theorem
  for V being finite-rank free Z_Module,
  i being Nat,
  a1 being Element of INT.Ring,
  a2 being Element of V,
  p1 being FinSequence of INT.Ring,
  p2 being FinSequence of V
  st i in dom (lmlt (p1,p2)) & a1 = p1 . i & a2 = p2 . i holds
  (lmlt (p1,p2)).i = a1 * a2 by FUNCOP_1:22;
