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

Lemma maxl_map_plus_le A f g (l : list A) :
maxl (map (fun x => f x + g x) l) <= maxl (map f l) + maxl (map g l).