
theorem Th24:
  for L being associative commutative well-unital distributive
  almost_left_invertible non empty doubleLoopStr, x being Element of L, n,m
  being Element of NAT holds pow(x, n * m) = pow(pow(x, n), m)
proof
  let L be associative commutative well-unital distributive
  almost_left_invertible non empty doubleLoopStr;
  let x be Element of L;
  let n,m be Element of NAT;
  pow(x, n*m) = x |^ (n*m) by Def2
    .= (x|^n) |^m by BINOM:11
    .= pow(x |^ n, m) by Def2
    .= pow(pow(x, n), m) by Def2;
  hence thesis;
end;
