Loogle!

Result

Found 508 declarations mentioning Equiv and Fin. Of these, 22 match your pattern(s).

• finCongr 📋 Mathlib.Data.Fin.Basic
  {n m : ℕ} (eq : n = m) : Fin n ≃ Fin m
• Fintype.equivFin 📋 Mathlib.Data.Fintype.EquivFin
  (α : Type u_4) [Fintype α] : α ≃ Fin (Fintype.card α)
• Fintype.equivFinOfCardEq 📋 Mathlib.Data.Fintype.EquivFin
  {α : Type u_1} [Fintype α] {n : ℕ} (h : Fintype.card α = n) : α ≃ Fin n
• Finset.equivFin 📋 Mathlib.Data.Fintype.EquivFin
  {α : Type u_1} (s : Finset α) : { x // x ∈ s } ≃ Fin s.card
• Finset.equivFinOfCardEq 📋 Mathlib.Data.Fintype.EquivFin
  {α : Type u_1} {s : Finset α} {n : ℕ} (h : s.card = n) : { x // x ∈ s } ≃ Fin n
• Finset.Nat.antidiagonalEquivFin 📋 Mathlib.Data.Finset.NatAntidiagonal
  (n : ℕ) : { x // x ∈ Finset.antidiagonal n } ≃ Fin (n + 1)
• Ideal.equivFinTwo 📋 Mathlib.RingTheory.Ideal.Basic
  (K : Type u_5) [DivisionSemiring K] [DecidableEq (Ideal K)] : Ideal K ≃ Fin 2
• finProdFinEquiv 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} : Fin m × Fin n ≃ Fin (m * n)
• finSumFinEquiv 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} : Fin m ⊕ Fin n ≃ Fin (m + n)
• finAddFlip 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} : Fin (m + n) ≃ Fin (n + m)
• finFunctionFinEquiv 📋 Mathlib.Algebra.BigOperators.Fin
  {m n : ℕ} : (Fin n → Fin m) ≃ Fin (m ^ n)
• finPiFinEquiv 📋 Mathlib.Algebra.BigOperators.Fin
  {m : ℕ} {n : Fin m → ℕ} : ((i : Fin m) → Fin (n i)) ≃ Fin (∏ i, n i)
• finSigmaFinEquiv 📋 Mathlib.Algebra.BigOperators.Fin
  {m : ℕ} {n : Fin m → ℕ} : (i : Fin m) × Fin (n i) ≃ Fin (∑ i, n i)
• Nat.equivFinOfCardPos 📋 Mathlib.SetTheory.Cardinal.Finite
  {α : Type u_3} (h : Nat.card α ≠ 0) : α ≃ Fin (Nat.card α)
• Finite.equivFin 📋 Mathlib.Data.Finite.Card
  (α : Type u_4) [Finite α] : α ≃ Fin (Nat.card α)
• Finite.equivFinOfCardEq 📋 Mathlib.Data.Finite.Card
  {α : Type u_1} [Finite α] {n : ℕ} (h : Nat.card α = n) : α ≃ Fin n
• Composition.blocksFinEquiv 📋 Mathlib.Combinatorics.Enumerative.Composition
  {n : ℕ} (c : Composition n) : (i : Fin c.length) × Fin (c.blocksFun i) ≃ Fin n
• Encodable.fintypeEquivFin 📋 Mathlib.Logic.Equiv.Finset
  {α : Type u_1} [Fintype α] [Encodable α] : α ≃ Fin (Fintype.card α)
• SSet.stdSimplex.obj₀Equiv 📋 Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
  {n : ℕ} : (SSet.stdSimplex.obj (SimplexCategory.mk n)).obj (Opposite.op (SimplexCategory.mk 0)) ≃ Fin (n + 1)
• DirectSum.IsInternal.sigmaOrthonormalBasisIndexEquiv 📋 Mathlib.Analysis.InnerProductSpace.PiL2
  {ι : Type u_7} {𝕜 : Type u_8} [RCLike 𝕜] {E : Type u_9} [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [Fintype ι] [FiniteDimensional 𝕜 E] {n : ℕ} (hn : Module.finrank 𝕜 E = n) [DecidableEq ι] {V : ι → Submodule 𝕜 E} (hV : DirectSum.IsInternal V) (hV' : OrthogonalFamily 𝕜 (fun i => ↥(V i)) fun i => (V i).subtypeₗᵢ) : (i : ι) × Fin (Module.finrank 𝕜 ↥(V i)) ≃ Fin n
• OrderedFinpartition.equivSigma 📋 Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno
  {n : ℕ} (c : OrderedFinpartition n) : (i : Fin c.length) × Fin (c.partSize i) ≃ Fin n
• FinEnum.equiv 📋 Mathlib.Data.FinEnum
  {α : Sort u_1} [self : FinEnum α] : α ≃ Fin (FinEnum.card α)

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 1bd7adb