X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2FZ%2Fz.ma;h=d18c80b23ac323b996280a835a52912fc2ffc8ce;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=997229763f5fc77f4a62790ffe009bd1d65cd0f0;hpb=5a702cea95883f7095c16b450e065ccb1714fc5a;p=helm.git

diff --git a/helm/matita/library/Z/z.ma b/helm/matita/library/Z/z.ma
index 997229763..d18c80b23 100644
--- a/helm/matita/library/Z/z.ma
+++ b/helm/matita/library/Z/z.ma
@@ -51,20 +51,20 @@ match z with
 theorem OZ_test_to_Prop :\forall z:Z.
 match OZ_test z with
 [true \Rightarrow z=OZ 
-|false \Rightarrow \lnot (z=OZ)].
+|false \Rightarrow z \neq OZ].
 intros.elim z.
 simplify.reflexivity.
-simplify.intros [H].
+simplify. unfold Not. intros (H).
 discriminate H.
-simplify.intros [H].
+simplify. unfold Not. intros (H).
 discriminate H.
 qed.
 
 (* discrimination *)
 theorem injective_pos: injective nat Z pos.
-simplify.
+unfold injective.
 intros.
-change with abs (pos x) = abs (pos y).
+change with (abs (pos x) = abs (pos y)).
 apply eq_f.assumption.
 qed.
 
@@ -72,32 +72,32 @@ variant inj_pos : \forall n,m:nat. pos n = pos m \to n = m
 \def injective_pos.
 
 theorem injective_neg: injective nat Z neg.
-simplify.
+unfold injective.
 intros.
-change with abs (neg x) = abs (neg y).
+change with (abs (neg x) = abs (neg y)).
 apply eq_f.assumption.
 qed.
 
 variant inj_neg : \forall n,m:nat. neg n = neg m \to n = m
 \def injective_neg.
 
-theorem not_eq_OZ_pos: \forall n:nat. \lnot (OZ = (pos n)).
-simplify.intros [n; H].
+theorem not_eq_OZ_pos: \forall n:nat. OZ \neq pos n.
+unfold Not.intros (n H).
 discriminate H.
 qed.
 
-theorem not_eq_OZ_neg :\forall n:nat. \lnot (OZ = (neg n)).
-simplify.intros [n; H].
+theorem not_eq_OZ_neg :\forall n:nat. OZ \neq neg n.
+unfold Not.intros (n H).
 discriminate H.
 qed.
 
-theorem not_eq_pos_neg :\forall n,m:nat. \lnot ((pos n) = (neg m)).
-simplify.intros [n; m; H].
+theorem not_eq_pos_neg :\forall n,m:nat. pos n \neq neg m.
+unfold Not.intros (n m H).
 discriminate H.
 qed.
 
 theorem decidable_eq_Z : \forall x,y:Z. decidable (x=y).
-intros.simplify.
+intros.unfold decidable.
 elim x.
 (* goal: x=OZ *)
   elim y.
@@ -110,25 +110,25 @@ elim x.
 (* goal: x=pos *)
   elim y.
   (* goal: x=pos y=OZ *)
-    right.intro.
-    apply not_eq_OZ_pos n. symmetry. assumption.
+    right.unfold Not.intro.
+    apply (not_eq_OZ_pos n). symmetry. assumption.
   (* goal: x=pos y=pos *)
-    elim (decidable_eq_nat n n1:(Or (n=n1) ((n=n1) \to False))).
+    elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
     left.apply eq_f.assumption.
-    right.intros [H_inj].apply H. injection H_inj. assumption.
+    right.unfold Not.intros (H_inj).apply H. injection H_inj. assumption.
   (* goal: x=pos y=neg *)
-    right.intro.apply not_eq_pos_neg n n1. assumption.
+    right.unfold Not.intro.apply (not_eq_pos_neg n n1). assumption.
 (* goal: x=neg *)
   elim y.
   (* goal: x=neg y=OZ *)
-    right.intro.
-    apply not_eq_OZ_neg n. symmetry. assumption.
+    right.unfold Not.intro.
+    apply (not_eq_OZ_neg n). symmetry. assumption.
   (* goal: x=neg y=pos *)
-    right. intro. apply not_eq_pos_neg n1 n. symmetry. assumption.
+    right. unfold Not.intro. apply (not_eq_pos_neg n1 n). symmetry. assumption.
   (* goal: x=neg y=neg *)
-    elim (decidable_eq_nat n n1:(Or (n=n1) ((n=n1) \to False))).
+    elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
     left.apply eq_f.assumption.
-    right.intro.apply H.apply injective_neg.assumption.
+    right.unfold Not.intro.apply H.apply injective_neg.assumption.
 qed.
 
 (* end discrimination *)