Theorems · Theorem · group theory
CoxeterSystem.isLeftDescent_iff_not_isLeftDescent_mul
∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) {w : W} {i : B},
cs.IsLeftDescent w i ↔ ¬cs.IsLeftDescent (cs.simple i * w) i- Defined in
- Mathlib.GroupTheory.Coxeter.Length
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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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.simplestatement and proof · cited by 73
- CoxeterSystem.lengthproof · cited by 41
- CoxeterSystem.IsLeftDescentstatement and proof · cited by 8
- CoxeterSystem.simple_mul_simple_cancel_leftproof · cited by 4
- CoxeterSystem.not_isLeftDescent_iffproof · cited by 1
- CoxeterSystem.isLeftDescent_iffproof · cited by 1
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