X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Forder.ma;h=473ac601d889d34fa47e01e64742d21ae1b7c3f1;hb=d9824956d9132109ed5f23380a0a1f9c5181d18a;hp=71de65d1d3f4e91c580c95b9e3d8ee5378e86235;hpb=295ad18b6a120d8317f0442d329a9d619a8cb53a;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/order.ma b/helm/software/matita/contribs/RELATIONAL/NLE/order.ma
index 71de65d1d..473ac601d 100644
--- a/helm/software/matita/contribs/RELATIONAL/NLE/order.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/order.ma
@@ -12,45 +12,41 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NLE/order".
+
 
 include "NLE/inv.ma".
 
-theorem nle_refl: \forall x. x <= x.
- intros; elim x; clear x; auto.
+theorem nle_refl: ∀x. x ≤ x.
+ intros; elim x; clear x; autobatch.
 qed.
 
-theorem nle_trans: \forall x,y. x <= y \to
-                   \forall z. y <= z \to x <= z.
- intros 3. elim H; clear H x y;
- [ auto
- | lapply linear nle_inv_succ_1 to H3. decompose. subst. 
-   auto
+theorem nle_trans: ∀x,y. x ≤ y → ∀z. y ≤ z → x ≤ z.
+ intros 3; elim H; clear H x y;
+ [ autobatch
+ | lapply linear nle_inv_succ_1 to H3. decompose. destruct. 
+   autobatch
  ].
 qed.
 
-theorem nle_false: \forall x,y. x <= y \to y < x \to False.
- intros 3; elim H; clear H x y; auto.
+theorem nle_false: ∀x,y. x ≤ y → y < x → False.
+ intros 3; elim H; clear H x y; autobatch.
 qed.
 
-theorem nle_irrefl: \forall x. x < x \to False.
- intros. auto.
+theorem nle_irrefl: ∀x. x < x → False.
+ intros. autobatch.
 qed.
 
-theorem nle_irrefl_ei: \forall x, z. z <= x \to z = succ x \to False.
- intros 3. elim H; clear H x z;
- [ destruct H1
- | destruct H3. clear H3. subst. auto.
- ].
+theorem nle_irrefl_ei: ∀x, z. z ≤ x → z = succ x → False.
+ intros 3; elim H; clear H x z; destruct; autobatch.
 qed.
 
-theorem nle_irrefl_smart: \forall x. x < x \to False.
- intros 1. elim x; clear x; auto.
+theorem nle_irrefl_smart: ∀x. x < x → False.
+ intros 1. elim x; clear x; autobatch.
 qed.
 
-theorem nle_lt_or_eq: \forall y, x. x <= y \to x < y \lor x = y.
- intros. elim H; clear H x y;
+theorem nle_lt_or_eq: ∀y, x. x ≤ y → x < y ∨ x = y.
+ intros; elim H; clear H x y;
  [ elim n; clear n
  | decompose
- ]; auto.
+ ]; autobatch.
 qed.