update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / clear / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma b/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma
index 68e250d761edb121096de84ccd2ef32a7f35848b..07e59e05d3be40b8c5510d9075d776f7f9f95293 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/clear/props.ma
@@ -14,9 +14,9 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/clear/fwd.ma".
+include "basic_1/clear/fwd.ma".
 
-theorem clear_clear:
+lemma clear_clear:
  \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (clear c2 c2)))
 \def
  \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to 
@@ -30,34 +30,6 @@ c2)).(eq_ind_r C (CHead c (Bind b) t) (\lambda (c0: C).(clear c0 c0))
 (clear_bind b c t) c2 (clear_gen_bind b c c2 t H1)))) (\lambda (f: 
 F).(\lambda (H1: (clear (CHead c (Flat f) t) c2)).(H c2 (clear_gen_flat f c 
 c2 t H1)))) k H0))))))) c1).
-(* COMMENTS
-Initial nodes: 199
-END *)
-
-theorem clear_mono:
- \forall (c: C).(\forall (c1: C).((clear c c1) \to (\forall (c2: C).((clear c 
-c2) \to (eq C c1 c2)))))
-\def
- \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (c1: C).((clear c0 c1) \to 
-(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2)))))) (\lambda (n: 
-nat).(\lambda (c1: C).(\lambda (_: (clear (CSort n) c1)).(\lambda (c2: 
-C).(\lambda (H0: (clear (CSort n) c2)).(clear_gen_sort c2 n H0 (eq C c1 
-c2))))))) (\lambda (c0: C).(\lambda (H: ((\forall (c1: C).((clear c0 c1) \to 
-(\forall (c2: C).((clear c0 c2) \to (eq C c1 c2))))))).(\lambda (k: 
-K).(\lambda (t: T).(\lambda (c1: C).(\lambda (H0: (clear (CHead c0 k t) 
-c1)).(\lambda (c2: C).(\lambda (H1: (clear (CHead c0 k t) c2)).(K_ind 
-(\lambda (k0: K).((clear (CHead c0 k0 t) c1) \to ((clear (CHead c0 k0 t) c2) 
-\to (eq C c1 c2)))) (\lambda (b: B).(\lambda (H2: (clear (CHead c0 (Bind b) 
-t) c1)).(\lambda (H3: (clear (CHead c0 (Bind b) t) c2)).(eq_ind_r C (CHead c0 
-(Bind b) t) (\lambda (c3: C).(eq C c1 c3)) (eq_ind_r C (CHead c0 (Bind b) t) 
-(\lambda (c3: C).(eq C c3 (CHead c0 (Bind b) t))) (refl_equal C (CHead c0 
-(Bind b) t)) c1 (clear_gen_bind b c0 c1 t H2)) c2 (clear_gen_bind b c0 c2 t 
-H3))))) (\lambda (f: F).(\lambda (H2: (clear (CHead c0 (Flat f) t) 
-c1)).(\lambda (H3: (clear (CHead c0 (Flat f) t) c2)).(H c1 (clear_gen_flat f 
-c0 c1 t H2) c2 (clear_gen_flat f c0 c2 t H3))))) k H0 H1))))))))) c).
-(* COMMENTS
-Initial nodes: 357
-END *)
 
 theorem clear_trans:
  \forall (c1: C).(\forall (c: C).((clear c1 c) \to (\forall (c2: C).((clear c 
@@ -78,11 +50,8 @@ c0 t H2)) in (eq_ind_r C (CHead c (Bind b) t) (\lambda (c3: C).(clear (CHead
 c (Bind b) t) c3)) (clear_bind b c t) c2 (clear_gen_bind b c c2 t H3))))) 
 (\lambda (f: F).(\lambda (H2: (clear (CHead c (Flat f) t) c0)).(clear_flat c 
 c2 (H c0 (clear_gen_flat f c c0 t H2) c2 H1) f t))) k H0))))))))) c1).
-(* COMMENTS
-Initial nodes: 299
-END *)
 
-theorem clear_ctail:
+lemma clear_ctail:
  \forall (b: B).(\forall (c1: C).(\forall (c2: C).(\forall (u2: T).((clear c1 
 (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1: T).(clear (CTail k 
 u1 c1) (CHead (CTail k u1 c2) (Bind b) u2))))))))
@@ -105,17 +74,15 @@ T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b) u2))))))))).(\lambda
 T).(K_ind (\lambda (k1: K).((clear (CHead c k1 t) (CHead c2 (Bind b) u2)) \to 
 (clear (CHead (CTail k0 u1 c) k1 t) (CHead (CTail k0 u1 c2) (Bind b) u2)))) 
 (\lambda (b0: B).(\lambda (H1: (clear (CHead c (Bind b0) t) (CHead c2 (Bind 
-b) u2))).(let H2 \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) u2) (CHead c (Bind b0) t) 
-(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in ((let H3 \def (f_equal 
-C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) 
-\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 in K return (\lambda (_: 
-K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2 
-(Bind b) u2) (CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) 
-u2) t H1)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e in C return 
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t0) 
-\Rightarrow t0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t) 
+b) u2))).(let H2 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u2) 
+(CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in 
+((let H3 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 with [(Bind b1) 
+\Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead c 
+(Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in ((let H4 
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | 
+(CHead _ _ t0) \Rightarrow t0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t) 
 (clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in (\lambda (H5: (eq B b 
 b0)).(\lambda (H6: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: T).(clear (CHead 
 (CTail k0 u1 c) (Bind b0) t) (CHead (CTail k0 u1 c2) (Bind b) t0))) (eq_ind_r 
@@ -126,27 +93,4 @@ k0 u1 c) t) b0 H5) c2 H6) u2 H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1:
 (clear (CHead c (Flat f) t) (CHead c2 (Bind b) u2))).(clear_flat (CTail k0 u1 
 c) (CHead (CTail k0 u1 c2) (Bind b) u2) (H c2 u2 (clear_gen_flat f c (CHead 
 c2 (Bind b) u2) t H1) k0 u1) f t))) k H0)))))))))) c1)).
-(* COMMENTS
-Initial nodes: 819
-END *)
-
-theorem clear_cle:
- \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (cle c2 c1)))
-\def
- \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to 
-(le (cweight c2) (cweight c))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda 
-(H: (clear (CSort n) c2)).(clear_gen_sort c2 n H (le (cweight c2) O))))) 
-(\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (le (cweight 
-c2) (cweight c)))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: 
-C).(\lambda (H0: (clear (CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear 
-(CHead c k0 t) c2) \to (le (cweight c2) (plus (cweight c) (tweight t))))) 
-(\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t) c2)).(eq_ind_r C 
-(CHead c (Bind b) t) (\lambda (c0: C).(le (cweight c0) (plus (cweight c) 
-(tweight t)))) (le_n (plus (cweight c) (tweight t))) c2 (clear_gen_bind b c 
-c2 t H1)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t) 
-c2)).(le_plus_trans (cweight c2) (cweight c) (tweight t) (H c2 
-(clear_gen_flat f c c2 t H1))))) k H0))))))) c1).
-(* COMMENTS
-Initial nodes: 247
-END *)