-theorem nle_gen_succ_1: \forall x,y. x < y \to
- \exists z. y = succ z \land x <= z.
- unfold NLE.
- intros. decompose.
- lapply linear nplus_gen_succ_2 to H1 as H.
- decompose. 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.
- lapply linear nle_gen_succ_1 to H as H0. decompose H0.
- lapply linear eq_gen_succ_succ to H1 as H. subst.
+ lapply linear nle_inv_succ_1 to H. decompose.
+ lapply linear eq_gen_succ_succ to H1. subst.