X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2FZ%2Fz.ma;h=31c3a7003bdffca309780ce3e38122712efe4368;hb=6d297b12c480352eb2f156ab4515f73921ea2e81;hp=ea50a2cd9c3b70729df6c8c6bb4b16d661d80d41;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git

diff --git a/helm/software/matita/library/Z/z.ma b/helm/software/matita/library/Z/z.ma
index ea50a2cd9..31c3a7003 100644
--- a/helm/software/matita/library/Z/z.ma
+++ b/helm/software/matita/library/Z/z.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/Z/z".
-
 include "datatypes/bool.ma".
 include "nat/nat.ma".
 
@@ -22,24 +20,31 @@ inductive Z : Set \def
 | pos : nat \to Z
 | neg : nat \to Z.
 
+interpretation "Integers" 'Z = Z.
+
 definition Z_of_nat \def
 \lambda n. match n with
 [ O \Rightarrow  OZ 
 | (S n)\Rightarrow  pos n].
 
-coercion cic:/matita/Z/z/Z_of_nat.con.
+coercion Z_of_nat.
 
 definition neg_Z_of_nat \def
 \lambda n. match n with
 [ O \Rightarrow  OZ 
 | (S n)\Rightarrow  neg n].
 
+lemma pos_n_eq_S_n : \forall n : nat.
+  (pos n) = (S n).
+intro.reflexivity. 
+qed.
+
 definition abs \def
 \lambda z.
  match z with 
 [ OZ \Rightarrow O
-| (pos n) \Rightarrow n
-| (neg n) \Rightarrow n].
+| (pos n) \Rightarrow (S n)
+| (neg n) \Rightarrow (S n)].
 
 definition OZ_test \def
 \lambda z.
@@ -55,15 +60,16 @@ match OZ_test z with
 intros.elim z.
 simplify.reflexivity.
 simplify. unfold Not. intros (H).
-discriminate H.
+destruct H.
 simplify. unfold Not. intros (H).
-discriminate H.
+destruct H.
 qed.
 
 (* discrimination *)
 theorem injective_pos: injective nat Z pos.
 unfold injective.
 intros.
+apply inj_S.
 change with (abs (pos x) = abs (pos y)).
 apply eq_f.assumption.
 qed.
@@ -74,6 +80,7 @@ variant inj_pos : \forall n,m:nat. pos n = pos m \to n = m
 theorem injective_neg: injective nat Z neg.
 unfold injective.
 intros.
+apply inj_S.
 change with (abs (neg x) = abs (neg y)).
 apply eq_f.assumption.
 qed.
@@ -83,17 +90,17 @@ variant inj_neg : \forall n,m:nat. neg n = neg m \to n = m
 
 theorem not_eq_OZ_pos: \forall n:nat. OZ \neq pos n.
 unfold Not.intros (n H).
-discriminate H.
+destruct H.
 qed.
 
 theorem not_eq_OZ_neg :\forall n:nat. OZ \neq neg n.
 unfold Not.intros (n H).
-discriminate H.
+destruct H.
 qed.
 
 theorem not_eq_pos_neg :\forall n,m:nat. pos n \neq neg m.
 unfold Not.intros (n m H).
-discriminate H.
+destruct H.
 qed.
 
 theorem decidable_eq_Z : \forall x,y:Z. decidable (x=y).
@@ -115,7 +122,7 @@ elim x.
   (* goal: x=pos y=pos *)
     elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
     left.apply eq_f.assumption.
-    right.unfold Not.intros (H_inj).apply H. injection H_inj. assumption.
+    right.unfold Not.intros (H_inj).apply H. destruct H_inj. reflexivity.
   (* goal: x=pos y=neg *)
     right.unfold Not.intro.apply (not_eq_pos_neg n n1). assumption.
 (* goal: x=neg *)