NLE is now derived fron NPlus rather than being a stand-alone relation

[helm.git] / helm / software / matita / contribs / RELATIONAL / NLE / props.ma

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
index bd76c2754b61db4aa5b540735245ae49eea16331..b571dfc6b46f9e8ab9385bef2462baf354e1d286 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
@@ -16,12 +16,27 @@ 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.
 
 theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros. elim H; clear H x y; intros; auto new timeout=100.
+ 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.
+ ].
 qed.
 
 theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.