Theorems · Theorem · group theory
CoxeterSystem.length_mul_mod_two
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (w₁ w₂ : W),
cs.length (w₁ * w₂) % 2 = (cs.length w₁ + cs.length w₂) % 2- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 1 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.
Cites10
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
- map_mulproof · cited by 1,137
- ZModproof · cited by 1,024
- Nat.cast_addproof · cited by 586
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.lengthstatement and proof · cited by 41
- CoxeterSystem.lengthParityproof · cited by 8
- CoxeterSystem.lengthParity_eq_ofAdd_lengthproof · cited by 5
- ZMod.natCast_eq_natCast_iff'proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CoxeterSystem.length_mul_simple_neproof · cited by 2