Theorems · Theorem · order theory
Set.biInter_eq_iInter
∀ {α : Type u_1} {β : Type u_2} (s : Set α) (t : (x : α) → x ∈ s → Set β), ⋂ x, ⋂ (h : x ∈ s), t x h = ⋂ x, t ↑x ⋯- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 19 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.
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.Elemstatement · cited by 7,166
- Set.iInterstatement · cited by 1,084
- iInf_subtype'proof · cited by 34
Cited by19
Results whose statement or proof uses this declaration.
- IsCompact.exists_isLeastproof · cited by 9
- countable_bInter_memproof · cited by 4
- Filter.pi_mem_piproof · cited by 4
- IsGδ.biInterproof · cited by 3
- MeasureTheory.tendsto_measure_biInter_gtproof · cited by 3
- Set.biInter_interproof · cited by 2
- Filter.EventuallyLE.countable_bInterproof · cited by 2
- omegaLimit_eq_iInter_interproof · cited by 2
- Set.iUnion_pi_of_monotoneproof · cited by 1
- Filter.EventuallyLE.cardinal_bInterproof · cited by 1
- Filter.cardinal_bInter_memproof · cited by 1
- omegaLimit_eq_iInterproof · cited by 1