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

theorem Th62:
  for s being set holds [0,s] in IBB implies s = 1
proof
  let s be set;
  assume [0,s] in IBB;
  then consider a, b being Point of I[01] such that
A1: [0,s] = [a,b] and
A2: b >= 1 - 2 * a and
  b >= 2 * a - 1 by Def9;
A3: b <= 1 by BORSUK_1:43;
  a = 0 & b = s by A1,XTUPLE_0:1;
  hence thesis by A2,A3,XXREAL_0:1;
end;
