Theorems · Theorem · group theory

AddSubgroup.leftCoset_cover_filter_FiniteIndex

∀ {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 →
    ∀ [inst_1 : DecidablePred AddSubgroup.FiniteIndex], ⋃ k ∈ {i ∈ s | (H i).FiniteIndex}, g k +ᵥ ↑(H k) = Set.univ

Defined in: Mathlib.GroupTheory.CosetCover
Cited by: 0 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup DecidablePred

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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
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.filterstatement · cited by 949
Set.vaddSetstatement · cited by 403
AddSubgroup.FiniteIndexstatement and proof · cited by 66
AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3

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