
theorem Th10:
  for L being associative non empty doubleLoopStr, k,l being
  Element of L, seq being sequence of L holds k * (l * seq) = (k * l) * seq
proof
  let L be associative non empty doubleLoopStr, k,l be Element of L, seq be
  sequence of L;
  now
    let i be Element of NAT;
    thus (k * (l * seq)).i = k * (l * seq).i by POLYNOM5:def 4
      .= k * (l * seq.i) by POLYNOM5:def 4
      .= (k * l) * seq.i by GROUP_1:def 3
      .= ((k * l) * seq).i by POLYNOM5:def 4;
  end;
  hence thesis by FUNCT_2:63;
end;
