theorem PROJ4:
  for V being free Z_Module, B being Basis of V, u being Vector of V
  holds Coordinate(u,B).(0.V) = 0
  proof
    let V be free Z_Module,
    B be Basis of V,
    u be Vector of V;
    set f = Coordinate(u,B);
    f.(0.V) = f.(0.V + 0.V)
    .= f.(0.V) +f.(0.V) by defCoord;
    hence f.(0.V) = 0;
end;
