Loogle!

Result

Found 8 declarations mentioning Coe.coe.

• Coe.coe 📋 Init.Coe
  {α : semiOutParam (Sort u)} {β : Sort v} [self : Coe α β] : α → β
• PNat.coe_coeMonoidHom 📋 Mathlib.Data.PNat.Basic
  : ⇑PNat.coeMonoidHom = Coe.coe
• GenContFract.Pair.coe_toPair 📋 Mathlib.Algebra.ContinuedFractions.Basic
  {α : Type u_1} {β : Type u_2} [Coe α β] {a b : α} : ↑{ a := a, b := b } = { a := Coe.coe a, b := Coe.coe b }
• GenContFract.coe_toGenContFract 📋 Mathlib.Algebra.ContinuedFractions.Basic
  {α : Type u_1} {β : Type u_2} [Coe α β] {g : GenContFract α} : ↑g = { h := Coe.coe g.h, s := Stream'.Seq.map GenContFract.Pair.coeFn g.s }
• GenContFract.IntFractPair.coe_to_intFractPair 📋 Mathlib.Algebra.ContinuedFractions.Computation.Basic
  {K : Type u_1} {β : Type u_2} [Coe K β] {b : ℤ} {fr : K} : ↑{ b := b, fr := fr } = { b := b, fr := Coe.coe fr }
• AlgebraicGeometry.morphismRestrict_base_coe 📋 Mathlib.AlgebraicGeometry.Restrict
  {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (U : Y.Opens) (x : ↑↑(↑((TopologicalSpace.Opens.map f.base).obj U)).toPresheafedSpace) : Coe.coe ((CategoryTheory.ConcreteCategory.hom (f ∣_ U).base) x) = (CategoryTheory.ConcreteCategory.hom f.base) ↑x
• MvPolynomial.coe_injective 📋 Mathlib.RingTheory.MvPowerSeries.Basic
  (σ : Type u_1) (R : Type u_2) [CommSemiring R] : Function.Injective Coe.coe
• Polynomial.coe_injective 📋 Mathlib.RingTheory.PowerSeries.Basic
  (R : Type u_1) [Semiring R] : Function.Injective Coe.coe

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 c3b95a7