theorem
  a is NonUnit of A implies ex m be maximal Ideal of A st a in m
  proof
    assume a is NonUnit of A; then
    {a}-Ideal <> [#] A by RING_2:20; then
    {a}-Ideal is proper; then
    consider m be maximal Ideal of A such that
A2: {a}-Ideal c= m by Th10;
    a in m by A2,IDEAL_1:66;
    hence thesis;
  end;
