Theorems · Theorem · group theory
AddSubgroup.iInf_normalizer_le_normalizer_iSup
∀ {G : Type u_2} [inst : AddGroup G] {ι : Sort u_5} (H : ι → AddSubgroup G),
⨅ i, AddSubgroup.normalizer ↑(H i) ≤ AddSubgroup.normalizer ↑(⨆ i, H i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- iSupstatement and proof · cited by 2,415
- iInfstatement and proof · cited by 1,690
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- AddSubgroup.normalizerstatement and proof · cited by 59
- AddAut.addConjproof · cited by 34
- AddSubgroup.mem_normalizer_iff_map_addConj_eqproof · cited by 6
- AddSubgroup.mem_iInfproof · cited by 4
- AddSubgroup.map_iSupproof · cited by 1
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