  For unital AF algebras with faithful tracial states, we provide criteria for
convergence in the quantum Gromov-Hausdorff propinquity. For any unital AF
algebra, we introduce new Leibniz Lip-norms using quotient norms. Next, we show
that any unital AF algebra is the limit of its defining inductive sequence of
finite dimensional C*-algebras in quantum propinquity given any Lip-norm
defined on the inductive sequence. We also establish sufficient conditions for
when a *-isomorphism between two AF algebras produces a quantum isometry in the
context of various Lip-norms.
