Theorems · Theorem · group theory
AddSubgroup.mem_iInf
∀ {G : Type u_1} [inst : AddGroup G] {ι : Sort u_2} {S : ι → AddSubgroup G} {x : G}, x ∈ ⨅ i, S i ↔ ∀ (i : ι), x ∈ S i- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- iInfstatement · cited by 1,690
- Set.forall_mem_rangeproof · cited by 135
- AddSubgroup.mem_sInfproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroupproof · cited by 4
- AddSubgroup.normal_iInf_normalproof · cited by 1
- AddSubgroup.centralizer_eq_iInfproof · cited by 1
- AddSubgroup.iInf_normalizer_le_normalizer_iSupproof · cited by 0