  This short note can be considered as a mathematical supplement to [Phys. Rev.
Lett. 106, 217206 (2011)], namely explaining in more detail how rigorous bound
on high-temperature spin stiffness is established in thermodynamic limit using
the almost-conserved Z-operator resulting from solving the boundary driven
Lindblad equation for the anisotropic Heisenberg (XXZ) spin 1/2 chain . No
reference to techniques used in Suzuki's proofs of Mazur's bound is made, but
quasi-local spin C* algebras and Lieb-Robinson bounds are invoked instead.
