Theorems · Theorem · general topology

Filter.pi_inf_principal_univ_pi_eq_bot

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {s : (i : ι) → Set (α i)},
  Filter.pi f ⊓ Filter.principal (Set.univ.pi s) = ⊥ ↔ ∃ i, f i ⊓ Filter.principal (s i) = ⊥

Defined in

Mathlib.Order.Filter.Pi

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound