Loogle!

Result

Found 21 declarations mentioning NonUnitalSubring.map.

• NonUnitalSubring.map 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (f : F) (s : NonUnitalSubring R) : NonUnitalSubring S
• NonUnitalSubring.map_id 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} [NonUnitalNonAssocRing R] (s : NonUnitalSubring R) : NonUnitalSubring.map (NonUnitalRingHom.id R) s = s
• NonUnitalSubring.map.congr_simp 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (f f✝ : F) (e_f : f = f✝) (s s✝ : NonUnitalSubring R) (e_s : s = s✝) : NonUnitalSubring.map f s = NonUnitalSubring.map f✝ s✝
• NonUnitalRingHom.range_eq_map 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] (f : R →ₙ+* S) : f.range = NonUnitalSubring.map f ⊤
• NonUnitalSubring.coe_map 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (f : F) (s : NonUnitalSubring R) : ↑(NonUnitalSubring.map f s) = ⇑f '' ↑s
• NonUnitalSubring.map_bot 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] (f : R →ₙ+* S) : NonUnitalSubring.map f ⊥ = ⊥
• NonUnitalSubring.gc_map_comap 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (f : F) : GaloisConnection (NonUnitalSubring.map f) (NonUnitalSubring.comap f)
• NonUnitalSubring.map_iInf 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] {ι : Sort u_1} [Nonempty ι] (f : F) (hf : Function.Injective ⇑f) (s : ι → NonUnitalSubring R) : NonUnitalSubring.map f (iInf s) = ⨅ i, NonUnitalSubring.map f (s i)
• NonUnitalSubring.mem_map 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] {f : F} {s : NonUnitalSubring R} {y : S} : y ∈ NonUnitalSubring.map f s ↔ ∃ x ∈ s, f x = y
• NonUnitalSubring.map_iSup 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] {ι : Sort u_1} (f : F) (s : ι → NonUnitalSubring R) : NonUnitalSubring.map f (iSup s) = ⨆ i, NonUnitalSubring.map f (s i)
• NonUnitalRingHom.map_closure 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] (f : R →ₙ+* S) (s : Set R) : NonUnitalSubring.map f (NonUnitalSubring.closure s) = NonUnitalSubring.closure (⇑f '' s)
• NonUnitalSubring.map_inf 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (s t : NonUnitalSubring R) (f : F) (hf : Function.Injective ⇑f) : NonUnitalSubring.map f (s ⊓ t) = NonUnitalSubring.map f s ⊓ NonUnitalSubring.map f t
• NonUnitalRingHom.map_range 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} {T : Type u_1} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [NonUnitalNonAssocRing T] (g : S →ₙ+* T) (f : R →ₙ+* S) : NonUnitalSubring.map g f.range = (g.comp f).range
• NonUnitalSubring.map_le_iff_le_comap 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] {f : F} {s : NonUnitalSubring R} {t : NonUnitalSubring S} : NonUnitalSubring.map f s ≤ t ↔ s ≤ NonUnitalSubring.comap f t
• NonUnitalSubring.map_sup 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (s t : NonUnitalSubring R) (f : F) : NonUnitalSubring.map f (s ⊔ t) = NonUnitalSubring.map f s ⊔ NonUnitalSubring.map f t
• NonUnitalSubring.map_map 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} {T : Type u_1} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [NonUnitalNonAssocRing T] (s : NonUnitalSubring R) (g : S →ₙ+* T) (f : R →ₙ+* S) : NonUnitalSubring.map g (NonUnitalSubring.map f s) = NonUnitalSubring.map (g.comp f) s
• NonUnitalSubring.equivMapOfInjective 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (s : NonUnitalSubring R) (f : F) (hf : Function.Injective ⇑f) : ↥s ≃+* ↥(NonUnitalSubring.map f s)
• NonUnitalSubring.mem_map_equiv 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] {f : R ≃+* S} {K : NonUnitalSubring R} {x : S} : x ∈ NonUnitalSubring.map (↑f) K ↔ f.symm x ∈ K
• NonUnitalSubring.comap_equiv_eq_map_symm 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] (f : R ≃+* S) (K : NonUnitalSubring S) : NonUnitalSubring.comap (↑f) K = NonUnitalSubring.map f.symm K
• NonUnitalSubring.map_equiv_eq_comap_symm 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] (f : R ≃+* S) (K : NonUnitalSubring R) : NonUnitalSubring.map (↑f) K = NonUnitalSubring.comap f.symm K
• NonUnitalSubring.coe_equivMapOfInjective_apply 📋 Mathlib.RingTheory.NonUnitalSubring.Basic
  {F : Type w} {R : Type u} {S : Type v} [NonUnitalNonAssocRing R] [NonUnitalNonAssocRing S] [FunLike F R S] [NonUnitalRingHomClass F R S] (s : NonUnitalSubring R) (f : F) (hf : Function.Injective ⇑f) (x : ↥s) : ↑((s.equivMapOfInjective f hf) x) = f ↑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 ee8c038 serving mathlib revision 7a9e177