proposition: Lemma add_below_bindings x e m : x < m -> bindings (add x e m) = (x, e) :: bindings m.
proof: Proof. functional induction (add x e m); simpl; intros; cleanf; trivial; invlt; try (intuition; order). rewrite bal_bindings. unfold create. rewrite !bindings_node. now rewrite IHt0. Qed.
imports: Coq(Bool PeanoNat BinInt FunInd Int) Coq(Orders OrdersFacts OrdersLists) MMaps(Utils Interface OrdList GenTree)