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Theorems · Theorem · order theory

Set.iUnion_univ_pi

∀ {α : Type u_1} {π : α → Type u_12} {ι : α → Type u_13} (t : (a : α) → ι a → Set (π a)),
  (⋃ x, Set.univ.pi fun a => t a (x a)) = Set.univ.pi fun a => ⋃ j, t a j
Defined in
Mathlib.Data.Set.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

generateFrom_pi_eq · cited by 1generateFrom_pi_eqIsCountablySpanning.pi · cited by 0IsCountablySpanning.piSet · cited by 53352SetSet.univ · cited by 3945Set.univSet.iUnion · cited by 2483Set.iUnionSet.ext · cited by 2266Set.extSet.pi · cited by 405Set.piSet.iUnion_univ_piCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Set.univstatement · cited by 3,945
  • Set.iUnionstatement · cited by 2,483
  • Set.extproof · cited by 2,266
  • Set.pistatement · cited by 405

Cited by2

Results whose statement or proof uses this declaration.