On the orthographic dimension of definable sets

A formula '(x 1 ; : : :; x n) conforms to a partition P of fx 1 ; : : :; x n g if it is equivalent to a Boolean combination of formulae that do not have free variables from more than one block of P. We show that if ' conforms to two partitions P 1 and P 2 , it also conforms to their greatest lower bound in the partition lattice. As a corollary, we obtain that the concept of orthographic dimension of a constraint-deenable set, introduced in the eld of constraint databases, is well-deened.