-theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.
- intros 1. elim y; clear y; intros;
- [ lapply linear nle_gen_zero_2 to H. auto
- | lapply linear nle_gen_succ_2 to H1. decompose;
- [ rewrite > H1. clear H1. auto
- | lapply linear H to H3 as H0. decompose;
- [ rewrite > H1. clear H1 x. auto
- | rewrite < H. clear H n. auto
- ]
- ]
+theorem nle_gt_or_le: \forall x, y. y > x \lor y <= x.
+ intros 2; elim y; clear y;
+ [ auto
+ | decompose;
+ [ lapply linear nle_inv_succ_1 to H1
+ | lapply linear nle_lt_or_eq to H1
+ ]; decompose; subst; auto depth = 4