Section suml.
Fixpoint suml (l : list nat) : nat :=
match l with
| nil => 0
| n :: l' => n + suml l'
end.

Lemma suml_map_plus (A : Type)(f g : A -> nat)(l : list A) : suml (map (fun x => f x + g x) l) = suml (map f l) + suml (map g l).