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_P4 :
forall (N:nat) (a b:R) (del:posreal) (i:nat),
(i < S N)%nat -> pos_Rl (SubEquiN (S N) a b del) i = a + INR i * del.