theorem Lm5:
  not 1.A in sqrt J
  proof
    assume 1.A in sqrt J; then
    1.A in {a where a is Element of A: ex n be Element of NAT st a|^n in J}
      by IDEAL_1:def 24; then
    consider a be Element of A such that
A3: 1.A = a and
A4: ex n be Element of NAT st a|^n in J;
    consider n1 be Element of NAT such that
A5: a|^n1 in J by A4;
    1.A = a|^n1 by A3,Lm4;
    hence contradiction by IDEAL_1:19, A5;
  end;
