(1) $\forall \, x, y \in X : f(x, y) \in X$ (D20: Enclosed binary operation)

(2) $\forall \, x, y \in X : g(x, y) \in X$ (D20: Enclosed binary operation)

(3) $\forall \, x, y, z \in X : g(x, f(y, z)) = f(g(x, y), g(x, z))$ (D555: Left-distributive binary operation)

(4) $\forall \, x, y, z \in X : g(f(x, y), z) = f(g(x, z), g(y, z))$ (D556: Right-distributive binary operation)

(5) $\forall \, x, y, z \in X : f(f(x, y), z) = f(x, f(y, z))$ (D488: Associative binary operation)

(6) $\forall \, x, y, z \in X : g(g(x, y), z) = g(x, g(y, z))$ (D488: Associative binary operation)