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
  -f/g = (-f)/g & f/(-g) = -f/g
proof
  thus -f/g = (-f)/g by Th39;
  thus f/(-g) = f (#) ((-g)^) by Th38
    .= f (#) ((-1r) (#) (g^)) by Lm2,Th35,COMPLEX1:def 4
    .= -(f (#) (g^)) by Th18,COMPLEX1:def 4
    .= -(f/g) by Th38;
end;
