reserve x,y,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for PartFunc of C,COMPLEX;
reserve r1,r2,p1 for Real;
reserve r,q,cr1,cr2 for Complex;

theorem
  f1/f - g1/g = (f1(#)g - g1(#)f)/(f(#)g)
proof
  thus f1/f - g1/g = f1/f + ((-1r)(#) g1)/g by Th39,COMPLEX1:def 4
    .= (f1(#)g + (-1r)(#) g1(#)f)/(f(#)g) by Th47
    .= (f1(#)g - (g1(#)f))/(f(#)g) by Th17,COMPLEX1:def 4;
end;
