
theorem Th13:
  for A being Subset of I[01], a, b being Real st a <= b &
  A = [.a,b.] holds 0 <= a & b <= 1
proof
  let A be Subset of I[01], a, b be Real;
  assume that
A1: a <= b and
A2: A = [.a,b.];
A3: b in A by A1,A2,XXREAL_1:1;
  a in A by A1,A2,XXREAL_1:1;
  hence thesis by A3,BORSUK_1:43;
end;
