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Theorems · Theorem · group theory

PresentedGroup.mk_eq_one_iff

∀ {α : Type u_1} {rels : Set (FreeGroup α)} {x : FreeGroup α},
  (PresentedGroup.mk rels) x = 1 ↔ x ∈ Subgroup.normalClosure rels
Defined in
Mathlib.GroupTheory.PresentedGroup
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

PresentedGroup.one_of_mem · cited by 3PresentedGroup.one_of_memDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMonoidHom · cited by 3629MonoidHomSubgroup · cited by 3593SubgroupFreeGroup · cited by 132FreeGroupSubgroup.normalClosure · cited by 35Subgroup.normalClosurePresentedGroup · cited by 21PresentedGroupQuotientGroup.eq_one_iff · cited by 18QuotientGroup.eq_one_iffPresentedGroup.mk · cited by 10PresentedGroup.mkPresentedGroup.mk_eq_one_iffCITED BYCITES

Cites9

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Cited by1

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