proposition: Lemma MapsTo_In : forall {A: Type} key (val: A) tree, MapsTo key val tree -> In key tree.
proof: Proof. intros. rewrite elements_in_iff. rewrite elements_mapsto_iff in *. eauto. Qed.
imports: Coq.FSets.FMapInterface Coq.FSets.FMapFacts Coq.Program.Program Coq.Structures.OrderedTypeEx Fiat.Common Fiat.Common.SetEq Fiat.Common.SetEqProperties Fiat.Common.List.ListFacts Fiat.Common.List.ListMorphisms Fiat.Common.LogicFacts Fiat.Common.SetoidClassInstances