Loogle!

Result

Found 10 declarations mentioning WittVector.map.

• WittVector.map 📋 Mathlib.RingTheory.WittVector.Basic
  {p : ℕ} {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] (f : R →+* S) : WittVector p R →+* WittVector p S
• WittVector.map_injective 📋 Mathlib.RingTheory.WittVector.Basic
  {p : ℕ} {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] (f : R →+* S) (hf : Function.Injective ⇑f) : Function.Injective ⇑(WittVector.map f)
• WittVector.map_surjective 📋 Mathlib.RingTheory.WittVector.Basic
  {p : ℕ} {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] (f : R →+* S) (hf : Function.Surjective ⇑f) : Function.Surjective ⇑(WittVector.map f)
• WittVector.map_coeff 📋 Mathlib.RingTheory.WittVector.Basic
  {p : ℕ} {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] (f : R →+* S) (x : WittVector p R) (n : ℕ) : ((WittVector.map f) x).coeff n = f (x.coeff n)
• WittVector.IsPoly.map 📋 Mathlib.RingTheory.WittVector.IsPoly
  {p : ℕ} {R S : Type u} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] {f : ⦃R : Type u⦄ → [CommRing R] → WittVector p R → WittVector p R} (hf : WittVector.IsPoly p f) (g : R →+* S) (x : WittVector p R) : (WittVector.map g) (f x) = f ((WittVector.map g) x)
• WittVector.IsPoly₂.map 📋 Mathlib.RingTheory.WittVector.IsPoly
  {p : ℕ} {R S : Type u} [CommRing R] [CommRing S] [Fact (Nat.Prime p)] {f : ⦃R : Type u⦄ → [CommRing R] → WittVector p R → WittVector p R → WittVector p R} (hf : WittVector.IsPoly₂ p f) (g : R →+* S) (x y : WittVector p R) : (WittVector.map g) (f x y) = f ((WittVector.map g) x) ((WittVector.map g) y)
• WittVector.frobenius_eq_map_frobenius 📋 Mathlib.RingTheory.WittVector.Frobenius
  (p : ℕ) {R : Type u_1} [hp : Fact (Nat.Prime p)] [CommRing R] [CharP R p] : WittVector.frobenius = WittVector.map (frobenius R p)
• WittVector.frobeniusEquiv_symm_apply 📋 Mathlib.RingTheory.WittVector.Frobenius
  (p : ℕ) (R : Type u_1) [hp : Fact (Nat.Prime p)] [CommRing R] [CharP R p] [PerfectRing R p] : ⇑(WittVector.frobeniusEquiv p R).symm = ⇑(WittVector.map ↑(frobeniusEquiv R p).symm)
• WittVector.map_verschiebung 📋 Mathlib.RingTheory.WittVector.Verschiebung
  {p : ℕ} {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] [hp : Fact (Nat.Prime p)] (f : R →+* S) (x : WittVector p R) : (WittVector.map f) (WittVector.verschiebung x) = WittVector.verschiebung ((WittVector.map f) x)
• WittVector.map_teichmuller 📋 Mathlib.RingTheory.WittVector.Teichmuller
  (p : ℕ) {R : Type u_1} {S : Type u_2} [hp : Fact (Nat.Prime p)] [CommRing R] [CommRing S] (f : R →+* S) (r : R) : (WittVector.map f) ((WittVector.teichmuller p) r) = (WittVector.teichmuller p) (f r)

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