## If $(\alpha,\beta)$ is the factor pair congruences of algebra $\mathbb{A},$ ia $(\forall \gamma\in ConA)\alpha\circ\gamma=\gamma\circ\beta?$

Let $$\mathbb{A}$$ be an algebra such that $$ConA$$ is the distributive lattice. If $$(\alpha,\beta)$$ is the factor pair congruences of algebra $$\mathbb{A},$$ prove that $$(\forall \gamma\in ConA)\alpha\circ\gamma=\gamma\circ\beta.$$