The type DHashMap.Raw itself is defined in the module Std.Data.DHashmap.RawDef for import structure reasons.

@[inline]

def Std.DHashMap.Raw.empty {α : Type u} {β : α → Type v} (capacity : optParam Nat 8) : Std.DHashMap.Raw α β

Creates a new empty hash map. The optional parameter capacity can be supplied to presize the map so that it can hold the given number of mappings without reallocating. It is also possible to use the empty collection notations ∅ and {} to create an empty hash map with the default capacity.

Equations

• Std.DHashMap.Raw.empty capacity = (Std.DHashMap.Internal.Raw₀.empty capacity).val

instance Std.DHashMap.Raw.instEmptyCollection {α : Type u} {β : α → Type v} : EmptyCollection (Std.DHashMap.Raw α β)

Equations

• Std.DHashMap.Raw.instEmptyCollection = { emptyCollection := Std.DHashMap.Raw.empty }

instance Std.DHashMap.Raw.instInhabited {α : Type u} {β : α → Type v} : Inhabited (Std.DHashMap.Raw α β)

Equations

• Std.DHashMap.Raw.instInhabited = { default := ∅ }

@[inline]

def Std.DHashMap.Raw.insert {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) (b : β a) : Std.DHashMap.Raw α β

Inserts the given mapping into the map, replacing an existing mapping for the key if there is one.

Equations

• m.insert a b = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.insert ⟨m, h⟩ a b).val else m

@[inline]

def Std.DHashMap.Raw.insertIfNew {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) (b : β a) : Std.DHashMap.Raw α β

If there is no mapping for the given key, inserts the given mapping into the map. Otherwise, returns the map unaltered.

Equations

• m.insertIfNew a b = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.insertIfNew ⟨m, h⟩ a b).val else m

@[inline]

def Std.DHashMap.Raw.containsThenInsert {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) (b : β a) : Bool × Std.DHashMap.Raw α β

Checks whether a key is present in a map, and unconditionally inserts a value for the key.

Equivalent to (but potentially faster than) calling contains followed by insert.

Equations

• m.containsThenInsert a b = if h : 0 < m.buckets.size then match Std.DHashMap.Internal.Raw₀.containsThenInsert ⟨m, h⟩ a b with | (replaced, ⟨r, property⟩) => (replaced, r) else (false, m)

@[inline]

def Std.DHashMap.Raw.getThenInsertIfNew? {α : Type u} {β : α → Type v} [BEq α] [Hashable α] [LawfulBEq α] (m : Std.DHashMap.Raw α β) (a : α) (b : β a) : Option (β a) × Std.DHashMap.Raw α β

Checks whether a key is present in a map, returning the associated value, and inserts a value for the key if it was not found.

If the returned value is some v, then the returned map is unaltered. If it is none, then the returned map has a new value inserted.

Equivalent to (but potentially faster than) calling get? followed by insertIfNew.

Uses the LawfulBEq instance to cast the retrieved value to the correct type.

Equations

• m.getThenInsertIfNew? a b = if h : 0 < m.buckets.size then match Std.DHashMap.Internal.Raw₀.getThenInsertIfNew? ⟨m, h⟩ a b with | (previous, ⟨r, property⟩) => (previous, r) else (none, m)

@[inline]

def Std.DHashMap.Raw.containsThenInsertIfNew {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) (b : β a) : Bool × Std.DHashMap.Raw α β

Checks whether a key is present in a map and inserts a value for the key if it was not found.

If the returned Bool is true, then the returned map is unaltered. If the Bool is false, then the returned map has a new value inserted.

Equivalent to (but potentially faster than) calling contains followed by insertIfNew.

Equations

• One or more equations did not get rendered due to their size.

@[inline]

def Std.DHashMap.Raw.get? {α : Type u} {β : α → Type v} [BEq α] [LawfulBEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) : Option (β a)

Tries to retrieve the mapping for the given key, returning none if no such mapping is present.

Uses the LawfulBEq instance to cast the retrieved value to the correct type.

Equations

• m.get? a = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.get? ⟨m, h⟩ a else none

@[inline]

def Std.DHashMap.Raw.contains {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) : Bool

Returns true if there is a mapping for the given key. There is also a Prop-valued version of this: a ∈ m is equivalent to m.contains a = true.

Observe that this is different behavior than for lists: for lists, ∈ uses = and contains uses == for comparisons, while for hash maps, both use ==.

Equations

• m.contains a = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.contains ⟨m, h⟩ a else false

instance Std.DHashMap.Raw.instMembershipOfBEqOfHashable {α : Type u} {β : α → Type v} [BEq α] [Hashable α] : Membership α (Std.DHashMap.Raw α β)

Equations

• Std.DHashMap.Raw.instMembershipOfBEqOfHashable = { mem := fun (m : Std.DHashMap.Raw α β) (a : α) => m.contains a = true }

instance Std.DHashMap.Raw.instDecidableMem {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} : Decidable (a ∈ m)

Equations

• Std.DHashMap.Raw.instDecidableMem = inferInstanceAs (Decidable (m.contains a = true))

@[inline]

def Std.DHashMap.Raw.get {α : Type u} {β : α → Type v} [BEq α] [Hashable α] [LawfulBEq α] (m : Std.DHashMap.Raw α β) (a : α) (h : a ∈ m) : β a

Retrieves the mapping for the given key. Ensures that such a mapping exists by requiring a proof of a ∈ m.

Uses the LawfulBEq instance to cast the retrieved value to the correct type.

Equations

• m.get a h = Std.DHashMap.Internal.Raw₀.get ⟨m, ⋯⟩ a ⋯

@[inline]

def Std.DHashMap.Raw.getD {α : Type u} {β : α → Type v} [BEq α] [Hashable α] [LawfulBEq α] (m : Std.DHashMap.Raw α β) (a : α) (fallback : β a) : β a

Tries to retrieve the mapping for the given key, returning fallback if no such mapping is present.

Uses the LawfulBEq instance to cast the retrieved value to the correct type.

Equations

• m.getD a fallback = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.getD ⟨m, h⟩ a fallback else fallback

@[inline]

def Std.DHashMap.Raw.get! {α : Type u} {β : α → Type v} [BEq α] [Hashable α] [LawfulBEq α] (m : Std.DHashMap.Raw α β) (a : α) [Inhabited (β a)] : β a

Tries to retrieve the mapping for the given key, panicking if no such mapping is present.

Uses the LawfulBEq instance to cast the retrieved value to the correct type.

Equations

• m.get! a = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.get! ⟨m, h⟩ a else default

@[inline]

def Std.DHashMap.Raw.erase {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) (a : α) : Std.DHashMap.Raw α β

Removes the mapping for the given key if it exists.

Equations

• m.erase a = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.erase ⟨m, h⟩ a).val else m

@[inline]

def Std.DHashMap.Raw.Const.get? {α : Type u} {β : Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α fun (x : α) => β) (a : α) : Option β

Tries to retrieve the mapping for the given key, returning none if no such mapping is present.

Equations

• Std.DHashMap.Raw.Const.get? m a = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.Const.get? ⟨m, h⟩ a else none

@[inline]

def Std.DHashMap.Raw.Const.get {α : Type u} {β : Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α fun (x : α) => β) (a : α) (h : a ∈ m) : β

Retrieves the mapping for the given key. Ensures that such a mapping exists by requiring a proof of a ∈ m.

Equations

• Std.DHashMap.Raw.Const.get m a h = Std.DHashMap.Internal.Raw₀.Const.get ⟨m, ⋯⟩ a ⋯

@[inline]

def Std.DHashMap.Raw.Const.getD {α : Type u} {β : Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α fun (x : α) => β) (a : α) (fallback : β) : β

Tries to retrieve the mapping for the given key, returning fallback if no such mapping is present.

Equations

• Std.DHashMap.Raw.Const.getD m a fallback = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.Const.getD ⟨m, h⟩ a fallback else fallback

@[inline]

def Std.DHashMap.Raw.Const.get! {α : Type u} {β : Type v} [BEq α] [Hashable α] [Inhabited β] (m : Std.DHashMap.Raw α fun (x : α) => β) (a : α) : β

Tries to retrieve the mapping for the given key, panicking if no such mapping is present.

Equations

• Std.DHashMap.Raw.Const.get! m a = if h : 0 < m.buckets.size then Std.DHashMap.Internal.Raw₀.Const.get! ⟨m, h⟩ a else default

@[inline]

def Std.DHashMap.Raw.Const.getThenInsertIfNew? {α : Type u} {β : Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α fun (x : α) => β) (a : α) (b : β) : Option β × Std.DHashMap.Raw α fun (x : α) => β

Equivalent to (but potentially faster than) calling Const.get? followed by insertIfNew.

Checks whether a key is present in a map, returning the associated value, and inserts a value for the key if it was not found.

If the returned value is some v, then the returned map is unaltered. If it is none, then the returned map has a new value inserted.

Equations

• One or more equations did not get rendered due to their size.

@[inline]

def Std.DHashMap.Raw.isEmpty {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : Bool

Returns true if the hash map contains no mappings.

Note that if your BEq instance is not reflexive or your Hashable instance is not lawful, then it is possible that this function returns false even though is not possible to get anything out of the hash map.

Equations

• m.isEmpty = (m.size == 0)

We currently do not provide lemmas for the functions below.

@[inline]

def Std.DHashMap.Raw.filterMap {α : Type u} {β : α → Type v} {γ : α → Type w} (f : (a : α) → β a → Option (γ a)) (m : Std.DHashMap.Raw α β) : Std.DHashMap.Raw α γ

Updates the values of the hash map by applying the given function to all mappings, keeping only those mappings where the function returns some value.

Equations

• Std.DHashMap.Raw.filterMap f m = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.filterMap f ⟨m, h⟩).val else ∅

@[inline]

def Std.DHashMap.Raw.map {α : Type u} {β : α → Type v} {γ : α → Type w} (f : (a : α) → β a → γ a) (m : Std.DHashMap.Raw α β) : Std.DHashMap.Raw α γ

Updates the values of the hash map by applying the given function to all mappings.

Equations

• Std.DHashMap.Raw.map f m = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.map f ⟨m, h⟩).val else ∅

@[inline]

def Std.DHashMap.Raw.filter {α : Type u} {β : α → Type v} (f : (a : α) → β a → Bool) (m : Std.DHashMap.Raw α β) : Std.DHashMap.Raw α β

Removes all mappings of the hash map for which the given function returns false.

Equations

• Std.DHashMap.Raw.filter f m = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.filter f ⟨m, h⟩).val else ∅

@[inline]

def Std.DHashMap.Raw.foldM {α : Type u} {β : α → Type v} {δ : Type w} {m : Type w → Type w} [Monad m] (f : δ → (a : α) → β a → m δ) (init : δ) (b : Std.DHashMap.Raw α β) : m δ

Monadically computes a value by folding the given function over the mappings in the hash map in some order.

Equations

• Std.DHashMap.Raw.foldM f init b = Array.foldlM (fun (acc : δ) (l : Std.DHashMap.Internal.AssocList α β) => Std.DHashMap.Internal.AssocList.foldlM f acc l) init b.buckets

@[inline]

def Std.DHashMap.Raw.fold {α : Type u} {β : α → Type v} {δ : Type w} (f : δ → (a : α) → β a → δ) (init : δ) (b : Std.DHashMap.Raw α β) : δ

Folds the given function over the mappings in the hash map in some order.

Equations

• Std.DHashMap.Raw.fold f init b = (Std.DHashMap.Raw.foldM f init b).run

@[inline]

def Std.DHashMap.Raw.forM {α : Type u} {β : α → Type v} {m : Type w → Type w} [Monad m] (f : (a : α) → β a → m PUnit) (b : Std.DHashMap.Raw α β) : m PUnit

Carries out a monadic action on each mapping in the hash map in some order.

Equations

• Std.DHashMap.Raw.forM f b = Array.forM (Std.DHashMap.Internal.AssocList.forM f) b.buckets

@[inline]

def Std.DHashMap.Raw.forIn {α : Type u} {β : α → Type v} {δ : Type w} {m : Type w → Type w} [Monad m] (f : (a : α) → β a → δ → m (ForInStep δ)) (init : δ) (b : Std.DHashMap.Raw α β) : m δ

Support for the for loop construct in do blocks.

Equations

• Std.DHashMap.Raw.forIn f init b = b.buckets.forIn init fun (bucket : Std.DHashMap.Internal.AssocList α β) (acc : δ) => bucket.forInStep acc f

instance Std.DHashMap.Raw.instForMSigma {α : Type u} {β : α → Type v} {m : Type w → Type w} : ForM m (Std.DHashMap.Raw α β) ((a : α) × β a)

Equations

• Std.DHashMap.Raw.instForMSigma = { forM := fun [Monad m] (m_1 : Std.DHashMap.Raw α β) (f : (a : α) × β a → m PUnit) => Std.DHashMap.Raw.forM (fun (a : α) (b : β a) => f ⟨a, b⟩) m_1 }

instance Std.DHashMap.Raw.instForInSigma {α : Type u} {β : α → Type v} {m : Type w → Type w} : ForIn m (Std.DHashMap.Raw α β) ((a : α) × β a)

Equations

• One or more equations did not get rendered due to their size.

@[inline]

def Std.DHashMap.Raw.toList {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : List ((a : α) × β a)

Transforms the hash map into a list of mappings in some order.

Equations

• m.toList = Std.DHashMap.Raw.fold (fun (acc : List ((a : α) × β a)) (k : α) (v : β k) => ⟨k, v⟩ :: acc) [] m

@[inline]

def Std.DHashMap.Raw.toArray {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : Array ((a : α) × β a)

Transforms the hash map into an array of mappings in some order.

Equations

• m.toArray = Std.DHashMap.Raw.fold (fun (acc : Array ((a : α) × β a)) (k : α) (v : β k) => acc.push ⟨k, v⟩) #[] m

@[inline]

def Std.DHashMap.Raw.Const.toList {α : Type u} {β : Type v} (m : Std.DHashMap.Raw α fun (x : α) => β) : List (α × β)

Transforms the hash map into a list of mappings in some order.

Equations

• Std.DHashMap.Raw.Const.toList m = Std.DHashMap.Raw.fold (fun (acc : List (α × β)) (k : α) (v : β) => (k, v) :: acc) [] m

@[inline]

def Std.DHashMap.Raw.Const.toArray {α : Type u} {β : Type v} (m : Std.DHashMap.Raw α fun (x : α) => β) : Array (α × β)

Transforms the hash map into an array of mappings in some order.

Equations

• Std.DHashMap.Raw.Const.toArray m = Std.DHashMap.Raw.fold (fun (acc : Array (α × β)) (k : α) (v : β) => acc.push (k, v)) #[] m

@[inline]

def Std.DHashMap.Raw.keys {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : List α

Returns a list of all keys present in the hash map in some order.

Equations

• m.keys = Std.DHashMap.Raw.fold (fun (acc : List α) (k : α) (x : β k) => k :: acc) [] m

@[inline]

def Std.DHashMap.Raw.keysArray {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : Array α

Returns an array of all keys present in the hash map in some order.

Equations

• m.keysArray = Std.DHashMap.Raw.fold (fun (acc : Array α) (k : α) (x : β k) => acc.push k) #[] m

@[inline]

def Std.DHashMap.Raw.values {α : Type u} {β : Type v} (m : Std.DHashMap.Raw α fun (x : α) => β) : List β

Returns a list of all values present in the hash map in some order.

Equations

• m.values = Std.DHashMap.Raw.fold (fun (acc : List β) (x : α) (v : β) => v :: acc) [] m

@[inline]

def Std.DHashMap.Raw.valuesArray {α : Type u} {β : Type v} (m : Std.DHashMap.Raw α fun (x : α) => β) : Array β

Returns an array of all values present in the hash map in some order.

Equations

• m.valuesArray = Std.DHashMap.Raw.fold (fun (acc : Array β) (x : α) (v : β) => acc.push v) #[] m

@[inline]

def Std.DHashMap.Raw.insertMany {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ ((a : α) × β a)] (m : Std.DHashMap.Raw α β) (l : ρ) : Std.DHashMap.Raw α β

Inserts multiple mappings into the hash map by iterating over the given collection and calling insert. If the same key appears multiple times, the last occurrence takes precendence.

Equations

• m.insertMany l = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.insertMany ⟨m, h⟩ l).val.val else m

@[inline]

def Std.DHashMap.Raw.Const.insertMany {α : Type u} {β : Type v} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ (α × β)] (m : Std.DHashMap.Raw α fun (x : α) => β) (l : ρ) : Std.DHashMap.Raw α fun (x : α) => β

Inserts multiple mappings into the hash map by iterating over the given collection and calling insert. If the same key appears multiple times, the last occurrence takes precendence.

Equations

• Std.DHashMap.Raw.Const.insertMany m l = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.Const.insertMany ⟨m, h⟩ l).val.val else m

@[inline]

def Std.DHashMap.Raw.Const.insertManyUnit {α : Type u} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ α] (m : Std.DHashMap.Raw α fun (x : α) => Unit) (l : ρ) : Std.DHashMap.Raw α fun (x : α) => Unit

Inserts multiple keys with the value () into the hash map by iterating over the given collection and calling insert. If the same key appears multiple times, the last occurrence takes precedence.

This is mainly useful to implement HashSet.insertMany, so if you are considering using this, HashSet or HashSet.Raw might be a better fit for you.

Equations

• Std.DHashMap.Raw.Const.insertManyUnit m l = if h : 0 < m.buckets.size then (Std.DHashMap.Internal.Raw₀.Const.insertManyUnit ⟨m, h⟩ l).val.val else m

@[inline]

def Std.DHashMap.Raw.ofList {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (l : List ((a : α) × β a)) : Std.DHashMap.Raw α β

Creates a hash map from a list of mappings. If the same key appears multiple times, the last occurrence takes precedence.

Equations

• Std.DHashMap.Raw.ofList l = ∅.insertMany l

@[inline]

def Std.DHashMap.Raw.Const.ofList {α : Type u} {β : Type v} [BEq α] [Hashable α] (l : List (α × β)) : Std.DHashMap.Raw α fun (x : α) => β

Creates a hash map from a list of mappings. If the same key appears multiple times, the last occurrence takes precedence.

Equations

• Std.DHashMap.Raw.Const.ofList l = Std.DHashMap.Raw.Const.insertMany ∅ l

@[inline]

def Std.DHashMap.Raw.Const.unitOfList {α : Type u} [BEq α] [Hashable α] (l : List α) : Std.DHashMap.Raw α fun (x : α) => Unit

Creates a hash map from a list of keys, associating the value () with each key.

This is mainly useful to implement HashSet.ofList, so if you are considering using this, HashSet or HashSet.Raw might be a better fit for you.

Equations

• Std.DHashMap.Raw.Const.unitOfList l = Std.DHashMap.Raw.Const.insertManyUnit ∅ l

def Std.DHashMap.Raw.Internal.numBuckets {α : Type u} {β : α → Type v} (m : Std.DHashMap.Raw α β) : Nat

Returns the number of buckets in the internal representation of the hash map. This function may be useful for things like monitoring system health, but it should be considered an internal implementation detail.

Equations

• Std.DHashMap.Raw.Internal.numBuckets m = m.buckets.size

instance Std.DHashMap.Raw.instRepr {α : Type u} {β : α → Type v} [Repr α] [(a : α) → Repr (β a)] : Repr (Std.DHashMap.Raw α β)

Equations

• Std.DHashMap.Raw.instRepr = { reprPrec := fun (m : Std.DHashMap.Raw α β) (prec : Nat) => Repr.addAppParen (Std.Format.text "Std.DHashMap.Raw.ofList " ++ reprArg m.toList) prec }

inductive Std.DHashMap.Raw.WF {α : Type u} {β : α → Type v} [BEq α] [Hashable α] : Std.DHashMap.Raw α β → Prop

Well-formedness predicate for hash maps. Users of DHashMap will not need to interact with this. Users of DHashMap.Raw will need to provide proofs of WF to lemmas and should use lemmas like WF.empty and WF.insert (which are always named exactly like the operations they are about) to show that map operations preserve well-formedness. The constructors of this type are internal implementation details and should not be accessed by users.

• wf: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β}, 0 < m.buckets.size → (∀ [inst_2 : EquivBEq α] [inst_3 : LawfulHashable α], Std.DHashMap.Internal.Raw.WFImp m) → m.WF

  Internal implementation detail of the hash map

• empty₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {c : Nat}, (Std.DHashMap.Internal.Raw₀.empty c).val.WF

  Internal implementation detail of the hash map

• insert₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α} {b : β a}, m.WF → (Std.DHashMap.Internal.Raw₀.insert ⟨m, h⟩ a b).val.WF

  Internal implementation detail of the hash map

• containsThenInsert₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α} {b : β a}, m.WF → (Std.DHashMap.Internal.Raw₀.containsThenInsert ⟨m, h⟩ a b).snd.val.WF

  Internal implementation detail of the hash map

• containsThenInsertIfNew₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α} {b : β a}, m.WF → (Std.DHashMap.Internal.Raw₀.containsThenInsertIfNew ⟨m, h⟩ a b).snd.val.WF

  Internal implementation detail of the hash map

• erase₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α}, m.WF → (Std.DHashMap.Internal.Raw₀.erase ⟨m, h⟩ a).val.WF

  Internal implementation detail of the hash map

• insertIfNew₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α} {b : β a}, m.WF → (Std.DHashMap.Internal.Raw₀.insertIfNew ⟨m, h⟩ a b).val.WF

  Internal implementation detail of the hash map

• getThenInsertIfNew?₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] [inst_2 : LawfulBEq α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {a : α} {b : β a}, m.WF → (Std.DHashMap.Internal.Raw₀.getThenInsertIfNew? ⟨m, h⟩ a b).snd.val.WF

  Internal implementation detail of the hash map

• filter₀: ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α β} {h : 0 < m.buckets.size} {f : (a : α) → β a → Bool}, m.WF → (Std.DHashMap.Internal.Raw₀.filter f ⟨m, h⟩).val.WF

  Internal implementation detail of the hash map

• constGetThenInsertIfNew?₀: ∀ {α : Type u} {β : Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.DHashMap.Raw α fun (x : α) => β} {h : 0 < m.buckets.size} {a : α} {b : β}, m.WF → (Std.DHashMap.Internal.Raw₀.Const.getThenInsertIfNew? ⟨m, h⟩ a b).snd.val.WF

  Internal implementation detail of the hash map

theorem Std.DHashMap.Raw.WF.size_buckets_pos {α : Type u} {β : α → Type v} [BEq α] [Hashable α] (m : Std.DHashMap.Raw α β) : m.WF → 0 < m.buckets.size

Internal implementation detail of the hash map

@[simp]

theorem Std.DHashMap.Raw.WF.empty {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {c : Nat} : (Std.DHashMap.Raw.empty c).WF

@[simp]

theorem Std.DHashMap.Raw.WF.emptyc {α : Type u} {β : α → Type v} [BEq α] [Hashable α] : ∅.WF

theorem Std.DHashMap.Raw.WF.insert {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} {b : β a} (h : m.WF) : (m.insert a b).WF

theorem Std.DHashMap.Raw.WF.containsThenInsert {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} {b : β a} (h : m.WF) : (m.containsThenInsert a b).snd.WF

theorem Std.DHashMap.Raw.WF.containsThenInsertIfNew {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} {b : β a} (h : m.WF) : (m.containsThenInsertIfNew a b).snd.WF

theorem Std.DHashMap.Raw.WF.erase {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} (h : m.WF) : (m.erase a).WF

theorem Std.DHashMap.Raw.WF.insertIfNew {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {a : α} {b : β a} (h : m.WF) : (m.insertIfNew a b).WF

theorem Std.DHashMap.Raw.WF.getThenInsertIfNew? {α : Type u} {β : α → Type v} [BEq α] [Hashable α] [LawfulBEq α] {m : Std.DHashMap.Raw α β} {a : α} {b : β a} (h : m.WF) : (m.getThenInsertIfNew? a b).snd.WF

theorem Std.DHashMap.Raw.WF.filter {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α β} {f : (a : α) → β a → Bool} (h : m.WF) : (Std.DHashMap.Raw.filter f m).WF

theorem Std.DHashMap.Raw.WF.Const.getThenInsertIfNew? {α : Type u} {β : Type v} [BEq α] [Hashable α] {m : Std.DHashMap.Raw α fun (x : α) => β} {a : α} {b : β} (h : m.WF) : (Std.DHashMap.Raw.Const.getThenInsertIfNew? m a b).snd.WF

theorem Std.DHashMap.Raw.WF.insertMany {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ ((a : α) × β a)] {m : Std.DHashMap.Raw α β} {l : ρ} (h : m.WF) : (m.insertMany l).WF

theorem Std.DHashMap.Raw.WF.Const.insertMany {α : Type u} {β : Type v} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ (α × β)] {m : Std.DHashMap.Raw α fun (x : α) => β} {l : ρ} (h : m.WF) : (Std.DHashMap.Raw.Const.insertMany m l).WF

theorem Std.DHashMap.Raw.WF.Const.insertManyUnit {α : Type u} [BEq α] [Hashable α] {ρ : Type w} [ForIn Id ρ α] {m : Std.DHashMap.Raw α fun (x : α) => Unit} {l : ρ} (h : m.WF) : (Std.DHashMap.Raw.Const.insertManyUnit m l).WF

theorem Std.DHashMap.Raw.WF.ofList {α : Type u} {β : α → Type v} [BEq α] [Hashable α] {l : List ((a : α) × β a)} : (Std.DHashMap.Raw.ofList l).WF

theorem Std.DHashMap.Raw.WF.Const.ofList {α : Type u} {β : Type v} [BEq α] [Hashable α] {l : List (α × β)} : (Std.DHashMap.Raw.Const.ofList l).WF

theorem Std.DHashMap.Raw.WF.Const.unitOfList {α : Type u} [BEq α] [Hashable α] {l : List α} : (Std.DHashMap.Raw.Const.unitOfList l).WF