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

theorem Th7:
  x in [.p,q.] implies x in [.p,q.[ or x = q
proof
  assume
A1: x in [.p,q.];
  then reconsider s = x as ExtReal;
A2: p <= s by A1,Th1;
  s <= q by A1,Th1;
  then q = s or s < q by XXREAL_0:1;
  hence thesis by A2,Th3;
end;
