Congruences

Abstract

Let a, b, c, d be elements of a lattice L. If

$$\displaystyle{\mbox{ $a \equiv b\!\pmod {\boldsymbol{\alpha }}$ implies that $c \equiv d\!\pmod {\boldsymbol{\alpha }}$,}}$$

for any congruence relation $\boldsymbol{\alpha }$ of L, then we can say that a ≡ b congruence-forces c ≡ d.