Theorems · Theorem · general topology
Filter.mem_prod_top
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {s : Set (α × β)}, s ∈ f ×ˢ ⊤ ↔ {a | ∀ (b : β), (a, b) ∈ s} ∈ f- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- SProd.sprodstatement and proof · cited by 1,750
- Filter.principal_univproof · cited by 46
- Filter.mem_prod_principalproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- UniformFun.gcproof · cited by 2