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;

theorem
  the carrier of L = the carrier of L.: & the L_join of L = the L_meet
  of L.: & the L_meet of L = the L_join of L.:;
