- bug fix in destruct

[helm.git] / matita / contribs / RELATIONAL / NLE / inv.ma

diff --git a/matita/contribs/RELATIONAL/NLE/inv.ma b/matita/contribs/RELATIONAL/NLE/inv.ma
index bc878009c2ac3b3129b814fc1ef39ad067815397..013cd67f1d936476f690528b58d934ea24d82e30 100644 (file)
--- a/matita/contribs/RELATIONAL/NLE/inv.ma
+++ b/matita/contribs/RELATIONAL/NLE/inv.ma
@@ -18,37 +18,23 @@ include "NLE/defs.ma".
 
 theorem nle_inv_succ_1: \forall x,y. x < y \to 
                         \exists z. y = succ z \land x <= z.
- intros. inversion H; clear H; intros; subst;
- [ destruct H
- | destruct H2. clear H2. subst. auto
- ]
+ intros. inversion H; clear H; intros; destruct. autobatch.
 qed.
 
 theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
- intros. inversion H; clear H; intros; subst;
- [ destruct H
- | destruct H2. destruct H3. clear H2 H3. subst. auto
- ]
+ intros. inversion H; clear H; intros; destruct. autobatch.
 qed.
 
 theorem nle_inv_succ_zero: \forall x. x < zero \to False.
- intros. inversion H; clear H; intros; subst;
- [ destruct H
- | destruct H3
- ]
+ intros. inversion H; clear H; intros; destruct.
 qed.
 
 theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
- intros. inversion H; clear H; intros; subst;
- [ auto
- | destruct H3
- ].
+ 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. inversion H; clear H; intros; subst;
- [ auto
- | destruct H3. clear H3. subst. auto depth = 4
- ].
+ intros. inversion H; clear H; intros; destruct;
+ autobatch depth = 4.
 qed.