Theorems · Definition · group theory
CoxeterSystem.simple
{B : Type u_1} → {W : Type u_3} → [inst : Group W] → {M : CoxeterMatrix B} → CoxeterSystem M W → B → WThe simple reflection of W at the index i.
- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 73 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MulEquiv.symmproof · cited by 482
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- PresentedGroup.ofproof · cited by 12
- CoxeterSystem.mulEquivproof · cited by 8
Cited by78
Results whose statement or proof uses this declaration.
- CoxeterSystem.wordProdproof · cited by 42
- CoxeterSystem.IsReflectionproof · cited by 17
- CoxeterSystem.inv_simplestatement · cited by 12
- CoxeterSystem.simple_mul_simple_selfstatement · cited by 9
- CoxeterSystem.wordProd_consstatement and proof · cited by 9
- CoxeterSystem.IsLeftDescentproof · cited by 8
- CoxeterSystem.IsRightDescentproof · cited by 8
- CoxeterSystem.lengthParity_eq_ofAdd_lengthproof · cited by 5
- CoxeterSystem.lengthParity_simplestatement · cited by 5
- CoxeterSystem.length_simplestatement and proof · cited by 5
- CoxeterSystem.wordProd_appendproof · cited by 5
- CoxeterSystem.wordProd_singletonstatement and proof · cited by 5