Theorems · Theorem · group theory
AddSubgroup.closure_pi
∀ {η : Type u_3} {f : η → Type u_4} [inst : (i : η) → AddGroup (f i)] [Finite η] {s : (i : η) → Set (f i)},
(∀ (i : η), 0 ∈ s i) →
AddSubgroup.closure (Set.univ.pi fun i => s i) = AddSubgroup.pi Set.univ fun i => AddSubgroup.closure (s i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement and proof · cited by 3,945
- AddSubgroupstatement · cited by 3,232
- Finitestatement and proof · cited by 3,029
- le_antisymmproof · cited by 2,068
- Set.pistatement and proof · cited by 405
- AddSubgroup.closurestatement and proof · cited by 156
- Pi.single_eq_sameproof · cited by 144
- AddSubgroup.comapproof · cited by 123
- Pi.single_eq_of_neproof · cited by 116
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