X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FRELATIONAL%2FNLE%2Fprops.ma;h=db1476309eeca1e40e17833d0705519e1e49c6b8;hb=a2f9236b189b39bb5e7d864991cae29c9f9cb67f;hp=549eae418c2762cca71c10f6e8de7a706ba87719;hpb=2f857bf7f4d1bb73d08d270af9d7ad36a365a3c4;p=helm.git

diff --git a/matita/contribs/RELATIONAL/NLE/props.ma b/matita/contribs/RELATIONAL/NLE/props.ma
index 549eae418..db1476309 100644
--- a/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/matita/contribs/RELATIONAL/NLE/props.ma
@@ -14,38 +14,18 @@
 
 set "baseuri" "cic:/matita/RELATIONAL/NLE/props".
 
-include "NLE/fwd.ma".
-
-theorem nle_zero: \forall q. zero <= q.
- unfold NLE.
- intros. apply ex_intro; auto. (**)
-qed.
-
-theorem nle_succ: \forall p,q. p <= q \to succ p <= succ q.
- unfold NLE.
- intros. decompose.
- apply ex_intro; [|auto] (**)
-qed.
-
-theorem nle_refl: \forall x. x <= x.
- intros 1; elim x; clear x; intros; auto new timeout=100.
-qed.
+include "NLE/order.ma".
 
 theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros 1. elim x; clear x; intros; 
- [ auto new timeout=100.
- | lapply linear nle_gen_succ_1 to H1 as H0. decompose H0. subst.
-   auto new timeout=100.
- ].
+ intros. elim H; clear H x y; auto.
 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 timeout=100
- | lapply linear nle_gen_succ_2 to H1. decompose;
-   [ subst. auto new timeout=100
-   | lapply linear H to H3 as H0. decompose;
-     subst; auto new timeout=100
-   ]
+theorem nle_gt_or_le: \forall x, y. y > x \lor y <= x.
+ intros 2; elim y; clear y;
+ [ auto
+ | decompose;
+   [ lapply linear nle_inv_succ_1 to H1
+   | lapply linear nle_lt_or_eq to H1
+   ]; decompose; subst; auto depth = 4
  ].
 qed.