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;
reserve L for 0_Lattice,
  f,g for Function of A, the carrier of L,
  u for Element of L;
reserve L for 1_Lattice,
  f,g for Function of A, the carrier of L,
  u for Element of L;
reserve L for D0_Lattice,
  f,g for (Function of A, the carrier of L),
  u for Element of L;

theorem
  u "/\" FinJoin(B,f) = FinJoin(B, (the L_meet of L)[;](u, f)) by Th64;
