Theorems · Theorem · group theory
CoxeterSystem.length_wordProd_le
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (ω : List B),
cs.length (cs.wordProd ω) ≤ ω.length- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 89 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.
Cites6
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.wordProdstatement and proof · cited by 42
- CoxeterSystem.lengthstatement · cited by 41
- Nat.find_min'proof · cited by 28
Cited by9
Results whose statement or proof uses this declaration.
- CoxeterSystem.length_invproof · cited by 7
- CoxeterSystem.length_simpleproof · cited by 5
- CoxeterSystem.length_mul_leproof · cited by 3
- CoxeterSystem.length_oneproof · cited by 3
- CoxeterSystem.IsReduced.nodup_rightInvSeqproof · cited by 1
- CoxeterSystem.exists_leftDescent_of_ne_oneproof · cited by 1
- CoxeterSystem.not_isReduced_alternatingWordproof · cited by 0
- CoxeterSystem.isLeftInversion_of_mem_leftInvSeqproof · cited by 0
- CoxeterSystem.isRightInversion_of_mem_rightInvSeqproof · cited by 0