Theorems · Theorem · group theory
CoxeterSystem.IsReflection.not_isLeftInversion_mul_right_iff
∀ {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.IsLeftInversion (t * w) t ↔ cs.IsLeftInversion w t- Defined in
- Mathlib.GroupTheory.Coxeter.Inversion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites7
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
- Iff.not_leftproof · cited by 49
- CoxeterSystem.IsReflectionstatement and proof · cited by 17
- CoxeterSystem.IsLeftInversionstatement · cited by 6
- CoxeterSystem.IsReflection.isLeftInversion_mul_right_iffproof · cited by 1
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