
theorem thdegLC:
for R being Ring, p being Polynomial of R holds LC (LM p) = LC p
proof
let R be Ring, p be Polynomial of R;
thus LC(LM p) = (LM p).(len(LM p)-'1) by RATFUNC1:def 6
        .= (LM p).(len(p)-'1) by POLYNOM4:15
        .= p.(len(p)-'1) by POLYNOM4:def 1
        .= LC p by RATFUNC1:def 6;
end;
