(** Specialization of inbetween for two consecutive integers. *)
Definition inbetween_int m x l :=
inbetween (Z2R m) (Z2R (m + 1)) x l.

Theorem inbetween_float_unique :
forall x e m l m' l',
inbetween_float m e x l ->
inbetween_float m' e x l' ->
m = m' /\ l = l'.