On this page we look at proving things in different theories, such as,

- Set Theory
- Type Theory
- Topology
- Homotopy Type Theory
- Category Theory

In many areas, such as set theory, we use a logic over the theory. When proving things we usually use Intuitionistic logic (see page here). Although there is also a connection between set theory and boolean logic which can be seen nicely in Venn diagrams. |

In type theory, types can represent both the structure and the logic within type theory. |