Section dimension_one.
Variable A : nat -> Prop.
Variable YA : (nat -> nat) -> nat.
Definition FYA (x n : nat) := n + S (enumerate YA x).
unfold increasing, FYA in |- *.
intros; apply plus_lt_compat_r; trivial with arith.
Qed.
Hint Resolve increasing_FYA.

Lemma enumerate_YA : full A YA -> forall x : nat, A (enumerate YA x).