Theorems · Theorem · general topology

Filter.mem_of_pi_mem_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {s : (i : ι) → Set (α i)} [∀ (i : ι), (f i).NeBot]
  {I : Set ι}, I.pi s ∈ Filter.pi f → ∀ {i : ι}, i ∈ I → s i ∈ f i

Defined in

Mathlib.Order.Filter.Pi

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Filter.NeBot