The properties of closure under addition and multiplication, associativity, commutativity and distributivity are easily seen. Multiplication follows the usual laws of associativity and distributivity. Extending this relation by associativity and distributivity allows explicitly constructing the Weyl algebra.. The following logical equivalences demonstrate that distributivity is a property of particular connectives. This notion requires but a single operation, and generalizes the distributivity condition for lattices. This is weaker than distributivity; e.g. the above-shown lattice "M" is modular, but not distributive. This is the case of distributivity or trigonometric identities. In several mathematical areas, generalized distributivity laws are considered. The principle of distributivity is valid in classical logic, but invalid in quantum logic. See the entry distributivity (order theory). See also the article on distributivity (order theory). See also the articles on complete distributivity and distributivity (order theory). Repeated application of distributivity may exponentially increase the size of a formula. Distributivity in turn is just the preservation of binary suprema by formula 6. For the distributivity, the computer function that applies this rewriting rule is generally called "expand".