A few changes to factorization and gcd.

[helm.git] / helm / matita / library / Z / z.ma

diff --git a/helm/matita/library/Z/z.ma b/helm/matita/library/Z/z.ma
index 207457a913e4e9c91574cf2e630ea61f3f2feb93..8ce0047e169f6b6a8b014d4614877e6e9c2eb7c4 100644 (file)
--- a/helm/matita/library/Z/z.ma
+++ b/helm/matita/library/Z/z.ma
@@ -14,8 +14,8 @@
 
 set "baseuri" "cic:/matita/Z/z".
 
+include "datatypes/bool.ma".
 include "nat/nat.ma".
-include "higher_order_defs/functions.ma".
 
 inductive Z : Set \def
   OZ : Z
@@ -51,7 +51,7 @@ 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].
@@ -81,17 +81,17 @@ 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)).
+theorem not_eq_OZ_pos: \forall n:nat. OZ \neq pos n.
 simplify.intros [n; H].
 discriminate H.
 qed.
 
-theorem not_eq_OZ_neg :\forall n:nat. \lnot (OZ = (neg n)).
+theorem not_eq_OZ_neg :\forall n:nat. OZ \neq neg n.
 simplify.intros [n; H].
 discriminate H.
 qed.
 
-theorem not_eq_pos_neg :\forall n,m:nat. \lnot ((pos n) = (neg m)).
+theorem not_eq_pos_neg :\forall n,m:nat. pos n \neq neg m.
 simplify.intros [n; m; H].
 discriminate H.
 qed.
@@ -113,7 +113,7 @@ elim x.
     right.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.
   (* goal: x=pos y=neg *)
@@ -126,7 +126,7 @@ elim x.
   (* goal: x=neg y=pos *)
     right. 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.
 qed.