
theorem Th6:
  for x being Point of I[01] holds 1/2 * x is Point of I[01]
proof
  let x be Point of I[01];
  x <= 1 by BORSUK_1:43;
  then 1/2 * x <= 1/2 * 1 by XREAL_1:64;
  then x >= 0 & 1/2 * x <= 1 by BORSUK_1:43,XXREAL_0:2;
  hence thesis by BORSUK_1:43;
end;
