version 0.7.1

[helm.git] / helm / matita / library / nat.ma

diff --git a/helm/matita/library/nat.ma b/helm/matita/library/nat.ma
index 3ab39d9e485883e51868263d0b47c64cb42aebff..c125e6775b7a2f48604f5912dad0f7c2c5defde6 100644 (file)
--- a/helm/matita/library/nat.ma
+++ b/helm/matita/library/nat.ma
@@ -36,8 +36,8 @@ qed.
 theorem injective_S : \forall n,m:nat. 
 (eq nat (S n) (S m)) \to (eq nat n m).
 intros;
-rewrite > pred_Sn n;
-rewrite > pred_Sn m;
+rewrite > pred_Sn;
+rewrite > pred_Sn m.
 apply f_equal; assumption.
 qed.
 
@@ -103,8 +103,8 @@ theorem times_n_Sm :
 \forall n,m:nat. eq nat (plus n (times n  m)) (times n (S m)).
 intros.elim n.simplify.reflexivity.
 simplify.apply f_equal.rewrite < H.
-transitivity (plus (plus e m) (times e m)).symmetry.
-apply assoc_plus.transitivity (plus (plus m e) (times e m)).
+transitivity (plus (plus e1 m) (times e1 m)).symmetry.
+apply assoc_plus.transitivity (plus (plus m e1) (times e1 m)).
 apply f_equal2.
 apply sym_plus.reflexivity.apply assoc_plus.
 qed.
@@ -112,7 +112,7 @@ qed.
 theorem sym_times : 
 \forall n,m:nat. eq nat (times n m) (times m n).
 intros.elim n.simplify.apply times_n_O.
-simplify.rewrite < sym_eq ? ? ? H.apply times_n_Sm.
+simplify.rewrite > H.apply times_n_Sm.
 qed.
 
 let rec minus n m \def 
@@ -188,7 +188,7 @@ qed.
 
 theorem le_Sn_n : \forall n:nat. Not (le (S n) n).
 intros.elim n.apply le_Sn_O.simplify.intros.
-cut le (S e) e.apply H.assumption.apply le_S_n.assumption.
+cut le (S e1) e1.apply H.assumption.apply le_S_n.assumption.
 qed.
 
 theorem le_antisym : \forall n,m:nat. (le n m) \to (le m n) \to (eq nat n m).