ocaml 3.09 transition

[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 e36c1beaa95303f52e693f11e4ac7f3d913b6928..a75032d7123b7018f40af65285712d5c3c4da9c1 100644 (file)
--- a/helm/matita/library/nat/nat.ma
+++ b/helm/matita/library/nat/nat.ma
@@ -30,10 +30,10 @@ intros. reflexivity.
 qed.
 
 theorem injective_S : injective nat nat S.
-simplify.
+unfold injective.
 intros.
 rewrite > pred_Sn.
-rewrite > pred_Sn y.
+rewrite > (pred_Sn y).
 apply eq_f. assumption.
 qed.
 
@@ -42,7 +42,7 @@ theorem inj_S : \forall n,m:nat.(S n)=(S m) \to n=m
 
 theorem not_eq_S  : \forall n,m:nat. 
 \lnot n=m \to S n \neq S m.
-intros. simplify. intros.
+intros. unfold Not. intros.
 apply H. apply injective_S. assumption.
 qed.
 
@@ -53,7 +53,7 @@ definition not_zero : nat \to Prop \def
   | (S p) \Rightarrow True ].
 
 theorem not_eq_O_S : \forall n:nat. O \neq S n.
-intros. simplify. intros.
+intros. unfold Not. intros.
 cut (not_zero O).
 exact Hcut.
 rewrite > H.exact I.
@@ -86,18 +86,18 @@ theorem nat_elim2 :
 (\forall n,m:nat. R n m \to R (S n) (S m)) \to \forall n,m:nat. R n m.
 intros 5.elim n.
 apply H.
-apply nat_case m.apply H1.
+apply (nat_case m).apply H1.
 intros.apply H2. apply H3.
 qed.
 
 theorem decidable_eq_nat : \forall n,m:nat.decidable (n=m).
-intros.simplify.
-apply nat_elim2 (\lambda n,m.(Or (n=m) ((n=m) \to False))).
+intros.unfold decidable.
+apply (nat_elim2 (\lambda n,m.(Or (n=m) ((n=m) \to False)))).
 intro.elim n1.
 left.reflexivity.
 right.apply not_eq_O_S.
 intro.right.intro.
-apply not_eq_O_S n1.
+apply (not_eq_O_S n1).
 apply sym_eq.assumption.
 intros.elim H.
 left.apply eq_f. assumption.