reserve x for set,
  D for non empty set,
  k, n for Element of NAT,
  z for Nat;
reserve N for with_zero set,
  S for
    IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
  i for Element of the InstructionsF of S,
  l, l1, l2, l3 for Element of NAT,
  s for State of S;
reserve ss for Element of product the_Values_of S;
reserve T for weakly_standard
 IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N;

theorem Th28:
  for F being non empty
   NAT-defined (the InstructionsF of T)-valued finite Function
   holds LastLoc F in dom F
proof
  let F be non empty
    NAT-defined (the InstructionsF of T)-valued finite Function;
  consider M being finite non empty natural-membered set such that
A1: M = { locnum(l,T) where l is Element of NAT : l in dom F } and
A2: LastLoc F = il.(T, max M) by Def11;
  max M in M by XXREAL_2:def 8;
  then
  ex l being Element of NAT st max M = locnum(l,T) & l in dom F
  by A1;
  hence thesis by A2,Def5;
end;
