Assume also that under this Poisson bracket, formula_18 (note that it's not true that formula_19in general for this "extended Poisson bracket" anymore) and formula_20 on the submanifold of zeros of (If these brackets also happen to be zero everywhere, then we say the constraints close off shell). It turns out the right invertibility condition and the commutativity of flows conditions are "independent" of the choice of connection. So, we can drop the connection provided we are working solely with the restricted subspace.