Loogle!

Result

Found 4 declarations mentioning Ideal.ResidueField.map.

• Ideal.ResidueField.map 📋 Mathlib.RingTheory.LocalRing.ResidueField.Ideal
  {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] (I : Ideal R) [I.IsPrime] (J : Ideal S) [J.IsPrime] (f : R →+* S) (hf : I = Ideal.comap f J) : I.ResidueField →+* J.ResidueField
• Ideal.ResidueField.map.congr_simp 📋 Mathlib.RingTheory.LocalRing.ResidueField.Ideal
  {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] (I : Ideal R) [I.IsPrime] (J : Ideal S) [J.IsPrime] (f f✝ : R →+* S) (e_f : f = f✝) (hf : I = Ideal.comap f J) : Ideal.ResidueField.map I J f hf = Ideal.ResidueField.map I J f✝ ⋯
• Ideal.ResidueField.map_algebraMap 📋 Mathlib.RingTheory.LocalRing.ResidueField.Ideal
  {R : Type u_1} {S : Type u_2} [CommRing R] [CommRing S] (I : Ideal R) [I.IsPrime] (J : Ideal S) [J.IsPrime] (f : R →+* S) (hf : I = Ideal.comap f J) (r : R) : (Ideal.ResidueField.map I J f hf) ((algebraMap R I.ResidueField) r) = (algebraMap S J.ResidueField) (f r)
• Ideal.ResidueField.mapₐ_apply 📋 Mathlib.RingTheory.LocalRing.ResidueField.Ideal
  {R : Type u_1} {A : Type u_3} {B : Type u_4} [CommRing R] [CommRing A] [CommRing B] [Algebra R A] [Algebra R B] (I : Ideal A) [I.IsPrime] (J : Ideal B) [J.IsPrime] (f : A →ₐ[R] B) (hf : I = Ideal.comap f.toRingHom J) (x : I.ResidueField) : (Ideal.ResidueField.mapₐ I J f hf) x = (Ideal.ResidueField.map I J f.toRingHom hf) x

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 6ff4759 serving mathlib revision edaf32c