End FinType.
End BigBool.
Section NatConst.
Variables (I : finType) (A : pred I).

(* Specifications: *)
Lemma sum_nat_const n : \sum_(i in A) n = #|A| * n.
Lemma leq_sum I r (P : pred I) (E1 E2 : I -> nat) :
(forall i, P i -> E1 i <= E2 i) ->
\sum_(i <- r | P i) E1 i <= \sum_(i <- r | P i) E2 i.
Lemma bigmax_sup (I : finType) i0 (P : pred I) m F :
P i0 -> m <= F i0 -> m <= \max_(i | P i) F i.