Loogle!

Result

Found 8 declarations mentioning tsum and ENat.

• contDiff_tsum 📋 Mathlib.Analysis.Calculus.SmoothSeries
  {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [NontriviallyNormedField 𝕜] [IsRCLikeNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [CompleteSpace F] [NormedSpace 𝕜 F] {f : α → E → F} {v : ℕ → α → ℝ} {N : ℕ∞} (hf : ∀ (i : α), ContDiff 𝕜 (↑N) (f i)) (hv : ∀ (k : ℕ), ↑k ≤ N → Summable (v k)) (h'f : ∀ (k : ℕ) (i : α) (x : E), ↑k ≤ N → ‖iteratedFDeriv 𝕜 k (f i) x‖ ≤ v k i) : ContDiff 𝕜 ↑N fun x => ∑' (i : α), f i x
• contDiff_tsum_of_eventually 📋 Mathlib.Analysis.Calculus.SmoothSeries
  {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [NontriviallyNormedField 𝕜] [IsRCLikeNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [CompleteSpace F] [NormedSpace 𝕜 F] {f : α → E → F} {v : ℕ → α → ℝ} {N : ℕ∞} (hf : ∀ (i : α), ContDiff 𝕜 (↑N) (f i)) (hv : ∀ (k : ℕ), ↑k ≤ N → Summable (v k)) (h'f : ∀ (k : ℕ), ↑k ≤ N → ∀ᶠ (i : α) in Filter.cofinite, ∀ (x : E), ‖iteratedFDeriv 𝕜 k (f i) x‖ ≤ v k i) : ContDiff 𝕜 ↑N fun x => ∑' (i : α), f i x
• iteratedFDeriv_tsum 📋 Mathlib.Analysis.Calculus.SmoothSeries
  {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [NontriviallyNormedField 𝕜] [IsRCLikeNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [CompleteSpace F] [NormedSpace 𝕜 F] {f : α → E → F} {v : ℕ → α → ℝ} {N : ℕ∞} (hf : ∀ (i : α), ContDiff 𝕜 (↑N) (f i)) (hv : ∀ (k : ℕ), ↑k ≤ N → Summable (v k)) (h'f : ∀ (k : ℕ) (i : α) (x : E), ↑k ≤ N → ‖iteratedFDeriv 𝕜 k (f i) x‖ ≤ v k i) {k : ℕ} (hk : ↑k ≤ N) : (iteratedFDeriv 𝕜 k fun y => ∑' (n : α), f n y) = fun x => ∑' (n : α), iteratedFDeriv 𝕜 k (f n) x
• iteratedFDeriv_tsum_apply 📋 Mathlib.Analysis.Calculus.SmoothSeries
  {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [NontriviallyNormedField 𝕜] [IsRCLikeNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [CompleteSpace F] [NormedSpace 𝕜 F] {f : α → E → F} {v : ℕ → α → ℝ} {N : ℕ∞} (hf : ∀ (i : α), ContDiff 𝕜 (↑N) (f i)) (hv : ∀ (k : ℕ), ↑k ≤ N → Summable (v k)) (h'f : ∀ (k : ℕ) (i : α) (x : E), ↑k ≤ N → ‖iteratedFDeriv 𝕜 k (f i) x‖ ≤ v k i) {k : ℕ} (hk : ↑k ≤ N) (x : E) : iteratedFDeriv 𝕜 k (fun y => ∑' (n : α), f n y) x = ∑' (n : α), iteratedFDeriv 𝕜 k (f n) x
• ContMDiff.sum_section_of_locallyFinite 📋 Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
  {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {H : Type u_3} [TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4} [TopologicalSpace M] [ChartedSpace H M] {F : Type u_5} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {n : WithTop ℕ∞} {V : M → Type u_6} [TopologicalSpace (Bundle.TotalSpace F V)] [(x : M) → TopologicalSpace (V x)] [FiberBundle F V] [(x : M) → AddCommGroup (V x)] [(x : M) → Module 𝕜 (V x)] [VectorBundle 𝕜 F V] {ι : Type u_7} {t : ι → (x : M) → V x} (ht : LocallyFinite fun i => {x | t i x ≠ 0}) (ht' : ∀ (i : ι), ContMDiff I (I.prod (modelWithCornersSelf 𝕜 F)) n fun x => Bundle.TotalSpace.mk' F x (t i x)) : ContMDiff I (I.prod (modelWithCornersSelf 𝕜 F)) n fun x => Bundle.TotalSpace.mk' F x (∑' (i : ι), t i x)
• ContMDiffAt.sum_section_of_locallyFinite 📋 Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
  {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {H : Type u_3} [TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4} [TopologicalSpace M] [ChartedSpace H M] {F : Type u_5} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {n : WithTop ℕ∞} {V : M → Type u_6} [TopologicalSpace (Bundle.TotalSpace F V)] [(x : M) → TopologicalSpace (V x)] [FiberBundle F V] [(x : M) → AddCommGroup (V x)] [(x : M) → Module 𝕜 (V x)] [VectorBundle 𝕜 F V] {x₀ : M} {ι : Type u_7} {t : ι → (x : M) → V x} (ht : LocallyFinite fun i => {x | t i x ≠ 0}) (ht' : ∀ (i : ι), ContMDiffAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (t i x)) x₀) : ContMDiffAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (∑' (i : ι), t i x)) x₀
• ContMDiffOn.sum_section_of_locallyFinite 📋 Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
  {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {H : Type u_3} [TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4} [TopologicalSpace M] [ChartedSpace H M] {F : Type u_5} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {n : WithTop ℕ∞} {V : M → Type u_6} [TopologicalSpace (Bundle.TotalSpace F V)] [(x : M) → TopologicalSpace (V x)] [FiberBundle F V] [(x : M) → AddCommGroup (V x)] [(x : M) → Module 𝕜 (V x)] [VectorBundle 𝕜 F V] {u : Set M} {ι : Type u_7} {t : ι → (x : M) → V x} (ht : LocallyFinite fun i => {x | t i x ≠ 0}) (ht' : ∀ (i : ι), ContMDiffOn I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (t i x)) u) : ContMDiffOn I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (∑' (i : ι), t i x)) u
• ContMDiffWithinAt.sum_section_of_locallyFinite 📋 Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
  {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {H : Type u_3} [TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4} [TopologicalSpace M] [ChartedSpace H M] {F : Type u_5} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {n : WithTop ℕ∞} {V : M → Type u_6} [TopologicalSpace (Bundle.TotalSpace F V)] [(x : M) → TopologicalSpace (V x)] [FiberBundle F V] [(x : M) → AddCommGroup (V x)] [(x : M) → Module 𝕜 (V x)] [VectorBundle 𝕜 F V] {u : Set M} {x₀ : M} {ι : Type u_7} {t : ι → (x : M) → V x} (ht : LocallyFinite fun i => {x | t i x ≠ 0}) (ht' : ∀ (i : ι), ContMDiffWithinAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (t i x)) u x₀) : ContMDiffWithinAt I (I.prod (modelWithCornersSelf 𝕜 F)) n (fun x => Bundle.TotalSpace.mk' F x (∑' (i : ι), t i x)) u x₀

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 06e7f72 serving mathlib revision 3df560d