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14
15
16
17 include "NLE/order.ma".
18
19 theorem nle_trans_succ: ∀x,y. x ≤ y → x ≤ succ y.
20  intros; elim H; clear H x y; autobatch.
21 qed.
22
23 theorem nle_gt_or_le: ∀x, y. y > x ∨ y ≤ x.
24  intros 2; elim y; clear y;
25  [ autobatch
26  | decompose;
27    [ lapply linear nle_inv_succ_1 to H1
28    | lapply linear nle_lt_or_eq to H1
29    ]; decompose; destruct; autobatch depth = 4
30  ].
31 qed.