theorem Th21:
  (for i holds l.i <= r.i) implies
  (x in cell(l,r) iff for i holds l.i <= x.i & x.i <= r.i)
proof
  assume
A1: for i holds l.i <= r.i;
  hereby
    assume x in cell(l,r);
    then (for i holds l.i <= x.i & x.i <= r.i) or
    ex i st r.i < l.i & (x.i <= r.i or l.i <= x.i) by Th20;
    hence for i holds l.i <= x.i & x.i <= r.i by A1;
  end;
  thus thesis;
end;
