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Theorems · Theorem · group theory

Set.center_pi

∀ {ι : Type u_2} {A : ι → Type u_3} [inst : (i : ι) → Mul (A i)],
  Set.center ((i : ι) → A i) = Set.univ.pi fun i => Set.center (A i)
Defined in
Mathlib.Algebra.Group.Center
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Mul
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Around this declaration

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

Subgroup.center_pi · cited by 0Subgroup.center_piSubalgebra.center_pi · cited by 0Subalgebra.center_piSubmonoid.center_pi · cited by 0Submonoid.center_piSet · cited by 53352SetSet.univ · cited by 3945Set.univSet.ext · cited by 2266Set.extFunction.update · cited by 502Function.updateSet.pi · cited by 405Set.piFunction.update_self · cited by 201Function.update_selfSet.center · cited by 49Set.centerSet.center_piCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.