Map of lattices

The concept of a lattice arises in order theory, a branch of mathematics. The Hasse diagram below depicts the inclusion relationships among some important subclasses of lattices. The concept of a lattice arises in order theory, a branch of mathematics. The Hasse diagram below depicts the inclusion relationships among some important subclasses of lattices. 1. A boolean algebra is a complemented distributive lattice. (def) 2. A boolean algebra is a heyting algebra. 3. A boolean algebra is orthocomplemented. 4. A distributive orthocomplemented lattice is orthomodular. 5. A boolean algebra is orthomodular. (1,3,4) 6. An orthomodular lattice is orthocomplemented. (def) 7. An orthocomplemented lattice is complemented. (def) 8. A complemented lattice is bounded. (def)