e/Minimal counterexample

Information
has gloss	eng: In mathematics, the method of considering a minimal counterexample (or minimal criminal) combines the ideas of inductive proof and proof by contradiction. Abstractly, in trying to prove a proposition P, one assumes that it is false, and that therefore there is at least one counterexample. With respect to some idea of size, which may need to be chosen skillfully, one assumes that there is such a counterexample C that is minimal. We expect that C is something quite hypothetical (since we are trying to prove P), but it may be possible to argue that if C existed, it would have some definite properties. From those we then try to get a contradiction.
lexicalization	eng: minimal counterexample
instance of	(noun) a formal series of statements showing that if one thing is true something else necessarily follows from it proof