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 is total implies (r(#)f)/.c = r * ((f/.c))
proof
  assume f is total;
  then r(#)f is total;
  then dom (r(#)f) = C;
  hence thesis by Th4;
end;
