The diamond lemmas constitute a of results about the existence of a unique normal form. Diamond lemmas exist in many diverse areas of mathematics, and as a result their technical contents can be quite different, but they are easily recognisable from their overall and basic idea — the “diamond” condition from which they inherit their name.
1 Newman’s Diamond Lemma
The basic diamond lemma, that of Newman [Newman], is today most easily presented in of binary relations.
Condition 1 can be graphically drawn as