reserve n for Nat;

theorem lcrpol:
for R being non degenerated Ring,
    a being Element of R,
    k being non zero Element of NAT holds LC rpoly(k,a) = 1.R
proof
let R be non degenerated Ring, a be Element of R, k be non zero Element of NAT;
deg rpoly(k,a) = len rpoly(k,a) - 1 by HURWITZ:def 2;
then k = len rpoly(k,a) - 1 by HURWITZ:27;
hence LC rpoly(k,a) = rpoly(k,a).k by XREAL_0:def 2
                   .= 1_R by HURWITZ:25
                   .= 1.R;
end;
