 reserve A, B, C, A1, B1, C1, A2, B2, C2, C3 for Point of TOP-REAL 2,
  lambda, mu, nu, alpha, beta, gamma for Real,
  X, Y, Z for Subset of TOP-REAL 2;

theorem
  Th1: (A + B) `1 = A `1 + B `1 & (A + B) `2 = A `2 + B `2
proof
  A + B = |[((A `1) + (B `1)), ((A `2) + (B `2))]| by EUCLID:55;
  hence thesis by EUCLID:52;
end;
