proposition: Lemma weak_heapOrdered_bounded_root_weak_heapOrdered: forall L j, weak_heapOrdered_bounded L root_idx j <-> weak_heapOrdered L j.
proof: Proof. split; intros [? ?]; split; auto. intros. apply H; auto. unfold root_idx; lia. Qed.
imports: Psatz List Arith.Div2 Even Relations RelationClasses PeanoNat Peano_dec Recdef Sorting Permutation Multiset