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 Th7:
  for l1, l2 being Element of NAT holds locnum(l1,T) =
  locnum(l2,T) implies l1 = l2
proof
  let l1, l2 be Element of NAT;
  assume
A1: locnum(l1,T) = locnum(l2,T);
  il.(T,locnum(l1,T)) = l1 by Def5;
  hence thesis by A1,Def5;
end;
