Theorems · Theorem · group theory
CoxeterSystem.IsReflection.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
- 1 results in Mathlib
- Foundations
- Depth 94 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.
Cites10
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
- mul_inv_revproof · cited by 270
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.IsReflectionstatement and proof · cited by 17
- CoxeterSystem.IsRightInversionproof · cited by 7
- CoxeterSystem.IsLeftInversionstatement and proof · cited by 6
- CoxeterSystem.IsReflection.invproof · cited by 4
- CoxeterSystem.IsReflection.isRightInversion_mul_left_iffproof · cited by 2
- CoxeterSystem.isRightInversion_inv_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CoxeterSystem.IsReflection.not_isLeftInversion_mul_right_iffproof · cited by 0