If John who is 18 is not too young to go to war, then a fortiori 19 year-old Peter is not too young.
A fortiori
Definition
A Latin term meaning literally 'from [the] stronger'. Translated into English and used in the particular context of legal writing, the term often means 'from [the] stronger [argument]'. If a particular fact is true, then one can infer that a second fact is also true.
Definition from Nolo’s Plain-English Law Dictionary
Definition provided by Nolo’s Plain-English Law Dictionary.
August 19, 2010, 5:10 pm
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.