Fixpoint SubEquiN (N:nat) (x y:R) (del:posreal) : list R :=
match N with
| O => cons y nil
| S p => cons x (SubEquiN p (x + del) y del)
end.
Definition max_N (a b:R) (del:posreal) (h:a < b) : nat :=
let (N,_) := maxN del h in N.
Definition SubEqui (a b:R) (del:posreal) (h:a < b) : list R :=
SubEquiN (S (max_N del h)) a b del.

Lemma SubEqui_P9 :
forall (a b:R) (del:posreal) (f:R -> R) (h:a < b),
{ g:StepFun a b |
g b = f b /\
(forall i:nat,
(i < pred (length (SubEqui del h)))%nat ->
constant_D_eq g
(co_interval (pos_Rl (SubEqui del h) i)
(pos_Rl (SubEqui del h) (S i)))
(f (pos_Rl (SubEqui del h) i))) }.