reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem Th228:
  p in REAL & q in REAL implies [.p,q.] c= REAL
proof
  assume that
A1: p in REAL and
A2: q in REAL;
  let x be ExtReal;
  assume
A3: x in [.p,q.];
  then
A4: p <= x by Th1;
  x <= q by A3,Th1;
  hence thesis by A1,A2,A4,XXREAL_0:45;
end;
