Theorems · Theorem · general topology

Filter.prod_mem_prod_iff

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : Filter α} {g : Filter β} [f.NeBot] [g.NeBot],
  s ×ˢ t ∈ f ×ˢ g ↔ s ∈ f ∧ t ∈ g

Defined in

Mathlib.Order.Filter.Prod

Cited by

2 results in Mathlib

Foundations

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

Assumes

Filter.NeBotFilter.NeBot