(** 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_eqA : forall l x y, eqA x y -> InA x l -> InA y l.
#[local]
Hint Immediate InA_eqA : core.