Loogle!

Result

Found 8 declarations mentioning Array.mapFinIdxM.map.

• Array.mapFinIdxM.map 📋 Init.Data.Array.Basic
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (i : ℕ) → α → i < as.size → m β) (i j : ℕ) (inv : i + j = as.size) (bs : Array β) : m (Array β)
• Array.mapFinIdxM.eq_1 📋 Init.Data.Array.MapIdx
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (i : ℕ) → α → i < as.size → m β) : as.mapFinIdxM f = Array.mapFinIdxM.map as f as.size 0 ⋯ (Array.emptyWithCapacity as.size)
• Array.mapFinIdxM.map.eq_1 📋 Init.Data.Array.MapIdx
  {α : Type u} {β : Type v} {m : Type v → Type w} [inst : Monad m] (as : Array α) (f : (i : ℕ) → α → i < as.size → m β) (j : ℕ) (bs : Array β) (x : 0 + j = as.size) : Array.mapFinIdxM.map as f 0 j x bs = pure bs
• Array.mapFinIdxM.map.eq_2 📋 Init.Data.Array.MapIdx
  {α : Type u} {β : Type v} {m : Type v → Type w} [inst : Monad m] (as : Array α) (f : (i : ℕ) → α → i < as.size → m β) (j : ℕ) (bs : Array β) (i_2 : ℕ) (inv_2 : i_2 + 1 + j = as.size) : Array.mapFinIdxM.map as f i_2.succ j inv_2 bs = do let __do_lift ← f j as[j] ⋯ Array.mapFinIdxM.map as f i_2 (j + 1) ⋯ (bs.push __do_lift)
• Array.mapFinIdx_induction.go 📋 Init.Data.Array.MapIdx
  {α : Type u_1} {β : Type u_2} (xs : Array α) (f : (i : ℕ) → α → i < xs.size → β) (motive : ℕ → Prop) (p : (i : ℕ) → β → i < xs.size → Prop) (hs : ∀ (i : ℕ) (h : i < xs.size), motive i → p i (f i xs[i] h) h ∧ motive (i + 1)) {bs : Array β} {i j : ℕ} {h : i + j = xs.size} (h₁ : j = bs.size) (h₂ : ∀ (i : ℕ) (h : i < xs.size) (h' : i < bs.size), p i bs[i] h) (hm : motive j) : let as := Array.mapFinIdxM.map xs f i j h bs; motive xs.size ∧ ∃ (eq : as.size = xs.size), ∀ (i_1 : ℕ) (h_1 : i_1 < xs.size), p i_1 as[i_1] h_1
• List.mapFinIdxM_toArray.go 📋 Init.Data.Array.MapIdx
  {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] [LawfulMonad m] {l : List α} {f : (i : ℕ) → α → i < l.length → m β} (i : ℕ) (acc : Array β) (inv : i + acc.size = l.length) : Array.mapFinIdxM.map l.toArray f i acc.size inv acc = List.toArray <$> List.mapFinIdxM.go l f (List.drop acc.size l) acc ⋯
• Vector.toArray_mapFinIdxM.go 📋 Init.Data.Vector.MapIdx
  {m : Type u_1 → Type u_2} {α : Type u_3} {n : ℕ} {β : Type u_1} [Monad m] [LawfulMonad m] {xs : Vector α n} {f : (i : ℕ) → α → i < n → m β} (i j : ℕ) (inv : i + j = n) (bs : Vector β (n - i)) : Vector.toArray <$> Vector.mapFinIdxM.map xs f i j inv bs = Array.mapFinIdxM.map xs.toArray (fun i x h => f i x ⋯) i j ⋯ bs.toArray
• Array.SatisfiesM_mapFinIdxM.go 📋 Batteries.Data.Array.Monadic
  {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] [LawfulMonad m] (as : Array α) (f : (i : ℕ) → α → i < as.size → m β) (motive : ℕ → Prop) (p : (i : ℕ) → β → i < as.size → Prop) (hs : ∀ (i : ℕ) (h : i < as.size), motive i → SatisfiesM (fun x => p i x h ∧ motive (i + 1)) (f i as[i] h)) {bs : Array β} {i j : ℕ} {h : i + j = as.size} (h₁ : j = bs.size) (h₂ : ∀ (i : ℕ) (h : i < as.size) (h' : i < bs.size), p i bs[i] h) (hm : motive j) : SatisfiesM (fun arr => motive as.size ∧ ∃ (eq : arr.size = as.size), ∀ (i_1 : ℕ) (h : i_1 < as.size), p i_1 arr[i_1] h) (Array.mapFinIdxM.map as f i j h bs)

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