Theorems · Theorem · group theory
CoxeterSystem.length_simple
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i : B),
cs.length (cs.simple i) = 1- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 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.
Cites16
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
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- ZModproof · cited by 1,024
- Multiplicativeproof · cited by 875
- Multiplicative.ofAddproof · cited by 237
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.simplestatement and proof · cited by 73
- CoxeterSystem.lengthstatement and proof · cited by 41
- CoxeterSystem.length_wordProd_leproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- CoxeterSystem.length_mul_simpleproof · cited by 3
- CoxeterSystem.length_mul_simple_neproof · cited by 2
- CoxeterSystem.not_isLeftDescent_oneproof · cited by 0
- CoxeterSystem.length_eq_one_iffproof · cited by 0
- CoxeterSystem.not_isRightDescent_oneproof · cited by 0