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 e961f5a9ced40c39a053ab7d7d07f88455a91bc8..b571dfc6b46f9e8ab9385bef2462baf354e1d286 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
@@ -16,23 +16,36 @@ 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.
+ 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.
+ 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.
  intros 1. elim y; clear y; intros;
- [ lapply linear nle_gen_zero_2 to H. auto
+ [ lapply linear nle_gen_zero_2 to H. auto new timeout=100
  | lapply linear nle_gen_succ_2 to H1. decompose;
-   [ rewrite > H1. clear H1. auto
+   [ subst. auto new timeout=100
    | lapply linear H to H3 as H0. decompose;
-     [ rewrite > H1. clear H1 x. auto
-     | rewrite < H. clear H n. auto
-     ]
+     subst; auto new timeout=100
    ]
  ].
 qed.