update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_1 / ext / tactics.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_1/ext/tactics.ma b/matita/matita/contribs/lambdadelta/ground_1/ext/tactics.ma
index a868d6db8c53a5f15dc620389313368086c02ca8..c2dff1889f818761797bfb517f05adf4f0d8960a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_1/ext/tactics.ma
+++ b/matita/matita/contribs/lambdadelta/ground_1/ext/tactics.ma
@@ -16,28 +16,26 @@
 
 include "ground_1/preamble.ma".
 
-theorem insert_eq:
+lemma insert_eq:
  \forall (S: Type[0]).(\forall (x: S).(\forall (P: ((S \to Prop))).(\forall 
 (G: ((S \to Prop))).(((\forall (y: S).((P y) \to ((eq S y x) \to (G y))))) 
 \to ((P x) \to (G x))))))
 \def
  \lambda (S: Type[0]).(\lambda (x: S).(\lambda (P: ((S \to Prop))).(\lambda 
 (G: ((S \to Prop))).(\lambda (H: ((\forall (y: S).((P y) \to ((eq S y x) \to 
-(G y)))))).(\lambda (H0: (P x)).(let TMP_1 \def (refl_equal S x) in (H x H0 
-TMP_1))))))).
+(G y)))))).(\lambda (H0: (P x)).(H x H0 (refl_equal S x))))))).
 
-theorem unintro:
+lemma unintro:
  \forall (A: Type[0]).(\forall (a: A).(\forall (P: ((A \to Prop))).(((\forall 
 (x: A).(P x))) \to (P a))))
 \def
  \lambda (A: Type[0]).(\lambda (a: A).(\lambda (P: ((A \to Prop))).(\lambda 
 (H: ((\forall (x: A).(P x)))).(H a)))).
 
-theorem xinduction:
+lemma xinduction:
  \forall (A: Type[0]).(\forall (t: A).(\forall (P: ((A \to Prop))).(((\forall 
 (x: A).((eq A t x) \to (P x)))) \to (P t))))
 \def
  \lambda (A: Type[0]).(\lambda (t: A).(\lambda (P: ((A \to Prop))).(\lambda 
-(H: ((\forall (x: A).((eq A t x) \to (P x))))).(let TMP_2 \def (refl_equal A 
-t) in (H t TMP_2))))).
+(H: ((\forall (x: A).((eq A t x) \to (P x))))).(H t (refl_equal A t))))).