Formalization of Coxeter groups with Lean 4

This repository formalizes the Coxeter groups in Lean 4.

Files sorted by dependencies:

• Aux_ : Auxiliary lemmas about List, Nat.
• OrderTwoGen : More lemmas.
• CoxeterSystem : Defined by exchange property.
• CoxeterMatrix, CoxeterMatrix1 : Defined by group presentation. Currently, work with CoxeterMatrix1. The aim here is to prove the strong exchange property.
• Morphism : Prove equivalence of Coxeter systems and Coxeter matrixes, as well as results about other maps.
• BruhatOrder : Prove things about Bruhat order.

Some notes for developers:

• We are using the Feature Branch workflow. Create a new branch to formalize in, then send a pull request to the master branch.
• ⟨i, hi : i < n⟩ is a Fin n, we can rcases to get the parts, or simply .1 or .val it to take the value out and .2 or .prop to get the inequality out.
• Consider using @[deprecated] if you want to change some stuff.
• Try to follow the conventional formatting of Mathematics in Lean.