Theorems · Theorem · general topology

Filter.eventually_prod_iff

∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {g : Filter β} {p : α × β → Prop},
  (∀ᶠ (x : α × β) in f ×ˢ g, p x) ↔
    ∃ pa, (∀ᶠ (x : α) in f, pa x) ∧ ∃ pb, (∀ᶠ (y : β) in g, pb y) ∧ ∀ {x : α}, pa x → ∀ {y : β}, pb y → p (x, y)

Defined in

Mathlib.Order.Filter.Prod

Cited by

12 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound