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Theorems · Theorem · group theory

CoxeterSystem.wordProd_singleton

∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i : B),
  cs.wordProd [i] = cs.simple i
Defined in
Mathlib.GroupTheory.Coxeter.Basic
Cited by
5 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Group
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CoxeterSystem.length_simple · cited by 5CoxeterSystem.length_simp…CoxeterSystem.wordProd_mul_getD_rightInvSeq · cited by 2CoxeterSystem.wordProd_mu…CoxeterSystem.getD_leftInvSeq_mul_wordProd · cited by 1CoxeterSystem.getD_leftIn…CoxeterSystem.getElem_leftInvSeq_alternatingWord · cited by 0CoxeterSystem.getElem_lef…CoxeterSystem.length_eq_one_iff · cited by 0CoxeterSystem.length_eq_o…Group · cited by 6238Groupmul_one · cited by 3885mul_oneCoxeterMatrix · cited by 140CoxeterMatrixCoxeterSystem · cited by 126CoxeterSystemCoxeterSystem.simple · cited by 73CoxeterSystem.simpleCoxeterSystem.wordProd · cited by 42CoxeterSystem.wordProdCoxeterSystem.wordProd_single…CITED BYCITES

Cites6

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Cited by5

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