(** Moreover, [eqlistA] implies [equivlistA]. A reverse result will be proved later for sorted list without duplicates. *)
Global Instance eqlistA_equivlistA : subrelation eqlistA equivlistA.
(** InA is compatible with eqA (for its first arg) and with equivlistA (and hence eqlistA) for its second arg *)
Global Instance InA_compat : Proper (eqA==>equivlistA==>iff) InA.
(** For compatibility, an immediate consequence of [InA_compat] *)

Lemma InA_split : forall l x, InA x l ->
exists l1 y l2, eqA x y /\ l = l1++y::l2.