In the paper "On the Foundations of Combinatorial Theory I. Theory of Miibius Functions" published in 1964, Gian Carlo Rota laid down te means for the widespread use of the Mobius inversion formula in combinatorics and lattice theory. I have a VERY specific question about this. What are the applications of Proposition 1 of Section 6 and are there other proofs of it in texts?
Here follows the link to the paper (thanks to amrsa) : http://www.maths.ed.ac.uk/~aar/papers/rota1.pdf