theorem
  r <= s implies [.r,s.] \ {s} = [.r,s.[
proof
  assume r <= s;
  then
A1: [.r,s.] = [.r,s.[ \/ {s} by Th129;
  not s in [.r,s.[ by Th3;
  hence thesis by A1,ZFMISC_1:117;
end;
