theorem Th59:
  (for x st x in B holds u [= f.x) implies u [= FinMeet(B,f)
proof
  reconsider f9 = f as Function of A, the carrier of L.:;
  reconsider u9 = u as Element of L.:;
  assume for x st x in B holds u [= f.x;
  then
A1: for x st x in B holds f9.x [= u9 by Th38;
  L.: is 0_Lattice by Th49;
  then FinJoin(B,f9) [= u9 by A1,Th54;
  hence thesis by Th39;
end;
