Section UnityRoots.
Variable n : nat.
(* Showing the existence of a primitive root requires the theory in cyclic. *)
Variable z : F.
Hypothesis prim_z : n.-primitive_root z.
Let zn := [seq z ^+ i | i <- index_iota 0 n].

Lemma prim_rootP x : x ^+ n = 1 -> {i : 'I_n | x = z ^+ i}.