Loogle!

Result

Found 11 declarations mentioning HahnSeries.map.

• HahnSeries.map 📋 Mathlib.RingTheory.HahnSeries.Basic
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [Zero R] [Zero S] (x : HahnSeries Γ R) {F : Type u_5} [FunLike F R S] [ZeroHomClass F R S] (f : F) : HahnSeries Γ S
• HahnSeries.map_coeff 📋 Mathlib.RingTheory.HahnSeries.Basic
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [Zero R] [Zero S] (x : HahnSeries Γ R) {F : Type u_5} [FunLike F R S] [ZeroHomClass F R S] (f : F) (g : Γ) : (x.map f).coeff g = f (x.coeff g)
• HahnSeries.map_zero 📋 Mathlib.RingTheory.HahnSeries.Basic
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [Zero R] [Zero S] (f : ZeroHom R S) : HahnSeries.map 0 f = 0
• HahnSeries.map_single 📋 Mathlib.RingTheory.HahnSeries.Basic
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [Zero R] {a : Γ} {r : R} [Zero S] (f : ZeroHom R S) : ((HahnSeries.single a) r).map f = (HahnSeries.single a) (f r)
• HahnSeries.map_neg 📋 Mathlib.RingTheory.HahnSeries.Addition
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [AddGroup R] [AddGroup S] (f : R →+ S) {x : HahnSeries Γ R} : (-x).map f = -x.map f
• HahnSeries.map_add 📋 Mathlib.RingTheory.HahnSeries.Addition
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [AddMonoid R] [AddMonoid S] (f : R →+ S) {x y : HahnSeries Γ R} : (x + y).map f = x.map f + y.map f
• HahnSeries.map_sub 📋 Mathlib.RingTheory.HahnSeries.Addition
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [PartialOrder Γ] [AddGroup R] [AddGroup S] (f : R →+ S) {x y : HahnSeries Γ R} : (x - y).map f = x.map f - y.map f
• HahnSeries.map_smul 📋 Mathlib.RingTheory.HahnSeries.Addition
  {Γ : Type u_1} {R : Type u_3} {U : Type u_5} {V : Type u_6} [PartialOrder Γ] [Semiring R] [AddCommMonoid V] [Module R V] [AddCommMonoid U] [Module R U] (f : U →ₗ[R] V) {r : R} {x : HahnSeries Γ U} : (r • x).map f = r • x.map f
• HahnSeries.map_one 📋 Mathlib.RingTheory.HahnSeries.Multiplication
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [Zero Γ] [PartialOrder Γ] [MonoidWithZero R] [MonoidWithZero S] (f : R →*₀ S) : HahnSeries.map 1 f = 1
• HahnSeries.map_C 📋 Mathlib.RingTheory.HahnSeries.Multiplication
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [AddCommMonoid Γ] [PartialOrder Γ] [IsOrderedCancelAddMonoid Γ] [NonAssocSemiring R] [NonAssocSemiring S] (a : R) (f : R →+* S) : (HahnSeries.C a).map f = HahnSeries.C (f a)
• HahnSeries.map_mul 📋 Mathlib.RingTheory.HahnSeries.Multiplication
  {Γ : Type u_1} {R : Type u_3} {S : Type u_4} [AddCommMonoid Γ] [PartialOrder Γ] [IsOrderedCancelAddMonoid Γ] [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S] (f : R →ₙ+* S) {x y : HahnSeries Γ R} : (x * y).map f = x.map f * y.map f

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 40fea08