
theorem Th25:
  for C being non empty closed_interval Subset of REAL
   holds lower_bound C <= upper_bound C
proof
  let C be non empty closed_interval Subset of REAL;
  set c = the Element of C;
A1: c <= upper_bound C by INTEGRA2:1;
  lower_bound C <= c by INTEGRA2:1;
  hence thesis by A1,XXREAL_0:2;
end;
