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;

theorem Th23:
  -f = (-1r)(#)f
proof
A1: dom (-f) = dom f by VFUNCT_1:def 5
    .= dom ((-1r)(#)f) by Def2;
  now
    let c be Element of M;
    assume
A2: c in dom ((-1r)(#)f);
    hence (-f)/.c = -(f/.c) by A1,VFUNCT_1:def 5
      .= (-1r) * f/.c by CLVECT_1:3
      .= ((-1r)(#)f)/.c by A2,Def2;
  end;
  hence thesis by A1,PARTFUN2:1;
end;
