
theorem TrivialBetween:
  for M being trivial non empty MetrSpace,
      a, b, c being Element of M holds
    a is_Between b,c
  proof
    let M be trivial non empty MetrSpace,
        a, b, c be Element of M;
    a = b & b = c by STRUCT_0:def 10; then
    dist (b,a) = 0 & dist (a,c) = 0 &
      dist (b,c) = 0 by METRIC_1:1; then
    a is_Between b,c;
    hence thesis;
  end;
