« Lemma means “auxiliary theorem”. The word is of Greek origin; a more literal translation would be “what is assumed”. We are trying to prove a theorem, say, A. We are led to suspect another theorem, say, B; if B were true we could perhaps, using it, prove A. We assume provisionally, postponing its proof, and go ahead with the proof of A. Such a theorem B is assumed, and is an auxiliary theorem to the original proposed theorem A. Our little story is fairly typical and explains the present meaning of the word “lemma”. »
~ “How to solve it”. G. Polya.