Proof using.
induction xs; simpl; auto using f_equal2.
Qed.

(* Specifications: *)
Lemma filter_except_one : forall (f g : A -> bool) x xs,
(forall y, In y xs ->
x <> y ->
f y = g y) ->
g x = false ->
filter f (remove A_eq_dec x xs) = filter g xs.