reserve a, b, c, d, e for Complex;

theorem :: REAL_1'41_2
  b <> 0 & d <> 0 implies a / b - c / d = (a * d - c * b) / (b * d)
proof
  assume
A1: b<>0;
  assume
A2: d<>0;
  thus a/b - c/d =a/b + -c/d .=a/b + (-c)/d by Lm17
    .=(a*d + (-c)*b)/(b*d) by A1,A2,Th116
    .=(a*d - c*b)/(b*d);
end;
