WHEN A RELATION WITH ALL BOREL SECTIONS WILL BE BOREL SOMEWHERE?

In ZFC, if there is a measurable cardinal with infinitely many Woodin cardinals below it, then for every binary relation R is an element of L(R) on R with all sections Delta(1)(1) (Sigma(1)(1) or Pi(1)(1)) and every sigma-ideal I on R so that the associated forcing P-I of I+ Delta(1)(1) subsets is proper, there exists some I+ Delta(1)(1) set C so that R boolean AND (C x R) is Delta(1)(1) (Sigma(1)(1) or Pi(1)(1), respectively).