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.

Lemma wBetween_next (n : nat)
: forall m, wBetween n m -> P m -> wBetween n (S m).