Hypothesis (Hnb_steps : (1 < nb_steps)%Z).

Lemma middle_odd :
forall k,
(2 * k + 1 = nb_steps)%Z ->
(((start + Z2R k * step) + (start + Z2R (k + 1) * step))/2 = start + Z2R nb_steps /2 * step)%R.