update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma
index 824b1b181ec439cb334d1b08f3624c4137d909a2..64e3319056d3485767193b8ae5ddb090b8145832 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/getl/getl.ma
@@ -18,20 +18,18 @@ include "basic_1/getl/drop.ma".
 
 include "basic_1/getl/clear.ma".
 
-theorem getl_conf_le:
+lemma getl_conf_le:
  \forall (i: nat).(\forall (a: C).(\forall (c: C).((getl i c a) \to (\forall 
 (e: C).(\forall (h: nat).((getl h c e) \to ((le h i) \to (getl (minus i h) e 
 a))))))))
 \def
  \lambda (i: nat).(\lambda (a: C).(\lambda (c: C).(\lambda (H: (getl i c 
 a)).(\lambda (e: C).(\lambda (h: nat).(\lambda (H0: (getl h c e)).(\lambda 
-(H1: (le h i)).(let H2 \def (getl_gen_all c e h H0) in (let TMP_1 \def 
-(\lambda (e0: C).(drop h O c e0)) in (let TMP_2 \def (\lambda (e0: C).(clear 
-e0 e)) in (let TMP_3 \def (minus i h) in (let TMP_4 \def (getl TMP_3 e a) in 
-(let TMP_7 \def (\lambda (x: C).(\lambda (H3: (drop h O c x)).(\lambda (H4: 
-(clear x e)).(let TMP_5 \def (minus i h) in (let TMP_6 \def 
-(getl_drop_conf_ge i a c H x h O H3 H1) in (getl_clear_conf TMP_5 x a TMP_6 e 
-H4)))))) in (ex2_ind C TMP_1 TMP_2 TMP_4 TMP_7 H2)))))))))))))).
+(H1: (le h i)).(let H2 \def (getl_gen_all c e h H0) in (ex2_ind C (\lambda 
+(e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e)) (getl (minus i h) e 
+a) (\lambda (x: C).(\lambda (H3: (drop h O c x)).(\lambda (H4: (clear x 
+e)).(getl_clear_conf (minus i h) x a (getl_drop_conf_ge i a c H x h O H3 H1) 
+e H4)))) H2))))))))).
 
 theorem getl_trans:
  \forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall (h: nat).((getl 
@@ -40,19 +38,14 @@ e2)))))))
 \def
  \lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda (h: 
 nat).(\lambda (H: (getl h c1 c2)).(\lambda (e2: C).(\lambda (H0: (getl i c2 
-e2)).(let H1 \def (getl_gen_all c2 e2 i H0) in (let TMP_1 \def (\lambda (e: 
-C).(drop i O c2 e)) in (let TMP_2 \def (\lambda (e: C).(clear e e2)) in (let 
-TMP_3 \def (plus i h) in (let TMP_4 \def (getl TMP_3 c1 e2) in (let TMP_14 
-\def (\lambda (x: C).(\lambda (H2: (drop i O c2 x)).(\lambda (H3: (clear x 
-e2)).(let TMP_6 \def (\lambda (n: nat).((drop n O c2 x) \to (let TMP_5 \def 
-(plus n h) in (getl TMP_5 c1 e2)))) in (let TMP_10 \def (\lambda (H4: (drop O 
-O c2 x)).(let TMP_7 \def (\lambda (c: C).(clear c e2)) in (let TMP_8 \def 
-(drop_gen_refl c2 x H4) in (let H5 \def (eq_ind_r C x TMP_7 H3 c2 TMP_8) in 
-(let TMP_9 \def (plus O h) in (getl_clear_trans TMP_9 c1 c2 H e2 H5)))))) in 
-(let TMP_13 \def (\lambda (i0: nat).(\lambda (_: (((drop i0 O c2 x) \to (getl 
-(plus i0 h) c1 e2)))).(\lambda (H4: (drop (S i0) O c2 x)).(let H_y \def 
-(getl_drop_trans c1 c2 h H x i0 H4) in (let TMP_11 \def (S i0) in (let TMP_12 
-\def (plus TMP_11 h) in (getl_intro TMP_12 c1 e2 x H_y H3))))))) in (nat_ind 
-TMP_6 TMP_10 TMP_13 i H2))))))) in (ex2_ind C TMP_1 TMP_2 TMP_4 TMP_14 
-H1))))))))))))).
+e2)).(let H1 \def (getl_gen_all c2 e2 i H0) in (ex2_ind C (\lambda (e: 
+C).(drop i O c2 e)) (\lambda (e: C).(clear e e2)) (getl (plus i h) c1 e2) 
+(\lambda (x: C).(\lambda (H2: (drop i O c2 x)).(\lambda (H3: (clear x 
+e2)).(nat_ind (\lambda (n: nat).((drop n O c2 x) \to (getl (plus n h) c1 
+e2))) (\lambda (H4: (drop O O c2 x)).(let H5 \def (eq_ind_r C x (\lambda (c: 
+C).(clear c e2)) H3 c2 (drop_gen_refl c2 x H4)) in (getl_clear_trans (plus O 
+h) c1 c2 H e2 H5))) (\lambda (i0: nat).(\lambda (_: (((drop i0 O c2 x) \to 
+(getl (plus i0 h) c1 e2)))).(\lambda (H4: (drop (S i0) O c2 x)).(let H_y \def 
+(getl_drop_trans c1 c2 h H x i0 H4) in (getl_intro (plus (S i0) h) c1 e2 x 
+H_y H3))))) i H2)))) H1)))))))).