Loogle!

Result

Found 4 declarations mentioning Trunc.map.

• Trunc.map 📋 Mathlib.Data.Quot
  {α : Sort u_1} {β : Sort u_2} (f : α → β) (q : Trunc α) : Trunc β
• Trunc.finChoiceEquiv_symm_apply 📋 Mathlib.Data.Fintype.Quotient
  {ι : Type u_1} [DecidableEq ι] [Fintype ι] {α : ι → Sort u_2} (q : Trunc ((i : ι) → α i)) (i : ι) : Trunc.finChoiceEquiv.symm q i = Trunc.map (fun x => x i) q
• DirectSum.addEquivProdDirectSum_symm_apply_support' 📋 Mathlib.Algebra.DirectSum.Basic
  {ι : Type v} {α : Option ι → Type w} [(i : Option ι) → AddCommMonoid (α i)] (f : (fun i => α i) none × Π₀ (i : ι), (fun i => α i) (some i)) : (DirectSum.addEquivProdDirectSum.symm f).support' = Trunc.map (fun s => ⟨none ::ₘ Multiset.map some ↑s, ⋯⟩) f.2.support'
• MultilinearMap.dfinsuppFamily_apply_support' 📋 Mathlib.LinearAlgebra.Multilinear.DFinsupp
  {ι : Type uι} {κ : ι → Type uκ} {R : Type uR} {M : (i : ι) → κ i → Type uM} {N : ((i : ι) → κ i) → Type uN} [DecidableEq ι] [Fintype ι] [Semiring R] [(i : ι) → (k : κ i) → AddCommMonoid (M i k)] [(p : (i : ι) → κ i) → AddCommMonoid (N p)] [(i : ι) → (k : κ i) → Module R (M i k)] [(p : (i : ι) → κ i) → Module R (N p)] (f : (p : (i : ι) → κ i) → MultilinearMap R (fun i => M i (p i)) (N p)) (x : (i : ι) → Π₀ (j : κ i), M i j) : ((MultilinearMap.dfinsuppFamily f) x).support' = Trunc.map (fun s => ⟨Multiset.map (fun f i => f i ⋯) (Finset.univ.val.pi fun i => ↑(s i)), ⋯⟩) (Trunc.finChoice fun i => (x i).support')

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