reserve a,b,c,x,y,z for Real;

theorem Th11:
  for a, b being Complex st a^2-b^2 <> 0 holds 1/(a-b) = (a+b)/(a^2-b^2)
proof
  let a, b be Complex;
  assume a^2-b^2 <> 0;
  then (a+b)*(a-b) <> 0;
  then (a+b) <> 0;
  hence 1/(a-b) = (1*(a+b))/((a-b)*(a+b)) by XCMPLX_1:91
    .= (a+b)/(a^2-b^2);
end;
