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

theorem Th224:
  REAL = ].-infty,+infty.[
proof
  let x be ExtReal;
  thus x in REAL implies x in ].-infty,+infty.[
  proof
    assume
A1: x in REAL;
    then
A2: -infty < x by XXREAL_0:12;
    x < +infty by A1,XXREAL_0:9;
    hence thesis by A2,Th4;
  end;
  assume
A3: x in ].-infty,+infty.[;
  then
A4: -infty < x by Th4;
  x < +infty by A3,Th4;
  hence thesis by A4,XXREAL_0:14;
end;
