Theorems · Theorem · group theory
CoxeterSystem.wordProd_nil
∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W), cs.wordProd [] = 1- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 83 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.wordProdstatement · cited by 42
Cited by11
Results whose statement or proof uses this declaration.
- CoxeterSystem.wordProd_reverseproof · cited by 4
- CoxeterSystem.getD_leftInvSeqproof · cited by 3
- CoxeterSystem.getD_rightInvSeqproof · cited by 3
- CoxeterSystem.prod_alternatingWord_eq_mul_powproof · cited by 1
- CoxeterSystem.prod_rightInvSeqproof · cited by 1
- CoxeterSystem.exists_leftDescent_of_ne_oneproof · cited by 1
- CoxeterSystem.rightInvSeq_singletonproof · cited by 1
- CoxeterSystem.getElem_leftInvSeq_alternatingWordproof · cited by 0
- CoxeterSystem.length_eq_zero_iffproof · cited by 0
- CoxeterSystem.wordProd_surjectiveproof · cited by 0
- CoxeterSystem.rightInvSeq_concatproof · cited by 0