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 f + (z,T) = g + (z,T)
   holds f = g
proof
  let f, g be Element of NAT;
  assume f + (z,T) = g + (z,T);
  then locnum(f,T) + z = locnum(g,T) + z by Th5;
  hence thesis by Th7;
end;
