Loogle!

Result

Found 25 declarations mentioning Std.DTreeMap.getD.

• Std.DTreeMap.getD 📋 Std.Data.DTreeMap.Basic
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} [Std.LawfulEqCmp cmp] (t : Std.DTreeMap α β cmp) (a : α) (fallback : β a) : β a
• Std.DTreeMap.getD_emptyc 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : ∅.getD a fallback = fallback
• Std.DTreeMap.getD_erase_self 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k : α} {fallback : β k} : (t.erase k).getD k fallback = fallback
• Std.DTreeMap.Const.getD_eq_getD 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.DTreeMap α (fun x => β) cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β} : Std.DTreeMap.Const.getD t a fallback = t.getD a fallback
• Std.DTreeMap.getD_insert_self 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback b : β a} : (t.insert a b).getD a fallback = b
• Std.DTreeMap.getD_of_isEmpty 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : t.isEmpty = true → t.getD a fallback = fallback
• Std.DTreeMap.getD_eq_fallback_of_contains_eq_false 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : t.contains a = false → t.getD a fallback = fallback
• Std.DTreeMap.getD_eq_getD_get? 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : t.getD a fallback = (t.get? a).getD fallback
• Std.DTreeMap.get!_eq_getD_default 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} [Inhabited (β a)] : t.get! a = t.getD a default
• Std.DTreeMap.getD_eq_fallback 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : a ∉ t → t.getD a fallback = fallback
• Std.DTreeMap.get?_eq_some_getD_of_contains 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : t.contains a = true → t.get? a = some (t.getD a fallback)
• Std.DTreeMap.get_eq_getD 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} {h : a ∈ t} : t.get a h = t.getD a fallback
• Std.DTreeMap.get?_eq_some_getD 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : a ∈ t → t.get? a = some (t.getD a fallback)
• Std.DTreeMap.getD_alter_self 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k : α} {fallback : β k} {f : Option (β k) → Option (β k)} : (t.alter k f).getD k fallback = (f (t.get? k)).getD fallback
• Std.DTreeMap.getD_modify_self 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k : α} {fallback : β k} {f : β k → β k} : (t.modify k f).getD k fallback = (Option.map f (t.get? k)).getD fallback
• Std.DTreeMap.getD_erase 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k a : α} {fallback : β a} : (t.erase k).getD a fallback = if cmp k a = Ordering.eq then fallback else t.getD a fallback
• Std.DTreeMap.getD_ofList_of_contains_eq_false 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] [BEq α] [Std.LawfulBEqCmp cmp] {l : List ((a : α) × β a)} {k : α} {fallback : β k} (contains_eq_false : (List.map Sigma.fst l).contains k = false) : (Std.DTreeMap.ofList l cmp).getD k fallback = fallback
• Std.DTreeMap.getD_insert 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k a : α} {fallback : β a} {v : β k} : (t.insert k v).getD a fallback = if h : cmp k a = Ordering.eq then cast ⋯ v else t.getD a fallback
• Std.DTreeMap.getD_insertMany_list_of_contains_eq_false 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] [BEq α] [Std.LawfulBEqCmp cmp] {l : List ((a : α) × β a)} {k : α} {fallback : β k} (contains_eq_false : (List.map Sigma.fst l).contains k = false) : (t.insertMany l).getD k fallback = t.getD k fallback
• Std.DTreeMap.getD_alter 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k k' : α} {fallback : β k'} {f : Option (β k) → Option (β k)} : (t.alter k f).getD k' fallback = if heq : cmp k k' = Ordering.eq then (Option.map (cast ⋯) (f (t.get? k))).getD fallback else t.getD k' fallback
• Std.DTreeMap.getD_modify 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k k' : α} {fallback : β k'} {f : β k → β k} : (t.modify k f).getD k' fallback = if heq : cmp k k' = Ordering.eq then (Option.map (cast ⋯) (Option.map f (t.get? k))).getD fallback else t.getD k' fallback
• Std.DTreeMap.getD_ofList_of_mem 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {l : List ((a : α) × β a)} {k k' : α} (k_eq : cmp k k' = Ordering.eq) {v : β k} {fallback : β k'} (distinct : List.Pairwise (fun a b => ¬cmp a.fst b.fst = Ordering.eq) l) (mem : ⟨k, v⟩ ∈ l) : (Std.DTreeMap.ofList l cmp).getD k' fallback = cast ⋯ v
• Std.DTreeMap.getD_insertIfNew 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {k a : α} {fallback : β a} {v : β k} : (t.insertIfNew k v).getD a fallback = if h : cmp k a = Ordering.eq ∧ k ∉ t then cast ⋯ v else t.getD a fallback
• Std.DTreeMap.getD_insertMany_list_of_mem 📋 Std.Data.DTreeMap.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {l : List ((a : α) × β a)} {k k' : α} (k_eq : cmp k k' = Ordering.eq) {v : β k} {fallback : β k'} (distinct : List.Pairwise (fun a b => ¬cmp a.fst b.fst = Ordering.eq) l) (mem : ⟨k, v⟩ ∈ l) : (t.insertMany l).getD k' fallback = cast ⋯ v
• Std.DTreeMap.Raw.getD_emptyc 📋 Std.Data.DTreeMap.Raw.Lemmas
  {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {a : α} {fallback : β a} : ∅.getD a fallback = 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