Loogle!

Result

Found 36 declarations mentioning Std.DHashMap.Const.getD.

• Std.DHashMap.Const.getD 📋 Std.Data.DHashMap.Basic
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} (m : Std.DHashMap α fun x => β) (a : α) (fallback : β) : β
• Std.DHashMap.Const.getD_unitOfList 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {l : List α} {k : α} {fallback : Unit} : Std.DHashMap.Const.getD (Std.DHashMap.Const.unitOfList l) k fallback = ()
• Std.DHashMap.Const.getD_emptyWithCapacity 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {a : α} {fallback : β} {c : ℕ} : Std.DHashMap.Const.getD (Std.DHashMap.emptyWithCapacity c) a fallback = fallback
• Std.DHashMap.Const.getD_empty 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {a : α} {fallback : β} : Std.DHashMap.Const.getD ∅ a fallback = fallback
• Std.DHashMap.Const.getD_emptyc 📋 Std.Data.DHashMap.Lemmas
  {α : Type u_1} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type u_2} {a : α} {fallback : β} : Std.DHashMap.Const.getD ∅ a fallback = fallback
• Std.DHashMap.Const.getD_eq_getD 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [LawfulBEq α] {a : α} {fallback : β} : Std.DHashMap.Const.getD m a fallback = m.getD a fallback
• Std.DHashMap.Const.getD_erase_self 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k : α} {fallback : β} : Std.DHashMap.Const.getD (m.erase k) k fallback = fallback
• Std.DHashMap.Const.getD_eq_getD_get? 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : Std.DHashMap.Const.getD m a fallback = (Std.DHashMap.Const.get? m a).getD fallback
• Std.DHashMap.Const.getD_insert_self 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k : α} {fallback v : β} : Std.DHashMap.Const.getD (m.insert k v) k fallback = v
• Std.DHashMap.Const.get!_eq_getD_default 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] [Inhabited β] {a : α} : Std.DHashMap.Const.get! m a = Std.DHashMap.Const.getD m a default
• Std.DHashMap.Const.getD_of_isEmpty 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : m.isEmpty = true → Std.DHashMap.Const.getD m a fallback = fallback
• Std.DHashMap.Const.getD_eq_fallback_of_contains_eq_false 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : m.contains a = false → Std.DHashMap.Const.getD m a fallback = fallback
• Std.DHashMap.Const.getD_congr 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a b : α} {fallback : β} (hab : (a == b) = true) : Std.DHashMap.Const.getD m a fallback = Std.DHashMap.Const.getD m b fallback
• Std.DHashMap.Const.getD_insertManyIfNewUnit_list 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {m : Std.DHashMap α fun x => Unit} {l : List α} {k : α} {fallback : Unit} : Std.DHashMap.Const.getD (Std.DHashMap.Const.insertManyIfNewUnit m l) k fallback = ()
• Std.DHashMap.Const.getD_eq_fallback 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : a ∉ m → Std.DHashMap.Const.getD m a fallback = fallback
• Std.DHashMap.Const.getD_ofList_of_contains_eq_false 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k : α} {fallback : β} (contains_eq_false : (List.map Prod.fst l).contains k = false) : Std.DHashMap.Const.getD (Std.DHashMap.Const.ofList l) k fallback = fallback
• Std.DHashMap.Const.get?_eq_some_getD_of_contains 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : m.contains a = true → Std.DHashMap.Const.get? m a = some (Std.DHashMap.Const.getD m a fallback)
• Std.DHashMap.Const.getD_alter_self 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k : α} {fallback : β} {f : Option β → Option β} : Std.DHashMap.Const.getD (Std.DHashMap.Const.alter m k f) k fallback = (f (Std.DHashMap.Const.get? m k)).getD fallback
• Std.DHashMap.Equiv.constGetD_eq 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m₁ m₂ : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k : α} {fallback : β} (h : m₁.Equiv m₂) : Std.DHashMap.Const.getD m₁ k fallback = Std.DHashMap.Const.getD m₂ k fallback
• Std.DHashMap.Const.getD_modify_self 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k : α} {fallback : β} {f : β → β} : Std.DHashMap.Const.getD (Std.DHashMap.Const.modify m k f) k fallback = (Option.map f (Std.DHashMap.Const.get? m k)).getD fallback
• Std.DHashMap.Const.get_eq_getD 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} {h : a ∈ m} : Std.DHashMap.Const.get m a h = Std.DHashMap.Const.getD m a fallback
• Std.DHashMap.Const.get?_eq_some_getD 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {a : α} {fallback : β} : a ∈ m → Std.DHashMap.Const.get? m a = some (Std.DHashMap.Const.getD m a fallback)
• Std.DHashMap.Const.getD_erase 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : β} : Std.DHashMap.Const.getD (m.erase k) a fallback = if (k == a) = true then fallback else Std.DHashMap.Const.getD m a fallback
• Std.DHashMap.Const.getD_insert 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} : Std.DHashMap.Const.getD (m.insert k v) a fallback = if (k == a) = true then v else Std.DHashMap.Const.getD m a fallback
• Std.DHashMap.Const.getD_filter_of_getKey?_eq_some 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {f : α → β → Bool} {k k' : α} {fallback : β} : m.getKey? k = some k' → Std.DHashMap.Const.getD (Std.DHashMap.filter f m) k fallback = (Option.filter (fun x => f k' x) (Std.DHashMap.Const.get? m k)).getD fallback
• Std.DHashMap.Const.getD_filterMap_of_getKey?_eq_some 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {γ : Type w} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {f : α → β → Option γ} {k k' : α} {fallback : γ} (h : m.getKey? k = some k') : Std.DHashMap.Const.getD (Std.DHashMap.filterMap f m) k fallback = ((Std.DHashMap.Const.get? m k).bind (f k')).getD fallback
• Std.DHashMap.Const.getD_map_of_getKey?_eq_some 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {γ : Type w} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] [Inhabited γ] {f : α → β → γ} {k k' : α} {fallback : γ} (h : m.getKey? k = some k') : Std.DHashMap.Const.getD (Std.DHashMap.map f m) k fallback = (Option.map (f k') (Std.DHashMap.Const.get? m k)).getD fallback
• Std.DHashMap.Const.getD_alter 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β} {f : Option β → Option β} : Std.DHashMap.Const.getD (Std.DHashMap.Const.alter m k f) k' fallback = if (k == k') = true then (f (Std.DHashMap.Const.get? m k)).getD fallback else Std.DHashMap.Const.getD m k' fallback
• Std.DHashMap.Const.getD_modify 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k k' : α} {fallback : β} {f : β → β} : Std.DHashMap.Const.getD (Std.DHashMap.Const.modify m k f) k' fallback = if (k == k') = true then (Option.map f (Std.DHashMap.Const.get? m k)).getD fallback else Std.DHashMap.Const.getD m k' fallback
• Std.DHashMap.Const.getD_ofList_of_mem 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k k' : α} (k_beq : (k == k') = true) {v fallback : β} (distinct : List.Pairwise (fun a b => (a.1 == b.1) = false) l) (mem : (k, v) ∈ l) : Std.DHashMap.Const.getD (Std.DHashMap.Const.ofList l) k' fallback = v
• Std.DHashMap.Const.getD_insertMany_list_of_contains_eq_false 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k : α} {fallback : β} (contains_eq_false : (List.map Prod.fst l).contains k = false) : Std.DHashMap.Const.getD (Std.DHashMap.Const.insertMany m l) k fallback = Std.DHashMap.Const.getD m k fallback
• Std.DHashMap.Const.getD_filter 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {f : α → β → Bool} {k : α} {fallback : β} : Std.DHashMap.Const.getD (Std.DHashMap.filter f m) k fallback = ((Std.DHashMap.Const.get? m k).pfilter fun x h' => f (m.getKey k ⋯) x).getD fallback
• Std.DHashMap.Const.getD_insertMany_list_of_mem 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k k' : α} (k_beq : (k == k') = true) {v fallback : β} (distinct : List.Pairwise (fun a b => (a.1 == b.1) = false) l) (mem : (k, v) ∈ l) : Std.DHashMap.Const.getD (Std.DHashMap.Const.insertMany m l) k' fallback = v
• Std.DHashMap.Const.getD_filterMap 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {γ : Type w} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {f : α → β → Option γ} {k : α} {fallback : γ} : Std.DHashMap.Const.getD (Std.DHashMap.filterMap f m) k fallback = ((Std.DHashMap.Const.get? m k).pbind fun x h' => f (m.getKey k ⋯) x).getD fallback
• Std.DHashMap.Const.getD_insertIfNew 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {k a : α} {fallback v : β} : Std.DHashMap.Const.getD (m.insertIfNew k v) a fallback = if (k == a) = true ∧ k ∉ m then v else Std.DHashMap.Const.getD m a fallback
• Std.DHashMap.Const.getD_map 📋 Std.Data.DHashMap.Lemmas
  {α : Type u} {x✝ : BEq α} {x✝¹ : Hashable α} {β : Type v} {γ : Type w} {m : Std.DHashMap α fun x => β} [EquivBEq α] [LawfulHashable α] {f : α → β → γ} {k : α} {fallback : γ} : Std.DHashMap.Const.getD (Std.DHashMap.map f m) k fallback = (Option.pmap (fun v h => f (m.getKey k h) v) (Std.DHashMap.Const.get? m k) ⋯).getD fallback

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 bce1d65