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.
End BETWEEN.

Lemma Between_ind (P : nat -> Prop) (a : nat) (b : nat)
(H_Between : Between (fun n => P (S n) -> P n) a b)
: P b -> P a.