(\lambda 
+(H: ((\forall (c2: C).(\forall (i: nat).((drop (S i) O c c2) \to (ex2_3 B C T 
+(\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear c (CHead e (Bind b) 
+v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e 
+c2)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (i: 
+nat).(\lambda (H0: (drop (S i) O (CHead c k t) c2)).(K_ind (\lambda (k0: 
+K).((drop (r k0 i) O c c2) \to (ex2_3 B C T (\lambda (b: B).(\lambda (e: 
+C).(\lambda (v: T).(clear (CHead c k0 t) (CHead e (Bind b) v))))) (\lambda 
+(_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2))))))) (\lambda (b: 
+B).(\lambda (H1: (drop (r (Bind b) i) O c c2)).(ex2_3_intro B C T (\lambda 
+(b0: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c (Bind b) t) (CHead e 
+(Bind b0) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e 
+c2)))) b c t (clear_bind b c t) H1))) (\lambda (f: F).(\lambda (H1: (drop (r 
+(Flat f) i) O c c2)).(let H2 \def (H c2 i H1) in (ex2_3_ind B C T (\lambda 
+(b: B).(\lambda (e: C).(\lambda (v: T).(clear c (CHead e (Bind b) v))))) 
+(\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2)))) (ex2_3 B C 
+T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear (CHead c (Flat f) t) 
+(CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: 
+T).(drop i O e c2))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: 
+T).(\lambda (H3: (clear c (CHead x1 (Bind x0) x2))).(\lambda (H4: (drop i O 
+x1 c2)).(ex2_3_intro B C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: 
+T).(clear (CHead c (Flat f) t) (CHead e (Bind b) v))))) (\lambda (_: 
+B).(\lambda (e: C).(\lambda (_: T).(drop i O e c2)))) x0 x1 x2 (clear_flat c 
+(CHead x1 (Bind x0) x2) H3 f t) H4)))))) H2)))) k (drop_gen_drop k c c2 t i 
+H0))))))))) c1).
 
-theorem drop_clear_O:
+lemma drop_clear_O:
  \forall (b: B).(\forall (c: C).(\forall (e1: C).(\forall (u: T).((clear c 
 (CHead e1 (Bind b) u)) \to (\forall (e2: C).(\forall (i: nat).((drop i O e1 
 e2) \to (drop (S i) O c e2))))))))
@@ -85,29 +82,24 @@ T).(\lambda (H0: (clear (CHead c0 k t) (CHead e1 (Bind b) u))).(\lambda (e2:
 C).(\lambda (i: nat).(\lambda (H1: (drop i O e1 e2)).(K_ind (\lambda (k0: 
 K).((clear (CHead c0 k0 t) (CHead e1 (Bind b) u)) \to (drop (S i) O (CHead c0 
 k0 t) e2))) (\lambda (b0: B).(\lambda (H2: (clear (CHead c0 (Bind b0) t) 
-(CHead e1 (Bind b) u))).(let H3 \def (f_equal C C (\lambda (e: C).(match e in 
-C return (\lambda (_: C).C) with [(CSort _) \Rightarrow e1 | (CHead c1 _ _) 
-\Rightarrow c1])) (CHead e1 (Bind b) u) (CHead c0 (Bind b0) t) 
-(clear_gen_bind b0 c0 (CHead e1 (Bind b) u) t H2)) in ((let H4 \def (f_equal 
-C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) 
-\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: 
-K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e1 
+(CHead e1 (Bind b) u))).(let H3 \def (f_equal C C (\lambda (e: C).(match e 
+with [(CSort _) \Rightarrow e1 | (CHead c1 _ _) \Rightarrow c1])) (CHead e1 
 (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 (Bind b) 
-u) t H2)) in ((let H5 \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 e1 (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 
-(CHead e1 (Bind b) u) t H2)) in (\lambda (H6: (eq B b b0)).(\lambda (H7: (eq 
-C e1 c0)).(let H8 \def (eq_ind C e1 (\lambda (c1: C).(drop i O c1 e2)) H1 c0 
-H7) in (eq_ind B b (\lambda (b1: B).(drop (S i) O (CHead c0 (Bind b1) t) e2)) 
-(drop_drop (Bind b) i c0 e2 H8 t) b0 H6))))) H4)) H3)))) (\lambda (f: 
-F).(\lambda (H2: (clear (CHead c0 (Flat f) t) (CHead e1 (Bind b) 
-u))).(drop_drop (Flat f) i c0 e2 (H e1 u (clear_gen_flat f c0 (CHead e1 (Bind 
-b) u) t H2) e2 i H1) t))) k H0))))))))))) c)).
-(* COMMENTS
-Initial nodes: 619
-END *)
+u) t H2)) in ((let H4 \def (f_equal C B (\lambda (e: C).(match e with [(CSort 
+_) \Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1) 
+\Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e1 (Bind b) u) (CHead c0 
+(Bind b0) t) (clear_gen_bind b0 c0 (CHead e1 (Bind b) u) t H2)) in ((let H5 
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u | 
+(CHead _ _ t0) \Rightarrow t0])) (CHead e1 (Bind b) u) (CHead c0 (Bind b0) t) 
+(clear_gen_bind b0 c0 (CHead e1 (Bind b) u) t H2)) in (\lambda (H6: (eq B b 
+b0)).(\lambda (H7: (eq C e1 c0)).(let H8 \def (eq_ind C e1 (\lambda (c1: 
+C).(drop i O c1 e2)) H1 c0 H7) in (eq_ind B b (\lambda (b1: B).(drop (S i) O 
+(CHead c0 (Bind b1) t) e2)) (drop_drop (Bind b) i c0 e2 H8 t) b0 H6))))) H4)) 
+H3)))) (\lambda (f: F).(\lambda (H2: (clear (CHead c0 (Flat f) t) (CHead e1 
+(Bind b) u))).(drop_drop (Flat f) i c0 e2 (H e1 u (clear_gen_flat f c0 (CHead 
+e1 (Bind b) u) t H2) e2 i H1) t))) k H0))))))))))) c)).
 
-theorem drop_clear_S:
+lemma drop_clear_S:
  \forall (x2: C).(\forall (x1: C).(\forall (h: nat).(\forall (d: nat).((drop 
 h (S d) x1 x2) \to (\forall (b: B).(\forall (c2: C).(\forall (u: T).((clear 
 x2 (CHead c2 (Bind b) u)) \to (ex2 C (\lambda (c1: C).(clear x1 (CHead c1 
@@ -141,15 +133,13 @@ c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2)))) (K_ind
 t)) (CHead c1 (Bind b) (lift h d u)))) (\lambda (c1: C).(drop h d c1 c2)))))) 
 (\lambda (b0: B).(\lambda (H4: (clear (CHead c (Bind b0) t) (CHead c2 (Bind 
 b) u))).(\lambda (H5: (drop h (r (Bind b0) d) x c)).(let H6 \def (f_equal C C 
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) 
-\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u) 
-(CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in 
-((let H7 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: 
-C).B) with [(CSort _) \Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 in 
-K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) 
-\Rightarrow b])])) (CHead c2 (Bind b) u) (CHead c (Bind b0) t) 
-(clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in ((let H8 \def (f_equal C 
-T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) 
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) 
+\Rightarrow c0])) (CHead c2 (Bind b) u) (CHead c (Bind b0) t) (clear_gen_bind 
+b0 c (CHead c2 (Bind b) u) t H4)) in ((let H7 \def (f_equal C B (\lambda (e: 
+C).(match e with [(CSort _) \Rightarrow b | (CHead _ k0 _) \Rightarrow (match 
+k0 with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2 
+(Bind b) u) (CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u) 
+t H4)) in ((let H8 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _) 
 \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead c2 (Bind b) u) (CHead 
 c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u) t H4)) in (\lambda 
 (H9: (eq B b b0)).(\lambda (H10: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: 
@@ -175,7 +165,4 @@ u)))).(\lambda (H8: (drop h d x0 c2)).(ex_intro2 C (\lambda (c1: C).(clear
 u)))) (\lambda (c1: C).(drop h d c1 c2)) x0 (clear_flat x (CHead x0 (Bind b) 
 (lift h d u)) H7 f (lift h (r (Flat f) d) t)) H8)))) H6))))) k H1 H3) x1 
 H2)))) (drop_gen_skip_r c x1 t h d k H0)))))))))))))) x2).
-(* COMMENTS
-Initial nodes: 1449
-END *)