theorem Th41:
  (ex x st x in B & f.x [= u) implies FinMeet(B,f)[= u
proof
  given x such that
A1: x in B and
A2: f.x [= u;
  reconsider u9 = u as Element of L.:;
  reconsider f9 = f as Function of A, the carrier of L.:;
  u9 [= f9.x by A2,Th38;
  then u9 [= FinJoin(B,f9) by A1,Th29;
  hence thesis by Th39;
end;
