-theorem nle_gen_succ_1: \forall x,y. x < y \to
- \exists z. y = succ z \land x <= z.
- intros. inversion H; clear H; intros;
- [ apply (eq_gen_succ_zero ? ? H)
- | lapply linear eq_gen_succ_succ to H2 as H0.
- subst.
- apply ex_intro; [|auto] (**)
- ].
+theorem nle_inv_succ_1: \forall x,y. x < y \to
+ \exists z. y = succ z \land x <= z.
+ intros. elim H.
+ lapply linear nplus_gen_succ_2 to H1.
+ decompose. subst. auto depth = 4.