added hmysql

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

diff --git a/helm/matita/library/nat/nat.ma b/helm/matita/library/nat/nat.ma
index aae6434e7e55657890c883550dc380d2db86275f..e36c1beaa95303f52e693f11e4ac7f3d913b6928 100644 (file)
--- a/helm/matita/library/nat/nat.ma
+++ b/helm/matita/library/nat/nat.ma
@@ -26,7 +26,7 @@ definition pred: nat \to nat \def
 | (S p) \Rightarrow p ].
 
 theorem pred_Sn : \forall n:nat.n=(pred (S n)).
-intros; reflexivity.
+intros. reflexivity.
 qed.
 
 theorem injective_S : injective nat nat S.
@@ -41,7 +41,7 @@ theorem inj_S : \forall n,m:nat.(S n)=(S m) \to n=m
 \def injective_S.
 
 theorem not_eq_S  : \forall n,m:nat. 
-\lnot n=m \to \lnot (S n = S m).
+\lnot n=m \to S n \neq S m.
 intros. simplify. intros.
 apply H. apply injective_S. assumption.
 qed.
@@ -52,14 +52,14 @@ definition not_zero : nat \to Prop \def
   [ O \Rightarrow False
   | (S p) \Rightarrow True ].
 
-theorem not_eq_O_S : \forall n:nat. \lnot O=S n.
+theorem not_eq_O_S : \forall n:nat. O \neq S n.
 intros. simplify. intros.
 cut (not_zero O).
 exact Hcut.
 rewrite > H.exact I.
 qed.
 
-theorem not_eq_n_Sn : \forall n:nat. \lnot n=S n.
+theorem not_eq_n_Sn : \forall n:nat. n \neq S n.
 intros.elim n.
 apply not_eq_O_S.
 apply not_eq_S.assumption.