Theorems · Theorem · group theory

CoxeterSystem.getElem_succ_leftInvSeq_alternatingWord

∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i j : B) (p k : ℕ)
  (h : k + 1 < 2 * p),
  (cs.leftInvSeq (CoxeterSystem.alternatingWord i j (2 * p)))[k + 1] =
    (MulAut.conj (cs.simple i)) (cs.leftInvSeq (CoxeterSystem.alternatingWord j i (2 * p)))[k]

Defined in

Mathlib.GroupTheory.Coxeter.Inversion

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Group