Loogle!

Result

Found 15 declarations mentioning Filter.Germ.map.

• Filter.Germ.map 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {l : Filter α} (op : β → γ) : l.Germ β → l.Germ γ
• Filter.Germ.map_id 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {l : Filter α} : Filter.Germ.map id = id
• Filter.Germ.map_const 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} (l : Filter α) (a : β) (f : β → γ) : Filter.Germ.map f ↑a = ↑(f a)
• Filter.Germ.instInv.eq_1 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {l : Filter α} {G : Type u_6} [Inv G] : Filter.Germ.instInv = { inv := Filter.Germ.map Inv.inv }
• Filter.Germ.instNeg.eq_1 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {l : Filter α} {G : Type u_6} [Neg G] : Filter.Germ.instNeg = { neg := Filter.Germ.map Neg.neg }
• Filter.Germ.map_coe 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {l : Filter α} (op : β → γ) (f : α → β) : Filter.Germ.map op ↑f = ↑(op ∘ f)
• Filter.Germ.coe_compTendsto' 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {l : Filter α} (f : α → β) {lc : Filter γ} {g : lc.Germ α} (hg : g.Tendsto l) : (↑f).compTendsto' g hg = Filter.Germ.map f g
• Filter.Germ.map_map 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {l : Filter α} (op₁ : γ → δ) (op₂ : β → γ) (f : l.Germ β) : Filter.Germ.map op₁ (Filter.Germ.map op₂ f) = Filter.Germ.map (op₁ ∘ op₂) f
• Filter.Germ.instSMul.eq_1 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {l : Filter α} {M : Type u_5} {G : Type u_6} [SMul M G] : Filter.Germ.instSMul = { smul := fun n => Filter.Germ.map fun x => n • x }
• Filter.Germ.instVAdd.eq_1 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {l : Filter α} {M : Type u_5} {G : Type u_6} [VAdd M G] : Filter.Germ.instVAdd = { vadd := fun n => Filter.Germ.map fun x => n +ᵥ x }
• Filter.Germ.instPow.eq_1 📋 Mathlib.Order.Filter.Germ.Basic
  {α : Type u_1} {l : Filter α} {M : Type u_5} {G : Type u_6} [Pow G M] : Filter.Germ.instPow = { pow := fun f n => Filter.Germ.map (fun x => x ^ n) f }
• MeasureTheory.AEEqFun.comp_toGerm 📋 Mathlib.MeasureTheory.Function.AEEqFun
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [MeasurableSpace α] {μ : MeasureTheory.Measure α} [TopologicalSpace β] [TopologicalSpace γ] (g : β → γ) (hg : Continuous g) (f : α →ₘ[μ] β) : (MeasureTheory.AEEqFun.comp g hg f).toGerm = Filter.Germ.map g f.toGerm
• MeasureTheory.AEEqFun.compMeasurable_toGerm 📋 Mathlib.MeasureTheory.Function.AEEqFun
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [MeasurableSpace α] {μ : MeasureTheory.Measure α} [TopologicalSpace β] [TopologicalSpace γ] [MeasurableSpace β] [BorelSpace β] [TopologicalSpace.PseudoMetrizableSpace β] [TopologicalSpace.PseudoMetrizableSpace γ] [SecondCountableTopology γ] [MeasurableSpace γ] [OpensMeasurableSpace γ] (g : β → γ) (hg : Measurable g) (f : α →ₘ[μ] β) : (MeasureTheory.AEEqFun.compMeasurable g hg f).toGerm = Filter.Germ.map g f.toGerm
• Filter.Germ.abs_def 📋 Mathlib.Order.Filter.FilterProduct
  {α : Type u} {β : Type v} {φ : Ultrafilter α} [AddCommGroup β] [LinearOrder β] (x : (↑φ).Germ β) : |x| = Filter.Germ.map abs x
• Hyperreal.IsSt.map 📋 Mathlib.Data.Real.Hyperreal
  {x : ℝ*} {r : ℝ} (hxr : x.IsSt r) {f : ℝ → ℝ} (hf : ContinuousAt f r) : Hyperreal.IsSt (Filter.Germ.map f x) (f r)

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 19971e9 serving mathlib revision bce1d65