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# What is a lemma?

Lemma and theorem are two different concepts in mathematics and cannot be termed the same.

## Answer: A lemma is a proven statement, used to prove other statements.

Let us go through the example to have a better understanding of the given term.

**Explanation:**

A lemma is nothing but a proven statement that is used to prove other statements. In other words, we can also say that a theorem is a result you're interested in, a corollary is a result that follows from a theorem, and a lemma is a result that you use to prove a theorem.

A lemma is like a mini-theorem that helps you prove a bigger theorem or statement. In other words, it's a small building block to your final destination with respect to proof.

Example:

**EUCLID'S DIVISION LEMMA: **

Euclid's division lemma gives us a systematic procedure to compute the HCF of any two positive integers which is termed as the Euclid division algorithm.

Euclid's division lemma states that for any two positive integers a and b, there exist two unique whole numbers say q and r, such that

a = bq + r , where 0 ≤ r < b

Here, a = Dividend , b = Divisor , q = Quotient , r = Remainder

It can be written as,

Dividend = (Divisor × Quotient) + Remainder

### Thus, a lemma is a proven statement, use to prove other proven statements.

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