
theorem lemconst:
for R being domRing
for p being Polynomial of R holds p is monic constant iff p = 1_.R
proof
let F be domRing, p be Polynomial of F;
reconsider q = p as Element of the carrier of Polynom-Ring F
   by POLYNOM3:def 10;
now assume B: p is monic constant; then
  H: LC q = 1.F by RATFUNC1:def 7;
  deg p <= 0 by B,RATFUNC1:def 2; then
  consider a being Element of F such that
  A: q = a|F by RING_4:def 4,RING_4:20;
  1.F = a by H,A,RING_5:6;
  hence p = 1_.F by A,RING_4:14;
  end;
hence thesis;
end;
