Section PossiblyTrivial.
Variable (n : nat).
Definition porderMixin := [porderMixin of 'I_n by <:].
Canonical porderType := POrderType ord_display 'I_n (porderMixin).
Definition orderMixin := [totalOrderMixin of 'I_n by <:].
Canonical latticeType := LatticeType 'I_n orderMixin.
Canonical distrLatticeType := DistrLatticeType 'I_n orderMixin.
Canonical orderType  := OrderType 'I_n orderMixin.
Canonical finPOrderType := [finPOrderType of 'I_n].

Lemma leEord : (le : rel 'I_n) = leq. Proof. by []. Qed.
Lemma ltEord : (lt : rel 'I_n) = (fun m n => m < n)%N. Proof. by []. Qed.