Loogle!

Result

Found 5 declarations mentioning PontryaginDual.map.

• PontryaginDual.map 📋 Mathlib.Topology.Algebra.PontryaginDual
  {A : Type u_1} {B : Type u_2} [Monoid A] [Monoid B] [TopologicalSpace A] [TopologicalSpace B] (f : A →ₜ* B) : PontryaginDual B →ₜ* PontryaginDual A
• PontryaginDual.map_apply 📋 Mathlib.Topology.Algebra.PontryaginDual
  {A : Type u_1} {B : Type u_2} [Monoid A] [Monoid B] [TopologicalSpace A] [TopologicalSpace B] (f : A →ₜ* B) (x : PontryaginDual B) (y : A) : ((PontryaginDual.map f) x) y = x (f y)
• PontryaginDual.map_comp 📋 Mathlib.Topology.Algebra.PontryaginDual
  {A : Type u_1} {B : Type u_2} {C : Type u_3} [Monoid A] [Monoid B] [Monoid C] [TopologicalSpace A] [TopologicalSpace B] [TopologicalSpace C] (g : B →ₜ* C) (f : A →ₜ* B) : PontryaginDual.map (g.comp f) = (PontryaginDual.map f).comp (PontryaginDual.map g)
• PontryaginDual.map_one 📋 Mathlib.Topology.Algebra.PontryaginDual
  {A : Type u_1} {B : Type u_2} [Monoid A] [Monoid B] [TopologicalSpace A] [TopologicalSpace B] : PontryaginDual.map 1 = 1
• PontryaginDual.map_mul 📋 Mathlib.Topology.Algebra.PontryaginDual
  {A : Type u_1} {G : Type u_4} [Monoid A] [CommGroup G] [TopologicalSpace A] [TopologicalSpace G] [IsTopologicalGroup G] (f g : A →ₜ* G) : PontryaginDual.map (f * g) = PontryaginDual.map f * PontryaginDual.map g

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 40fea08