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

theorem Th227:
  q in REAL implies ].p,q.] c= REAL
proof
  assume
A1: q in REAL;
  let x be ExtReal;
  assume
A2: x in ].p,q.];
  then
A3: p < x by Th2;
  x <= q by A2,Th2;
  hence thesis by A1,A3,XXREAL_0:47;
end;
