Loogle!

Result

Found 11 declarations mentioning Norm.norm, nhds, Filter.atTop, Iff, and Filter.Tendsto. Of these, 4 match your pattern(s).

• NormedAddCommGroup.tendsto_atTop 📋 Mathlib.Analysis.Normed.Ring.Basic
  {α : Type u_2} [Nonempty α] [Preorder α] [IsDirectedOrder α] {β : Type u_5} [SeminormedAddCommGroup β] {f : α → β} {b : β} : Filter.Tendsto f Filter.atTop (nhds b) ↔ ∀ (ε : ℝ), 0 < ε → ∃ N, ∀ (n : α), N ≤ n → ‖f n - b‖ < ε
• NormedAddCommGroup.tendsto_atTop' 📋 Mathlib.Analysis.Normed.Ring.Basic
  {α : Type u_2} [Nonempty α] [Preorder α] [IsDirectedOrder α] [NoMaxOrder α] {β : Type u_5} [SeminormedAddCommGroup β] {f : α → β} {b : β} : Filter.Tendsto f Filter.atTop (nhds b) ↔ ∀ (ε : ℝ), 0 < ε → ∃ N, ∀ (n : α), N < n → ‖f n - b‖ < ε
• tendsto_pow_atTop_nhds_zero_iff_norm_lt_one 📋 Mathlib.Analysis.SpecificLimits.Normed
  {R : Type u_2} [SeminormedRing R] [NormMulClass R] {x : R} : Filter.Tendsto (fun n => x ^ n) Filter.atTop (nhds 0) ↔ ‖x‖ < 1
• PointwiseConvergenceCLM.tendsto_nhds_atTop 📋 Mathlib.Analysis.LocallyConvex.PointwiseConvergence
  {α : Type u_1} {𝕜₁ : Type u_3} {𝕜₂ : Type u_4} [NormedField 𝕜₁] [NormedField 𝕜₂] {σ : 𝕜₁ →+* 𝕜₂} {E : Type u_7} {F : Type u_8} [AddCommGroup E] [TopologicalSpace E] [Module 𝕜₁ E] [NormedAddCommGroup F] [NormedSpace 𝕜₂ F] [SemilatticeSup α] [Nonempty α] (u : α → E →SLₚₜ[σ] F) (y₀ : E →SLₚₜ[σ] F) : Filter.Tendsto u Filter.atTop (nhds y₀) ↔ ∀ (x : E) (ε : ℝ), 0 < ε → ∃ k₀, ∀ (k : α), k₀ ≤ k → ‖(u k) x - y₀ x‖ < ε

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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 128218b serving mathlib revision 2ff4632