Theorems · Theorem · group theory
AddSubgroup.exists_finiteIndex_of_leftCoset_cover
∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_2} {H : ι → AddSubgroup G} {g : ι → G} {s : Finset ι},
⋃ i ∈ s, g i +ᵥ ↑(H i) = Set.univ → ∃ k ∈ s, (H k).FiniteIndex- Defined in
- Mathlib.GroupTheory.CosetCover
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 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.
Cites21
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement and proof · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- Set.iUnionstatement and proof · cited by 2,483
- HVAdd.hVAddstatement and proof · cited by 1,820
- Finset.Nonemptyproof · cited by 1,001
- Finset.filterproof · cited by 949
- Set.vaddSetstatement · cited by 403
- Finset.mem_filterproof · cited by 185
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Submodule.exists_finiteIndex_of_coverproof · cited by 1