1 Introduction  
2 Poset  
2.1 Zorn’s Lemma  
2.2 Möbius Algebra  
3 Lattice  
3.1 Generalities on Lattice  
3.2 Distributive Lattice  
4 Valuation on Lattice  
4.1 Valuation Module  
4.2 Valuation Algebra  
4.3 Identities on Valuation Algebra  
5 Dissection Theory  
6 Face Counting for Submanifold Arrangement