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

theorem
  x in [.p,q.[ implies x in ].p,q.] & x <> q or x = p
proof
  assume
A1: x in [.p,q.[;
  then reconsider s = x as ExtReal;
A2: p <= s by A1,Th3;
A3: s < q by A1,Th3;
  p = s or p < s by A2,XXREAL_0:1;
  hence thesis by A3,Th2;
end;
