Section Maxl.
Fixpoint maxl (l : list nat) : nat :=
match l with
| nil => 0
| n :: l' => max n (maxl l')
end.

Lemma maxl_le_maxl A f g (l : list A) :
(forall x, In x l -> f x <= g x) -> maxl (map f l) <= maxl (map g l).