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

theorem
  r <= s & s <= t implies not r in ].s,t.[ \/ ].t,p.[
proof
  assume that
A1: r <= s and
A2: s <= t;
  assume r in ].s,t.[ \/ ].t,p.[;
  then r in ].s,t.[ or r in ].t,p.[ by XBOOLE_0:def 3;
  then s < r & r < t or t < r & r < p by Th4;
  hence contradiction by A1,A2,XXREAL_0:2;
end;
