Fractional congruence

The congruence $ \eta / \theta $ of a quotient system $ \mathbf A / \theta $ defined by the formula

$$ [ x ] _ \theta ( \eta / \theta ) [ y ] _ \theta \iff x \eta y , $$

where $ \eta $ is some congruence of the algebraic system $ \mathbf A $ containing the given congruence $ \theta $ and $ [ a] _ \theta = \{ {x \in \mathbf A } : {x \theta a } \} $. The quotient system $ ( \mathbf A / \theta ) / ( \eta / \theta ) $ is isomorphic to the system $ \mathbf A / \eta $.