(* This file is distributed under the terms of the MIT License, also known as the X11 Licence.  A copy of this license is in the README file that accompanied the original distribution of this file.  Based on code written by: Brian Aydemir *)
(* *********************************************************************** *)
(** * Examples *)
(** The examples go through more smoothly if we declare [eq_nat_dec] as a hint. *)
Hint Resolve eq_nat_dec : eq_dec.
(* *********************************************************************** *)
(** ** Predicates on natural numbers *)
Scheme le_ind' := Induction for le Sort Prop.

Lemma le_unique : forall (x y : nat) (p q: x <= y), p = q.
Section Uniqueness_Of_SetoidList_Proofs.