Theorems · Definition · group theory
CoxeterSystem.IsLeftDescent
{B : Type u_1} → {W : Type u_2} → [inst : Group W] → {M : CoxeterMatrix B} → CoxeterSystem M W → W → B → PropThe proposition that i is a left descent of w; that is, $\ell(s_i w) < \ell(w)$.
- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 8 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.simpleproof · cited by 73
- CoxeterSystem.lengthproof · cited by 41
Cited by8
Results whose statement or proof uses this declaration.
- CoxeterSystem.not_isLeftDescent_iffstatement · cited by 1
- CoxeterSystem.isLeftDescent_iffstatement · cited by 1
- CoxeterSystem.isLeftDescent_inv_iffstatement · cited by 1
- CoxeterSystem.exists_leftDescent_of_ne_onestatement · cited by 1
- CoxeterSystem.isRightDescent_inv_iffstatement and proof · cited by 0
- CoxeterSystem.not_isLeftDescent_onestatement · cited by 0
- CoxeterSystem.isLeftDescent_iff_not_isLeftDescent_mulstatement and proof · cited by 0
- CoxeterSystem.isLeftInversion_simple_iff_isLeftDescentstatement · cited by 0