Theorems · Theorem · group theory
CoxeterSystem.simple_mul_simple_pow
∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i i' : B),
(cs.simple i * cs.simple i') ^ M.M i i' = 1- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 1 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.
Cites17
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
- map_powproof · cited by 503
- 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
- QuotientGroup.eq_one_iffproof · cited by 18
- CoxeterMatrix.Mstatement and proof · cited by 13
- PresentedGroup.ofproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- CoxeterSystem.simple_mul_simple_pow'proof · cited by 1