Formal verification methods model systems by Kripke structures. In order to model live behaviors of systems, Kripke structures are augmented with
. Such conditions partition the computations of the systems into fair computations, with respect to which verification proceeds, and unfair computations, which are ignored. Reasoning about Kripke structures augmented with fairness is typically harder than reasoning about non-fair Kripke structures. We consider the
condition, where a computation
is fair iff each transition that is enabled in
infinitely often is also taken in
infinitely often. Transition fairness is a natural and useful fairness condition. We show that reasoning about Kripke structures augmented with transition fairness is not harder than reasoning about non-fair Kripke structures. We demonstrate it for fair CTL and LTL model checking, and the problem of calculating the dominators and postdominators.