update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / pc3 / subst1.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/pc3/subst1.ma b/matita/matita/contribs/lambdadelta/basic_1/pc3/subst1.ma
index 75a8794fd3f1772eacd6fd7e727f8d9cecf2874e..1df35129b7e4e61eea5d4032d87389c2998593a7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/pc3/subst1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/pc3/subst1.ma
@@ -18,7 +18,7 @@ include "basic_1/pc3/props.ma".
 
 include "basic_1/pr3/subst1.ma".
 
-theorem pc3_gen_cabbr:
+lemma pc3_gen_cabbr:
  \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to (\forall 
 (e: C).(\forall (u: T).(\forall (d: nat).((getl d c (CHead e (Bind Abbr) u)) 
 \to (\forall (a0: C).((csubst1 d u c a0) \to (\forall (a: C).((drop (S O) d 
@@ -30,24 +30,16 @@ t2)).(\lambda (e: C).(\lambda (u: T).(\lambda (d: nat).(\lambda (H0: (getl d
 c (CHead e (Bind Abbr) u))).(\lambda (a0: C).(\lambda (H1: (csubst1 d u c 
 a0)).(\lambda (a: C).(\lambda (H2: (drop (S O) d a0 a)).(\lambda (x1: 
 T).(\lambda (H3: (subst1 d u t1 (lift (S O) d x1))).(\lambda (x2: T).(\lambda 
-(H4: (subst1 d u t2 (lift (S O) d x2))).(let H5 \def H in (let TMP_1 \def 
-(\lambda (t: T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t: T).(pr3 c t2 
-t)) in (let TMP_3 \def (pc3 a x1 x2) in (let TMP_20 \def (\lambda (x: 
-T).(\lambda (H6: (pr3 c t1 x)).(\lambda (H7: (pr3 c t2 x)).(let TMP_6 \def 
-(\lambda (x3: T).(let TMP_4 \def (S O) in (let TMP_5 \def (lift TMP_4 d x3) 
-in (subst1 d u x TMP_5)))) in (let TMP_7 \def (\lambda (x3: T).(pr3 a x2 x3)) 
-in (let TMP_8 \def (pc3 a x1 x2) in (let TMP_18 \def (\lambda (x0: 
-T).(\lambda (H8: (subst1 d u x (lift (S O) d x0))).(\lambda (H9: (pr3 a x2 
-x0)).(let TMP_11 \def (\lambda (x3: T).(let TMP_9 \def (S O) in (let TMP_10 
-\def (lift TMP_9 d x3) in (subst1 d u x TMP_10)))) in (let TMP_12 \def 
-(\lambda (x3: T).(pr3 a x1 x3)) in (let TMP_13 \def (pc3 a x1 x2) in (let 
-TMP_16 \def (\lambda (x3: T).(\lambda (H10: (subst1 d u x (lift (S O) d 
-x3))).(\lambda (H11: (pr3 a x1 x3)).(let TMP_14 \def (\lambda (t: T).(pr3 a 
-x1 t)) in (let TMP_15 \def (subst1_confluence_lift x x3 u d H10 x0 H8) in 
-(let H12 \def (eq_ind T x3 TMP_14 H11 x0 TMP_15) in (pc3_pr3_t a x1 x0 H12 x2 
-H9))))))) in (let TMP_17 \def (pr3_gen_cabbr c t1 x H6 e u d H0 a0 H1 a H2 x1 
-H3) in (ex2_ind T TMP_11 TMP_12 TMP_13 TMP_16 TMP_17))))))))) in (let TMP_19 
-\def (pr3_gen_cabbr c t2 x H7 e u d H0 a0 H1 a H2 x2 H4) in (ex2_ind T TMP_6 
-TMP_7 TMP_8 TMP_18 TMP_19))))))))) in (ex2_ind T TMP_1 TMP_2 TMP_3 TMP_20 
-H5))))))))))))))))))))).
+(H4: (subst1 d u t2 (lift (S O) d x2))).(let H5 \def H in (ex2_ind T (\lambda 
+(t: T).(pr3 c t1 t)) (\lambda (t: T).(pr3 c t2 t)) (pc3 a x1 x2) (\lambda (x: 
+T).(\lambda (H6: (pr3 c t1 x)).(\lambda (H7: (pr3 c t2 x)).(ex2_ind T 
+(\lambda (x3: T).(subst1 d u x (lift (S O) d x3))) (\lambda (x3: T).(pr3 a x2 
+x3)) (pc3 a x1 x2) (\lambda (x0: T).(\lambda (H8: (subst1 d u x (lift (S O) d 
+x0))).(\lambda (H9: (pr3 a x2 x0)).(ex2_ind T (\lambda (x3: T).(subst1 d u x 
+(lift (S O) d x3))) (\lambda (x3: T).(pr3 a x1 x3)) (pc3 a x1 x2) (\lambda 
+(x3: T).(\lambda (H10: (subst1 d u x (lift (S O) d x3))).(\lambda (H11: (pr3 
+a x1 x3)).(let H12 \def (eq_ind T x3 (\lambda (t: T).(pr3 a x1 t)) H11 x0 
+(subst1_confluence_lift x x3 u d H10 x0 H8)) in (pc3_pr3_t a x1 x0 H12 x2 
+H9))))) (pr3_gen_cabbr c t1 x H6 e u d H0 a0 H1 a H2 x1 H3))))) 
+(pr3_gen_cabbr c t2 x H7 e u d H0 a0 H1 a H2 x2 H4))))) H5))))))))))))))))).