Canonical comp_poly_linear p := Linear (comp_poly_is_linear p).

(* Specifications: *)
Lemma comp_poly0 p : 0 \Po p = 0.
Lemma comp_polyXaddC_K p z : (p \Po ('X + z%:P)) \Po ('X - z%:P) = p.
Lemma size_comp_poly_leq p q :
size (p \Po q) <= ((size p).-1 * (size q).-1).+1.