reserve x,A for set, i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set, z for Nat;
reserve S for COM-Struct;
reserve ins for Element of the InstructionsF of S;
reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set;
reserve i, j, k for Nat,
  n for Nat,
  l,il for Nat;

theorem Th21:
  for k being Nat holds
  for p being finite NAT-defined (the InstructionsF of S)-valued Function
   holds dom Reloc(p,k) = { j+k where j is Nat:j in dom p }
proof
  let k be Nat;
  let p be finite NAT-defined (the InstructionsF of S)-valued Function;
  thus dom Reloc(p,k) = dom Shift(p,k) by Th20
    .= { j+k where j is Nat:j in dom p } by VALUED_1:def 12;
end;
