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 Th9:
  for N,T
  for l1, l2 being Element of NAT holds locnum(l1,T) <=
  locnum(l2,T) iff l1 <= l2, T
proof let N,T;
  let l1, l2 be Element of NAT;
  il.(T,locnum(l1,T)) = l1 & il.(T,locnum(l2,T)) = l2 by Def5;
  hence thesis by Th8;
end;
