0. Definition

Recall that a modular lattice is a lattice that obeys the modular law

(M)   $x \leq z \Rightarrow x \vee (y \wedge z) = (x \vee y) \wedge z$, or equivalently,

(M$'$)   $(x \vee y) \wedge (x \vee z) = x \vee (y \wedge (z \vee x))$.