
theorem Th9:
  for L be associative well-unital non empty doubleLoopStr for p
  being sequence of L holds 1.L*p = p
proof
  let L be associative well-unital non empty doubleLoopStr;
  let p be sequence of L;
  for i being Element of NAT holds ((1.L)*p).i = p.i
  proof
    let i be Element of NAT;
    thus ((1.L)*p).i = (1.L)*p.i by POLYNOM5:def 4
      .= p.i;
  end;
  hence thesis by FUNCT_2:63;
end;
