Theorems · Theorem · group theory
Subgroup.coe_iInf
∀ {G : Type u_1} [inst : Group G] {ι : Sort u_2} {S : ι → Subgroup G}, ↑(⨅ i, S i) = ⋂ i, ↑(S i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- iInfstatement · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Set.biInter_rangeproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- ProfiniteGrp.denseRange_toLimitproof · cited by 1
- Subgroup.normalCore_isClosedproof · cited by 1
- Subgroup.map_iInfproof · cited by 1