reserve n for Nat;

theorem prl0a:
for R being domRing,
    p being Polynomial of R
for a being Element of R holds LC(a * p) = a * LC(p)
proof
let R be domRing, p be Polynomial of R; let a be Element of R;
per cases;
suppose A1: a = 0.R;
  a * p = 0_.(R) by A1,POLYNOM5:26;
  hence thesis by A1,FUNCOP_1:7;
  end;
suppose a <> 0.R;
  then A3: a is non zero;
  thus LC(a * p) = a * (p.(len(a*p)-'1)) by POLYNOM5:def 4
                .= a * LC(p) by A3,Th25a;
  end;
end;
