Global Instance InfA_compat : Proper (eqA==>eqlistA==>iff) InfA.
Proof using eqA_equiv ltA_compat. (* and not ltA_strorder *)
intros x x' Hxx' l l' Hll'.
inversion_clear Hll'.
- intuition.
- split; intro; inv; constructor.
+ match goal with H : eqA _ _ |- _ => rewrite <- Hxx', <- H; auto end.
+ match goal with H : eqA _ _ |- _ => rewrite Hxx', H; auto end.
Qed.

(** For compatibility, can be deduced from [InfA_compat] *)
Lemma InfA_eqA l x y : eqA x y -> InfA y l -> InfA x l.
Proof using eqA_equiv ltA_compat.