Theorems · Theorem · group theory
Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq
∀ {G : Type u_1} [inst : Group G] {ι : Type u_2} {s : Finset ι} {H : Subgroup G} {g : ι → G},
⋃ i ∈ s, g i • ↑H = Set.univ → H.index = s.card → (↑s).PairwiseDisjoint fun x => g x • ↑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
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Groupstatement and proof · cited by 6,238
- Set.univstatement and proof · cited by 3,945
- Subgroupstatement and proof · cited by 3,593
- Set.iUnionstatement and proof · cited by 2,483
- Finset.cardstatement and proof · cited by 2,327
- HasQuotient.Quotientproof · cited by 2,301
- Fintype.cardproof · cited by 1,386
- Function.Bijectiveproof · cited by 863
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3