Loogle!

Result

Found 21 declarations mentioning Sym.map.

• Sym.map 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) (x : Sym α n) : Sym β n
• Sym.map_id 📋 Mathlib.Data.Sym.Basic
  {α : Type u_3} {n : ℕ} (s : Sym α n) : Sym.map id s = s
• Sym.map_id' 📋 Mathlib.Data.Sym.Basic
  {α : Type u_3} {n : ℕ} (s : Sym α n) : Sym.map (fun x => x) s = s
• Sym.map_injective 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {f : α → β} (hf : Function.Injective f) (n : ℕ) : Function.Injective (Sym.map f)
• Sym.coe_map 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (s : Sym α n) (f : α → β) : ↑(Sym.map f s) = Multiset.map f ↑s
• Sym.map_cons 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) (a : α) (s : Sym α n) : Sym.map f (a ::ₛ s) = f a ::ₛ Sym.map f s
• Sym.map_map 📋 Mathlib.Data.Sym.Basic
  {α : Type u_3} {β : Type u_4} {γ : Type u_5} {n : ℕ} (g : β → γ) (f : α → β) (s : Sym α n) : Sym.map g (Sym.map f s) = Sym.map (g ∘ f) s
• Sym.attach_map_coe 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {n : ℕ} (s : Sym α n) : Sym.map Subtype.val s.attach = s
• Sym.map_congr 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} {f g : α → β} {s : Sym α n} (h : ∀ x ∈ s, f x = g x) : Sym.map f s = Sym.map g s
• Sym.mem_map 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} {f : α → β} {b : β} {l : Sym α n} : b ∈ Sym.map f l ↔ ∃ a ∈ l, f a = b
• SymOptionSuccEquiv.decode_inr 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {n : ℕ} (s : Sym α n.succ) : SymOptionSuccEquiv.decode (Sum.inr s) = Sym.map (⇑Function.Embedding.some) s
• SymOptionSuccEquiv.decode.eq_2 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {n : ℕ} (s : Sym α n.succ) : SymOptionSuccEquiv.decode (Sum.inr s) = Sym.map (⇑Function.Embedding.some) s
• Sym.map.eq_1 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) (x : Sym α n) : Sym.map f x = ⟨Multiset.map f ↑x, ⋯⟩
• Sym.map_zero 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} (f : α → β) : Sym.map f 0 = 0
• Sym.equivCongr_apply 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (e : α ≃ β) (x : Sym α n) : (Sym.equivCongr e) x = Sym.map (⇑e) x
• Sym.equivCongr_symm_apply 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (e : α ≃ β) (x : Sym β n) : (Sym.equivCongr e).symm x = Sym.map (⇑e.symm) x
• Sym.map_mk 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} {f : α → β} {m : Multiset α} {hc : m.card = n} : Sym.map f (Sym.mk m hc) = Sym.mk (Multiset.map f m) ⋯
• Sym.attach_cons 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {n : ℕ} (x : α) (s : Sym α n) : (x ::ₛ s).attach = ⟨x, ⋯⟩ ::ₛ Sym.map (fun x_1 => ⟨↑x_1, ⋯⟩) s.attach
• SymOptionSuccEquiv.encode_of_not_none_mem 📋 Mathlib.Data.Sym.Basic
  {α : Type u_1} {n : ℕ} [DecidableEq α] (s : Sym (Option α) n.succ) (h : none ∉ s) : SymOptionSuccEquiv.encode s = Sum.inr (Sym.map (fun o => (↑o).get ⋯) s.attach)
• List.sym_map 📋 Mathlib.Data.List.Sym
  {α : Type u_1} {β : Type u_3} (f : α → β) (n : ℕ) (xs : List α) : List.sym n (List.map f xs) = List.map (Sym.map f) (List.sym n xs)
• Nat.Partition.ofSym_map 📋 Mathlib.Combinatorics.Enumerative.Partition
  {n : ℕ} {σ : Type u_1} {τ : Type u_2} [DecidableEq σ] [DecidableEq τ] (e : σ ≃ τ) (s : Sym σ n) : Nat.Partition.ofSym (Sym.map (⇑e) s) = Nat.Partition.ofSym s

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