
theorem Th15:
  for L being associative commutative well-unital distributive
  almost_left_invertible non empty doubleLoopStr, x being Element of L holds
  pow(x,-1) = x"
proof
  let L be associative commutative well-unital distributive
  almost_left_invertible non empty doubleLoopStr, x be Element of L;
  |.-1 .| = --1 by ABSVALUE:def 1;
  hence pow(x, -1) = (pow(x, 1))" by Lm3
    .= x" by Th14;
end;
