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

theorem Th63:
  for s being set holds [s,1] in ICC implies s = 1
proof
  let s be set;
  assume [s,1] in ICC;
  then consider a, b being Point of I[01] such that
A1: [s,1] = [a,b] and
A2: b <= 2 * a - 1 by Def10;
  b = 1 by A1,XTUPLE_0:1;
  then 1 + 1 <= 2 * a by A2,XREAL_1:19;
  then
A3: 2/2 <= (2 * a)/2 by XREAL_1:72;
  a <= 1 & a = s by A1,BORSUK_1:43,XTUPLE_0:1;
  hence thesis by A3,XXREAL_0:1;
end;
