Section NonTrivial.
Variable (n' : nat).
Let n := n'.+1.
Canonical bLatticeType :=
BLatticeType 'I_n (BottomMixin (leq0n : forall x, ord0 <= x)).
Canonical bDistrLatticeType := [bDistrLatticeType of 'I_n].
Canonical tbLatticeType :=
TBLatticeType 'I_n (TopMixin (@leq_ord _ : forall x, x <= ord_max)).
Canonical tbDistrLatticeType := [tbDistrLatticeType of 'I_n].
Canonical finLatticeType := [finLatticeType of 'I_n].
Canonical finDistrLatticeType := [finDistrLatticeType of 'I_n].
Canonical finOrderType := [finOrderType of 'I_n].

Lemma botEord : 0%O = ord0. Proof. by []. Qed.
Lemma topEord : 1%O = ord_max. Proof. by []. Qed.