Loogle!

Result

Found 7 declarations mentioning Norm.norm, Filter.Eventually, LE.le, Filter.Tendsto, and OfNat.ofNat. Of these, 4 match your pattern(s).

• squeeze_one_norm' 📋 Mathlib.Analysis.Normed.Group.Continuity
  {α : Type u_1} {E : Type u_4} [SeminormedGroup E] {f : α → E} {a : α → ℝ} {t₀ : Filter α} (h : ∀ᶠ (n : α) in t₀, ‖f n‖ ≤ a n) (h' : Filter.Tendsto a t₀ (nhds 0)) : Filter.Tendsto f t₀ (nhds 1)
• squeeze_zero_norm' 📋 Mathlib.Analysis.Normed.Group.Continuity
  {α : Type u_1} {E : Type u_4} [SeminormedAddGroup E] {f : α → E} {a : α → ℝ} {t₀ : Filter α} (h : ∀ᶠ (n : α) in t₀, ‖f n‖ ≤ a n) (h' : Filter.Tendsto a t₀ (nhds 0)) : Filter.Tendsto f t₀ (nhds 0)
• MeasureTheory.tendsto_lintegral_norm_of_dominated_convergence 📋 Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral
  {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [NormedAddCommGroup β] {F : ℕ → α → β} {f : α → β} {bound : α → ℝ} (F_measurable : ∀ (n : ℕ), MeasureTheory.AEStronglyMeasurable (F n) μ) (bound_hasFiniteIntegral : MeasureTheory.HasFiniteIntegral bound μ) (h_bound : ∀ (n : ℕ), ∀ᵐ (a : α) ∂μ, ‖F n a‖ ≤ bound a) (h_lim : ∀ᵐ (a : α) ∂μ, Filter.Tendsto (fun n => F n a) Filter.atTop (nhds (f a))) : Filter.Tendsto (fun n => ∫⁻ (a : α), ENNReal.ofReal ‖F n a - f a‖ ∂μ) Filter.atTop (nhds 0)
• MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub 📋 Mathlib.MeasureTheory.Integral.Average
  {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [NormedAddCommGroup E] [NormedSpace ℝ E] {μ : MeasureTheory.Measure α} [CompleteSpace E] {ι : Type u_4} {a : ι → Set α} {l : Filter ι} {f : α → E} {c : E} {g : ι → α → ℝ} (K : ℝ) (hf : Filter.Tendsto (fun i => ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (nhds 0)) (f_int : ∀ᶠ (i : ι) in l, MeasureTheory.IntegrableOn f (a i) μ) (hg : Filter.Tendsto (fun i => ∫ (y : α), g i y ∂μ) l (nhds 1)) (g_supp : ∀ᶠ (i : ι) in l, Function.support (g i) ⊆ a i) (g_bound : ∀ᶠ (i : ι) in l, ∀ (x : α), |g i x| ≤ K / μ.real (a i)) : Filter.Tendsto (fun i => ∫ (y : α), g i y • f y ∂μ) l (nhds c)

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 401c76f serving mathlib revision b87935d