reserve n for Element of NAT,
  a, b for Real;

theorem Th8:
  for T being non empty interval SubSpace of R^1, a, b being Point
  of T holds [. a, b .] c= the carrier of T
proof
  let T be non empty interval SubSpace of R^1, a, b be Point of T;
  reconsider a1 = a, b1 = b as Point of R^1 by PRE_TOPC:25;
  [#]T is interval Subset of T by Def3;
  then [. a1, b1 .] c= the carrier of T by XXREAL_2:def 12;
  hence thesis;
end;
