Loogle!

Result

Found 20 declarations mentioning ENat.map.

• ENat.map 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) (k : ℕ∞) : WithTop α
• ENat.map_top 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) : ENat.map f ⊤ = ⊤
• ENat.map_coe 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) (a : ℕ) : ENat.map f ↑a = ↑(f a)
• ENat.map_eq_top_iff 📋 Mathlib.Data.ENat.Basic
  {n : ℕ∞} {α : Type u_1} {f : ℕ → α} : ENat.map f n = ⊤ ↔ n = ⊤
• ENat.map_zero 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) : ENat.map f 0 = ↑(f 0)
• ENat.map_ofNat 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) (n : ℕ) [n.AtLeastTwo] : ENat.map f (OfNat.ofNat n) = ↑(f n)
• ENat.map_one 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} (f : ℕ → α) : ENat.map f 1 = ↑(f 1)
• ENat.monotone_map_iff 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} {f : ℕ → α} [Preorder α] : Monotone (ENat.map f) ↔ Monotone f
• ENat.strictMono_map_iff 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} {f : ℕ → α} [Preorder α] : StrictMono (ENat.map f) ↔ StrictMono f
• ENat.map_natCast_injective 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} [AddMonoidWithOne α] [PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α] : Function.Injective (ENat.map Nat.cast)
• ENat.map_natCast_inj 📋 Mathlib.Data.ENat.Basic
  {m n : ℕ∞} {α : Type u_1} [AddMonoidWithOne α] [PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α] : ENat.map Nat.cast m = ENat.map Nat.cast n ↔ m = n
• ENat.map_natCast_strictMono 📋 Mathlib.Data.ENat.Basic
  {α : Type u_1} [AddMonoidWithOne α] [PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α] : StrictMono (ENat.map Nat.cast)
• ENat.map_natCast_nonneg 📋 Mathlib.Data.ENat.Basic
  {n : ℕ∞} {α : Type u_1} [AddMonoidWithOne α] [PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] : 0 ≤ ENat.map Nat.cast n
• AddHom.ENatMap_apply 📋 Mathlib.Data.ENat.Basic
  {N : Type u_2} [Add N] (f : ℕ →ₙ+ N) : ⇑f.ENatMap = ENat.map ⇑f
• ENat.map_natCast_eq_zero 📋 Mathlib.Data.ENat.Basic
  {n : ℕ∞} {α : Type u_1} [AddMonoidWithOne α] [PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α] : ENat.map Nat.cast n = 0 ↔ n = 0
• ENat.map_add 📋 Mathlib.Data.ENat.Basic
  {β : Type u_2} {F : Type u_3} [Add β] [FunLike F ℕ β] [AddHomClass F ℕ β] (f : F) (a b : ℕ∞) : ENat.map (⇑f) (a + b) = ENat.map (⇑f) a + ENat.map (⇑f) b
• AddMonoidHom.ENatMap_apply 📋 Mathlib.Data.ENat.Basic
  {N : Type u_2} [AddZeroClass N] (f : ℕ →+ N) : ⇑f.ENatMap = ENat.map ⇑f
• MonoidWithZeroHom.ENatMap_apply 📋 Mathlib.Data.ENat.Basic
  {S : Type u_2} [MulZeroOneClass S] [DecidableEq S] [Nontrivial S] (f : ℕ →*₀ S) (hf : Function.Injective ⇑f) : ⇑(f.ENatMap hf) = ENat.map ⇑f
• ENat.map_coe_nnreal 📋 Mathlib.Data.Real.ENatENNReal
  : ENat.map Nat.cast = ENat.toENNReal
• AnalyticAt.meromorphicAt_order 📋 Mathlib.Analysis.Meromorphic.Order
  {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜} (hf : AnalyticAt 𝕜 f x) : ⋯.order = ENat.map Nat.cast hf.order

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