Loogle!

Result

Found 8 declarations mentioning FreeAbelianGroup.map.

• FreeAbelianGroup.map 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} {β : Type v} (f : α → β) : FreeAbelianGroup α →+ FreeAbelianGroup β
• FreeAbelianGroup.map_id 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} : FreeAbelianGroup.map id = AddMonoidHom.id (FreeAbelianGroup α)
• FreeAbelianGroup.map_id_apply 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} (x : FreeAbelianGroup α) : (FreeAbelianGroup.map id) x = x
• FreeAbelianGroup.map_of_apply 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} {β : Type v} {f : α → β} (a : α) : (FreeAbelianGroup.map f) (FreeAbelianGroup.of a) = FreeAbelianGroup.of (f a)
• FreeAbelianGroup.map_comp 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} {β : Type v} {γ : Type w} {f : α → β} {g : β → γ} : FreeAbelianGroup.map (g ∘ f) = (FreeAbelianGroup.map g).comp (FreeAbelianGroup.map f)
• FreeAbelianGroup.map.eq_1 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} {β : Type v} (f : α → β) : FreeAbelianGroup.map f = FreeAbelianGroup.lift (FreeAbelianGroup.of ∘ f)
• FreeAbelianGroup.map_comp_apply 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u} {β : Type v} {γ : Type w} {f : α → β} {g : β → γ} (x : FreeAbelianGroup α) : (FreeAbelianGroup.map (g ∘ f)) x = (FreeAbelianGroup.map g) ((FreeAbelianGroup.map f) x)
• FreeAbelianGroup.lift_comp 📋 Mathlib.GroupTheory.FreeAbelianGroup
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [AddCommGroup γ] (f : α → β) (g : β → γ) (x : FreeAbelianGroup α) : (FreeAbelianGroup.lift (g ∘ f)) x = (FreeAbelianGroup.lift g) ((FreeAbelianGroup.map 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 19971e9 serving mathlib revision 40fea08