reserve m,j,p,q,n,l for Element of NAT;
reserve e1,e2 for ExtReal;

theorem
  for F being non empty NAT-defined finite Function
  holds dom F = dom CutLastLoc F \/ {LastLoc F}
proof
  let F be non empty NAT-defined finite Function;
  LastLoc F in dom F by XXREAL_2:def 8;
  then
A1: {LastLoc F} c= dom F by ZFMISC_1:31;
  dom CutLastLoc F = (dom F) \ {LastLoc F} by Th35;
  hence thesis by A1,XBOOLE_1:45;
end;
