Notation member := (in_dec eq_nat_dec).

Lemma fold_left_for_each_not_in : forall (f : A -> B -> A) (g : A -> B -> C), (forall a b b', b <> b' -> g (f a b') b = g a b) -> forall l a b, ~ In b l -> g (fold_left f l a) b = g a b.