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
  for f1,f2 being complex-valued Function holds
  r(#)(f1 - f2) = r(#)f1 - r(#)f2
proof
  let f1,f2 be complex-valued Function;
  r(#)(-f2) = -r(#)f2 by T2;
  hence thesis by T111;
end;
