(** ** A proper filter on SF_seq *)

Lemma Riemann_fine_unif_part :
forall (f : R -> R -> R) (a b : R) (n : nat),
(forall a b, a <= b -> a <= f a b <= b) ->
a <= b ->
seq_step (SF_lx (SF_seq_f2 f (unif_part a b n))) <= (b - a) / (INR n + 1) /\
pointed_subdiv (SF_seq_f2 f (unif_part a b n)) /\
SF_h (SF_seq_f2 f (unif_part a b n)) = a /\
last (SF_h (SF_seq_f2 f (unif_part a b n))) (SF_lx (SF_seq_f2 f (unif_part a b n))) = b.