(** ** Order-based induction principles *)
Variable z : t.
Let Rlt (n m : t) := z <= n < m.
Let Rgt (n m : t) := m < n <= z.
Instance Rlt_wd : Proper (eq ==> eq ==> iff) Rlt.
Instance Rgt_wd : Proper (eq ==> eq ==> iff) Rgt.

(* Specifications: *)
Theorem lt_wf : well_founded Rlt.
Theorem gt_wf : well_founded Rgt.
End WF.