reserve M for non empty set;
reserve V for ComplexNormSpace;
reserve f,f1,f2,f3 for PartFunc of M,V;
reserve z,z1,z2 for Complex;
reserve X,Y for set;

theorem
  for x be Element of M st f is total holds (z(#)f)/.x = z * (f/.x)
proof
  let x be Element of M;
  assume f is total;
  then z(#)f is total by Th34;
  then dom (z(#)f) = M;
  hence thesis by Def2;
end;
