Section OrdinalSub.
Variable n : nat.
Inductive ordinal : predArgType := Ordinal m of m < n.
Coercion nat_of_ord i := let: Ordinal m _ := i in m.
Canonical ordinal_subType := [subType for nat_of_ord].
Definition ordinal_eqMixin := Eval hnf in [eqMixin of ordinal by <:].
Canonical ordinal_eqType := Eval hnf in EqType ordinal ordinal_eqMixin.
Definition ordinal_choiceMixin := [choiceMixin of ordinal by <:].
Canonical ordinal_choiceType :=
Eval hnf in ChoiceType ordinal ordinal_choiceMixin.
Definition ordinal_countMixin := [countMixin of ordinal by <:].
Canonical ordinal_countType := Eval hnf in CountType ordinal ordinal_countMixin.
Canonical ordinal_subCountType := [subCountType of ordinal].

Lemma ltn_ord (i : ordinal) : i < n. Proof. exact: valP i. Qed.