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

Lemma list_beq_refl (A : Type) (A_beq : A -> A -> bool) l : (forall a1 a2 : A, In a1 l -> In a2 l -> (A_beq a1 a2 = true <-> a1 = a2)) -> list_beq _ A_beq l l = true.