theorem Th17:
 for F being non empty NAT-defined finite Function
  holds not LastLoc F in dom CutLastLoc F
 proof let F be non empty NAT-defined finite Function;
   LastLoc F in dom F by VALUED_1:30;
   then F|{LastLoc F} = LastLoc F .--> F.LastLoc F by FUNCT_7:6;
   then
A1:  dom CutLastLoc F = dom F \ {LastLoc F} by RELAT_1:177;
   LastLoc F in {LastLoc F} by TARSKI:def 1;
  hence thesis by A1,XBOOLE_0:def 5;
 end;
