Require Export Bool.
Require Export Arith.
Require Export Compare_dec.
Require Export Peano_dec.
Require Export MyList.
Require Export MyRelations.
Set Implicit Arguments.
Unset Strict Implicit.
Definition max_nat (n m : nat) :=
match le_gt_dec n m with
| left _ => m
| right _ => n
end.

Lemma least_upper_bound_max_nat :
forall n m p : nat, n <= p -> m <= p -> max_nat n m <= p.