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

(* Specifications: *)
Lemma ordered_steps :
forall k,
(start + Z2R k * step < start + Z2R (k + 1) * step)%R.
Lemma middle_range :
forall k,
((start + (start + Z2R k * step)) / 2 = start + (Z2R k / 2 * step))%R.
Lemma ordered_steps :
forall k,
(start + Z2R k * step < start + Z2R (k + 1) * step)%R.
Lemma middle_range :
forall k,
((start + (start + Z2R k * step)) / 2 = start + (Z2R k / 2 * step))%R.