A lattice is called distributive if, for all , , and in , we find that ∧ ( ∨ ) = ( ∧ ) ∨ ( ∧ ). This condition is known to be equivalent to its order dual. A meet- semilattice is distributive if for all elements , and , ∧ ≤ implies the existence of elements ≥ and ≥ such that ∧ = . See also completely distributive.