proposition: Lemma build_heap_helper_downwards: forall L n, weak_heapOrdered_bounded L n n -> heapOrdered (build_heap_helper L n).
proof: Proof. intros L n. revert L. induction n; intros. apply heapOrdered_bounded_root_heapOrdered. simpl. apply sink_hO_bounded. apply H. simpl. apply IHn, sink_downwards_crawl, H. Qed.
imports: Psatz List Arith.Div2 Even Relations RelationClasses PeanoNat Peano_dec Recdef Sorting Permutation Multiset