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;
reserve I,J for Program of S;
reserve i for Instruction of S,
        I for Program of S;
reserve loc for Nat;

theorem Th49:
  loc in dom I implies Shift(stop I,n).(loc+n)=Shift(I,n).(loc+n)
proof
A1: dom I c= dom (stop I) by AFINSQ_1:21;
  reconsider l = loc as Element of NAT by ORDINAL1:def 12;
  assume
A2: loc in dom I;
  hence Shift(I,n).(loc+n)=I.l by VALUED_1:def 12
    .=(stop I).l by A2,AFINSQ_1:def 3
    .=Shift(stop I,n).(loc+n) by A2,A1,VALUED_1:def 12;
end;
