proposition: Lemma equiv_eq_key : forall elt, Equivalence (eq_key (elt:=elt)).
proof: Proof. intros; unfold eq_key; split; intuition. unfold Transitive; firstorder. transitivity (fst y); trivial. 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