X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Finv.ma;h=649a5b8a4cd4b6f6044aaf998a4e8942d4919d60;hb=d9824956d9132109ed5f23380a0a1f9c5181d18a;hp=67a18d820de92b2201c5abe9403d7a7181678b7b;hpb=b7503f874120f581c9679deabe45bd3c333f1b0c;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/inv.ma b/helm/software/matita/contribs/RELATIONAL/NLE/inv.ma
index 67a18d820..649a5b8a4 100644
--- a/helm/software/matita/contribs/RELATIONAL/NLE/inv.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/inv.ma
@@ -12,43 +12,29 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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_inv_succ_2 to H1.
- decompose. subst. auto depth = 4.
+theorem nle_inv_succ_1: ∀x,y. x < y → 
+                        ∃z. y = succ z ∧ x ≤ z.
+ intros; inversion H; clear H; intros; destruct. autobatch.
 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.
+theorem nle_inv_succ_succ: ∀x,y. x < succ y → x ≤ y.
+ intros; inversion H; clear H; intros; destruct. autobatch.
 qed.
 
-theorem nle_inv_succ_zero: \forall x. x < zero \to False.
- intros.
- lapply linear nle_inv_succ_1 to H. decompose.
- destruct H1.
+theorem nle_inv_succ_zero: ∀x. x < zero → False.
+ intros. inversion H; clear H; intros; destruct.
 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.
- ].
+theorem nle_inv_zero_2: ∀x. x ≤ zero → x = zero.
+ intros; inversion H; clear H; intros; destruct. autobatch.
 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.
- ].
+theorem nle_inv_succ_2: ∀y,x. x ≤ succ y →
+                        x = zero ∨ ∃z. x = succ z ∧ z ≤ y.
+ intros; inversion H; clear H; intros; destruct;
+ autobatch depth = 4.
 qed.