reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;
reserve L for non empty LattStr,
  a,b,c for Element of L;
reserve L for Lattice;
reserve a,b,c,u,v for Element of L;
reserve A for non empty set,
  x for Element of A,
  B for Element of Fin A,
  f,g for Function of A, the carrier of L;

theorem
  for L being Lattice, B being Element of Fin A for f being Function
  of A, the carrier of L, f9 being Function of A, the carrier of L.: st f = f9
  holds FinJoin(B,f) = FinMeet(B,f9) & FinMeet(B,f) = FinJoin(B,f9);
