theorem Th8:
    (D|^(n+1)) = (D*D|^n) & dom D = the carrier of R &
    dom (D|^n) = the carrier of R & D|^n is (the carrier of R)-valued Function
    proof
      D|^1 = D by VECTSP11:19;
      hence thesis by FUNCT_2:def 1,VECTSP11:20;
    end;
