Theorems · Theorem · group theory
CoxeterSystem.IsReflection.length_mul_left_ne
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} {cs : CoxeterSystem M W} {t : W},
cs.IsReflection t → ∀ (w : W), cs.length (w * t) ≠ cs.length w- Defined in
- Mathlib.GroupTheory.Coxeter.Inversion
- 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.
Cites14
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
- map_mulproof · cited by 1,137
- Multiplicative.ofAddproof · cited by 237
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- map_invproof · cited by 95
- CoxeterSystem.simpleproof · cited by 73
- CoxeterSystem.lengthstatement and proof · cited by 41
- CoxeterSystem.IsReflectionstatement and proof · cited by 17
- mul_inv_cancel_commproof · cited by 13
- CoxeterSystem.lengthParityproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- CoxeterSystem.IsReflection.isRightInversion_mul_left_iffproof · cited by 2