
theorem Added:
  for V being non empty UNITSTR,
      u being Point of V,
      x being FinSequence of V,
      i being Nat st 1 <= i <= len x
   holds ((u.|.x)(*)x).i = (u .|. (x/.i)) * (x/.i)
  proof
    let V be non empty UNITSTR,
    u be Point of V,
    x be FinSequence of V,
    i be Nat such that
A1: 1 <= i <= len x;
    len (u.|.x) = len x by DefSK; then
    i in dom (u.|.x) by A1,FINSEQ_3:25; then
A2: (u.|.x).i = (u.|.x)/.i by PARTFUN1:def 6;
    thus ((u.|.x)(*)x).i = (u.|.x)/.i * (x/.i) by A1,DefR
    .= (u .|. (x/.i)) * (x/.i) by A1,A2,DefSK;
  end;
