Theorems · Theorem · group theory

Subgroup.closure_pi

∀ {η : Type u_3} {f : η → Type u_4} [inst : (i : η) → Group (f i)] [Finite η] {s : (i : η) → Set (f i)},
  (∀ (i : η), 1 ∈ s i) →
    Subgroup.closure (Set.univ.pi fun i => s i) = Subgroup.pi Set.univ fun i => Subgroup.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
Assumes: Group Finite

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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
Groupstatement and proof · cited by 6,238
Set.univstatement and proof · cited by 3,945
Subgroupstatement · cited by 3,593
Finitestatement and proof · cited by 3,029
le_antisymmproof · cited by 2,068
Set.pistatement and proof · cited by 405
Subgroup.closurestatement and proof · cited by 196
Subgroup.comapproof · cited by 154
Subgroup.subset_closureproof · cited by 53
Subgroup.closure_leproof · cited by 31

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