Theorems · Theorem · group theory
CoxeterSystem.lengthParity_eq_ofAdd_length
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (w : W),
cs.lengthParity w = Multiplicative.ofAdd ↑(cs.length w)- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 5 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- ZModstatement and proof · cited by 1,024
- Multiplicativestatement and proof · cited by 875
- Multiplicative.ofAddstatement and proof · cited by 237
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.simpleproof · cited by 73
- CoxeterSystem.wordProdproof · cited by 42
- CoxeterSystem.lengthstatement · cited by 41
Cited by5
Results whose statement or proof uses this declaration.
- CoxeterSystem.length_simpleproof · cited by 5
- CoxeterSystem.length_mul_mod_twoproof · cited by 1
- CoxeterSystem.IsReflection.length_mul_left_neproof · cited by 1
- CoxeterSystem.IsReflection.length_mul_right_neproof · cited by 0
- CoxeterSystem.IsReflection.odd_lengthproof · cited by 0