update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / getl / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
index b378f61fc55862e5bb3643960a68be53fc2d4c25..7390775d31d6dbec7e5c7406af4242b028aa649c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
@@ -14,13 +14,23 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/getl/defs.ma".
+include "basic_1/getl/defs.ma".
 
-include "Basic-1/drop/fwd.ma".
+include "basic_1/drop/fwd.ma".
 
-include "Basic-1/clear/fwd.ma".
+include "basic_1/clear/fwd.ma".
 
-theorem getl_gen_all:
+implied lemma getl_ind:
+ \forall (h: nat).(\forall (c1: C).(\forall (c2: C).(\forall (P: 
+Prop).(((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to P)))) \to 
+((getl h c1 c2) \to P)))))
+\def
+ \lambda (h: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda (P: 
+Prop).(\lambda (f: ((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to 
+P))))).(\lambda (g: (getl h c1 c2)).(match g with [(getl_intro x x0 x1) 
+\Rightarrow (f x x0 x1)])))))).
+
+lemma getl_gen_all:
  \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex2 
 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e c2))))))
 \def
@@ -29,11 +39,8 @@ c2)).(getl_ind i c1 c2 (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e:
 C).(clear e c2))) (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda 
 (H1: (clear e c2)).(ex_intro2 C (\lambda (e0: C).(drop i O c1 e0)) (\lambda 
 (e0: C).(clear e0 c2)) e H0 H1)))) H)))).
-(* COMMENTS
-Initial nodes: 95
-END *)
 
-theorem getl_gen_sort:
+lemma getl_gen_sort:
  \forall (n: nat).(\forall (h: nat).(\forall (x: C).((getl h (CSort n) x) \to 
 (\forall (P: Prop).P))))
 \def
@@ -46,11 +53,8 @@ e x)) P (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) x0)).(\lambda (H2:
 (eq nat O O)).(let H6 \def (eq_ind C x0 (\lambda (c: C).(clear c x)) H2 
 (CSort n) H3) in (clear_gen_sort x n H6 P))))) (drop_gen_sort n h O x0 
 H1))))) H0)))))).
-(* COMMENTS
-Initial nodes: 179
-END *)
 
-theorem getl_gen_O:
+lemma getl_gen_O:
  \forall (e: C).(\forall (x: C).((getl O e x) \to (clear e x)))
 \def
  \lambda (e: C).(\lambda (x: C).(\lambda (H: (getl O e x)).(let H0 \def 
@@ -58,11 +62,8 @@ theorem getl_gen_O:
 (\lambda (e0: C).(clear e0 x)) (clear e x) (\lambda (x0: C).(\lambda (H1: 
 (drop O O e x0)).(\lambda (H2: (clear x0 x)).(let H3 \def (eq_ind_r C x0 
 (\lambda (c: C).(clear c x)) H2 e (drop_gen_refl e x0 H1)) in H3)))) H0)))).
-(* COMMENTS
-Initial nodes: 99
-END *)
 
-theorem getl_gen_S:
+lemma getl_gen_S:
  \forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: 
 nat).((getl (S h) (CHead c k u) x) \to (getl (r k h) c x))))))
 \def
@@ -72,11 +73,8 @@ nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let H0 \def (getl_gen_all
 k u) e)) (\lambda (e: C).(clear e x)) (getl (r k h) c x) (\lambda (x0: 
 C).(\lambda (H1: (drop (S h) O (CHead c k u) x0)).(\lambda (H2: (clear x0 
 x)).(getl_intro (r k h) c x x0 (drop_gen_drop k c x0 u h H1) H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 145
-END *)
 
-theorem getl_gen_2:
+lemma getl_gen_2:
  \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex_3 
 B C T (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind 
 b) v)))))))))
@@ -97,11 +95,8 @@ x0) x2) (\lambda (c: C).(ex_3 B C T (\lambda (b: B).(\lambda (c0: C).(\lambda
 B).(\lambda (c: C).(\lambda (v: T).(eq C (CHead x1 (Bind x0) x2) (CHead c 
 (Bind b) v))))) x0 x1 x2 (refl_equal C (CHead x1 (Bind x0) x2))) c2 H4)))))) 
 H3))))) H0))))).
-(* COMMENTS
-Initial nodes: 325
-END *)
 
-theorem getl_gen_flat:
+lemma getl_gen_flat:
  \forall (f: F).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: 
 nat).((getl i (CHead e (Flat f) v) d) \to (getl i e d))))))
 \def
@@ -112,11 +107,8 @@ e d))) (\lambda (H: (getl O (CHead e (Flat f) v) d)).(getl_intro O e d e
 H)))) (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Flat f) v) d) \to 
 (getl n e d)))).(\lambda (H0: (getl (S n) (CHead e (Flat f) v) 
 d)).(getl_gen_S (Flat f) e d v n H0)))) i))))).
-(* COMMENTS
-Initial nodes: 155
-END *)
 
-theorem getl_gen_bind:
+lemma getl_gen_bind:
  \forall (b: B).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: 
 nat).((getl i (CHead e (Bind b) v) d) \to (or (land (eq nat i O) (eq C d 
 (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat i (S j))) (\lambda 
@@ -142,7 +134,21 @@ v))) (ex2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: nat).(getl
 j e d))) (ex_intro2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: 
 nat).(getl j e d)) n (refl_equal nat (S n)) (getl_gen_S (Bind b) e d v n 
 H0)))))) i))))).
-(* COMMENTS
-Initial nodes: 525
-END *)
+
+theorem getl_mono:
+ \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to 
+(\forall (x2: C).((getl h c x2) \to (eq C x1 x2))))))
+\def
+ \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c 
+x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all 
+c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: 
+C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c 
+x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in 
+(ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq 
+C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear 
+x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0 
+(drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0: 
+C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def 
+(eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0 
+H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))).