
theorem id2:
for R being comRing,
    I being Ideal of R,
    a being Element of R holds a in I implies {a}-Ideal c= I
proof
let R be comRing, I be Ideal of R, a be Element of R;
assume AS: a in I;
now let x be Element of R;
  assume A: x in {a}-Ideal;
  {a}-Ideal = the set of all a*r where r is Element of R by IDEAL_1:64;
  then ex r being Element of R st x = a * r by A;
  hence x in I by AS,IDEAL_1:def 2;
  end;
hence thesis;
end;
