e/Elementary proof

Information
has gloss	eng: In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these results have been reproved using only elementary techniques.
lexicalization	eng: elementary proof
instance of	(noun) a formal series of statements showing that if one thing is true something else necessarily follows from it proof