reserve T for non empty TopSpace,
  a, b, c, d for Point of T;

theorem Th65:
  for x being Point of I[01] holds [x,1] in IBB
proof
  let x be Point of I[01];
  x <= 1 by BORSUK_1:43;
  then 2 * x <= 2 * 1 by XREAL_1:64;
  then
A1: 1 is Point of I[01] & 2 * x - 1 <= 2 * 1 - 1 by BORSUK_1:43,XREAL_1:13;
  x >= 0 by BORSUK_1:43;
  then 1 - 2 * x <= 1 - 2 * 0 by XREAL_1:13;
  hence thesis by A1,Def9;
end;
