Question

What is a lemma?

Answer 1

A proven statement used as a stepping-stone toward the proof of another statement is called lemma.

For example:

Euclid’s Division Lemma: Let a and b be any two positive integers.

Then, there exist unique integers q and r such that 

`a=bq+r `, `0 ≤ r < b`

If `b|a` then  `r=0`.

Otherwise, r satisfies the stronger inequality `0 < r< b.`.