Loogle!

Result

Found 16 declarations whose name contains "℘".

• PeriodPair.℘ 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (z : ℂ) : ℂ
• PeriodPair.℘Except 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ z : ℂ) : ℂ
• PeriodPair.℘_neg 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (z : ℂ) : L.℘ (-z) = L.℘ z
• PeriodPair.℘Except_neg 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ z : ℂ) : L.℘Except l₀ (-z) = L.℘Except (-l₀) z
• PeriodPair.differentiableOn_℘ 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) : DifferentiableOn ℂ L.℘ (↑L.lattice)ᶜ
• PeriodPair.℘Except_of_notMem 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ : ℂ) (hl : l₀ ∉ L.lattice) : L.℘Except l₀ = L.℘
• PeriodPair.differentiableOn_℘Except 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ : ℂ) : DifferentiableOn ℂ (L.℘Except l₀) (↑L.lattice \ {l₀})ᶜ
• PeriodPair.℘_bound 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (r : ℝ) (hr : r > 0) (s : ℂ) (hs : ‖s‖ < r) (l : ℂ) (h : 2 * r ≤ ‖l‖) : ‖1 / (s - l) ^ 2 - 1 / l ^ 2‖ ≤ 10 * r * ‖l‖ ^ (-3)
• PeriodPair.℘Except_add 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ : ↥L.lattice) (z : ℂ) : L.℘Except (↑l₀) z + (1 / (z - ↑l₀) ^ 2 - 1 / ↑l₀ ^ 2) = L.℘ z
• PeriodPair.℘Except_def 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ : ↥L.lattice) (z : ℂ) : L.℘Except (↑l₀) z = L.℘ z + (1 / ↑l₀ ^ 2 - 1 / (z - ↑l₀) ^ 2)
• PeriodPair.hasSumLocallyUniformly_℘ 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) : HasSumLocallyUniformly (fun l z => 1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2) L.℘
• PeriodPair.hasSum_℘ 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (z : ℂ) : HasSum (fun l => 1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2) (L.℘ z)
• PeriodPair.℘.eq_1 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (z : ℂ) : L.℘ z = ∑' (l : ↥L.lattice), (1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2)
• PeriodPair.hasSumLocallyUniformly_℘Except 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ : ℂ) : HasSumLocallyUniformly (fun l z => if ↑l = l₀ then 0 else 1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2) (L.℘Except l₀)
• PeriodPair.hasSum_℘Except 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ z : ℂ) : HasSum (fun l => if ↑l = l₀ then 0 else 1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2) (L.℘Except l₀ z)
• PeriodPair.℘Except.eq_1 📋 Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass
  (L : PeriodPair) (l₀ z : ℂ) : L.℘Except l₀ z = ∑' (l : ↥L.lattice), if ↑l = l₀ then 0 else 1 / (z - ↑l) ^ 2 - 1 / ↑l ^ 2

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 0ac13cd serving mathlib revision 91b78e4