theorem Th46:
  B <> {} & (for x st x in B holds u [= f.x) implies u [= FinMeet( B,f)
proof
  assume that
A1: B <> {} and
A2: for x st x in B holds u [= f.x;
  reconsider u9 = u as Element of L.:;
  reconsider f9 = f as Function of A, the carrier of L.:;
  for x st x in B holds f9.x [= u9 by A2,Th38;
  then FinJoin(B,f9) [= u9 by A1,Th32;
  hence thesis by Th39;
end;
