include "NLE/fwd.ma".
theorem nle_refl: \forall x. x <= x.
- intros 1; elim x; clear x; intros; auto.
+ intros 1; elim x; clear x; intros; auto new.
qed.
theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros. elim H; clear H x y; intros; auto.
+ intros. elim H; clear H x y; intros; auto new.
qed.
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_zero_2 to H. auto new
| lapply linear nle_gen_succ_2 to H1. decompose;
- [ rewrite > H1. clear H1. auto
+ [ subst. auto new
| lapply linear H to H3 as H0. decompose;
- [ rewrite > H1. clear H1 x. auto
- | rewrite < H. clear H n. auto
- ]
+ subst; auto new
]
].
qed.