In lattice we have the following equivalences
$ x \vee y \le z \Longleftrightarrow {x \le z } \space \& \space { y \le z} $
and, dually
$ z \le x \wedge y \Longleftrightarrow z \le x \space \& \space z \le y $
However, I'm unable to decompose constraints
$ z \le x \vee y $
$ x \wedge y \le z $
and wonder why this skew of symmetry? Naively, I've expected logical disjunction, and more generally, is it possible to decompose lattice constraint into disjunction?