Loogle!

Result

Found 16 declarations mentioning Countable and Not. Of these, 8 match your pattern(s).

• not_countable 📋 Mathlib.Data.Countable.Defs
  {α : Sort u} [Uncountable α] : ¬Countable α
• Uncountable.mk 📋 Mathlib.Data.Countable.Defs
  {α : Sort u_1} (not_countable : ¬Countable α) : Uncountable α
• Uncountable.not_countable 📋 Mathlib.Data.Countable.Defs
  {α : Sort u_1} [self : Uncountable α] : ¬Countable α
• not_countable_iff 📋 Mathlib.Data.Countable.Defs
  {α : Sort u} : ¬Countable α ↔ Uncountable α
• uncountable_iff_not_countable 📋 Mathlib.Data.Countable.Defs
  (α : Sort u_1) : Uncountable α ↔ ¬Countable α
• PolishSpace.measurableEquivNatBoolOfNotCountable 📋 Mathlib.MeasureTheory.Constructions.Polish.Basic
  {α : Type u_4} [MeasurableSpace α] [StandardBorelSpace α] (h : ¬Countable α) : α ≃ᵐ (ℕ → Bool)
• PolishSpace.measurableEquivOfNotCountable 📋 Mathlib.MeasureTheory.Constructions.Polish.Basic
  {α : Type u_4} {β : Type u_6} [MeasurableSpace α] [MeasurableSpace β] [StandardBorelSpace α] [StandardBorelSpace β] (hα : ¬Countable α) (hβ : ¬Countable β) : α ≃ᵐ β
• ProbabilityTheory.Kernel.condKernel_def 📋 Mathlib.Probability.Kernel.Disintegration.StandardBorel
  {α : Type u_5} {β : Type u_6} {Ω : Type u_7} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {mΩ : MeasurableSpace Ω} [StandardBorelSpace Ω] [Nonempty Ω] [h : MeasurableSpace.CountableOrCountablyGenerated α β] (κ : ProbabilityTheory.Kernel α (β × Ω)) [ProbabilityTheory.IsFiniteKernel κ] : κ.condKernel = if hα : Countable α then ProbabilityTheory.Kernel.condKernelCountable (fun a => (κ a).condKernel) ⋯ else κ.condKernelBorel

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 401c76f serving mathlib revision b87935d