proposition: Lemma right_child_inj: forall i j, right_child i = right_child j -> i = j.
proof: Proof. unfold right_child, left_child; intros; lia. Qed.
imports: Psatz List Arith.Div2 Even Relations RelationClasses PeanoNat Peano_dec Recdef Sorting Permutation Multiset