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Theorems · Theorem · group theory

AddSubgroup.index_iInf_ne_zero

∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_3} [Finite ι] {f : ι → AddSubgroup G},
  (∀ (i : ι), (f i).index ≠ 0) → (⨅ i, f i).index ≠ 0
Defined in
Mathlib.GroupTheory.Index
Cited by
1 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupFinite
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AddSubgroup.finiteIndex_iInf · cited by 2AddSubgroup.finiteIndex_i…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupFinite · cited by 3029FiniteiInf · cited by 1690iInfAddSubgroup.index · cited by 104AddSubgroup.indexAddSubgroup.relIndex_top_right · cited by 7AddSubgroup.relIndex_top_…AddSubgroup.relIndex_iInf_ne_zero · cited by 1AddSubgroup.relIndex_iInf…AddSubgroup.index_iInf_ne_zeroCITED BYCITES

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