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;
reserve i, j, k for Nat,
  n for Element of NAT,
  N for with_zero set,
  S for weakly_standard IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N,
  l for Element of NAT,
  f for FinPartState of S;

theorem
  l + (k,S) -' (k,S) = l
proof
  thus l + (k,S) -' (k,S) = il.(S,locnum(l,S) + k -' k) by Def5
    .= il.(S,locnum(l,S)) by NAT_D:34
    .= l by Def5;
end;
