Loogle!

Result

Found 789 declarations whose name contains "sort". Of these, only the first 200 are shown.

• instInhabitedSort 📋 Init.Prelude
  : Inhabited (Sort u)
• coeSortNotation 📋 Init.Coe
  : Lean.ParserDescr
• boolToSort 📋 Init.Coe
  : CoeSort Bool Prop
• CoeSort 📋 Init.Coe
  (α : Sort u) (β : outParam (Sort v)) : Sort (max (max 1 u) v)
• instCoeOutOfCoeSort 📋 Init.Coe
  {α : Sort u_1} {β : Sort u_2} [CoeSort α β] : CoeOut α β
• CoeSort.coe 📋 Init.Coe
  {α : Sort u} {β : outParam (Sort v)} [self : CoeSort α β] : α → β
• CoeSort.mk 📋 Init.Coe
  {α : Sort u} {β : outParam (Sort v)} (coe : α → β) : CoeSort α β
• Nat.Internal.Linear.Poly.denote_sort 📋 Init.Data.Nat.Internal.Linear
  (ctx : Nat.Internal.Linear.Context) (m : Nat.Internal.Linear.Poly) : Nat.Internal.Linear.Poly.denote ctx m.norm = Nat.Internal.Linear.Poly.denote ctx m
• Nat.Internal.SOM.Poly.insertSorted 📋 Init.Data.Nat.Internal.SOM
  (k : ℕ) (m : Nat.Internal.SOM.Mon) (p : Nat.Internal.SOM.Poly) : Nat.Internal.SOM.Poly
• Nat.Internal.SOM.Poly.denote_insertSorted 📋 Init.Data.Nat.Internal.SOM
  (ctx : Nat.Internal.Linear.Context) (k : ℕ) (m : Nat.Internal.SOM.Mon) (p : Nat.Internal.SOM.Poly) : Nat.Internal.SOM.Poly.denote ctx (Nat.Internal.SOM.Poly.insertSorted k m p) = Nat.Internal.SOM.Poly.denote ctx p + k * Nat.Internal.SOM.Mon.denote ctx m
• Lean.Data.AC.sort 📋 Init.Data.AC
  (xs : List ℕ) : List ℕ
• Lean.Data.AC.sort.loop 📋 Init.Data.AC
  : List ℕ → List ℕ → List ℕ
• Lean.Data.AC.Context.sort_loop_nonEmpty 📋 Init.Data.AC
  {ys : List ℕ} (xs : List ℕ) (h : xs ≠ []) : Lean.Data.AC.sort.loop xs ys ≠ []
• Lean.Data.AC.Context.evalList_sort 📋 Init.Data.AC
  {α : Sort u_1} (ctx : Lean.Data.AC.Context α) (h : Lean.Data.AC.ContextInformation.isComm ctx = true) (e : List ℕ) : Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort e) = Lean.Data.AC.evalList α ctx e
• Lean.Data.AC.Context.evalList_sort_cons 📋 Init.Data.AC
  {α : Sort u_1} (ctx : Lean.Data.AC.Context α) (h : Std.Commutative ctx.op) (x : ℕ) (xs : List ℕ) : Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort (x :: xs)) = Lean.Data.AC.evalList α ctx (x :: Lean.Data.AC.sort xs)
• Lean.Data.AC.Context.evalList_sort_loop_swap 📋 Init.Data.AC
  {α : Sort u_1} {y : ℕ} (ctx : Lean.Data.AC.Context α) (h : Std.Commutative ctx.op) (xs ys : List ℕ) : Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort.loop xs (y :: ys)) = Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort.loop (y :: xs) ys)
• Lean.Data.AC.Context.evalList_sort_congr 📋 Init.Data.AC
  {α : Sort u_1} {a b c : List ℕ} (ctx : Lean.Data.AC.Context α) (h : Std.Commutative ctx.op) (h₂ : Lean.Data.AC.evalList α ctx a = Lean.Data.AC.evalList α ctx b) (h₃ : a ≠ []) (h₄ : b ≠ []) : Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort.loop a c) = Lean.Data.AC.evalList α ctx (Lean.Data.AC.sort.loop b c)
• Lean.Grind.CommRing.Poly.isSorted 📋 Init.Grind.Ring.CommSolver
  : Lean.Grind.CommRing.Poly → Bool
• Lean.Grind.AC.Seq.sort 📋 Init.Grind.AC
  (s : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq
• Lean.Grind.AC.Seq.sort_k 📋 Init.Grind.AC
  (s : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq
• Lean.Grind.AC.Seq.sort' 📋 Init.Grind.AC
  (s acc : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq
• Lean.Grind.AC.Seq.sort'_k 📋 Init.Grind.AC
  (s : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq → Lean.Grind.AC.Seq
• Lean.Grind.AC.Seq.sort_k_eq_sort 📋 Init.Grind.AC
  (s : Lean.Grind.AC.Seq) : s.sort_k = s.sort
• Lean.Grind.AC.Seq.sort'_k_eq_sort' 📋 Init.Grind.AC
  (s acc : Lean.Grind.AC.Seq) : s.sort'_k acc = s.sort' acc
• Lean.Grind.AC.Seq.denote_sort 📋 Init.Grind.AC
  {α : Sort u_1} (ctx : Lean.Grind.AC.Context α) {inst₁ : Std.Associative ctx.op} {inst₂ : Std.Commutative ctx.op} (s : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq.denote ctx s.sort = Lean.Grind.AC.Seq.denote ctx s
• Lean.Grind.AC.Seq.denote_sort' 📋 Init.Grind.AC
  {α : Sort u_1} (ctx : Lean.Grind.AC.Context α) {inst₁ : Std.Associative ctx.op} {inst₂ : Std.Commutative ctx.op} (s acc : Lean.Grind.AC.Seq) : Lean.Grind.AC.Seq.denote ctx (s.sort' acc) = ctx.op (Lean.Grind.AC.Seq.denote ctx s) (Lean.Grind.AC.Seq.denote ctx acc)
• List.mergeSort 📋 Init.Data.List.Sort.Basic
  {α : Type u_1} (xs : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α
• List.MergeSort.Internal.splitInTwo 📋 Init.Data.List.Sort.Basic
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : { l // l.length = (n + 1) / 2 } × { l // l.length = n / 2 }
• List.mergeSort_perm 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} (l : List α) (le : α → α → Bool) : (l.mergeSort le).Perm l
• List.mergeSort_nil 📋 Init.Data.List.Sort.Lemmas
  {α✝ : Type u_1} {r : α✝ → α✝ → Bool} : [].mergeSort r = []
• List.length_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (l : List α) : (l.mergeSort le).length = l.length
• List.mergeSort_singleton 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {r : α → α → Bool} (a : α) : [a].mergeSort r = [a]
• List.mergeSort_of_pairwise 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {l : List α} : List.Pairwise (fun a b => le a b = true) l → l.mergeSort le = l
• List.mem_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {a : α} {l : List α} : a ∈ l.mergeSort le ↔ a ∈ l
• List.mergeSort_zipIdx 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {l : List α} : List.map (fun x => x.1) (l.zipIdx.mergeSort (List.zipIdxLE le)) = l.mergeSort le
• List.mergeSort_pair 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (a b : α) : [a, b].mergeSort le = if le a b = true then [a, b] else [b, a]
• List.pairwise_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) (l : List α) : List.Pairwise (fun a b => le a b = true) (l.mergeSort le)
• List.map_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_2} {β : Type u_1} {r : α → α → Bool} {s : β → β → Bool} {f : α → β} {l : List α} (hl : ∀ a ∈ l, ∀ b ∈ l, r a b = s (f a) (f b)) : List.map f (l.mergeSort r) = (List.map f l).mergeSort s
• List.sublist_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {xs : List α} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) {ys : List α} : List.Pairwise (fun a b => le a b = true) ys → ys.Sublist xs → ys.Sublist (xs.mergeSort le)
• List.mergeSort_append 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (l₁ l₂ : List α) (h₁ : l₂.length ≤ l₁.length) (h₂ : l₁.length ≤ l₂.length + 1) : (l₁ ++ l₂).mergeSort le = (l₁.mergeSort le).merge (l₂.mergeSort le) le
• List.pair_sublist_mergeSort 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {a b : α} {l : List α} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) (hab : le a b = true) (h : [a, b].Sublist l) : [a, b].Sublist (l.mergeSort le)
• List.mergeSort_cons 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) (a : α) (l : List α) : ∃ l₁ l₂, (a :: l).mergeSort le = l₁ ++ a :: l₂ ∧ l.mergeSort le = l₁ ++ l₂ ∧ ∀ b ∈ l₁, (!le a b) = true
• List.MergeSort.Internal.splitInTwo_snd_pairwise 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} {le : α → α → Prop} (l : { l // l.length = n }) (h : List.Pairwise le ↑l) : List.Pairwise le ↑(List.MergeSort.Internal.splitInTwo l).2
• List.MergeSort.Internal.splitInTwo_fst_pairwise 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} {le : α → α → Prop} (l : { l // l.length = n }) (h : List.Pairwise le ↑l) : List.Pairwise le ↑(List.MergeSort.Internal.splitInTwo l).1
• List.MergeSort.Internal.splitInTwo_snd 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitInTwo l).2 = ⟨List.drop ((n + 1) / 2) ↑l, ⋯⟩
• List.MergeSort.Internal.splitInTwo_fst 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitInTwo l).1 = ⟨List.take ((n + 1) / 2) ↑l, ⋯⟩
• List.MergeSort.Internal.splitInTwo_fst_append_splitInTwo_snd 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : ↑(List.MergeSort.Internal.splitInTwo l).1 ++ ↑(List.MergeSort.Internal.splitInTwo l).2 = ↑l
• List.MergeSort.Internal.splitInTwo_fst_le_splitInTwo_snd 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {n : ℕ} {le : α → α → Prop} {l : { l // l.length = n }} (h : List.Pairwise le ↑l) (a b : α) : a ∈ ↑(List.MergeSort.Internal.splitInTwo l).1 → b ∈ ↑(List.MergeSort.Internal.splitInTwo l).2 → le a b
• List.MergeSort.Internal.splitInTwo_cons_cons_zipIdx_fst 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {a b : α} (i : ℕ) (l : List α) : ↑(List.MergeSort.Internal.splitInTwo ⟨(a, i) :: (b, i + 1) :: l.zipIdx (i + 2), ⋯⟩).1 = (↑(List.MergeSort.Internal.splitInTwo ⟨a :: b :: l, ⋯⟩).1).zipIdx i
• List.MergeSort.Internal.splitInTwo_cons_cons_zipIdx_snd 📋 Init.Data.List.Sort.Lemmas
  {α : Type u_1} {a b : α} (i : ℕ) (l : List α) : ↑(List.MergeSort.Internal.splitInTwo ⟨(a, i) :: (b, i + 1) :: l.zipIdx (i + 2), ⋯⟩).2 = (↑(List.MergeSort.Internal.splitInTwo ⟨a :: b :: l, ⋯⟩).2).zipIdx (i + (l.length + 3) / 2)
• List.MergeSort.Internal.splitRevAt 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} (n : ℕ) (l : List α) : List α × List α
• List.MergeSort.Internal.mergeSortTR 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α
• List.MergeSort.Internal.mergeSortTR₂ 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α
• List.MergeSort.Internal.mergeTR 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} (l₁ l₂ : List α) (le : α → α → Bool) : List α
• List.MergeSort.Internal.mergeSort_eq_mergeSortTR 📋 Init.Data.List.Sort.Impl
  : @List.mergeSort = @List.MergeSort.Internal.mergeSortTR
• List.MergeSort.Internal.mergeSort_eq_mergeSortTR₂ 📋 Init.Data.List.Sort.Impl
  : @List.mergeSort = @List.MergeSort.Internal.mergeSortTR₂
• List.MergeSort.Internal.merge_eq_mergeTR 📋 Init.Data.List.Sort.Impl
  : @List.merge = @List.MergeSort.Internal.mergeTR
• List.MergeSort.Internal.splitRevAt_eq 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} (i : ℕ) (l : List α) : List.MergeSort.Internal.splitRevAt i l = ((List.take i l).reverse, List.drop i l)
• List.MergeSort.Internal.splitRevInTwo 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : { l // l.length = (n + 1) / 2 } × { l // l.length = n / 2 }
• List.MergeSort.Internal.splitRevInTwo' 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : { l // l.length = n / 2 } × { l // l.length = (n + 1) / 2 }
• List.MergeSort.Internal.splitRevInTwo_snd 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitRevInTwo l).2 = ⟨↑(List.MergeSort.Internal.splitInTwo l).2, ⋯⟩
• List.MergeSort.Internal.splitRevInTwo'_fst 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitRevInTwo' l).1 = ⟨↑(List.MergeSort.Internal.splitInTwo ⟨(↑l).reverse, ⋯⟩).2, ⋯⟩
• List.MergeSort.Internal.splitRevInTwo_fst 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitRevInTwo l).1 = ⟨(↑(List.MergeSort.Internal.splitInTwo l).1).reverse, ⋯⟩
• List.MergeSort.Internal.splitRevInTwo'_snd 📋 Init.Data.List.Sort.Impl
  {α : Type u_1} {n : ℕ} (l : { l // l.length = n }) : (List.MergeSort.Internal.splitRevInTwo' l).2 = ⟨(↑(List.MergeSort.Internal.splitInTwo ⟨(↑l).reverse, ⋯⟩).1).reverse, ⋯⟩
• Array.qsortOrd 📋 Init.Data.Array.QSort.Basic
  {α : Type u_1} [ord : Ord α] (xs : Array α) : Array α
• Array.qsort 📋 Init.Data.Array.QSort.Basic
  {α : Type u_1} (as : Array α) (lt : α → α → Bool := by exact (· < ·)) (lo : ℕ := 0) (hi : ℕ := as.size - 1) : Array α
• Array.insertionSort 📋 Init.Data.Array.InsertionSort
  {α : Type u_1} (xs : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α
• Array.mergeSort 📋 Init.Data.Array.Sort.Basic
  {α : Type u_1} (xs : Array α) (le : α → α → Bool := by exact (· ≤ ·)) : Array α
• Subarray.mergeSort 📋 Init.Data.Array.Sort.Basic
  {α : Type u_1} (xs : Subarray α) (le : α → α → Bool := by exact (· ≤ ·)) : Array α
• Array.mergeSort_perm 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Array α} {le : α → α → Bool} : (xs.mergeSort le).Perm xs
• Array.size_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {xs : Array α} : (xs.mergeSort le).size = xs.size
• Array.mergeSort_empty 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {r : α → α → Bool} : #[].mergeSort r = #[]
• Array.mergeSort_eq_toArray_mergeSort_toList 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Array α} {le : α → α → Bool} : xs.mergeSort le = (xs.toList.mergeSort le).toArray
• Array.toList_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Array α} {le : α → α → Bool} : (xs.mergeSort le).toList = xs.toList.mergeSort le
• Array.mergeSort_singleton 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {r : α → α → Bool} {a : α} : #[a].mergeSort r = #[a]
• Array.mem_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {a : α} {xs : Array α} : a ∈ xs.mergeSort le ↔ a ∈ xs
• Array.mergeSort_of_pairwise 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {xs : Array α} : List.Pairwise (fun x1 x2 => le x1 x2 = true) xs.toList → xs.mergeSort le = xs
• Subarray.mergeSort_eq_mergeSort_toArray 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Subarray α} {le : α → α → Bool} : xs.mergeSort le = (Std.Slice.toArray xs).mergeSort le
• Subarray.mergeSort_toArray 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Subarray α} {le : α → α → Bool} : (Std.Slice.toArray xs).mergeSort le = xs.mergeSort le
• Subarray.toList_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Subarray α} {le : α → α → Bool} : (xs.mergeSort le).toList = (Std.Slice.toList xs).mergeSort le
• Array.pairwise_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) {xs : Array α} : List.Pairwise (fun x1 x2 => le x1 x2 = true) (xs.mergeSort le).toList
• Array.map_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {β : Type u_2} {r : α → α → Bool} {s : β → β → Bool} {f : α → β} {xs : Array α} (hxs : ∀ a ∈ xs, ∀ b ∈ xs, r a b = s (f a) (f b)) : Array.map f (xs.mergeSort r) = (Array.map f xs).mergeSort s
• Array.mergeSort_zipIdx 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {xs : Array α} : Array.map (fun x => x.1) ((Array.map (fun x => match x with | (a, i) => (a, i)) xs.zipIdx).mergeSort (List.zipIdxLE le)) = xs.mergeSort le
• Array.sublist_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {xs : Array α} {le : α → α → Bool} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) {ys : List α} : List.Pairwise (fun x1 x2 => le x1 x2 = true) ys → ys.Sublist xs.toList → ys.Sublist (xs.mergeSort le).toList
• Array.pair_sublist_mergeSort 📋 Init.Data.Array.Sort.Lemmas
  {α : Type u_1} {le : α → α → Bool} {a b : α} {xs : Array α} (trans : ∀ (a b c : α), le a b = true → le b c = true → le a c = true) (total : ∀ (a b : α), (le a b || le b a) = true) (hab : le a b = true) (h : [a, b].Sublist xs.toList) : [a, b].Sublist (xs.mergeSort le).toList
• Lean.mkSort 📋 Lean.Expr
  (u : Lean.Level) : Lean.Expr
• Lean.mkSortEx 📋 Lean.Expr
  : Lean.Level → Lean.Expr
• Lean.Expr.isSort 📋 Lean.Expr
  : Lean.Expr → Bool
• Lean.Expr.sort 📋 Lean.Expr
  (u : Lean.Level) : Lean.Expr
• Lean.Expr.sortLevel! 📋 Lean.Expr
  : Lean.Expr → Lean.Level
• Lean.Expr.updateSort! 📋 Lean.Expr
  (e : Lean.Expr) (newLevel : Lean.Level) : Lean.Expr
• Lean.LocalContext.sortFVarsByContextOrder 📋 Lean.LocalContext
  (lctx : Lean.LocalContext) (hyps : Array Lean.FVarId) : Array Lean.FVarId
• Lean.getErrorExplanationsSorted 📋 Lean.ErrorExplanation
  {m : Type → Type} [Monad m] [Lean.MonadEnv m] : m (Array (Lean.Name × Lean.ErrorExplanation))
• Lean.Meta.sortFVarIds 📋 Lean.Meta.Basic
  (fvarIds : Array Lean.FVarId) : Lean.MetaM (Array Lean.FVarId)
• Lean.Meta.CoeFnType.coeSort 📋 Lean.Meta.CoeAttr
  : Lean.Meta.CoeFnType
• Lean.Parser.Term.sort 📋 Lean.Parser.Term
  : Lean.Parser.Parser
• Lean.PrettyPrinter.Delaborator.delabSort 📋 Lean.PrettyPrinter.Delaborator.Builtins
  : Lean.PrettyPrinter.Delaborator.Delab
• _private.Lean.Meta.Closure.0.Lean.Meta.Closure.TopoSort.doneMark 📋 Lean.Meta.Closure
  (self : Lean.Meta.Closure.TopoSort✝) : Lean.FVarIdHashSet
• _private.Lean.Meta.Closure.0.Lean.Meta.Closure.TopoSort.tempMark 📋 Lean.Meta.Closure
  (self : Lean.Meta.Closure.TopoSort✝) : Lean.FVarIdHashSet
• _private.Lean.Meta.Closure.0.Lean.Meta.Closure.TopoSort.newArgs 📋 Lean.Meta.Closure
  (self : Lean.Meta.Closure.TopoSort✝) : Array Lean.Expr
• _private.Lean.Meta.Closure.0.Lean.Meta.Closure.TopoSort.newDecls 📋 Lean.Meta.Closure
  (self : Lean.Meta.Closure.TopoSort✝) : Array Lean.LocalDecl
• Lean.sortExprs 📋 Lean.Util.SortExprs
  (es : Array Lean.Expr) (lt : Bool := true) : Array Lean.Expr × Lean.Perm
• Lean.HeadIndex.sort 📋 Lean.HeadIndex
  : Lean.HeadIndex
• Lean.Meta.coerceToSort? 📋 Lean.Meta.Coe
  (expr : Lean.Expr) : Lean.MetaM (Option Lean.Expr)
• Lean.Elab.Term.ToDepElimPattern.TopSort.State 📋 Lean.Elab.Match
  : Type
• Lean.Elab.Term.ToDepElimPattern.TopSortM 📋 Lean.Elab.Match
  (α : Type) : Type
• Lean.Elab.Term.ToDepElimPattern.TopSort.State.visitedFVars 📋 Lean.Elab.Match
  (self : Lean.Elab.Term.ToDepElimPattern.TopSort.State) : Lean.FVarIdSet
• Lean.Elab.Term.ToDepElimPattern.TopSort.State.visitedMVars 📋 Lean.Elab.Match
  (self : Lean.Elab.Term.ToDepElimPattern.TopSort.State) : Lean.MVarIdSet
• Lean.Elab.Term.ToDepElimPattern.TopSort.State.result 📋 Lean.Elab.Match
  (self : Lean.Elab.Term.ToDepElimPattern.TopSort.State) : Array Lean.Expr
• Lean.Elab.Term.ToDepElimPattern.TopSort.State.mk 📋 Lean.Elab.Match
  (visitedFVars : Lean.FVarIdSet) (visitedMVars : Lean.MVarIdSet) (result : Array Lean.Expr) : Lean.Elab.Term.ToDepElimPattern.TopSort.State
• Lean.Elab.Tactic.sortMVarIdArrayByIndex 📋 Lean.Elab.Tactic.ElabTerm
  {m : Type → Type} [Lean.MonadMCtx m] [Monad m] (mvarIds : Array Lean.MVarId) : m (Array Lean.MVarId)
• Lean.Elab.Tactic.sortMVarIdsByIndex 📋 Lean.Elab.Tactic.ElabTerm
  {m : Type → Type} [Lean.MonadMCtx m] [Monad m] (mvarIds : Array Lean.MVarId) : m (Array Lean.MVarId)
• Lean.Lsp.CompletionItem.sortText? 📋 Lean.Data.Lsp.LanguageFeatures
  (self : Lean.Lsp.CompletionItem) : Option String
• Lean.Lsp.ResolvableCompletionItem.sortText? 📋 Lean.Data.Lsp.LanguageFeatures
  (self : Lean.Lsp.ResolvableCompletionItem) : Option String
• Lean.Elab.Term.elabSort 📋 Lean.Elab.BuiltinTerm
  : Lean.Elab.Term.TermElab
• Lean.Elab.Term.elabCoeSortNotation 📋 Lean.Elab.BuiltinNotation
  : Lean.Elab.Term.TermElab
• Array.dedupSorted 📋 Batteries.Data.Array.Merge
  {α : Type u_1} [eq : BEq α] (xs : Array α) : Array α
• Array.sortDedup 📋 Batteries.Data.Array.Merge
  {α : Type u_1} [ord : Ord α] (xs : Array α) : Array α
• Array.mergeUnsortedDedup 📋 Batteries.Data.Array.Merge
  {α : Type u_1} [eq : BEq α] (xs ys : Array α) : Array α
• Array.mergeUnsortedDedup.go 📋 Batteries.Data.Array.Merge
  {α : Type u_1} [eq : BEq α] (xs ys : Array α) : Array α
• Array.heapSort 📋 Batteries.Data.BinaryHeap.Basic
  {α : Type u_1} (a : Array α) (lt : α → α → Bool) : Array α
• Batteries.Tactic.Lint.sortResults 📋 Batteries.Tactic.Lint.Frontend
  {α : Type} (results : Std.HashMap Lean.Name α) : Lean.CoreM (Array (Lean.Name × α))
• RBTree.RBSet.toList_sorted 📋 Batteries.Recycling.RBTree.Lemmas
  {α : Type u_1} {cmp : α → α → Ordering} {t : RBTree.RBSet α cmp} : List.Pairwise (RBTree.RBNode.cmpLT cmp) t.toList
• RBTree.RBNode.Ordered.toList_sorted 📋 Batteries.Recycling.RBTree.Lemmas
  {α : Type u_1} {cmp : α → α → Ordering} {t : RBTree.RBNode α} : RBTree.RBNode.Ordered cmp t → List.Pairwise (RBTree.RBNode.cmpLT cmp) t.toList
• RBTree.RBMap.toList_sorted 📋 Batteries.Recycling.RBTree.Lemmas
  {α : Type u_1} {β : Type u_2} {cmp : α → α → Ordering} {t : RBTree.RBMap α β cmp} : List.Pairwise (RBTree.RBNode.cmpLT fun x1 x2 => cmp x1.1 x2.1) t.toList
• Lean.Meta.sortFVarsByContextOrder 📋 Batteries.Lean.Meta.Basic
  {m : Type → Type} [Monad m] [Lean.MonadLCtx m] (hyps : Array Lean.FVarId) : m (Array Lean.FVarId)
• Lean.Elab.Command.getSortedAssertExists 📋 Lean.Elab.AssertExists
  (env : Lean.Environment) : Array Lean.Elab.Command.AssertExists
• Lean.Elab.sortDeclLevelParams 📋 Lean.Elab.DeclUtil
  (scopeParams allUserParams : List Lean.Name) (usedParams : Array Lean.Name) : Except String (List Lean.Name)
• Lean.Elab.Term.«termSort*» 📋 Mathlib.Tactic.TypeStar
  : Lean.ParserDescr
• Aesop.UnorderedArraySet.ofSortedArray 📋 Aesop.Util.UnorderedArraySet
  {α : Type u_1} [BEq α] (xs : Array α) : Aesop.UnorderedArraySet α
• Aesop.sortRuleStatsTotals 📋 Aesop.Stats.Basic
  (ts : Array (Aesop.DisplayRuleName × Aesop.RuleStatsTotals)) : Array (Aesop.DisplayRuleName × Aesop.RuleStatsTotals)
• Aesop.Script.sortDedupArrays 📋 Aesop.Script.UScriptToSScript
  {α : Type u_1} [Ord α] (as : Array (Array α)) : Array α
• Aesop.sortedMedianD 📋 Aesop.Stats.Report
  {α : Type u_1} (dflt : α) (xs : Array α) : α
• Aesop.sortedPercentileD 📋 Aesop.Stats.Report
  {α : Type u_1} (p : Aesop.Percent) (dflt : α) (xs : Array α) : α
• LinOrd.instCoeSortType 📋 Mathlib.Order.Defs.LinearOrder
  : CoeSort LinOrd (Type u_2)
• Qq.SortLocalDecls.Context 📋 Qq.SortLocalDecls
  : Type
• Qq.SortLocalDecls.State 📋 Qq.SortLocalDecls
  : Type
• Qq.SortLocalDecls.M 📋 Qq.SortLocalDecls
  (α : Type) : Type
• Qq.SortLocalDecls.State.visited 📋 Qq.SortLocalDecls
  (self : Qq.SortLocalDecls.State) : Lean.NameSet
• Qq.SortLocalDecls.visitExpr 📋 Qq.SortLocalDecls
  (e : Lean.Expr) : Qq.SortLocalDecls.M Unit
• Qq.SortLocalDecls.visitLocalDecl 📋 Qq.SortLocalDecls
  (localDecl : Lean.LocalDecl) : Qq.SortLocalDecls.M Unit
• Qq.SortLocalDecls.Context.localDecls 📋 Qq.SortLocalDecls
  (self : Qq.SortLocalDecls.Context) : Lean.NameMap Lean.LocalDecl
• Qq.SortLocalDecls.Context.mk 📋 Qq.SortLocalDecls
  (localDecls : Lean.NameMap Lean.LocalDecl) : Qq.SortLocalDecls.Context
• Qq.SortLocalDecls.State.result 📋 Qq.SortLocalDecls
  (self : Qq.SortLocalDecls.State) : Array Lean.LocalDecl
• Qq.SortLocalDecls.State.mk 📋 Qq.SortLocalDecls
  (visited : Lean.NameSet) (result : Array Lean.LocalDecl) : Qq.SortLocalDecls.State
• Qq.sortLocalDecls 📋 Qq.SortLocalDecls
  (localDecls : Array Lean.LocalDecl) : Lean.MetaM (Array Lean.LocalDecl)
• Bool.coe_sort_false 📋 Mathlib.Data.Bool.Basic
  : (false = true) = False
• Bool.coe_sort_true 📋 Mathlib.Data.Bool.Basic
  : (true = true) = True
• Set.instCoeSortType 📋 Mathlib.Data.Set.CoeSort
  {α : Type u} : CoeSort (Set α) (Type u)
• Set.Nonempty.coe_sort 📋 Mathlib.Data.Set.Basic
  {α : Type u} {s : Set α} : s.Nonempty → Nonempty ↑s
• Set.nonempty_coe_sort 📋 Mathlib.Data.Set.Basic
  {α : Type u} {s : Set α} : Nonempty ↑s ↔ s.Nonempty
• Set.isEmpty_coe_sort 📋 Mathlib.Data.Set.Basic
  {α : Type u} {s : Set α} : IsEmpty ↑s ↔ s = ∅
• Set.Nontrivial.coe_sort 📋 Mathlib.Data.Set.Subsingleton
  {α : Type u} {s : Set α} : s.Nontrivial → Nontrivial ↑s
• Set.Subsingleton.coe_sort 📋 Mathlib.Data.Set.Subsingleton
  {α : Type u} {s : Set α} : s.Subsingleton → Subsingleton ↑s
• Set.nontrivial_coe_sort 📋 Mathlib.Data.Set.Subsingleton
  {α : Type u} {s : Set α} : Nontrivial ↑s ↔ s.Nontrivial
• Lean.Meta.ensureIsSort 📋 Mathlib.Lean.Meta.Basic
  (e : Lean.Expr) : Lean.MetaM Lean.Expr
• Lean.Meta.RefinedDiscrTree.Key.sort 📋 Mathlib.Lean.Meta.RefinedDiscrTree.Basic
  : Lean.Meta.RefinedDiscrTree.Key
• Lean.Meta.Sym.Internal.mkSortS 📋 Lean.Meta.Sym.AlphaShareBuilder
  {m : Type → Type} [Lean.Meta.Sym.Internal.MonadShareCommon m] (u : Lean.Level) : m Lean.Expr
• Int.Internal.Linear.Poly.isSorted 📋 Lean.Meta.Tactic.Grind.Arith.Cutsat.Util
  (p : Int.Internal.Linear.Poly) : Bool
• Lean.Meta.Grind.TopSort.State 📋 Lean.Meta.Tactic.Grind.EqResolution
  : Type
• Lean.Meta.Grind.TopSortM 📋 Lean.Meta.Tactic.Grind.EqResolution
  (α : Type) : Type
• Lean.Meta.Grind.TopSort.State.result 📋 Lean.Meta.Tactic.Grind.EqResolution
  (self : Lean.Meta.Grind.TopSort.State) : Array Lean.Expr
• Lean.Meta.Grind.TopSort.State.permMark 📋 Lean.Meta.Tactic.Grind.EqResolution
  (self : Lean.Meta.Grind.TopSort.State) : Std.HashSet Lean.Expr
• Lean.Meta.Grind.TopSort.State.tempMark 📋 Lean.Meta.Tactic.Grind.EqResolution
  (self : Lean.Meta.Grind.TopSort.State) : Std.HashSet Lean.Expr
• Lean.Meta.Grind.TopSort.State.mk 📋 Lean.Meta.Tactic.Grind.EqResolution
  (tempMark permMark : Std.HashSet Lean.Expr) (result : Array Lean.Expr) : Lean.Meta.Grind.TopSort.State
• Lean.Grind.AC.Seq.isSorted 📋 Lean.Meta.Tactic.Grind.AC.Seq
  (s : Lean.Grind.AC.Seq) : Bool
• Mathlib.Tactic.LibraryRewrite.checkAndSortRewriteLemmas 📋 Mathlib.Tactic.Widget.LibraryRewrite
  (e : Lean.Expr) (rewrites : Array Mathlib.Tactic.LibraryRewrite.RewriteLemma) : Lean.MetaM (Array (Mathlib.Tactic.LibraryRewrite.Rewrite × Lean.Name))
• Mathlib.Tactic.Linarith.GlobalPreprocessorToGlobalBranchingPreprocessor 📋 Mathlib.Tactic.Linarith.Datatypes
  : Coe Mathlib.Tactic.Linarith.GlobalPreprocessor Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor
• Mathlib.Tactic.Linarith.PreprocessorToGlobalBranchingPreprocessor 📋 Mathlib.Tactic.Linarith.Datatypes
  : Coe Mathlib.Tactic.Linarith.Preprocessor Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor
• SetLike.instCoeSortType 📋 Mathlib.Data.SetLike.Basic
  {A : Type u_1} {B : Type u_2} [i : SetLike A B] : CoeSort A (Type u_2)
• SetLike.coe_sort_coe 📋 Mathlib.Data.SetLike.Basic
  {A : Type u_1} {B : Type u_2} [i : SetLike A B] (p : A) : ↑↑p = ↥p
• Finset.coe_sort_coe 📋 Mathlib.Data.Finset.Defs
  {α : Type u_1} (s : Finset α) : ↑↑s = ↥s
• List.Nodup.mergeSort 📋 Mathlib.Data.List.Nodup
  {α : Type u} {l : List α} {le : α → α → Bool} : l.Nodup → (l.mergeSort le).Nodup
• List.nodup_mergeSort 📋 Mathlib.Data.List.Nodup
  {α : Type u} {l : List α} {le : α → α → Bool} : (l.mergeSort le).Nodup ↔ l.Nodup
• Finset.Nonempty.coe_sort 📋 Mathlib.Data.Finset.Empty
  {α : Type u_1} {s : Finset α} : s.Nonempty → Nonempty ↥s
• Finset.nonempty_coe_sort 📋 Mathlib.Data.Finset.Empty
  {α : Type u_1} {s : Finset α} : Nonempty ↥s ↔ s.Nonempty
• Finset.isEmpty_coe_sort 📋 Mathlib.Data.Finset.Empty
  {α : Type u_1} {s : Finset α} : IsEmpty ↥s ↔ s = ∅
• Finset.fintypeCoeSort 📋 Mathlib.Data.Fintype.Sets
  {α : Type u} (s : Finset α) : Fintype ↥s
• List.SortedGE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] (l : List α) : Prop
• List.SortedGT 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] (l : List α) : Prop
• List.SortedLE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] (l : List α) : Prop
• List.SortedLT 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] (l : List α) : Prop
• List.sortedLT_range 📋 Mathlib.Data.List.Sort
  (n : ℕ) : (List.range n).SortedLT
• List.sortedGE_nil 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] : [].SortedGE
• List.sortedGT_nil 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] : [].SortedGT
• List.sortedLE_nil 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] : [].SortedLE
• List.sortedLT_nil 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] : [].SortedLT
• List.sortedLE_range' 📋 Mathlib.Data.List.Sort
  (a b s : ℕ) : (List.range' a b s).SortedLE
• List.sortedLT_finRange 📋 Mathlib.Data.List.Sort
  (n : ℕ) : (List.finRange n).SortedLT
• List.insertionSort 📋 Mathlib.Data.List.Sort
  {α : Type u_1} (r : α → α → Prop) [DecidableRel r] : List α → List α
• List.sortedLE_replicate 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] {a : α} (n : ℕ) : (List.replicate n a).SortedLE
• List.SortedGT.nodup 📋 Mathlib.Data.List.Sort
  {α : Type u_1} {l : List α} [Preorder α] (h : l.SortedGT) : l.Nodup
• List.SortedLT.nodup 📋 Mathlib.Data.List.Sort
  {α : Type u_1} {l : List α} [Preorder α] (h : l.SortedLT) : l.Nodup
• List.SortedGT.sortedGE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] {l : List α} (h : l.SortedGT) : l.SortedGE
• List.SortedLT.sortedLE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] {l : List α} (h : l.SortedLT) : l.SortedLE
• List.decidableSortedGE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] [DecidableLE α] : DecidablePred List.SortedGE
• List.decidableSortedGT 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] [DecidableLT α] : DecidablePred List.SortedGT
• List.decidableSortedLE 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] [DecidableLE α] : DecidablePred List.SortedLE
• List.decidableSortedLT 📋 Mathlib.Data.List.Sort
  {α : Type u_1} [Preorder α] [DecidableLT α] : DecidablePred List.SortedLT
• List.SortedGE.of_reverse 📋 Mathlib.Data.List.Sort
  {α : Type u_1} {l : List α} [Preorder α] : l.reverse.SortedGE → l.SortedLE

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using the Loogle command from the command palette. 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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 9f11169 serving mathlib revision 4f617dc