Definition Const c v := exists f, is_cipher_of f v /\ forall i, i < l -> f i = c.

(* Specifications: *)
Lemma Const_dio c v : Const c v <-> l = 0 /\ 1 < q /\ v = 0
\/ 0 < l /\ l+1 < q /\
exists p u u1, p = power q 2 /\ c < p /\ seqs_of_ones u u1 /\ v = c*u.