Loogle!

Result

Found 6 declarations mentioning Exists and Quot.

• Quot.exists_rep 📋 Init.Core
  {α : Sort u} {r : α → α → Prop} (q : Quot r) : ∃ a, Quot.mk r a = q
• Std.Iterators.IterM.QuotStep.restrict 📋 Std.Data.Iterators.Lemmas.Equivalence.StepCongr
  {α : Type u_1} {m : Type u_1 → Type u_2} {β : Type u_1} [Std.Iterators.Iterator α m β] [Monad m] [LawfulMonad m] {it : Std.IterM m β} (step : { s // ∃ s', s = (↑s').bundledQuotient }) : it.QuotStep
• Std.Iterators.IterM.Equiv.exists_step_of_step 📋 Std.Data.Iterators.Lemmas.Equivalence.StepCongr
  {α₁ : Type u_1} {m : Type u_1 → Type u_2} {β α₂ : Type u_1} [Std.Iterators.Iterator α₁ m β] [Std.Iterators.Iterator α₂ m β] [Monad m] [LawfulMonad m] {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) (s : ita.Step) : ∃ s', (↑s).bundledQuotient = (↑s').bundledQuotient
• Std.Iterators.IterStep.restrict_bundle 📋 Std.Data.Iterators.Lemmas.Equivalence.StepCongr
  {α₁ : Type u_1} {m : Type u_1 → Type u_2} {β α₂ : Type u_1} [Std.Iterators.Iterator α₁ m β] [Std.Iterators.Iterator α₂ m β] [Monad m] [LawfulMonad m] {ita : Std.IterM m β} {step : Std.Iterators.IterStep (Std.IterM m β) β} {h : ∃ s, step.bundledQuotient = (↑s).bundledQuotient} : Std.Iterators.IterM.QuotStep.restrict ⟨step.bundledQuotient, h⟩ = Quot.mk (fun s₁ s₂ => (↑s₁).bundledQuotient = (↑s₂).bundledQuotient) h.choose
• Std.Iterators.IterM.QuotStep.transportAlongEquiv.eq_1 📋 Std.Data.Iterators.Lemmas.Equivalence.StepCongr
  {α₁ : Type u_1} {m : Type u_1 → Type u_2} {β α₂ : Type u_1} [Std.Iterators.Iterator α₁ m β] [Std.Iterators.Iterator α₂ m β] [Monad m] [LawfulMonad m] {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : Std.Iterators.IterM.QuotStep.transportAlongEquiv h = Quot.lift (fun s₁ => have this := ⋯; Quot.mk (fun s₁ s₂ => (↑s₁).bundledQuotient = (↑s₂).bundledQuotient) this.choose) ⋯
• Multiset.exists_multiset_eq_map_quot_mk 📋 Mathlib.Data.Multiset.MapFold
  {α : Type u_1} {r : α → α → Prop} (s : Multiset (Quot r)) : ∃ t, s = Multiset.map (Quot.mk r) t

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 e086424 serving mathlib revision fd96d2d