theorem
  for L1,L2 being Lattice for F1 being Filter of L1, F2 being Filter of
  L2 st the LattStr of L1 = the LattStr of L2 & F1 = F2 holds latt F1 = latt F2
proof
  let L1,L2 be Lattice, F1 be Filter of L1, F2 be Filter of L2;
  ex o1,o2 being BinOp of F1 st o1 = (the L_join of L1)||F1 & o2 = (the
  L_meet of L1)||F1 & latt F1 = LattStr (#F1, o1, o2#) by FILTER_0:def 9;
  hence thesis by FILTER_0:def 9;
end;
