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Theorems · Theorem · order theory

Set.univ_pi_nonempty_iff

∀ {ι : Type u_1} {α : ι → Type u_2} {t : (i : ι) → Set (α i)}, (Set.univ.pi t).Nonempty ↔ ∀ (i : ι), (t i).Nonempty
Defined in
Mathlib.Data.Set.Prod
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.

IsPiSystem.pi · cited by 2IsPiSystem.piNumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSet · cited by 1fundamentalCone.zero_mem_…Set · cited by 53352SetSet.univ · cited by 3945Set.univSet.Nonempty · cited by 2627Set.NonemptySet.pi · cited by 405Set.piSet.univ_pi_nonempty_iffCITED BYCITES

Cites4

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.Nonemptystatement · cited by 2,627
  • Set.pistatement · cited by 405

Cited by2

Results whose statement or proof uses this declaration.