Loogle!

Result

Found 10 declarations mentioning WithOne.map.

• WithOne.map 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Mul α] [Mul β] (f : α →ₙ* β) : WithOne α →* WithOne β
• WithOne.map_id 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} [Mul α] : WithOne.map (MulHom.id α) = MonoidHom.id (WithOne α)
• WithOne.map_coe 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Mul α] [Mul β] (f : α →ₙ* β) (a : α) : (WithOne.map f) ↑a = ↑(f a)
• WithOne.map_comp 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} {γ : Type w} [Mul α] [Mul β] [Mul γ] (f : α →ₙ* β) (g : β →ₙ* γ) : WithOne.map (g.comp f) = (WithOne.map g).comp (WithOne.map f)
• MulEquiv.withOneCongr_apply 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Mul α] [Mul β] (e : α ≃* β) (a : WithOne α) : e.withOneCongr a = (WithOne.map e.toMulHom) a
• WithOne.map.eq_1 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Mul α] [Mul β] (f : α →ₙ* β) : WithOne.map f = WithOne.lift (WithOne.coeMulHom.comp f)
• WithOne.map_map 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} {γ : Type w} [Mul α] [Mul β] [Mul γ] (f : α →ₙ* β) (g : β →ₙ* γ) (x : WithOne α) : (WithOne.map g) ((WithOne.map f) x) = (WithOne.map (g.comp f)) x
• MulEquiv.withOneCongr.eq_1 📋 Mathlib.Algebra.Group.WithOne.Basic
  {α : Type u} {β : Type v} [Mul α] [Mul β] (e : α ≃* β) : e.withOneCongr = { toFun := ⇑(WithOne.map e.toMulHom), invFun := ⇑(WithOne.map e.symm.toMulHom), left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯ }
• MonCat.adjoinOne.eq_1 📋 Mathlib.Algebra.Category.MonCat.Adjunctions
  : MonCat.adjoinOne = { obj := fun S => MonCat.of (WithOne ↑S), map := fun {X Y} f => MonCat.ofHom (WithOne.map (Semigrp.Hom.hom f)), map_id := MonCat.adjoinOne._proof_1, map_comp := @MonCat.adjoinOne._proof_2 }
• MonCat.adjoinOne_map 📋 Mathlib.Algebra.Category.MonCat.Adjunctions
  {X✝ Y✝ : Semigrp} (f : X✝ ⟶ Y✝) : MonCat.adjoinOne.map f = MonCat.ofHom (WithOne.map (Semigrp.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