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Theorems · Theorem · group theory

CoxeterSystem.not_isLeftDescent_iff

∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) {w : W} {i : B},
  ¬cs.IsLeftDescent w i ↔ cs.length (cs.simple i * w) = cs.length w + 1
Defined in
Mathlib.GroupTheory.Coxeter.Length
Cited by
1 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Group
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Around this declaration

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CoxeterSystem.isLeftDescent_iff_not_isLeftDescent_mul · cited by 0CoxeterSystem.isLeftDesce…Group · cited by 6238GroupCoxeterMatrix · cited by 140CoxeterMatrixCoxeterSystem · cited by 126CoxeterSystemCoxeterSystem.simple · cited by 73CoxeterSystem.simpleCoxeterSystem.length · cited by 41CoxeterSystem.lengthCoxeterSystem.IsLeftDescent · cited by 8CoxeterSystem.IsLeftDesce…CoxeterSystem.length_simple_mul · cited by 2CoxeterSystem.length_simp…CoxeterSystem.not_isLeftDesce…CITED BYCITES

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