theorem
  E = M & P is reflexive implies E = P..E
proof
  assume
A1: E = M;
  assume P is reflexive;
  then
A2: E c= P..E;
  P..E in bool E by A1,MSSUBFAM:12;
  then P..E c= E by MBOOLEAN:18;
  hence thesis by A2,PBOOLE:146;
end;
