X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2FZ%2Fcompare.ma;h=4a5025975fe3d8d4b3f610563b565dce39be6bac;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=a8f8aca3918f12c1a7a60fb475338a81da32dfbe;hpb=78044035b4419e569df0d7f6a7f96fa32d21a19d;p=helm.git

diff --git a/helm/matita/library/Z/compare.ma b/helm/matita/library/Z/compare.ma
index a8f8aca39..4a5025975 100644
--- a/helm/matita/library/Z/compare.ma
+++ b/helm/matita/library/Z/compare.ma
@@ -14,8 +14,6 @@
 
 set "baseuri" "cic:/matita/Z/compare".
 
-include "datatypes/bool.ma".
-include "datatypes/compare.ma".
 include "Z/orders.ma".
 include "nat/compare.ma".
 
@@ -43,7 +41,7 @@ theorem eqZb_to_Prop:
 \forall x,y:Z. 
 match eqZb x y with
 [ true \Rightarrow x=y
-| false \Rightarrow \lnot x=y].
+| false \Rightarrow x \neq y].
 intros.
 elim x.
   elim y.
@@ -51,31 +49,31 @@ elim x.
     simplify.apply not_eq_OZ_pos.
     simplify.apply not_eq_OZ_neg.
   elim y.
-    simplify.intro.apply not_eq_OZ_pos n.apply sym_eq.assumption.
+    simplify.unfold Not.intro.apply (not_eq_OZ_pos n).apply sym_eq.assumption.
     simplify.apply eqb_elim.
       intro.simplify.apply eq_f.assumption.
-      intro.simplify.intro.apply H.apply inj_pos.assumption.
+      intro.simplify.unfold Not.intro.apply H.apply inj_pos.assumption.
     simplify.apply not_eq_pos_neg.
   elim y.
-    simplify.intro.apply not_eq_OZ_neg n.apply sym_eq.assumption.
-    simplify.intro.apply not_eq_pos_neg n1 n.apply sym_eq.assumption.
+    simplify.unfold Not.intro.apply (not_eq_OZ_neg n).apply sym_eq.assumption.
+    simplify.unfold Not.intro.apply (not_eq_pos_neg n1 n).apply sym_eq.assumption.
     simplify.apply eqb_elim.
       intro.simplify.apply eq_f.assumption.
-      intro.simplify.intro.apply H.apply inj_neg.assumption.
+      intro.simplify.unfold Not.intro.apply H.apply inj_neg.assumption.
 qed.
 
 theorem eqZb_elim: \forall x,y:Z.\forall P:bool \to Prop.
-(x=y \to (P true)) \to (\lnot x=y \to (P false)) \to P (eqZb x y).
+(x=y \to (P true)) \to (x \neq y \to (P false)) \to P (eqZb x y).
 intros.
 cut 
-match (eqZb x y) with
+(match (eqZb x y) with
 [ true \Rightarrow x=y
-| false \Rightarrow \lnot x=y] \to P (eqZb x y).
+| false \Rightarrow x \neq y] \to P (eqZb x y)).
 apply Hcut.
 apply eqZb_to_Prop.
 elim (eqZb).
-apply H H2.
-apply H1 H2.
+apply (H H2).
+apply (H1 H2).
 qed.
 
 definition Z_compare : Z \to Z \to compare \def
@@ -111,14 +109,14 @@ elim x.
   elim y.
     simplify.exact I.
     simplify.
-      cut match (nat_compare n n1) with
+      cut (match (nat_compare n n1) with
       [ LT \Rightarrow n<n1
       | EQ \Rightarrow n=n1
       | GT \Rightarrow n1<n] \to 
       match (nat_compare n n1) with
       [ LT \Rightarrow (S n) \leq n1
       | EQ \Rightarrow pos n = pos n1
-      | GT \Rightarrow (S n1) \leq n]. 
+      | GT \Rightarrow (S n1) \leq n]). 
         apply Hcut.apply nat_compare_to_Prop. 
         elim (nat_compare n n1).
           simplify.exact H.
@@ -129,14 +127,14 @@ elim x.
     simplify.exact I.
     simplify.exact I.
     simplify. 
-      cut match (nat_compare n1 n) with
+      cut (match (nat_compare n1 n) with
       [ LT \Rightarrow n1<n
       | EQ \Rightarrow n1=n
       | GT \Rightarrow n<n1] \to 
       match (nat_compare n1 n) with
       [ LT \Rightarrow (S n1) \leq n
       | EQ \Rightarrow neg n = neg n1
-      | GT \Rightarrow (S n) \leq n1]. 
+      | GT \Rightarrow (S n) \leq n1]). 
         apply Hcut. apply nat_compare_to_Prop. 
         elim (nat_compare n1 n).
           simplify.exact H.