Global Instance KH_fine_proper_filter a b : ProperFilter' (KH_fine a b).
Section is_KHInt.
Context {V : NormedModule R_AbsRing}.
Definition is_KHInt (f : R -> V) (a b : R) (If : V) :=
filterlim (fun ptd => scal (sign (b-a)) (Riemann_sum f ptd)) (KH_fine a b) (locally If).
Definition ex_KHInt f a b :=
exists If : V, is_KHInt f a b If.

Lemma is_KHInt_const :
forall (a b : R) (c : V),
is_KHInt (fun x : R => c) a b (scal (b-a) c).