Canonical itv_intersection_comoid := Monoid.ComLaw itv_intersectionC.
End IntervalOrdered.
Section IntervalField.
Variable R : realFieldType.

Lemma mid_in_itv : forall ba bb (xa xb : R), xa <= xb ?< if ba || bb
-> mid xa xb \in Interval (BOpen_if ba xa) (BOpen_if bb xb).