reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve p for Prime;
reserve a,b,c,d for Element of GF(p);
reserve K for Ring;
reserve a1,a2,a3,a4,a5,a6 for Element of K;

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;
