Theorems · Theorem · group theory
CoxeterSystem.exists_leftDescent_of_ne_one
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) {w : W},
w ≠ 1 → ∃ i, cs.IsLeftDescent w i- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 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.
Cites13
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.simpleproof · cited by 73
- CoxeterSystem.wordProdproof · cited by 42
- CoxeterSystem.lengthproof · cited by 41
- CoxeterSystem.IsReducedproof · cited by 19
- CoxeterSystem.wordProd_nilproof · cited by 11
- CoxeterSystem.wordProd_consproof · cited by 9
- CoxeterSystem.length_wordProd_leproof · cited by 9
- CoxeterSystem.IsLeftDescentstatement · cited by 8
- CoxeterSystem.exists_isReducedproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- CoxeterSystem.exists_rightDescent_of_ne_oneproof · cited by 0