intro; apply increasingbystep; unfold enumerate in |- *; auto with arith.
Qed.
Section dimension_one.
Variable A : nat -> Prop.
Variable YA : (nat -> nat) -> nat.
Definition FYA (x n : nat) := n + S (enumerate YA x).

Lemma increasing_FYA : forall x : nat, increasing (FYA x).
unfold increasing, FYA in |- *.