theorem Th65:
  equivalence_wrt F is_symmetric_in the carrier of L
proof
  let x,y be object;
  assume x in the carrier of L & y in the carrier of L;
  then reconsider p = x, q = y as Element of L;
  assume [x,y] in equivalence_wrt F;
  then p <=> q in F by Def11;
  then q <=> p in F;
  hence thesis by Def11;
end;
