reserve X for RealUnitarySpace;
reserve x, y, y1, y2 for Point of X;
reserve xd for set;
reserve i, j, n for Nat;

theorem
  x = 0.X iff for y holds x.|.y = 0
proof
  now
    assume for y holds x.|.y = 0;
    then x.|.x = 0;
    hence x = 0.X by BHSP_1:def 2;
  end;
  hence thesis by BHSP_1:14;
end;
