Loogle!

Result

Found 6 declarations mentioning Commute.map.

• Commute.map 📋 Mathlib.Algebra.Group.Commute.Hom
  {F : Type u_1} {M : Type u_2} {N : Type u_3} [Mul M] [Mul N] {x y : M} [FunLike F M N] [MulHomClass F M N] (h : Commute x y) (f : F) : Commute (f x) (f y)
• Finset.map_noncommProd 📋 Mathlib.Data.Finset.NoncommProd
  {F : Type u_1} {α : Type u_3} {β : Type u_4} {γ : Type u_5} [Monoid β] [Monoid γ] [FunLike F β γ] [MonoidHomClass F β γ] (s : Finset α) (f : α → β) (comm : (↑s).Pairwise (Function.onFun Commute f)) (g : F) : g (s.noncommProd f comm) = s.noncommProd (fun i => g (f i)) ⋯
• MonoidHom.comp_noncommPiCoprod 📋 Mathlib.GroupTheory.NoncommPiCoprod
  {M : Type u_1} [Monoid M] {ι : Type u_2} [Fintype ι] {N : ι → Type u_3} [(i : ι) → Monoid (N i)] (ϕ : (i : ι) → N i →* M) {hcomm : Pairwise fun i j => ∀ (x : N i) (y : N j), Commute ((ϕ i) x) ((ϕ j) y)} {P : Type u_4} [Monoid P] {f : M →* P} (hcomm' : Pairwise fun i j => ∀ (x : N i) (y : N j), Commute ((f.comp (ϕ i)) x) ((f.comp (ϕ j)) y) := ⋯) : f.comp (MonoidHom.noncommPiCoprod ϕ hcomm) = MonoidHom.noncommPiCoprod (fun i => f.comp (ϕ i)) hcomm'
• MulHom.comp_noncommCoprod 📋 Mathlib.GroupTheory.NoncommCoprod
  {M : Type u_1} {N : Type u_2} {P : Type u_3} [Mul M] [Mul N] [Semigroup P] (f : M →ₙ* P) (g : N →ₙ* P) {Q : Type u_4} [Semigroup Q] (h : P →ₙ* Q) (comm : ∀ (m : M) (n : N), Commute (f m) (g n)) : h.comp (f.noncommCoprod g comm) = (h.comp f).noncommCoprod (h.comp g) ⋯
• MonoidHom.noncommCoprod_unique 📋 Mathlib.GroupTheory.NoncommCoprod
  {M : Type u_1} {N : Type u_2} {P : Type u_3} [MulOneClass M] [MulOneClass N] [Monoid P] (f : M × N →* P) : (f.comp (MonoidHom.inl M N)).noncommCoprod (f.comp (MonoidHom.inr M N)) ⋯ = f
• MonoidHom.comp_noncommCoprod 📋 Mathlib.GroupTheory.NoncommCoprod
  {M : Type u_1} {N : Type u_2} {P : Type u_3} [MulOneClass M] [MulOneClass N] [Monoid P] (f : M →* P) (g : N →* P) (comm : ∀ (m : M) (n : N), Commute (f m) (g n)) {Q : Type u_4} [Monoid Q] (h : P →* Q) : h.comp (f.noncommCoprod g comm) = (h.comp f).noncommCoprod (h.comp g) ⋯

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