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
  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;
