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

Theorem inbetween_step_Hi :
forall x k l,
inbetween (start + IZR k * step) (start + IZR (k + 1) * step) x l ->
(nb_steps < 2 * k)%Z -> (k < nb_steps)%Z ->
inbetween start (start + IZR nb_steps * step) x (loc_Inexact Gt).