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
  for f, g being Element of NAT st NextLoc(f,T) = NextLoc(g,T)
  holds f = g
proof
  let f, g be Element of NAT such that
A1: NextLoc(f,T) = NextLoc(g,T);
  set m = locnum(g,T);
  set k = locnum(f,T);
  k+0 = k+1-1
    .= m+1-1 by A1,Th5
    .= m+0;
  hence thesis by Th7;
end;
