Section Fcalc_bracket_step.
Variable start step : R.
Variable nb_steps : Z.
Variable Hstep : (0 < step)%R.
Hypothesis (Hnb_steps : (1 < nb_steps)%Z).

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