Global Instance KH_fine_proper_filter a b : ProperFilter' (KH_fine a b).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 ex_KHInt_const : forall (a b : R) (c : V), ex_KHInt (fun x : R => c) a b.