
theorem Th5:
  for A being Subset of I[01], a, b being Real st a < b & A
  = ].a,b.[ holds [.a,b.] c= the carrier of I[01]
proof
  let A be Subset of I[01], a, b be Real;
  assume
A1: a < b;
  assume
A2: A = ].a,b.[;
  then
A3: b <= 1 by A1,BORSUK_1:40,XXREAL_1:51;
  0 <= a by A1,A2,BORSUK_1:40,XXREAL_1:51;
  hence thesis by A3,BORSUK_1:40,XXREAL_1:34;
end;
