Loogle!

Result

Found 10 declarations mentioning WithZero.map.

• WithZero.map 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Add α] [Add β] (f : α →ₙ+ β) : WithZero α →+ WithZero β
• WithZero.map_id 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} [Add α] : WithZero.map (AddHom.id α) = AddMonoidHom.id (WithZero α)
• WithZero.map_coe 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Add α] [Add β] (f : α →ₙ+ β) (a : α) : (WithZero.map f) ↑a = ↑(f a)
• WithZero.map_comp 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} {γ : Type w} [Add α] [Add β] [Add γ] (f : α →ₙ+ β) (g : β →ₙ+ γ) : WithZero.map (g.comp f) = (WithZero.map g).comp (WithZero.map f)
• AddEquiv.withZeroCongr_apply 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Add α] [Add β] (e : α ≃+ β) (a : WithZero α) : e.withZeroCongr a = (WithZero.map e.toAddHom) a
• WithZero.map.eq_1 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Add α] [Add β] (f : α →ₙ+ β) : WithZero.map f = WithZero.lift (WithZero.coeAddHom.comp f)
• WithZero.map_map 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} {γ : Type w} [Add α] [Add β] [Add γ] (f : α →ₙ+ β) (g : β →ₙ+ γ) (x : WithZero α) : (WithZero.map g) ((WithZero.map f) x) = (WithZero.map (g.comp f)) x
• AddEquiv.withZeroCongr.eq_1 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Add α] [Add β] (e : α ≃+ β) : e.withZeroCongr = { toFun := ⇑(WithZero.map e.toAddHom), invFun := ⇑(WithZero.map e.symm.toAddHom), left_inv := ⋯, right_inv := ⋯, map_add' := ⋯ }
• AddMonCat.adjoinZero.eq_1 📋 Mathlib.Algebra.Category.MonCat.Adjunctions
  : AddMonCat.adjoinZero = { obj := fun S => AddMonCat.of (WithZero ↑S), map := fun {X Y} f => AddMonCat.ofHom (WithZero.map (AddSemigrp.Hom.hom f)), map_id := AddMonCat.adjoinZero._proof_3, map_comp := @AddMonCat.adjoinZero._proof_4 }
• AddMonCat.adjoinZero_map 📋 Mathlib.Algebra.Category.MonCat.Adjunctions
  {X✝ Y✝ : AddSemigrp} (f : X✝ ⟶ Y✝) : AddMonCat.adjoinZero.map f = AddMonCat.ofHom (WithZero.map (AddSemigrp.Hom.hom 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 bce1d65