Loogle!

Result

Found 4 declarations mentioning RestrictedProduct.map.

• RestrictedProduct.map 📋 Mathlib.Topology.Algebra.RestrictedProduct
  {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂} {A₁ : (i : ι₁) → Set (R₁ i)} {A₂ : (i : ι₂) → Set (R₂ i)} (f : ι₂ → ι₁) (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) (φ : (j : ι₂) → R₁ (f j) → R₂ j) (hφ : ∀ᶠ (j : ι₂) in 𝓕₂, Set.MapsTo (φ j) (A₁ (f j)) (A₂ j)) (x : RestrictedProduct (fun i => R₁ i) (fun i => A₁ i) 𝓕₁) : RestrictedProduct (fun j => R₂ j) (fun j => A₂ j) 𝓕₂
• RestrictedProduct.map_apply 📋 Mathlib.Topology.Algebra.RestrictedProduct
  {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂} {A₁ : (i : ι₁) → Set (R₁ i)} {A₂ : (i : ι₂) → Set (R₂ i)} (f : ι₂ → ι₁) (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) (φ : (j : ι₂) → R₁ (f j) → R₂ j) (hφ : ∀ᶠ (j : ι₂) in 𝓕₂, Set.MapsTo (φ j) (A₁ (f j)) (A₂ j)) (x : RestrictedProduct (fun i => R₁ i) (fun i => A₁ i) 𝓕₁) (j : ι₂) : (RestrictedProduct.map R₁ R₂ f hf φ hφ x) j = φ j (x (f j))
• RestrictedProduct.mapAddMonoidHom.eq_1 📋 Mathlib.Topology.Algebra.RestrictedProduct
  {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂} {S₁ : ι₁ → Type u_7} {S₂ : ι₂ → Type u_8} [(i : ι₁) → SetLike (S₁ i) (R₁ i)] [(j : ι₂) → SetLike (S₂ j) (R₂ j)] {B₁ : (i : ι₁) → S₁ i} {B₂ : (j : ι₂) → S₂ j} (f : ι₂ → ι₁) (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) [(i : ι₁) → AddMonoid (R₁ i)] [(i : ι₂) → AddMonoid (R₂ i)] [∀ (i : ι₁), AddSubmonoidClass (S₁ i) (R₁ i)] [∀ (i : ι₂), AddSubmonoidClass (S₂ i) (R₂ i)] (φ : (j : ι₂) → R₁ (f j) →+ R₂ j) (hφ : ∀ᶠ (j : ι₂) in 𝓕₂, Set.MapsTo ⇑(φ j) ↑(B₁ (f j)) ↑(B₂ j)) : RestrictedProduct.mapAddMonoidHom R₁ R₂ f hf φ hφ = { toFun := RestrictedProduct.map R₁ R₂ f hf (fun j r => (φ j) r) hφ, map_zero' := ⋯, map_add' := ⋯ }
• RestrictedProduct.mapMonoidHom.eq_1 📋 Mathlib.Topology.Algebra.RestrictedProduct
  {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂} {S₁ : ι₁ → Type u_7} {S₂ : ι₂ → Type u_8} [(i : ι₁) → SetLike (S₁ i) (R₁ i)] [(j : ι₂) → SetLike (S₂ j) (R₂ j)] {B₁ : (i : ι₁) → S₁ i} {B₂ : (j : ι₂) → S₂ j} (f : ι₂ → ι₁) (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) [(i : ι₁) → Monoid (R₁ i)] [(i : ι₂) → Monoid (R₂ i)] [∀ (i : ι₁), SubmonoidClass (S₁ i) (R₁ i)] [∀ (i : ι₂), SubmonoidClass (S₂ i) (R₂ i)] (φ : (j : ι₂) → R₁ (f j) →* R₂ j) (hφ : ∀ᶠ (j : ι₂) in 𝓕₂, Set.MapsTo ⇑(φ j) ↑(B₁ (f j)) ↑(B₂ j)) : RestrictedProduct.mapMonoidHom R₁ R₂ f hf φ hφ = { toFun := RestrictedProduct.map R₁ R₂ f hf (fun j r => (φ j) r) hφ, map_one' := ⋯, map_mul' := ⋯ }

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