theorem Th21:
  x.t in still_not-bound_in p implies t < index p
proof
  assume
A1: x.t in still_not-bound_in p;
  now
    min NBI p in NBI p by QC_LANG1:def 35;
    then
A2: ex u st u = min NBI p & for t st u<=t holds not x.t in
    still_not-bound_in p;
    assume min (NBI p) <= t;
    hence contradiction by A1,A2;
  end;
  hence thesis by QC_LANG1:25;
end;
