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;
