Loogle!

Result

Found 37 declarations mentioning Std.TreeMap.Raw.getD.

• Std.TreeMap.Raw.getD 📋 Std.Data.TreeMap.Raw.Basic
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} (t : Std.TreeMap.Raw α β cmp) (a : α) (fallback : β) : β
• Std.TreeMap.Raw.getD_unitOfList 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {cmp : α → α → Ordering} {l : List α} {k : α} {fallback : Unit} : (Std.TreeMap.Raw.unitOfList l cmp).getD k fallback = ()
• Std.TreeMap.Raw.getD_emptyc 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] {a : α} {fallback : β} : ∅.getD a fallback = fallback
• Std.TreeMap.Raw.getD_erase_self 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k : α} {fallback : β} : (t.erase k).getD k fallback = fallback
• Std.TreeMap.Raw.getD_insert_self 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k : α} {fallback v : β} : (t.insert k v).getD k fallback = v
• Std.TreeMap.Raw.getD_of_isEmpty 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : t.isEmpty = true → t.getD a fallback = fallback
• Std.TreeMap.Raw.getD_eq_fallback_of_contains_eq_false 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : t.contains a = false → t.getD a fallback = fallback
• Std.TreeMap.Raw.getD_congr 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a b : α} {fallback : β} (hab : cmp a b = Ordering.eq) : t.getD a fallback = t.getD b fallback
• Std.TreeMap.Raw.getD_eq_fallback 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : a ∉ t → t.getD a fallback = fallback
• Std.TreeMap.Raw.getD_insertManyIfNewUnit_list 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α Unit cmp} {l : List α} {k : α} {fallback : Unit} : (t.insertManyIfNewUnit l).getD k fallback = ()
• Std.TreeMap.Raw.getElem?_eq_some_getD_of_contains 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : t.contains a = true → t.get? a = some (t.getD a fallback)
• Std.TreeMap.Raw.getD_ofList_of_contains_eq_false 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] [BEq α] [Std.LawfulBEqCmp cmp] {l : List (α × β)} {k : α} {fallback : β} (contains_eq_false : (List.map Prod.fst l).contains k = false) : (Std.TreeMap.Raw.ofList l cmp).getD k fallback = fallback
• Std.TreeMap.Raw.Equiv.getD_eq 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {k : α} {fallback : β} (h₁ : t₁.WF) (h₂ : t₂.WF) (h : t₁.Equiv t₂) : t₁.getD k fallback = t₂.getD k fallback
• Std.TreeMap.Raw.getD_erase 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k a : α} {fallback : β} : (t.erase k).getD a fallback = if cmp k a = Ordering.eq then fallback else t.getD a fallback
• Std.TreeMap.Raw.getD_insert 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k a : α} {fallback v : β} : (t.insert k v).getD a fallback = if cmp k a = Ordering.eq then v else t.getD a fallback
• Std.TreeMap.Raw.getD_eq_getD_getElem? 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : t.getD a fallback = t[a]?.getD fallback
• Std.TreeMap.Raw.getElem!_eq_getD_default 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [Inhabited β] (h : t.WF) {a : α} : t[a]! = t.getD a default
• Std.TreeMap.Raw.getD_alter_self 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k : α} {fallback : β} {f : Option β → Option β} : (t.alter k f).getD k fallback = (f t[k]?).getD fallback
• Std.TreeMap.Raw.getD_modify_self 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k : α} {fallback : β} {f : β → β} : (t.modify k f).getD k fallback = (Option.map f t[k]?).getD fallback
• Std.TreeMap.Raw.getElem?_eq_some_getD 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} : a ∈ t → t[a]? = some (t.getD a fallback)
• Std.TreeMap.Raw.getD_filter' 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {f : α → β → Bool} {k : α} {fallback : β} (h : t.WF) : (Std.TreeMap.Raw.filter f t).getD k fallback = (Option.filter (f k) t[k]?).getD fallback
• Std.TreeMap.Raw.getD_ofList_of_mem 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} [Std.TransCmp cmp] {l : List (α × β)} {k k' : α} (k_eq : cmp k k' = Ordering.eq) {v fallback : β} (distinct : List.Pairwise (fun a b => ¬cmp a.1 b.1 = Ordering.eq) l) (mem : (k, v) ∈ l) : (Std.TreeMap.Raw.ofList l cmp).getD k' fallback = v
• Std.TreeMap.Raw.getD_map 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {f : α → β → γ} {k : α} {fallback : γ} (h : t.WF) : (Std.TreeMap.Raw.map f t).getD k fallback = (Option.map (f k) t[k]?).getD fallback
• Std.TreeMap.Raw.getD_filterMap' 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp] {f : α → β → Option γ} {k : α} {fallback : γ} (h : t.WF) : (Std.TreeMap.Raw.filterMap f t).getD k fallback = (t[k]?.bind (f k)).getD fallback
• Std.TreeMap.Raw.getD_filter_of_getKey?_eq_some 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → Bool} {k k' : α} {fallback : β} (h : t.WF) : t.getKey? k = some k' → (Std.TreeMap.Raw.filter f t).getD k fallback = (Option.filter (fun x => f k' x) t[k]?).getD fallback
• Std.TreeMap.Raw.getD_map_of_getKey?_eq_some 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → γ} {k k' : α} {fallback : γ} (h : t.WF) (h' : t.getKey? k = some k') : (Std.TreeMap.Raw.map f t).getD k fallback = (Option.map (f k') t[k]?).getD fallback
• Std.TreeMap.Raw.getD_filterMap_of_getKey?_eq_some 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → Option γ} {k k' : α} {fallback : γ} (h : t.WF) : t.getKey? k = some k' → (Std.TreeMap.Raw.filterMap f t).getD k fallback = (t[k]?.bind fun x => f k' x).getD fallback
• Std.TreeMap.Raw.getD_alter 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k k' : α} {fallback : β} {f : Option β → Option β} : (t.alter k f).getD k' fallback = if cmp k k' = Ordering.eq then (f t[k]?).getD fallback else t.getD k' fallback
• Std.TreeMap.Raw.getD_modify 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k k' : α} {fallback : β} {f : β → β} : (t.modify k f).getD k' fallback = if cmp k k' = Ordering.eq then (Option.map f t[k]?).getD fallback else t.getD k' fallback
• Std.TreeMap.Raw.getElem_eq_getD 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {a : α} {fallback : β} {h' : a ∈ t} : t[a] = t.getD a fallback
• Std.TreeMap.Raw.getD_insertMany_list_of_contains_eq_false 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [BEq α] [Std.LawfulBEqCmp cmp] (h : t.WF) {l : List (α × β)} {k : α} {fallback : β} (contains_eq_false : (List.map Prod.fst l).contains k = false) : (t.insertMany l).getD k fallback = t.getD k fallback
• Std.TreeMap.Raw.getD_insertIfNew 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {k a : α} {fallback v : β} : (t.insertIfNew k v).getD a fallback = if cmp k a = Ordering.eq ∧ k ∉ t then v else t.getD a fallback
• Std.TreeMap.Raw.getD_insertMany_list_of_mem 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] (h : t.WF) {l : List (α × β)} {k k' : α} (k_eq : cmp k k' = Ordering.eq) {v fallback : β} (distinct : List.Pairwise (fun a b => ¬cmp a.1 b.1 = Ordering.eq) l) (mem : (k, v) ∈ l) : (t.insertMany l).getD k' fallback = v
• Std.TreeMap.Raw.getD_insertMany_list 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [BEq α] [Std.LawfulBEqCmp cmp] (h : t.WF) {l : List (α × β)} {k : α} {fallback : β} : (t.insertMany l).getD k fallback = (List.findSomeRev? (fun x => match x with | (a, b) => if cmp a k = Ordering.eq then some b else none) l).getD (t.getD k fallback)
• Std.TreeMap.Raw.getD_map' 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → γ} {k : α} {fallback : γ} (h : t.WF) : (Std.TreeMap.Raw.map f t).getD k fallback = (Option.pmap (fun v h => f (t.getKey k h) v) (t.get? k) ⋯).getD fallback
• Std.TreeMap.Raw.getD_filter 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → Bool} {k : α} {fallback : β} (h : t.WF) : (Std.TreeMap.Raw.filter f t).getD k fallback = (t[k]?.pfilter fun x h' => f (t.getKey k ⋯) x).getD fallback
• Std.TreeMap.Raw.getD_filterMap 📋 Std.Data.TreeMap.Raw.Lemmas
  {α : Type u} {β : Type v} {γ : Type w} {cmp : α → α → Ordering} {t : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] {f : α → β → Option γ} {k : α} {fallback : γ} (h : t.WF) : (Std.TreeMap.Raw.filterMap f t).getD k fallback = (t[k]?.pbind fun x h' => f (t.getKey k ⋯) x).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 187ba29 serving mathlib revision 6c19380