X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FRELATIONAL%2FNLE%2Finv.ma;h=54ab40ae776adbb6e0166678d452da575429dfbc;hb=77405663b295e36da4e322c6f8184a1d256f8b78;hp=e42eecde3ab305988f00002ac8f8cf12b83ec1a0;hpb=4d945e028b3787f5aa26bdb0ef1639cde3ac30fe;p=helm.git

diff --git a/matita/contribs/RELATIONAL/NLE/inv.ma b/matita/contribs/RELATIONAL/NLE/inv.ma
index e42eecde3..54ab40ae7 100644
--- a/matita/contribs/RELATIONAL/NLE/inv.ma
+++ b/matita/contribs/RELATIONAL/NLE/inv.ma
@@ -14,41 +14,26 @@
 
 set "baseuri" "cic:/matita/RELATIONAL/NLE/inv".
 
-include "NPlus/inv.ma".
 include "NLE/defs.ma".
 
 theorem nle_inv_succ_1: \forall x,y. x < y \to 
-                         \exists z. y = succ z \land x <= z.
- intros. elim H.
- lapply linear nplus_gen_succ_2 to H1.
- decompose. subst. auto depth = 4.
+                        \exists z. y = succ z \land x <= z.
+ intros. inversion H; clear H; intros; subst. auto.
 qed.
 
 theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
- intros.
- lapply linear nle_inv_succ_1 to H. decompose.
- destruct H1. clear H1. subst.
- auto.
+ intros. inversion H; clear H; intros; subst. auto.
 qed.
 
 theorem nle_inv_succ_zero: \forall x. x < zero \to False.
- intros.
- lapply linear nle_inv_succ_1 to H. decompose.
- destruct H1.
+ intros. inversion H; clear H; intros; subst.
 qed.
 
 theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
- intros 1. elim x; clear x; intros;
- [ auto
- | lapply linear nle_inv_succ_zero to H1. decompose.
- ].
+ intros. inversion H; clear H; intros; subst. auto.
 qed.
 
 theorem nle_inv_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
- | lapply linear nle_inv_succ_succ to H1.
-   auto depth = 4.
- ].
+ intros. inversion H; clear H; intros; subst; auto depth = 4.
 qed.