proposition: Lemma andb_len x1 x2 x3 x4 : (x1 <=? x2)%num && (x3 <=? x4)%num <-> (x1 <= x2)%num /\ (x3 <= x4)%num.
proof: Proof. destruct (x1 <=? x2)%num eqn:Heq1; simpl; split; try easy; destruct (x3 <=? x4)%num eqn:Heq2; simpl; try easy. - eapply N.leb_le in Heq1. eapply N.leb_le in Heq2. easy. - intros [H1 H2]. eapply N.leb_nle in Heq2. eauto. - intros [H1 H2]. eapply N.leb_nle in Heq1. eauto. - intros [H1 H2]. eapply N.leb_nle in Heq1. eauto. Qed.
imports: Coq(Arith Basics List Recdef ZArith Lia) mathcomp(ssrbool ssreflect ssrnat) QuickChick(Classes Sets Producer Enumerators Generators Tactics)