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Theorems · Theorem · order theory

Set.subset_pi_iff

∀ {ι : Type u_1} {α : ι → Type u_2} {s : Set ι} {t : (i : ι) → Set (α i)} {s' : Set ((i : ι) → α i)},
  s' ⊆ s.pi t ↔ ∀ i ∈ s, s' ⊆ (fun x => x i) ⁻¹' t i
Defined in
Mathlib.Data.Set.Prod
Cited by
4 results in Mathlib
Foundations
Depth 16 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.

AddSubgroup.le_pi_iff · cited by 1AddSubgroup.le_pi_iffSubgroup.le_pi_iff · cited by 1Subgroup.le_pi_iffAddSubmonoid.le_pi_iff · cited by 0AddSubmonoid.le_pi_iffSubmonoid.le_pi_iff · cited by 0Submonoid.le_pi_iffSet · cited by 53352SetSet.preimage · cited by 4946Set.preimageSet.pi · cited by 405Set.piSet.subset_pi_iffCITED BYCITES

Cites3

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.preimagestatement · cited by 4,946
  • Set.pistatement · cited by 405

Cited by4

Results whose statement or proof uses this declaration.