A technical lemma for congruences of finite lattices

TL;DR

This paper introduces a new technical lemma for congruences on finite lattices, which, despite its simplicity, has proven useful in various applications within lattice theory.

Contribution

It presents a novel technical lemma specifically for finite lattices' congruences, expanding the toolkit for lattice theory applications.

Findings

The lemma is simple to prove.

It has demonstrated usefulness in applications.

It enhances understanding of finite lattice congruences.

Abstract

The classical Technical Lemma for congruences is not difficult to prove but it is very efficient in its applications. We present here a Technical Lemma for congruences on \emph{finite lattices}. This is not difficult to prove either but it has already has proved its usefulness in some applications.