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

theorem Th4:
  t in ].r,s.[ iff r < t & t < s
proof
  hereby
    assume t in ].r,s.[;
    then ex a st a = t & r < a & a < s;
    hence r < t & t < s;
  end;
  t is Element of ExtREAL by XXREAL_0:def 1;
  hence thesis;
end;
