theorem
  (lambda * A - mu * B) `1 = lambda * A `1 - mu * B `1 &
  (lambda * A - mu * B) `2 = lambda * A `2 - mu * B `2
proof
  (lambda * A - mu * B) `1 = (lambda * A) `1 - (mu * B) `1 by EUCLID_6:41
  .= lambda * A `1 - (mu * B) `1 by Th2;
  hence (lambda * A - mu * B) `1 = lambda * A `1 - mu * B `1 by Th2;
  (lambda * A - mu * B) `2 = (lambda * A) `2 - (mu * B) `2 by EUCLID_6:41
  .= lambda * A `2 - (mu * B) `2 by Th2;
  hence thesis by Th2;
end;
