
theorem
  for a,b being Real st 0 < a * b holds 0 < a / b
  proof
    let a,b be Real;
    assume
A1: 0 < a * b; then
A2: b <> 0; then
    0 < b^2 by SQUARE_1:12;
    then 0 / b^2 < (a * b) / b^2 by A1;
    then 0 < (a * b) / (b * b) by SQUARE_1:def 1;
    then 0 < (a / b) * (b / b) by XCMPLX_1:76;
    then 0 < (a / b) * 1 by A2,XCMPLX_1:60;
    hence thesis;
  end;
