Loogle!

Result

Found 2853 declarations mentioning Filter.Tendsto. Of these, 23 have a name containing "const" and "add".

• Filter.Tendsto.atBot_of_add_const 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f : α → M} (C : M) (hf : Filter.Tendsto (fun x => f x + C) l Filter.atBot) : Filter.Tendsto f l Filter.atBot
• Filter.Tendsto.atBot_of_const_add 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f : α → M} (C : M) (hf : Filter.Tendsto (fun x => C + f x) l Filter.atBot) : Filter.Tendsto f l Filter.atBot
• Filter.Tendsto.atTop_of_add_const 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f : α → M} (C : M) (hf : Filter.Tendsto (fun x => f x + C) l Filter.atTop) : Filter.Tendsto f l Filter.atTop
• Filter.Tendsto.atTop_of_const_add 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f : α → M} (C : M) (hf : Filter.Tendsto (fun x => C + f x) l Filter.atTop) : Filter.Tendsto f l Filter.atTop
• Filter.Tendsto.atBot_of_add_const_le 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f g : α → M} (hg : ∃ C, ∀ (x : α), C ≤ g x) (hfg : Filter.Tendsto (fun x => f x + g x) l Filter.atBot) : Filter.Tendsto f l Filter.atBot
• Filter.Tendsto.atBot_of_const_le_add 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f g : α → M} (hf : ∃ C, ∀ (x : α), C ≤ f x) (hfg : Filter.Tendsto (fun x => f x + g x) l Filter.atBot) : Filter.Tendsto g l Filter.atBot
• Filter.Tendsto.atTop_of_add_le_const 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f g : α → M} (hg : ∃ C, ∀ (x : α), g x ≤ C) (hfg : Filter.Tendsto (fun x => f x + g x) l Filter.atTop) : Filter.Tendsto f l Filter.atTop
• Filter.Tendsto.atTop_of_le_const_add 📋 Mathlib.Order.Filter.AtTopBot.Monoid
  {α : Type u_1} {M : Type u_2} [AddCommMonoid M] [PartialOrder M] [IsOrderedCancelAddMonoid M] {l : Filter α} {f g : α → M} (hf : ∃ C, ∀ (x : α), f x ≤ C) (hfg : Filter.Tendsto (fun x => f x + g x) l Filter.atTop) : Filter.Tendsto g l Filter.atTop
• Filter.tendsto_atBot_add_const_left 📋 Mathlib.Order.Filter.AtTopBot.Group
  {α : Type u_1} {G : Type u_2} [AddCommGroup G] [PartialOrder G] [IsOrderedAddMonoid G] (l : Filter α) {f : α → G} (C : G) (hf : Filter.Tendsto f l Filter.atBot) : Filter.Tendsto (fun x => C + f x) l Filter.atBot
• Filter.tendsto_atBot_add_const_right 📋 Mathlib.Order.Filter.AtTopBot.Group
  {α : Type u_1} {G : Type u_2} [AddCommGroup G] [PartialOrder G] [IsOrderedAddMonoid G] (l : Filter α) {f : α → G} (C : G) (hf : Filter.Tendsto f l Filter.atBot) : Filter.Tendsto (fun x => f x + C) l Filter.atBot
• Filter.tendsto_atTop_add_const_left 📋 Mathlib.Order.Filter.AtTopBot.Group
  {α : Type u_1} {G : Type u_2} [AddCommGroup G] [PartialOrder G] [IsOrderedAddMonoid G] (l : Filter α) {f : α → G} (C : G) (hf : Filter.Tendsto f l Filter.atTop) : Filter.Tendsto (fun x => C + f x) l Filter.atTop
• Filter.tendsto_atTop_add_const_right 📋 Mathlib.Order.Filter.AtTopBot.Group
  {α : Type u_1} {G : Type u_2} [AddCommGroup G] [PartialOrder G] [IsOrderedAddMonoid G] (l : Filter α) {f : α → G} (C : G) (hf : Filter.Tendsto f l Filter.atTop) : Filter.Tendsto (fun x => f x + C) l Filter.atTop
• Filter.Tendsto.const_vadd 📋 Mathlib.Topology.Algebra.ConstMulAction
  {M : Type u_1} {α : Type u_2} {β : Type u_3} [TopologicalSpace α] [VAdd M α] [ContinuousConstVAdd M α] {f : β → α} {l : Filter β} {a : α} (hf : Filter.Tendsto f l (nhds a)) (c : M) : Filter.Tendsto (fun x => c +ᵥ f x) l (nhds (c +ᵥ a))
• tendsto_const_vadd_iff 📋 Mathlib.Topology.Algebra.ConstMulAction
  {α : Type u_2} {β : Type u_3} {G : Type u_4} [TopologicalSpace α] [AddGroup G] [AddAction G α] [ContinuousConstVAdd G α] {f : β → α} {l : Filter β} {a : α} (c : G) : Filter.Tendsto (fun x => c +ᵥ f x) l (nhds (c +ᵥ a)) ↔ Filter.Tendsto f l (nhds a)
• Filter.Tendsto.vadd_const 📋 Mathlib.Topology.Algebra.MulAction
  {M : Type u_1} {X : Type u_2} {α : Type u_4} [TopologicalSpace M] [TopologicalSpace X] [VAdd M X] [ContinuousVAdd M X] {f : α → M} {l : Filter α} {c : M} (hf : Filter.Tendsto f l (nhds c)) (a : X) : Filter.Tendsto (fun x => f x +ᵥ a) l (nhds (c +ᵥ a))
• Filter.Tendsto.add_const 📋 Mathlib.Topology.Algebra.Monoid
  {α : Type u_2} {M : Type u_3} [TopologicalSpace M] [Add M] [ContinuousAdd M] (b : M) {c : M} {f : α → M} {l : Filter α} (h : Filter.Tendsto (fun k => f k) l (nhds c)) : Filter.Tendsto (fun k => f k + b) l (nhds (c + b))
• Filter.Tendsto.const_add 📋 Mathlib.Topology.Algebra.Monoid
  {α : Type u_2} {M : Type u_3} [TopologicalSpace M] [Add M] [ContinuousAdd M] (b : M) {c : M} {f : α → M} {l : Filter α} (h : Filter.Tendsto (fun k => f k) l (nhds c)) : Filter.Tendsto (fun k => b + f k) l (nhds (b + c))
• tendsto_add_const_cobounded 📋 Mathlib.Topology.Bornology.BoundedOperation
  {R : Type u_1} [SeminormedAddCommGroup R] (x : R) : Filter.Tendsto (fun x_1 => x_1 + x) (Bornology.cobounded R) (Bornology.cobounded R)
• tendsto_const_add_cobounded 📋 Mathlib.Topology.Bornology.BoundedOperation
  {R : Type u_1} [SeminormedAddCommGroup R] (x : R) : Filter.Tendsto (fun x_1 => x + x_1) (Bornology.cobounded R) (Bornology.cobounded R)
• Asymptotics.IsEquivalent.add_const_of_norm_tendsto_atTop 📋 Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
  {α : Type u_1} {β : Type u_2} [NormedAddCommGroup β] {u v : α → β} {l : Filter α} {c : β} (huv : Asymptotics.IsEquivalent l u v) (hv : Filter.Tendsto (norm ∘ v) l Filter.atTop) : Asymptotics.IsEquivalent l (fun x => u x + c) v
• Asymptotics.IsEquivalent.const_add_of_norm_tendsto_atTop 📋 Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
  {α : Type u_1} {β : Type u_2} [NormedAddCommGroup β] {u v : α → β} {l : Filter α} {c : β} (huv : Asymptotics.IsEquivalent l u v) (hv : Filter.Tendsto (norm ∘ v) l Filter.atTop) : Asymptotics.IsEquivalent l (fun x => c + u x) v
• Filter.Tendsto.const_vadd_asymptoticNhds 📋 Mathlib.Topology.Algebra.AsymptoticCone
  {k : Type u_1} {V : Type u_2} {P : Type u_3} [Field k] [LinearOrder k] [AddCommGroup V] [Module k V] [AddTorsor V P] [TopologicalSpace V] {α : Type u_4} {l : Filter α} {f : α → P} {v : V} (u : V) (hf : Filter.Tendsto f l (AffineSpace.asymptoticNhds k P v)) : Filter.Tendsto (fun x => u +ᵥ f x) l (AffineSpace.asymptoticNhds k P v)
• Filter.Tendsto.asymptoticNhds_vadd_const 📋 Mathlib.Topology.Algebra.AsymptoticCone
  {k : Type u_1} {V : Type u_2} {P : Type u_3} [Field k] [LinearOrder k] [AddCommGroup V] [Module k V] [AddTorsor V P] [TopologicalSpace V] {α : Type u_4} {l : Filter α} {f : α → V} {v : V} (p : P) (hf : Filter.Tendsto f l (AffineSpace.asymptoticNhds k V v)) : Filter.Tendsto (fun x => f x +ᵥ p) l (AffineSpace.asymptoticNhds k P v)

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 ff5ab5e