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 (-f)/.x = - f/.x & (||.f.||)
  .x = ||. f/.x .||
proof
  let x be Element of M;
  assume
A1: f is total;
  then -f is total by Th35;
  then dom (-f) = M;
  hence (-f)/.x = - f/.x by VFUNCT_1:def 5;
  ||.f.|| is total by A1,Th36;
  then dom (||.f.||) = M;
  hence thesis by NORMSP_0:def 3;
end;
