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_InA : forall l x y, InA y (removeA x l) <-> InA y l /\ ~eqA x y.