Definition fmono (f: nat → nat):= ∀ x y, x ≤ y → f x ≤ f y.

Lemma forall_impl_and {A:Type} (R:A→Prop) (P Q:A→Prop): (∀ x, R x → P x ∧ Q x) ↔ ((∀ x, R x → P x) ∧ (∀ x, R x → Q x)).