update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubt/pc3.ma b/matita/matita/contribs/lambdadelta/basic_1/csubt/pc3.ma
index c27906d3a24536291f4f1f47d44553c7ccac6ef7..60a4452e3d9756d6590efeb42254263bf51c6a55 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubt/pc3.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubt/pc3.ma
@@ -18,45 +18,39 @@ include "basic_1/csubt/getl.ma".
 
 include "basic_1/pc3/left.ma".
 
-theorem csubt_pr2:
+lemma csubt_pr2:
  \forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((pr2 c1 
 t1 t2) \to (\forall (c2: C).((csubt g c1 c2) \to (pr2 c2 t1 t2)))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda 
-(H: (pr2 c1 t1 t2)).(let TMP_1 \def (\lambda (c: C).(\lambda (t: T).(\lambda 
-(t0: T).(\forall (c2: C).((csubt g c c2) \to (pr2 c2 t t0)))))) in (let TMP_2 
-\def (\lambda (c: C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H0: (pr0 t3 
-t4)).(\lambda (c2: C).(\lambda (_: (csubt g c c2)).(pr2_free c2 t3 t4 
-H0))))))) in (let TMP_9 \def (\lambda (c: C).(\lambda (d: C).(\lambda (u: 
-T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) 
-u))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H1: (pr0 t3 t4)).(\lambda 
-(t: T).(\lambda (H2: (subst0 i u t4 t)).(\lambda (c2: C).(\lambda (H3: (csubt 
-g c c2)).(let H4 \def (csubt_getl_abbr g c d u i H0 c2 H3) in (let TMP_3 \def 
-(\lambda (d2: C).(csubt g d d2)) in (let TMP_6 \def (\lambda (d2: C).(let 
-TMP_4 \def (Bind Abbr) in (let TMP_5 \def (CHead d2 TMP_4 u) in (getl i c2 
-TMP_5)))) in (let TMP_7 \def (pr2 c2 t3 t) in (let TMP_8 \def (\lambda (x: 
-C).(\lambda (_: (csubt g d x)).(\lambda (H6: (getl i c2 (CHead x (Bind Abbr) 
-u))).(pr2_delta c2 x u i H6 t3 t4 H1 t H2)))) in (ex2_ind C TMP_3 TMP_6 TMP_7 
-TMP_8 H4)))))))))))))))))) in (pr2_ind TMP_1 TMP_2 TMP_9 c1 t1 t2 H)))))))).
+(H: (pr2 c1 t1 t2)).(pr2_ind (\lambda (c: C).(\lambda (t: T).(\lambda (t0: 
+T).(\forall (c2: C).((csubt g c c2) \to (pr2 c2 t t0)))))) (\lambda (c: 
+C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H0: (pr0 t3 t4)).(\lambda (c2: 
+C).(\lambda (_: (csubt g c c2)).(pr2_free c2 t3 t4 H0))))))) (\lambda (c: 
+C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c 
+(CHead d (Bind Abbr) u))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H1: 
+(pr0 t3 t4)).(\lambda (t: T).(\lambda (H2: (subst0 i u t4 t)).(\lambda (c2: 
+C).(\lambda (H3: (csubt g c c2)).(let H4 \def (csubt_getl_abbr g c d u i H0 
+c2 H3) in (ex2_ind C (\lambda (d2: C).(csubt g d d2)) (\lambda (d2: C).(getl 
+i c2 (CHead d2 (Bind Abbr) u))) (pr2 c2 t3 t) (\lambda (x: C).(\lambda (_: 
+(csubt g d x)).(\lambda (H6: (getl i c2 (CHead x (Bind Abbr) u))).(pr2_delta 
+c2 x u i H6 t3 t4 H1 t H2)))) H4)))))))))))))) c1 t1 t2 H))))).
 
-theorem csubt_pc3:
+lemma csubt_pc3:
  \forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((pc3 c1 
 t1 t2) \to (\forall (c2: C).((csubt g c1 c2) \to (pc3 c2 t1 t2)))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda 
-(H: (pc3 c1 t1 t2)).(let TMP_1 \def (\lambda (t: T).(\lambda (t0: T).(\forall 
-(c2: C).((csubt g c1 c2) \to (pc3 c2 t t0))))) in (let TMP_2 \def (\lambda 
-(t: T).(\lambda (c2: C).(\lambda (_: (csubt g c1 c2)).(pc3_refl c2 t)))) in 
-(let TMP_6 \def (\lambda (t0: T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 t0 
-t3)).(\lambda (t4: T).(\lambda (_: (pc3 c1 t3 t4)).(\lambda (H2: ((\forall 
-(c2: C).((csubt g c1 c2) \to (pc3 c2 t3 t4))))).(\lambda (c2: C).(\lambda 
-(H3: (csubt g c1 c2)).(let TMP_3 \def (csubt_pr2 g c1 t0 t3 H0 c2 H3) in (let 
-TMP_4 \def (pc3_pr2_r c2 t0 t3 TMP_3) in (let TMP_5 \def (H2 c2 H3) in (pc3_t 
-t3 c2 t0 TMP_4 t4 TMP_5)))))))))))) in (let TMP_10 \def (\lambda (t0: 
-T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 t0 t3)).(\lambda (t4: T).(\lambda 
-(_: (pc3 c1 t0 t4)).(\lambda (H2: ((\forall (c2: C).((csubt g c1 c2) \to (pc3 
-c2 t0 t4))))).(\lambda (c2: C).(\lambda (H3: (csubt g c1 c2)).(let TMP_7 \def 
-(csubt_pr2 g c1 t0 t3 H0 c2 H3) in (let TMP_8 \def (pc3_pr2_x c2 t3 t0 TMP_7) 
-in (let TMP_9 \def (H2 c2 H3) in (pc3_t t0 c2 t3 TMP_8 t4 TMP_9)))))))))))) 
-in (pc3_ind_left c1 TMP_1 TMP_2 TMP_6 TMP_10 t1 t2 H))))))))).
+(H: (pc3 c1 t1 t2)).(pc3_ind_left c1 (\lambda (t: T).(\lambda (t0: 
+T).(\forall (c2: C).((csubt g c1 c2) \to (pc3 c2 t t0))))) (\lambda (t: 
+T).(\lambda (c2: C).(\lambda (_: (csubt g c1 c2)).(pc3_refl c2 t)))) (\lambda 
+(t0: T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 t0 t3)).(\lambda (t4: 
+T).(\lambda (_: (pc3 c1 t3 t4)).(\lambda (H2: ((\forall (c2: C).((csubt g c1 
+c2) \to (pc3 c2 t3 t4))))).(\lambda (c2: C).(\lambda (H3: (csubt g c1 
+c2)).(pc3_t t3 c2 t0 (pc3_pr2_r c2 t0 t3 (csubt_pr2 g c1 t0 t3 H0 c2 H3)) t4 
+(H2 c2 H3)))))))))) (\lambda (t0: T).(\lambda (t3: T).(\lambda (H0: (pr2 c1 
+t0 t3)).(\lambda (t4: T).(\lambda (_: (pc3 c1 t0 t4)).(\lambda (H2: ((\forall 
+(c2: C).((csubt g c1 c2) \to (pc3 c2 t0 t4))))).(\lambda (c2: C).(\lambda 
+(H3: (csubt g c1 c2)).(pc3_t t0 c2 t3 (pc3_pr2_x c2 t3 t0 (csubt_pr2 g c1 t0 
+t3 H0 c2 H3)) t4 (H2 c2 H3)))))))))) t1 t2 H))))).