theorem
  for D being MSClosureSystem of S for J being MSSetOp of the Sorts of D
  st for X being Element of bool the Sorts of D for SF being non-empty
  MSSubsetFamily of the Sorts of D st (for Y being ManySortedSet of the carrier
  of S holds Y in SF iff Y in the Family of D & X c= Y) holds J..X = meet SF
  holds J is MSClosureOperator of the Sorts of D by Th36,Th37;
