update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / sty1 / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/sty1/props.ma b/matita/matita/contribs/lambdadelta/basic_1/sty1/props.ma
index 46a807164378144319309e68a3b6fd3bd97db14d..0780b7eebed7895f0b9d15fca685f742f1838a61 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/sty1/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/sty1/props.ma
@@ -29,7 +29,7 @@ c t t3)).(sty1_sing g c t1 t H t3 H1))) (\lambda (t0: T).(\lambda (_: (sty1 g
 c t t0)).(\lambda (H2: (sty1 g c t1 t0)).(\lambda (t3: T).(\lambda (H3: (sty0 
 g c t0 t3)).(sty1_sing g c t1 t0 H2 t3 H3)))))) t2 H0))))))).
 
-theorem sty1_bind:
+lemma sty1_bind:
  \forall (g: G).(\forall (b: B).(\forall (c: C).(\forall (v: T).(\forall (t1: 
 T).(\forall (t2: T).((sty1 g (CHead c (Bind b) v) t1 t2) \to (sty1 g c (THead 
 (Bind b) v t1) (THead (Bind b) v t2))))))))
@@ -45,7 +45,7 @@ t1) (THead (Bind b) v t))).(\lambda (t3: T).(\lambda (H2: (sty0 g (CHead c
 (Bind b) v) t t3)).(sty1_sing g c (THead (Bind b) v t1) (THead (Bind b) v t) 
 H1 (THead (Bind b) v t3) (sty0_bind g b c v t t3 H2))))))) t2 H))))))).
 
-theorem sty1_appl:
+lemma sty1_appl:
  \forall (g: G).(\forall (c: C).(\forall (v: T).(\forall (t1: T).(\forall 
 (t2: T).((sty1 g c t1 t2) \to (sty1 g c (THead (Flat Appl) v t1) (THead (Flat 
 Appl) v t2)))))))
@@ -60,7 +60,7 @@ t1) (THead (Flat Appl) v t))).(\lambda (t3: T).(\lambda (H2: (sty0 g c t
 t3)).(sty1_sing g c (THead (Flat Appl) v t1) (THead (Flat Appl) v t) H1 
 (THead (Flat Appl) v t3) (sty0_appl g c v t t3 H2))))))) t2 H)))))).
 
-theorem sty1_lift:
+lemma sty1_lift:
  \forall (g: G).(\forall (e: C).(\forall (t1: T).(\forall (t2: T).((sty1 g e 
 t1 t2) \to (\forall (c: C).(\forall (h: nat).(\forall (d: nat).((drop h d c 
 e) \to (sty1 g c (lift h d t1) (lift h d t2))))))))))
@@ -78,7 +78,7 @@ c h d H1)))))))) (\lambda (t: T).(\lambda (_: (sty1 g e t1 t)).(\lambda (H1:
 (H3: (drop h d c e)).(sty1_sing g c (lift h d t1) (lift h d t) (H1 c h d H3) 
 (lift h d t3) (sty0_lift g e t t3 H2 c h d H3))))))))))) t2 H))))).
 
-theorem sty1_correct:
+lemma sty1_correct:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t: T).((sty1 g c 
 t1 t) \to (ex T (\lambda (t2: T).(sty0 g c t t2)))))))
 \def
@@ -89,7 +89,7 @@ t2)).(sty0_correct g c t1 t2 H0))) (\lambda (t0: T).(\lambda (_: (sty1 g c t1
 t0)).(\lambda (_: (ex T (\lambda (t2: T).(sty0 g c t0 t2)))).(\lambda (t2: 
 T).(\lambda (H2: (sty0 g c t0 t2)).(sty0_correct g c t0 t2 H2)))))) t H))))).
 
-theorem sty1_abbr:
+lemma sty1_abbr:
  \forall (g: G).(\forall (c: C).(\forall (d: C).(\forall (v: T).(\forall (i: 
 nat).((getl i c (CHead d (Bind Abbr) v)) \to (\forall (w: T).((sty1 g d v w) 
 \to (sty1 g c (TLRef i) (lift (S i) O w)))))))))
@@ -105,7 +105,7 @@ t2)).(sty1_sing g c (TLRef i) (lift (S i) O t) H2 (lift (S i) O t2)
 (sty0_lift g d t t2 H3 c (S i) O (getl_drop Abbr c d v i H)))))))) w 
 H0)))))))).
 
-theorem sty1_cast2:
+lemma sty1_cast2:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((sty1 g c 
 t1 t2) \to (\forall (v1: T).(\forall (v2: T).((sty0 g c v1 v2) \to (ex2 T 
 (\lambda (v3: T).(sty1 g c v1 v3)) (\lambda (v3: T).(sty1 g c (THead (Flat