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

theorem
  a <> 0 & b <> 0 implies a" - b" = (b - a)*(a*b)"
proof
  assume
A1: a <> 0 & b <> 0;
  thus a" - b" = a" + -(b") .= a" + (-b)" by Lm19
    .= (a + -b)*(a*-b)" by A1,Th211
    .= (a + -b)*(-a*b)"
    .= (a + -b)*-((a*b)") by Lm19
    .= (b - a)*(a*b)";
end;
