Loogle!

Result

Found 62 declarations mentioning Dvd.dvd and ZMod. Of these, 6 have a name containing "hom".

• ZMod.castHom 📋 Mathlib.Data.ZMod.Basic
  {n m : ℕ} (h : m ∣ n) (R : Type u_2) [Ring R] [CharP R m] : ZMod n →+* R
• ZMod.castHom_apply 📋 Mathlib.Data.ZMod.Basic
  {n : ℕ} {R : Type u_1} [Ring R] {m : ℕ} [CharP R m] {h : m ∣ n} (i : ZMod n) : (ZMod.castHom h R) i = i.cast
• ZMod.castHom_comp 📋 Mathlib.Data.ZMod.Basic
  {n m d : ℕ} (hm : n ∣ m) (hd : m ∣ d) : (ZMod.castHom hm (ZMod n)).comp (ZMod.castHom hd (ZMod m)) = ZMod.castHom ⋯ (ZMod n)
• ZMod.castHom.eq_1 📋 Mathlib.Data.ZMod.Basic
  {n m : ℕ} (h : m ∣ n) (R : Type u_2) [Ring R] [CharP R m] : ZMod.castHom h R = { toFun := ZMod.cast, map_one' := ⋯, map_mul' := ⋯, map_zero' := ⋯, map_add' := ⋯ }
• DirichletCharacter.changeLevel_toUnitHom 📋 Mathlib.NumberTheory.DirichletCharacter.Basic
  {R : Type u_1} [CommMonoidWithZero R] {n : ℕ} (χ : DirichletCharacter R n) {m : ℕ} (hm : n ∣ m) : MulChar.toUnitHom ((DirichletCharacter.changeLevel hm) χ) = (MulChar.toUnitHom χ).comp (ZMod.unitsMap hm)
• PadicInt.pow_dvd_nthHom_sub 📋 Mathlib.NumberTheory.Padics.RingHoms
  {R : Type u_1} [NonAssocSemiring R] {p : ℕ} {f : (k : ℕ) → R →+* ZMod (p ^ k)} [hp_prime : Fact (Nat.Prime p)] (f_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), (ZMod.castHom ⋯ (ZMod (p ^ k1))).comp (f k2) = f k1) (r : R) (i j : ℕ) (h : i ≤ j) : ↑p ^ i ∣ PadicInt.nthHom f r j - PadicInt.nthHom f r i

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 f167e8d