reserve i,j,k for Nat;

theorem Th21:
  for K being Abelian left_zeroed right_zeroed non empty
addLoopStr, R being Element of i-tuples_on the carrier of K holds R + (i|->(0.
  K)) = R & R = (i|->(0.K)) + R
proof
  let K be Abelian left_zeroed right_zeroed non empty addLoopStr, R be
  Element of i-tuples_on the carrier of K;
  thus R + (i|->(0.K)) = R by Lm2;
  hence thesis by FINSEQOP:33;
end;
