Theorems · Theorem · order theory

Filter.frequently_lt_of_liminf_lt

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLinearOrder β] {f : Filter α} {u : α → β} {b : β},
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.frequently_lt_of_liminf_lt._auto_1 →
    Filter.liminf u f < b → ∃ᶠ (x : α) in f, u x < b

Defined in

Mathlib.Order.LiminfLimsup

Cited by

7 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrder