X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2FZ%2Forders.ma;h=c39f693085398eedf4a95a9f15898f05e6cee264;hb=97c2d258a5c524eb5c4b85208899d80751a2c82f;hp=f97c47eba0c16c3442874145446bafd19f720fdf;hpb=80b8635f33060e4a925a96bf6dc60e0386c01903;p=helm.git

diff --git a/helm/matita/library/Z/orders.ma b/helm/matita/library/Z/orders.ma
index f97c47eba..c39f69308 100644
--- a/helm/matita/library/Z/orders.ma
+++ b/helm/matita/library/Z/orders.ma
@@ -68,12 +68,12 @@ interpretation "integer 'not less than'" 'nless x y =
   (cic:/matita/logic/connectives/Not.con (cic:/matita/Z/orders/Zlt.con x y)).
 
 theorem irreflexive_Zlt: irreflexive Z Zlt.
-change with \forall x:Z. x < x \to False.
+change with (\forall x:Z. x < x \to False).
 intro.elim x.exact H.
-cut neg n < neg n \to False.
-apply Hcut.apply H.simplify.apply not_le_Sn_n.
-cut pos n < pos n \to False.
-apply Hcut.apply H.simplify.apply not_le_Sn_n.
+cut (neg n < neg n \to False).
+apply Hcut.apply H.simplify.unfold lt.apply not_le_Sn_n.
+cut (pos n < pos n \to False).
+apply Hcut.apply H.simplify.unfold lt.apply not_le_Sn_n.
 qed.
 
 theorem irrefl_Zlt: irreflexive Z Zlt
@@ -100,23 +100,31 @@ simplify.apply H.
 qed.
 
 theorem Zlt_to_Zle: \forall x,y:Z. x < y \to Zsucc x \leq y.
-intros 2.elim x.
-cut OZ < y \to Zsucc OZ \leq y.
-apply Hcut. assumption.simplify.elim y.
-simplify.exact H1.
-simplify.exact H1.
-simplify.apply le_O_n.
-cut neg n < y \to Zsucc (neg n) \leq y.
-apply Hcut. assumption.elim n.
-cut neg O < y \to Zsucc (neg O) \leq y.
-apply Hcut. assumption.simplify.elim y.
-simplify.exact I.simplify.apply not_le_Sn_O n1 H2.
-simplify.exact I.
-cut neg (S n1) < y \to (Zsucc (neg (S n1))) \leq y.
-apply Hcut. assumption.simplify.
-elim y.
-simplify.exact I.
-simplify.apply le_S_S_to_le n2 n1 H3.
-simplify.exact I.
-exact H.
+intros 2.
+elim x.
+(* goal: x=OZ *)
+  cut (OZ < y \to Zsucc OZ \leq y).
+    apply Hcut. assumption.
+    simplify.elim y. 
+      simplify.exact H1.
+      simplify.apply le_O_n.
+      simplify.exact H1.
+(* goal: x=pos *)      
+  exact H.
+(* goal: x=neg *)      
+  cut (neg n < y \to Zsucc (neg n) \leq y).
+    apply Hcut. assumption.
+    elim n.
+      cut (neg O < y \to Zsucc (neg O) \leq y).
+        apply Hcut. assumption.
+        simplify.elim y.
+          simplify.exact I.
+          simplify.exact I.
+          simplify.apply (not_le_Sn_O n1 H2).
+      cut (neg (S n1) < y \to (Zsucc (neg (S n1))) \leq y).
+        apply Hcut. assumption.simplify.
+        elim y.
+          simplify.exact I.
+          simplify.exact I.
+          simplify.apply (le_S_S_to_le n2 n1 H3).
 qed.