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 Th20:
 for k being Nat holds
  for p being finite NAT-defined (the InstructionsF of S)-valued Function
   holds dom Reloc(p,k) = dom Shift(p,k)
proof let k be Nat;
 let p be finite NAT-defined (the InstructionsF of S)-valued Function;
A1: dom IncAddr(p,k) = dom p by Def9;
 thus dom Reloc(p,k)
          = { m+k where m is Nat :m in dom p} by A1,VALUED_1:def 12
         .= dom Shift(p,k) by VALUED_1:def 12;
end;
