∀ {R : Type u_1} {ι : Type u_2} [inst : LinearOrder R] [inst_1 : NonUnitalNonAssocSemiring R] [CanonicallyOrderedAdd R]
  [inst_3 : OrderBot R] (s : Finset ι) (f : ι → R) (a : R), s.sup f * a = s.sup fun x => f x * a