(** lists with same elements modulo [eqA] at the same place *)

Inductive eqlistA : list A -> list A -> Prop :=
  | eqlistA_nil : eqlistA nil nil
  | eqlistA_cons : forall x x' l l',
      eqA x x' -> eqlistA l l' -> eqlistA (x::l) (x'::l').(** lists with same elements modulo [eqA] at the same place *)

Inductive eqlistA : list A -> list A -> Prop :=
  | eqlistA_nil : eqlistA nil nil
  | eqlistA_cons : forall x x' l l',
      eqA x x' -> eqlistA l l' -> eqlistA (x::l) (x'::l').(** lists with same elements modulo [eqA] at the same place *)

Inductive eqlistA : list A -> list A -> Prop :=
  | eqlistA_nil : eqlistA nil nil
  | eqlistA_cons : forall x x' l l',
      eqA x x' -> eqlistA l l' -> eqlistA (x::l) (x'::l').

(* Specifications: *)
Lemma eqlistA_altdef : forall l l', eqlistA l l' <-> Forall2 eqA l l'.