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

Lemma suml_map_mult_le_suml_mult_maxl (A : Type) f g (l : list A) : suml (map (fun x => f x * g x) l) <= suml (map f l) * maxl (map g l).