Theorems · Theorem · order theory

Filter.bliminf_eq_iSup_biInf

∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β} {p : β → Prop} {u : β → α},
  Filter.bliminf u f p = ⨆ s ∈ f, ⨅ b, ⨅ (_ : p b ∧ b ∈ s), u b

Defined in

Mathlib.Order.LiminfLimsup

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompleteLattice