Theorems · Theorem · group theory
Subgroup.closure_iUnion
∀ {G : Type u_1} [inst : Group G] {ι : Sort u_2} (s : ι → Set G),
Subgroup.closure (⋃ i, s i) = ⨆ i, Subgroup.closure (s i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Subgroup.closurestatement · cited by 196
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_iSupproof · cited by 78
- Subgroup.giproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.mem_biSup_of_directedOnproof · cited by 1
- Subgroup.iSup_eq_closureproof · cited by 1
- Polynomial.Splits.surjective_toPermHom_of_iSup_inertia_eq_topproof · cited by 0