Loogle!

Result

Found 6 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.mapFinIdxM.map.congr_simp 📋 Init.Data.Array.MapIdx
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f f✝ : (i : ℕ) → α → i < as.size → m β) (e_f : f = f✝) (i i✝ : ℕ) (e_i : i = i✝) (j j✝ : ℕ) (e_j : j = j✝) (inv : i + j = as.size) (bs bs✝ : Array β) (e_bs : bs = bs✝) : Array.mapFinIdxM.map as f i j inv bs = Array.mapFinIdxM.map as f✝ i✝ j✝ ⋯ bs✝
• Array.mapFinIdxM.map.eq_def 📋 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) (i j : ℕ) (inv : i + j = as.size) (bs : Array β) : Array.mapFinIdxM.map as f i j inv bs = match i, inv with | 0, x => pure bs | i.succ, inv => have j_lt := ⋯; have this := ⋯; do let __do_lift ← f j as[j] j_lt Array.mapFinIdxM.map as f i (j + 1) this (bs.push __do_lift)

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 187ba29 serving mathlib revision 82dd791