### Abstract

This work contains a formalization of some topics in knot theory.
The concepts that were formalized include definitions of tangles, links,
framed links and link/tangle equivalence. The formalization is based on a
formulation of links in terms of tangles. We further construct and prove the
invariance of the Bracket polynomial. Bracket polynomial is an invariant of
framed links closely linked to the Jones polynomial. This is perhaps the first
attempt to formalize any aspect of knot theory in an interactive proof assistant.

### License

### Topics

### Session Knot_Theory

- Preliminaries
- Tangles
- Tangle_Algebra
- Tangle_Relation
- Tangle_Moves
- Link_Algebra
- Example
- Kauffman_Matrix
- Computations
- Linkrel_Kauffman
- Kauffman_Invariance
- Knot_Theory