Loogle!

Result

Found 8 declarations mentioning FunOnFinite.map.

• FunOnFinite.map 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} [Finite X] [Finite Y] (f : X → Y) (s : X → M) : Y → M
• FunOnFinite.map_id 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  (M : Type u_4) [AddCommMonoid M] {X : Type u_5} [Finite X] : FunOnFinite.map id = id
• FunOnFinite.map_apply_apply 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} [Fintype X] [Finite Y] [DecidableEq Y] (f : X → Y) (s : X → M) (y : Y) : FunOnFinite.map f s y = ∑ x with f x = y, s x
• FunOnFinite.map.congr_simp 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} [Finite X] [Finite Y] (f f✝ : X → Y) (e_f : f = f✝) (s s✝ : X → M) (e_s : s = s✝) (a✝ a✝¹ : Y) : a✝ = a✝¹ → FunOnFinite.map f s a✝ = FunOnFinite.map f✝ s✝ a✝¹
• FunOnFinite.map_comp 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} {Z : Type u_7} [Finite X] [Finite Y] [Finite Z] (g : Y → Z) (f : X → Y) : FunOnFinite.map (g ∘ f) = FunOnFinite.map g ∘ FunOnFinite.map f
• FunOnFinite.map_piSingle 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} [Finite X] [Finite Y] [DecidableEq X] [DecidableEq Y] (f : X → Y) (x : X) (m : M) : FunOnFinite.map f (Pi.single x m) = Pi.single (f x) m
• FunOnFinite.map.eq_1 📋 Mathlib.LinearAlgebra.Finsupp.Pi
  {M : Type u_4} [AddCommMonoid M] {X : Type u_5} {Y : Type u_6} [Finite X] [Finite Y] (f : X → Y) (s : X → M) : FunOnFinite.map f s = Finsupp.equivFunOnFinite (Finsupp.mapDomain f (Finsupp.equivFunOnFinite.symm s))
• FunOnFinite.continuous_map 📋 Mathlib.Topology.Algebra.Monoid.FunOnFinite
  (M : Type u_1) [AddCommMonoid M] [TopologicalSpace M] [ContinuousAdd M] {X : Type u_2} {Y : Type u_3} [Finite X] [Finite Y] (f : X → Y) : Continuous (FunOnFinite.map f)

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 ee8c038 serving mathlib revision 7a9e177