  Using Je\v{r}\'abek 's framework for probabilistic reasoning, we formalize
the correctness of two fundamental RNC^2 algorithms for bipartite perfect
matching within the theory VPV for polytime reasoning. The first algorithm is
for testing if a bipartite graph has a perfect matching, and is based on the
Schwartz-Zippel Lemma for polynomial identity testing applied to the Edmonds
polynomial of the graph. The second algorithm, due to Mulmuley, Vazirani and
Vazirani, is for finding a perfect matching, where the key ingredient of this
algorithm is the Isolating Lemma.
