update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubc / arity.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubc/arity.ma b/matita/matita/contribs/lambdadelta/basic_1/csubc/arity.ma
index 72943adfca646d9c1fdce2b47e991d4ad04d35dd..63593633a83fe42837254ab3565a63fcc93b8b37 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubc/arity.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubc/arity.ma
@@ -16,22 +16,21 @@
 
 include "basic_1/csubc/csuba.ma".
 
-theorem csubc_arity_conf:
+lemma csubc_arity_conf:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubc g c1 c2) \to 
 (\forall (t: T).(\forall (a: A).((arity g c1 t a) \to (arity g c2 t a)))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubc g c1 
-c2)).(\lambda (t: T).(\lambda (a: A).(\lambda (H0: (arity g c1 t a)).(let 
-TMP_1 \def (csubc_csuba g c1 c2 H) in (csuba_arity g c1 t a H0 c2 
-TMP_1)))))))).
+c2)).(\lambda (t: T).(\lambda (a: A).(\lambda (H0: (arity g c1 t 
+a)).(csuba_arity g c1 t a H0 c2 (csubc_csuba g c1 c2 H)))))))).
 
-theorem csubc_arity_trans:
+lemma csubc_arity_trans:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubc g c1 c2) \to 
 ((csubv c1 c2) \to (\forall (t: T).(\forall (a: A).((arity g c2 t a) \to 
 (arity g c1 t a))))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubc g c1 
 c2)).(\lambda (H0: (csubv c1 c2)).(\lambda (t: T).(\lambda (a: A).(\lambda 
-(H1: (arity g c2 t a)).(let TMP_1 \def (csubc_csuba g c1 c2 H) in 
-(csuba_arity_rev g c2 t a H1 c1 TMP_1 H0))))))))).
+(H1: (arity g c2 t a)).(csuba_arity_rev g c2 t a H1 c1 (csubc_csuba g c1 c2 
+H) H0)))))))).