End Fcalc_bracket_step.
Section Fcalc_bracket_scale.

(* Specifications: *)
Lemma inbetween_mult_aux :
forall x d s,
((x * s + d * s) / 2 = (x + d) / 2 * s)%R.
Theorem inbetween_mult_compat :
forall x d u l s,
(0 < s)%R ->
inbetween x d u l ->
inbetween (x * s) (d * s) (u * s) l.
Theorem inbetween_mult_reg :
forall x d u l s,
(0 < s)%R ->
inbetween (x * s) (d * s) (u * s) l ->
inbetween x d u l.
Lemma inbetween_mult_aux :
forall x d s,
((x * s + d * s) / 2 = (x + d) / 2 * s)%R.
Theorem inbetween_mult_compat :
forall x d u l s,
(0 < s)%R ->
inbetween x d u l ->
inbetween (x * s) (d * s) (u * s) l.
Theorem inbetween_mult_reg :
forall x d u l s,
(0 < s)%R ->
inbetween (x * s) (d * s) (u * s) l ->
inbetween x d u l.