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 Th40:
  x in B implies FinMeet(B,f) [= f.x
proof
  reconsider f9 = f as Function of A, the carrier of L.:;
  assume x in B;
  then f9.x [= FinJoin(B,f9) by Th28;
  hence thesis by Th39;
end;
