Loogle!

Result

Found 29 declarations mentioning Sum, Equiv and Fin. Of these, 8 match your pattern(s).

• finSumFinEquiv 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} : Fin m ⊕ Fin n ≃ Fin (m + n)
• finSumFinEquiv_apply_left 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} (i : Fin m) : finSumFinEquiv (Sum.inl i) = Fin.castAdd n i
• finSumFinEquiv_apply_right 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} (i : Fin n) : finSumFinEquiv (Sum.inr i) = Fin.natAdd m i
• finSigmaFinEquiv.eq_2 📋 Mathlib.Algebra.BigOperators.Fin
  (m_2 : ℕ) (n_2 : Fin m_2.succ → ℕ) : finSigmaFinEquiv = Trans.trans (Trans.trans (Trans.trans (Trans.trans finSumFinEquiv.sigmaCongrLeft.symm (Equiv.sumSigmaDistrib fun a => Fin (n_2 (finSumFinEquiv a)))) (finSigmaFinEquiv.sumCongr (Equiv.uniqueSigma fun i => Fin (n_2 (finSumFinEquiv (Sum.inr i)))))) finSumFinEquiv) (finCongr ⋯)
• finSumFinEquiv.eq_1 📋 Mathlib.Topology.Homeomorph.Lemmas
  {m n : ℕ} : finSumFinEquiv = { toFun := Sum.elim (Fin.castAdd n) (Fin.natAdd m), invFun := fun i => Fin.addCases Sum.inl Sum.inr i, left_inv := ⋯, right_inv := ⋯ }
• MultilinearMap.curryFinFinset_symm_apply 📋 Mathlib.LinearAlgebra.Multilinear.Curry
  {R : Type uR} {M₂ : Type v₂} {M' : Type v'} [CommSemiring R] [AddCommMonoid M'] [AddCommMonoid M₂] [Module R M'] [Module R M₂] {k l n : ℕ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sᶜ.card = l) (f : MultilinearMap R (fun x => M') (MultilinearMap R (fun x => M') M₂)) (m : Fin n → M') : ((MultilinearMap.curryFinFinset R M₂ M' hk hl).symm f) m = (f fun i => m ((finSumEquivOfFinset hk hl) (Sum.inl i))) fun i => m ((finSumEquivOfFinset hk hl) (Sum.inr i))
• ContinuousMultilinearMap.curryFinFinset_symm_apply 📋 Mathlib.Analysis.NormedSpace.Multilinear.Curry
  {𝕜 : Type u} {n : ℕ} {G : Type wG} {G' : Type wG'} [NontriviallyNormedField 𝕜] [NormedAddCommGroup G] [NormedSpace 𝕜 G] [NormedAddCommGroup G'] [NormedSpace 𝕜 G'] {k l : ℕ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sᶜ.card = l) (f : ContinuousMultilinearMap 𝕜 (fun i => G) (ContinuousMultilinearMap 𝕜 (fun i => G) G')) (m : Fin n → G) : ((ContinuousMultilinearMap.curryFinFinset 𝕜 G G' hk hl).symm f) m = (f fun i => m ((finSumEquivOfFinset hk hl) (Sum.inl i))) fun i => m ((finSumEquivOfFinset hk hl) (Sum.inr i))
• FirstOrder.Language.BoundedFormula.relabelAux.eq_1 📋 Mathlib.ModelTheory.Syntax
  {α : Type u'} {β : Type v'} {n : ℕ} (g : α → β ⊕ Fin n) (k : ℕ) : FirstOrder.Language.BoundedFormula.relabelAux g k = Sum.map id ⇑finSumFinEquiv ∘ ⇑(Equiv.sumAssoc β (Fin n) (Fin k)) ∘ Sum.map g id

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 40fea08