Theorems · Theorem · group theory
AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq
∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_2} {s : Finset ι} {H : AddSubgroup G} {g : ι → G},
⋃ i ∈ s, g i +ᵥ ↑H = Set.univ → H.index = s.card → (↑s).PairwiseDisjoint fun x => g x +ᵥ ↑H- Defined in
- Mathlib.GroupTheory.CosetCover
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 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.
Cites32
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
- Fintypeproof · cited by 7,736
- 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
- Finset.cardstatement and proof · cited by 2,327
- HasQuotient.Quotientproof · cited by 2,301
- HVAdd.hVAddstatement and proof · cited by 1,820
- Fintype.cardproof · cited by 1,386
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3