A fortiori

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In the Supreme Court case Gail Atwater, et al., Petitioners v. City of Lago Vista et al., , Justice Souter quotes the case Holyday v. Oxenbridge from 1631 that uses the term a fortiori:
"In Holyday v. Oxenbridge, Cro. Car. 234, 79 Eng. Rep. 805 (K.B. 1631), the Court of King’s Bench held that even a private person (and thus a fortiori a peace officer) needed no warrant to arrest a “common cheater” whom he discovered “cozen[ing] with false dice.” 

Using the example in Holyday, if it is true that any person can arrest a "common cheater". Then, of course we can safely infer that a police officer can arrest a "common cheater" because a police officer has even more of a right to arrest than an other person.