Theorems · Theorem · general topology
Filter.mem_pi
∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {s : Set ((i : ι) → α i)},
s ∈ Filter.pi f ↔ ∃ I, I.Finite ∧ ∃ t, (∀ (i : ι), t i ∈ f i) ∧ I.pi t ⊆ s- Defined in
- Mathlib.Order.Filter.Pi
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Filterstatement and proof · cited by 8,121
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- Set.Finitestatement and proof · cited by 1,814
- Set.iInterproof · cited by 1,084
- Set.pistatement and proof · cited by 405
- Filter.mem_of_supersetproof · cited by 308
- Function.evalproof · cited by 140
- Filter.pistatement · cited by 48
- Set.pi_defproof · cited by 14
- Set.iInter₂_monoproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- Filter.map_eval_piproof · cited by 2
- Filter.mem_of_pi_mem_piproof · cited by 2
- Pi.locallyConnectedSpace_of_finite_not_preconnectedSpaceproof · cited by 1
- Pi.locallyPathConnectedSpace_of_finite_not_pathConnectedSpaceproof · cited by 1
- Bornology.IsVonNBounded.image_multilinear'proof · cited by 1
- Filter.mem_pi'proof · cited by 0
- Pi.locallyConnectedSpace_iffproof · cited by 0
- Pi.locallyPathConnectedSpace_iffproof · cited by 0