Theorems · Theorem · group theory
CoxeterSystem.length_mul_le
∀ {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) ≤ cs.length w₁ + cs.length w₂- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 3 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.
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
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.wordProdproof · cited by 42
- CoxeterSystem.lengthstatement and proof · cited by 41
- CoxeterSystem.IsReducedproof · cited by 19
- CoxeterSystem.length_wordProd_leproof · cited by 9
- CoxeterSystem.exists_isReducedproof · cited by 8
- CoxeterSystem.wordProd_appendproof · cited by 5
- CoxeterSystem.IsReduced.eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- CoxeterSystem.length_mul_simpleproof · cited by 3
- CoxeterSystem.length_le_length_mul_add_rightproof · cited by 2
- CoxeterSystem.length_le_length_mul_add_leftproof · cited by 1