Theorems · Theorem · order theory
Set.subset_iInter_iff
∀ {α : Type u_1} {ι : Sort u_5} {s : Set α} {t : ι → Set α}, s ⊆ ⋂ i, t i ↔ ∀ (i : ι), s ⊆ t i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.iInterstatement · cited by 1,084
- le_iInf_iffproof · cited by 30
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isMulLeftInvariantproof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isAddLeftInvariantproof · cited by 1
- Subsemiring.isHomogeneous_iff_subset_iInterproof · cited by 0
- Ideal.isHomogeneous_iff_subset_iInterproof · cited by 0