Fixpoint removeA (x : A) (l : list A) : list A :=
  match l with
    | nil => nil
    | y::tl => if (eqA_dec x y) then removeA x tl else y::(removeA x tl)
  end.

Lemma removeA_equivlistA : forall l l' x, ~InA x l -> equivlistA (x :: l) l' -> equivlistA l (removeA x l').