Theorems · Theorem · group theory

Submonoid.closure_pi

∀ {η : Type u_1} {f : η → Type u_2} [inst : (i : η) → MulOneClass (f i)] [Finite η] {s : (i : η) → Set (f i)},
  (∀ (i : η), 1 ∈ s i) →
    Submonoid.closure (Set.univ.pi fun i => s i) = Submonoid.pi Set.univ fun i => Submonoid.closure (s i)

Defined in: Mathlib.Algebra.Group.Submonoid.Finite
Cited by: 0 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MulOneClass Finite

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

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
Set.univstatement and proof · cited by 3,945
Submonoidstatement · cited by 3,086
Finitestatement and proof · cited by 3,029
le_antisymmproof · cited by 2,068
MulOneClassstatement and proof · cited by 1,018
Set.pistatement · cited by 405
Submonoid.closurestatement and proof · cited by 167
Submonoid.subset_closureproof · cited by 46
Submonoid.closure_leproof · cited by 27
MonoidHom.mulSingleproof · cited by 21

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.