reserve i, x, I for set,
  A, M for ManySortedSet of I,
  f for Function,
  F for ManySortedFunction of I;
reserve P, R for MSSetOp of M,
  E, T for Element of bool M;

theorem
  P is reflexive & R is reflexive implies P ** R is reflexive
proof
  assume
A1: P is reflexive & R is reflexive;
  let X be Element of bool M;
  X c= R..X & R..X c= P..(R..X) by A1;
  then doms R = bool M & X c= P..(R..X) by MSSUBFAM:17,PBOOLE:13;
  hence thesis by Th4,MSSUBFAM:12;
end;
