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

theorem Th70:
  for x being Point of I[01] st x <= 1/2 holds [x,0] in IAA
proof
  let x be Point of I[01];
  assume x <= 1/2;
  then 2 * x <= 2 * (1/2) by XREAL_1:64;
  then
A1: 1 - 2 * x >= 1 - 2 * (1/2) by XREAL_1:13;
  0 is Point of I[01] by BORSUK_1:43;
  hence thesis by A1,Def8;
end;
