Theorems · Theorem · group theory
AddSubgroup.one_le_sum_inv_index_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 → 1 ≤ ∑ i ∈ s, (↑(H i).index)⁻¹- Defined in
- Mathlib.GroupTheory.CosetCover
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement · cited by 5,195
- 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
- Set.vaddSetstatement · cited by 403
- AddSubgroup.indexstatement · cited by 104
- AddSubgroup.FiniteIndexproof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.exists_index_le_card_of_leftCoset_coverproof · cited by 0