X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Fprops.ma;h=ba563b7af941c80e46916fe3b532b0b0652c2283;hb=d9824956d9132109ed5f23380a0a1f9c5181d18a;hp=066e056e0435f74c01f0dc43970bbce5a2575994;hpb=a05d8741ee9ec2484542f74a111043af207f70a3;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
index 066e056e0..ba563b7af 100644
--- a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
@@ -12,25 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NLE/props".
 
-include "NLE/fwd.ma".
 
-theorem nle_refl: \forall x. x <= x.
- intros 1; elim x; clear x; intros; auto new.
-qed.
+include "NLE/order.ma".
 
-theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros. elim H; clear H x y; intros; auto new.
+theorem nle_trans_succ: ∀x,y. x ≤ y → x ≤ succ y.
+ intros; elim H; clear H x y; autobatch.
 qed.
 
-theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.
- intros 1. elim y; clear y; intros;
- [ lapply linear nle_gen_zero_2 to H. auto new
- | lapply linear nle_gen_succ_2 to H1. decompose;
-   [ subst. auto new
-   | lapply linear H to H3 as H0. decompose;
-     subst; auto new
-   ]
+theorem nle_gt_or_le: ∀x, y. y > x ∨ y ≤ x.
+ intros 2; elim y; clear y;
+ [ autobatch
+ | decompose;
+   [ lapply linear nle_inv_succ_1 to H1
+   | lapply linear nle_lt_or_eq to H1
+   ]; decompose; destruct; autobatch depth = 4
  ].
 qed.