Theorems · Definition · group theory
CoxeterSystem.IsLeftInversion
{B : Type u_1} → {W : Type u_2} → [inst : Group W] → {M : CoxeterMatrix B} → CoxeterSystem M W → W → W → PropThe proposition that t is a left inversion of w; i.e., t is a reflection and
$\ell (t w) < \ell(w)$.
- Defined in
- Mathlib.GroupTheory.Coxeter.Inversion
- Cited by
- 6 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.
Cites5
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.lengthproof · cited by 41
- CoxeterSystem.IsReflectionproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- CoxeterSystem.isRightInversion_inv_iffstatement · cited by 2
- CoxeterSystem.IsReflection.isLeftInversion_mul_right_iffstatement and proof · cited by 1
- CoxeterSystem.isLeftInversion_inv_iffstatement and proof · cited by 0
- CoxeterSystem.isLeftInversion_of_mem_leftInvSeqstatement · cited by 0
- CoxeterSystem.isLeftInversion_simple_iff_isLeftDescentstatement · cited by 0
- CoxeterSystem.IsReflection.not_isLeftInversion_mul_right_iffstatement · cited by 0