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

theorem
  p <= r & s <= q implies [.p,q.] \ ([.p,r.] \/ [.s,q.]) = ].r,s.[
proof
  assume that
A1: p <= r and
A2: s <= q;
  thus [.p,q.] \ ([.p,r.] \/ [.s,q.])
  = [.p,q.] \ [.p,r.] \ [.s,q.] by XBOOLE_1:41
    .= ].r,q.] \ [.s,q.] by A1,Th182
    .= ].r,s.[ by A2,Th191;
end;
