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Proof rules for program verification rely on auxiliary assertions. We propose a (sound and relatively complete) proof rule whose auxiliary assertions are transition invariants. A transition invariant of a program is a binary relation over program states that contains the transitive closure of the transition relation of the program. A relation is disjunctively well-founded if it is a finite union of well-founded relations. We characterize the validity of termination or another liveness propertydoi:10.1109/lics.2004.1319598 dblp:conf/lics/PodelskiR04 fatcat:wk4bavbz3vax3ltcyk66k2hk3a