theorem Th21:
  for I being halt-ending Program of S
 holds CutLastLoc I = CutLastLoc J implies I = J
proof let I be halt-ending Program of S such that
A1: CutLastLoc I = CutLastLoc J;
 card I - 1 = card CutLastLoc J by A1,VALUED_1:38
   .= card J -1 by VALUED_1:38;
  then LastLoc I = card J -' 1 by AFINSQ_1:70
      .= LastLoc J by AFINSQ_1:70;
 hence I = CutLastLoc I +* (LastLoc J .--> halt S) by Th20
   .= J by A1,Th20;
end;
