Constraint algebra from local Poincaré symmetry

A rigorous derivation of the constraint algebra between lapse, shift and Lorentz Hamiltonians is presented assuming that only local Poincaré symmetry constraints are present in the theory. It is also shown that the Dirac-Arnowitt-Deser-Misner form of the Hamiltonian is merely a consequence of the local Poincaré symmetry identities.