X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Ffwd.ma;h=5ddeb41aff1b1efe28b47c639310f49cd8373f50;hb=c99cecf223de21ed2ebb32106d661ce8b4dac9a8;hp=19ad50b9b2aa7c11cae590a0f3ec987ec194e96d;hpb=883affb9b633393615ce3cb674834664c5b9c881;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma b/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
index 19ad50b9b..5ddeb41af 100644
--- a/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
@@ -16,47 +16,44 @@ set "baseuri" "cic:/matita/RELATIONAL/NLE/fwd".
 
 include "logic/connectives.ma".
 
-include "Nat/fwd.ma". 
+include "NPlus/fwd.ma". 
 include "NLE/defs.ma".
 
 theorem nle_gen_succ_1: \forall x,y. x < y \to 
                         \exists z. y = succ z \land x <= z.
- intros. inversion H; clear H; intros;
- [ apply (eq_gen_succ_zero ? ? H)
- | lapply linear eq_gen_succ_succ to H2 as H0.
-   rewrite > H0. clear H0.
-   apply ex_intro; [|auto] (**)
- ].
+ unfold NLE. 
+ intros. decompose.
+ lapply linear nplus_gen_succ_2 to H1 as H.
+ decompose. subst.
+ apply ex_intro; auto. (**)
 qed.
 
+
 theorem nle_gen_succ_succ: \forall x,y. x < succ y \to x <= y.
- intros; inversion H; clear H; intros;
- [ apply (eq_gen_succ_zero ? ? H)
- | lapply linear eq_gen_succ_succ to H2 as H0.
-   lapply linear eq_gen_succ_succ to H3 as H2.
-   rewrite > H0. rewrite > H2. clear H0 H2.
-   auto
- ].
+ intros.
+ lapply linear nle_gen_succ_1 to H as H0. decompose H0.
+ lapply linear eq_gen_succ_succ to H1 as H. subst.
+ auto.
 qed.
 
-theorem nle_gen_succ_zero: \forall (P:Prop). \forall x. x < zero \to P.
+theorem nle_gen_succ_zero: \forall x. x < zero \to False.
  intros.
  lapply linear nle_gen_succ_1 to H. decompose.
- apply (eq_gen_zero_succ ? ? H1).
+ lapply linear eq_gen_zero_succ to H1. decompose.
 qed.
 
 theorem nle_gen_zero_2: \forall x. x <= zero \to x = zero.
  intros 1. elim x; clear x; intros;
- [ auto
- | apply (nle_gen_succ_zero ? ? H1)
+ [ auto new timeout=30
+ | lapply linear nle_gen_succ_zero to H1. decompose.
  ].
 qed.
 
 theorem nle_gen_succ_2: \forall y,x. x <= succ y \to
                         x = zero \lor \exists z. x = succ z \land z <= y.
  intros 2; elim x; clear x; intros;
- [ auto
+ [ auto new timeout=30
  | lapply linear nle_gen_succ_succ to H1.
-   right. apply ex_intro; [|auto] (**)
+   right. apply ex_intro; [|auto new timeout=30] (**)
  ].
 qed.