
theorem div1:
for R being comRing,
    a,b being Element of R
holds a divides b iff {b}-Ideal c= {a}-Ideal
proof
let R be comRing, a,b be Element of R;
now assume {b}-Ideal c= {a}-Ideal;
  then b in {a}-Ideal by IDEAL_1:66;
  hence a divides b by div0;
  end;
hence thesis by div0,IDEAL_1:67;
end;
