theorem
  for K being associative commutative well-unital almost_left_invertible
  non degenerated doubleLoopStr holds
  (1.K)" = 1.K
  proof
   let K be associative commutative well-unital almost_left_invertible
   non degenerated doubleLoopStr;
    1.K <> 0.K;
    then (1.K)" * (1.K) = 1.K by VECTSP_1:def 10;
    hence thesis;
  end;
