Let A be an algebra and let $\alpha,\beta,\gamma$ congruence in A. How can I prove that the commutator is meet semidistributive in the second variable ( i.e. $[\beta,\alpha]=[\beta,\gamma]$ implies $[\beta,\alpha]=[\beta,\gamma\vee\alpha]$ ) ?
Def. For any $\alpha,\beta \in$ Con(A) there is a smallest congreunce $\delta$ with C$(\alpha,\beta;\delta)$; such congruence is called the commutator of $\alpha$ and $\beta$ and is denoted by $[\alpha,\beta]$.
C(x,y;z) is the centralizer