Module FinRootNameType (Import N : NatValue) (FN : FinNameType N) <: RootNameType FN.
Definition root (x : fin n) := fin_to_nat x = 0.
Definition root_dec (x : fin n) := Nat.eq_dec (fin_to_nat x) 0.

Lemma root_unique : forall x y, root x -> root y -> x = y.