X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Fprops.ma;h=ba563b7af941c80e46916fe3b532b0b0652c2283;hb=d9824956d9132109ed5f23380a0a1f9c5181d18a;hp=a6d0ca7a88dbac1fb0b3232c984ffe5a5c0c67c6;hpb=b7503f874120f581c9679deabe45bd3c333f1b0c;p=helm.git

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
index a6d0ca7a8..ba563b7af 100644
--- a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
@@ -12,67 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/RELATIONAL/NLE/props".
 
-include "NLE/inv.ma".
 
-theorem nle_zero_1: \forall q. zero <= q.
- intros. auto.
-qed.
-
-theorem nle_succ_succ: \forall p,q. p <= q \to succ p <= succ q.
- intros. elim H. clear H. auto.
-qed.
-
-theorem nle_ind: \forall P:(Nat \to Nat \to Prop).
-                 (\forall n:Nat.P zero n) \to 
-                 (\forall n,n1:Nat.
-                  n <= n1 \to P n n1 \to P (succ n) (succ n1)
-                 ) \to
-                \forall n,n1:Nat. n <= n1 \to P n n1.
- intros 4. elim n; clear n;
- [ auto
- | lapply linear nle_inv_succ_1 to H3. decompose; subst.
-   auto
- ].
-qed.
-
-theorem nle_refl: \forall x. x <= x.
- intros 1; elim x; clear x; intros; auto.
-qed.
+include "NLE/order.ma".
 
-theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros. elim H using nle_ind; clear H x y; auto.
-qed.
-
-theorem nle_false: \forall x,y. x <= y \to y < x \to False.
- intros 3; elim H using nle_ind; clear H x y; auto.
-qed.
-
-theorem nle_trans: \forall x,y. x <= y \to
-                   \forall z. y <= z \to x <= z.
- intros 3. elim H using nle_ind; clear H x y;
- [ auto
- | lapply linear nle_inv_succ_1 to H3. decompose. subst. 
-   auto
- ].
-qed.
-
-theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.
- intros. elim H using nle_ind; clear H x y;
- [ elim n; clear n; auto
- | decompose; subst; auto
- ].
+theorem nle_trans_succ: ∀x,y. x ≤ y → x ≤ succ y.
+ intros; elim H; clear H x y; autobatch.
 qed.
 
-theorem nle_gt_or_le: \forall x,y. y > x \lor y <= x.
+theorem nle_gt_or_le: ∀x, y. y > x ∨ y ≤ x.
  intros 2; elim y; clear y;
- [ auto
+ [ autobatch
  | decompose;
-   [ lapply linear nle_inv_succ_1 to H1. decompose.
-     subst. auto depth=4
-   | lapply linear nle_lt_or_eq to H1; decompose;
-     subst; auto
-   ]
+   [ lapply linear nle_inv_succ_1 to H1
+   | lapply linear nle_lt_or_eq to H1
+   ]; decompose; destruct; autobatch depth = 4
  ].
 qed.