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Theorems · Theorem · group theory

AddSubgroup.finiteIndex_iInf

∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_3} [Finite ι] {f : ι → AddSubgroup G},
  (∀ (i : ι), (f i).FiniteIndex) → (⨅ i, f i).FiniteIndex
Defined in
Mathlib.GroupTheory.Index
Cited by
2 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupFinite
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Around this declaration

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

AddSubgroup.finiteIndex_iInf' · cited by 1AddSubgroup.finiteIndex_i…ProfiniteAddGrp.ProfiniteCompletion.denseRange · cited by 1ProfiniteCompletion.dense…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupFinite · cited by 3029FiniteiInf · cited by 1690iInfAddSubgroup.FiniteIndex · cited by 66AddSubgroup.FiniteIndexAddSubgroup.FiniteIndex.index_ne_zero · cited by 10FiniteIndex.index_ne_zeroAddSubgroup.index_iInf_ne_zero · cited by 1AddSubgroup.index_iInf_ne…AddSubgroup.finiteIndex_iInfCITED BYCITES

Cites7

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Cited by2

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