
theorem Th4:
  for x being Point of I[01] st x >= 1/2 holds 2 * x - 1 is Point of I[01]
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: 2 * x - 1 <= 2 - 1 by XREAL_1:9;
  assume x >= 1/2;
  then 2 * x >= 2 * (1/2) by XREAL_1:64;
  then 2 * x - 1 >= 1 - 1 by XREAL_1:9;
  hence thesis by A1,BORSUK_1:43;
end;
