Theorems · Theorem · group theory
CoxeterSystem.simple_mul_simple_self
∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i : B),
cs.simple i * cs.simple i = 1- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 82 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- map_mulproof · cited by 1,137
- pow_oneproof · cited by 894
- MulEquiv.symmproof · cited by 482
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterSystem.simplestatement · cited by 73
- FreeGroup.ofproof · cited by 39
- PresentedGroupproof · cited by 21
- QuotientGroup.eq_one_iffproof · cited by 18
- PresentedGroup.ofproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- CoxeterSystem.inv_simpleproof · cited by 12
- CoxeterSystem.simple_mul_simple_cancel_leftproof · cited by 4
- CoxeterSystem.getD_leftInvSeqproof · cited by 3
- CoxeterSystem.prod_alternatingWord_eq_prod_alternatingWord_subproof · cited by 2
- CoxeterSystem.simple_mul_simple_cancel_rightproof · cited by 1
- CoxeterSystem.getD_rightInvSeq_mul_selfproof · cited by 1
- CoxeterSystem.simple_sqproof · cited by 1
- CoxeterSystem.IsReflection.mul_selfproof · cited by 1
- CoxeterSystem.getD_leftInvSeq_mul_selfproof · cited by 0