There are three lattice-theoretic properties that are generally used to open a discussion on sublattices of a free lattice:
(W) for all a, b, c, d, a Λ b ≦ c V d implies a A b ≦ c, a Λ b g rf, a ≦cVd,orb ≦ c V d;
(SDv) for all a, b, c, a V b = a V c implies a V b = a V (b Λ c ) ;
(SDΛ) for all a, b, c, a Λ b = a Λ c implies a Λ b = a Λ (b V c).