forall a b, a <= b -> cut_minus a b =N= 0. Proof. unfold cut_minus,nat_cut_minus. intros a b;revert a;induction b as [|b IH];intros [|a];simpl. - split. - intros E;destruct (not_lt_0 _ E). - split. - intros E. apply IH;apply le_S_S,E. Qed.
Require Import