for a, b being Subset of A holds f . (a \/ b) = (f . a) \/ (f . b) by ROUGHS_4:def 9;
then for a, b being Subset of A holds (Flip f) . (a /\ b) = ((Flip f) . a) /\ ((Flip f) . b) by ROUGHS_2:21;
hence Flip f is /\-preserving by ROUGHS_4:def 10; :: thesis: verum