proposition: Lemma in_elements_after_add_iff: forall {A: Type} key (added elem: A) tree, (~ In key tree) -> (List.In elem (GetValues (add key added tree)) <-> (elem = added \/ List.In elem (GetValues tree))).
proof: Proof. intros; split; eauto using in_elements_after_add, in_elements_after_add'. 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