Section BETWEEN. (* Reference: "https://github.com/DmxLarchey/Murec_Extraction/blob/murec_artifact/theories/between.v" *)
Variable P : nat -> Prop.
Definition wBetween (n : nat) (m : nat) : Prop :=
forall i, n <= i -> i < m -> P i.
Definition Between (n : nat) (m : nat) : Prop :=
n <= m /\ wBetween n m.

Lemma Between_next (n : nat)
: forall m, Between n m -> P m -> Between n (S m).