Theorems · Theorem · group theory
CoxeterSystem.inv_simple
∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i : B),
(cs.simple i)⁻¹ = cs.simple i- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 83 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.
Cites6
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 · cited by 73
- CoxeterSystem.simple_mul_simple_selfproof · cited by 9
- eq_inv_of_mul_eq_one_rightproof · cited by 7
Cited by12
Results whose statement or proof uses this declaration.
- CoxeterSystem.submonoid_closure_range_simpleproof · cited by 4
- CoxeterSystem.wordProd_reverseproof · cited by 4
- CoxeterSystem.IsReflection.invproof · cited by 4
- CoxeterSystem.getD_leftInvSeqproof · cited by 3
- CoxeterSystem.prod_alternatingWord_eq_prod_alternatingWord_subproof · cited by 2
- CoxeterSystem.length_simple_mulproof · cited by 2
- CoxeterSystem.getElem_succ_leftInvSeq_alternatingWordproof · cited by 1
- CoxeterSystem.isLeftDescent_inv_iffproof · cited by 1
- CoxeterSystem.prod_rightInvSeqproof · cited by 1
- CoxeterSystem.getElem_leftInvSeq_alternatingWordproof · cited by 0
- CoxeterSystem.rightInvSeq_concatproof · cited by 0
- CoxeterSystem.length_simple_mul_neproof · cited by 0