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 inbetween_step_not_Eq :
forall x k l l',
inbetween (start + IZR k * step) (start + IZR (k + 1) * step) x l ->
(0 < k < nb_steps)%Z ->
Rcompare x (start + (IZR nb_steps / 2 * step))%R = l' ->
inbetween start (start + IZR nb_steps * step) x (loc_Inexact l').