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;
reserve
  i,j,k for Instruction of S,
  I,J,K for Program of S;
reserve k1,k2 for Integer;
reserve l,l1,loc for Nat;
reserve i1,i2 for Instruction of S;
reserve
  i,j,k for Instruction of S,
  I,J,K for Program of S;
reserve m for Nat;

theorem
 for S being COM-Struct
 for p,q being finite NAT-defined (the InstructionsF of S)-valued Function,
     k be Nat
  holds Reloc(p+*q,k) = Reloc(p,k)+*Reloc(q,k)
proof
 let S be COM-Struct;
 let p,q be finite NAT-defined (the InstructionsF of S)-valued Function,
     k be Nat;
A1: Reloc(p+*q,k) = IncAddr(Shift(p+*q,k),k) by Th22;
A2: Reloc(p,k) = IncAddr(Shift(p,k),k) by Th22;
A3: Reloc(q,k) = IncAddr(Shift(q,k),k) by Th22;
 thus Reloc(p+*q,k)
      = IncAddr(Shift(p,k) +* Shift(q,k),k) by A1,VALUED_1:23
     .= Reloc(p,k)+*Reloc(q,k) by A2,A3,Th25;
end;
