
theorem Th20:
  for L be Abelian add-associative right_zeroed
  right_complementable well-unital commutative distributive non empty
  doubleLoopStr for n be Element of NAT holds 0_.(L)`^(n+1) = 0_.(L)
proof
  let L be Abelian add-associative right_zeroed right_complementable
  well-unital commutative distributive non empty doubleLoopStr;
  let n be Element of NAT;
  thus 0_.(L)`^(n+1) = (0_.(L)`^n)*'0_.(L) by Th19
    .= 0_.(L) by POLYNOM3:34;
end;
