reserve R,R1 for commutative Ring;
reserve A,B for non degenerated commutative Ring;
reserve o,o1,o2 for object;
reserve r,r1,r2 for Element of R;
reserve a,a1,a2,b,b1 for Element of A;
reserve f for Function of R, R1;
reserve p for Element of Spectrum A;

theorem Th2:
  1.A is not Zero_Divisor of A
  proof
    assume 1.A is Zero_Divisor of A; then
    consider b be Element of A such that
A2: b <> 0.A and
A3: 1.A * b = 0.A by Def1;
    thus contradiction by A2,A3;
  end;
