feat: tree map lemmas for modify (#7419)
This PR provides lemmas about the tree map function `modify` and its interactions with other functions for which lemmas already exist. --------- Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This commit is contained in:
Paul Reichert
GitHub
parent
e0fa6a1792
commit
f3c507ec57
7 changed files with 1061 additions and 3 deletions
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@ -85,7 +85,9 @@ private def modifyMap : Std.HashMap Name Name :=
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(`alter, ``toListModel_alter),
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(`alter!, ``toListModel_alter!),
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(`Const.alter, ``Const.toListModel_alter),
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(`Const.alter!, ``Const.toListModel_alter!)]
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(`Const.alter!, ``Const.toListModel_alter!),
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(`modify, ``toListModel_modify),
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(`Const.modify, ``Const.toListModel_modify)]
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private def congrNames : MacroM (Array (TSyntax `term)) := do
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return #[← `(_root_.List.Perm.isEmpty_eq), ← `(containsKey_of_perm),
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@ -3872,4 +3874,268 @@ end Const
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end Alter
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section Modify
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variable [TransOrd α]
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section Dependent
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variable [LawfulEqOrd α]
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@[simp]
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theorem isEmpty_modify (h : t.WF) {k : α} {f : β k → β k} :
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(t.modify k f).isEmpty = t.isEmpty := by
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simp_to_model [modify] using List.isEmpty_modifyKey
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theorem contains_modify (h : t.WF) {k k' : α} {f : β k → β k} :
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(t.modify k f).contains k' = t.contains k' := by
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simp_to_model [modify] using List.containsKey_modifyKey
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theorem mem_modify (h : t.WF) {k k' : α} {f : β k → β k} :
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k' ∈ t.modify k f ↔ k' ∈ t := by
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simp [mem_iff_contains, contains_modify h]
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theorem size_modify (h : t.WF) {k : α} {f : β k → β k} :
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(t.modify k f).size = t.size := by
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simp_to_model [modify] using List.length_modifyKey
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theorem get?_modify (h : t.WF) {k k' : α} {f : β k → β k} :
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(t.modify k f).get? k' =
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if h : compare k k' = .eq then
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(cast (congrArg (Option ∘ β) (compare_eq_iff_eq.mp h)) ((t.get? k).map f))
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else
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t.get? k' := by
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simp_to_model [modify] using List.getValueCast?_modifyKey
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@[simp]
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theorem get?_modify_self (h : t.WF) {k : α} {f : β k → β k} :
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(t.modify k f).get? k = (t.get? k).map f := by
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simp_to_model [modify] using List.getValueCast?_modifyKey_self
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theorem get_modify (h : t.WF) {k k' : α} {f : β k → β k} {hc : k' ∈ t.modify k f} :
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(t.modify k f).get k' hc =
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if heq : compare k k' = .eq then
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haveI h' : k ∈ t := by rwa [mem_modify h, ← compare_eq_iff_eq.mp heq] at hc
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cast (congrArg β (compare_eq_iff_eq.mp heq)) <| f (t.get k h')
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else
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haveI h' : k' ∈ t := by rwa [mem_modify h] at hc
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t.get k' h' := by
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simp_to_model [modify] using List.getValueCast_modifyKey
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@[simp]
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theorem get_modify_self (h : t.WF) {k : α} {f : β k → β k} {hc : k ∈ t.modify k f} :
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haveI h' : k ∈ t := mem_modify h |>.mp hc
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(t.modify k f).get k hc = f (t.get k h') := by
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simp_to_model [modify] using List.getValueCast_modifyKey_self
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theorem get!_modify (h : t.WF) {k k' : α} [hi : Inhabited (β k')] {f : β k → β k} :
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(t.modify k f).get! k' =
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if heq : compare k k' = .eq then
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t.get? k |>.map f |>.map (cast (congrArg β (compare_eq_iff_eq.mp heq))) |>.get!
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else
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t.get! k' := by
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simp_to_model [modify] using List.getValueCast!_modifyKey
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@[simp]
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theorem get!_modify_self (h : t.WF) {k : α} [Inhabited (β k)] {f : β k → β k} :
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(t.modify k f).get! k = ((t.get? k).map f).get! := by
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simp_to_model [modify] using List.getValueCast!_modifyKey_self
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theorem getD_modify (h : t.WF) {k k' : α} {fallback : β k'} {f : β k → β k} :
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(t.modify k f).getD k' fallback =
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if heq : compare k k' = .eq then
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t.get? k |>.map f |>.map (cast (congrArg β <| compare_eq_iff_eq.mp heq)) |>.getD fallback
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else
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t.getD k' fallback := by
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simp_to_model [modify] using List.getValueCastD_modifyKey
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@[simp]
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theorem getD_modify_self (h : t.WF) {k : α} {fallback : β k} {f : β k → β k} :
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(t.modify k f).getD k fallback = ((t.get? k).map f).getD fallback := by
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simp_to_model [modify] using List.getValueCastD_modifyKey_self
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theorem getKey?_modify (h : t.WF) {k k' : α} {f : β k → β k} :
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(t.modify k f).getKey? k' =
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if compare k k' = .eq then
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if k ∈ t then some k else none
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else
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t.getKey? k' := by
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simp_to_model [modify] using List.getKey?_modifyKey
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theorem getKey?_modify_self (h : t.WF) {k : α} {f : β k → β k} :
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(t.modify k f).getKey? k = if k ∈ t then some k else none := by
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simp_to_model [modify] using List.getKey?_modifyKey_self
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theorem getKey!_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β k → β k} :
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(t.modify k f).getKey! k' =
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if compare k k' = .eq then
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if k ∈ t then k else default
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else
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t.getKey! k' := by
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simp_to_model [modify] using List.getKey!_modifyKey
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theorem getKey!_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β k → β k} :
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(t.modify k f).getKey! k = if k ∈ t then k else default := by
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simp_to_model [modify] using List.getKey!_modifyKey_self
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theorem getKey_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β k → β k}
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{hc : k' ∈ t.modify k f} :
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(t.modify k f).getKey k' hc =
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if compare k k' = .eq then
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k
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else
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haveI h' : k' ∈ t := mem_modify h |>.mp hc
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t.getKey k' h' := by
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simp_to_model [modify] using List.getKey_modifyKey
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@[simp]
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theorem getKey_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β k → β k}
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{hc : k ∈ t.modify k f} : (t.modify k f).getKey k hc = k := by
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simp_to_model [modify] using List.getKey_modifyKey_self
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theorem getKeyD_modify (h : t.WF) {k k' fallback : α} {f : β k → β k} :
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(t.modify k f).getKeyD k' fallback =
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if compare k k' = .eq then
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if k ∈ t then k else fallback
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else
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t.getKeyD k' fallback := by
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simp_to_model [modify] using List.getKeyD_modifyKey
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theorem getKeyD_modify_self (h : t.WF) [Inhabited α] {k fallback : α} {f : β k → β k} :
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(t.modify k f).getKeyD k fallback = if k ∈ t then k else fallback := by
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simp_to_model [modify] using List.getKeyD_modifyKey_self
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end Dependent
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namespace Const
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variable {β : Type v} {t : Impl α β}
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@[simp]
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theorem isEmpty_modify (h : t.WF) {k : α} {f : β → β} :
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(modify k f t).isEmpty = t.isEmpty := by
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simp_to_model [Const.modify] using List.Const.isEmpty_modifyKey
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theorem contains_modify (h : t.WF) {k k' : α} {f : β → β} :
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(modify k f t).contains k' = t.contains k' := by
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simp_to_model [Const.modify] using List.Const.containsKey_modifyKey
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theorem mem_modify (h : t.WF) {k k' : α} {f : β → β} :
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k' ∈ modify k f t ↔ k' ∈ t := by
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simp [mem_iff_contains, contains_modify h]
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theorem size_modify (h : t.WF) {k : α} {f : β → β} :
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(modify k f t).size = t.size := by
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simp_to_model [Const.modify] using List.Const.length_modifyKey
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theorem get?_modify (h : t.WF) {k k' : α} {f : β → β} :
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get? (modify k f t) k' =
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if compare k k' = .eq then
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(get? t k).map f
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else
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get? t k' := by
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simp_to_model [Const.modify] using List.Const.getValue?_modifyKey
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@[simp]
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theorem get?_modify_self (h : t.WF) {k : α} {f : β → β} :
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get? (modify k f t) k = (get? t k).map f := by
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simp_to_model [Const.modify] using List.Const.getValue?_modifyKey_self
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theorem get_modify (h : t.WF) {k k' : α} {f : β → β} {hc : k' ∈ modify k f t} :
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get (modify k f t) k' hc =
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if heq : compare k k' = .eq then
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haveI h' : k ∈ t := mem_congr h heq |>.mpr <| mem_modify h |>.mp hc
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f (get t k h')
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else
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haveI h' : k' ∈ t := mem_modify h |>.mp hc
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get t k' h' := by
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simp_to_model [Const.modify] using List.Const.getValue_modifyKey
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@[simp]
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theorem get_modify_self (h : t.WF) {k : α} {f : β → β} {hc : k ∈ modify k f t} :
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haveI h' : k ∈ t := mem_modify h |>.mp hc
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get (modify k f t) k hc = f (get t k h') := by
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simp_to_model [Const.modify] using List.Const.getValue_modifyKey_self
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theorem get!_modify (h : t.WF) {k k' : α} [hi : Inhabited β] {f : β → β} :
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get! (modify k f t) k' =
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if compare k k' = .eq then
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get? t k |>.map f |>.get!
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else
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get! t k' := by
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simp_to_model [Const.modify] using List.Const.getValue!_modifyKey
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@[simp]
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theorem get!_modify_self (h : t.WF) {k : α} [Inhabited β] {f : β → β} :
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get! (modify k f t) k = ((get? t k).map f).get! := by
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simp_to_model [Const.modify] using List.Const.getValue!_modifyKey_self
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theorem getD_modify (h : t.WF) {k k' : α} {fallback : β} {f : β → β} :
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getD (modify k f t) k' fallback =
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if compare k k' = .eq then
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get? t k |>.map f |>.getD fallback
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else
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getD t k' fallback := by
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simp_to_model [Const.modify] using List.Const.getValueD_modifyKey
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@[simp]
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theorem getD_modify_self (h : t.WF) {k : α} {fallback : β} {f : β → β} :
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getD (modify k f t) k fallback = ((get? t k).map f).getD fallback := by
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simp_to_model [Const.modify] using List.Const.getValueD_modifyKey_self
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theorem getKey?_modify (h : t.WF) {k k' : α} {f : β → β} :
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(modify k f t).getKey? k' =
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if compare k k' = .eq then
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if k ∈ t then some k else none
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else
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t.getKey? k' := by
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simp_to_model [Const.modify] using List.Const.getKey?_modifyKey
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theorem getKey?_modify_self (h : t.WF) {k : α} {f : β → β} :
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(modify k f t).getKey? k = if k ∈ t then some k else none := by
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simp_to_model [Const.modify] using List.Const.getKey?_modifyKey_self
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theorem getKey!_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β → β} :
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(modify k f t).getKey! k' =
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if compare k k' = .eq then
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if k ∈ t then k else default
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else
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t.getKey! k' := by
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simp_to_model [Const.modify] using List.Const.getKey!_modifyKey
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theorem getKey!_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β → β} :
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(modify k f t).getKey! k = if k ∈ t then k else default := by
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simp_to_model [Const.modify] using List.Const.getKey!_modifyKey_self
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theorem getKey_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β → β}
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{hc : k' ∈ modify k f t} :
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(modify k f t).getKey k' hc =
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if compare k k' = .eq then
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k
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else
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haveI h' : k' ∈ t := mem_modify h |>.mp hc
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t.getKey k' h' := by
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simp_to_model [Const.modify] using List.Const.getKey_modifyKey
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@[simp]
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theorem getKey_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β → β}
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{hc : k ∈ modify k f t} : (modify k f t).getKey k hc = k := by
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simp_to_model [Const.modify] using List.Const.getKey_modifyKey_self
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theorem getKeyD_modify (h : t.WF) {k k' fallback : α} {f : β → β} :
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(modify k f t).getKeyD k' fallback =
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if compare k k' = .eq then
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if k ∈ t then k else fallback
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else
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t.getKeyD k' fallback := by
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simp_to_model [Const.modify] using List.Const.getKeyD_modifyKey
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theorem getKeyD_modify_self (h : t.WF) [Inhabited α] {k fallback : α} {f : β → β} :
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(modify k f t).getKeyD k fallback = if k ∈ t then k else fallback := by
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simp_to_model [Const.modify] using List.Const.getKeyD_modifyKey_self
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end Const
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end Modify
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end Std.DTreeMap.Internal.Impl
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@ -784,7 +784,7 @@ def modify [Ord α] [LawfulEqOrd α] (k : α) (f : β k → β k) (t : Impl α
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| .eq => .inner sz k (f <| cast (congrArg β <| compare_eq_iff_eq.mp h).symm v') l r
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@[Std.Internal.tree_tac]
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theorem size_modify [Ord α] [LawfulEqOrd α] {k f} {t : Impl α β} :
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theorem aux_size_modify [Ord α] [LawfulEqOrd α] {k f} {t : Impl α β} :
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(t.modify k f).size = t.size := by
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unfold modify
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split <;> (try split) <;> rfl
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@ -891,7 +891,7 @@ def modify [Ord α] (k : α) (f : β → β) (t : Impl α β) :
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| .eq => .inner sz k (f v') l r
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@[Std.Internal.tree_tac]
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theorem size_modify [Ord α] {k f} {t : Impl α β} :
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theorem aux_size_modify [Ord α] {k f} {t : Impl α β} :
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(modify k f t).size = t.size := by
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unfold modify
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split <;> (try split) <;> rfl
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@ -1116,6 +1116,11 @@ theorem ordered_modify [Ord α] [TransOrd α] [LawfulEqOrd α] {t : Impl α β}
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(htb : t.Balanced) (hto : t.Ordered) : (modify a f t).Ordered :=
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modify_eq_alter htb ▸ ordered_alter htb hto
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theorem toListModel_modify [Ord α] [TransOrd α] [LawfulEqOrd α] {t : Impl α β} {a f}
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(htb : t.Balanced) (hto : t.Ordered) :
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List.Perm (modify a f t).toListModel (modifyKey a f t.toListModel) := by
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simpa only [modify_eq_alter htb, modifyKey_eq_alterKey] using toListModel_alter htb hto
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/-!
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### mergeWith
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-/
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@ -1365,6 +1370,11 @@ theorem ordered_modify [Ord α] [TransOrd α] {t : Impl α β} {a f}
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(htb : t.Balanced) (hto : t.Ordered) : (modify a f t).Ordered :=
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modify_eq_alter htb ▸ ordered_alter htb hto
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theorem toListModel_modify [Ord α] [TransOrd α] {t : Impl α β} {a f}
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(htb : t.Balanced) (hto : t.Ordered) :
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List.Perm (modify a f t).toListModel (Const.modifyKey a f t.toListModel) := by
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simpa only [modify_eq_alter htb, Const.modifyKey_eq_alterKey] using toListModel_alter htb hto
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/-!
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### mergeWith
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-/
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@ -2443,4 +2443,268 @@ end Const
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end Alter
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section Modify
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variable [TransCmp cmp]
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section Dependent
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variable [LawfulEqCmp cmp]
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@[simp]
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theorem isEmpty_modify {k : α} {f : β k → β k} :
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(t.modify k f).isEmpty = t.isEmpty :=
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Impl.isEmpty_modify t.wf
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theorem contains_modify {k k' : α} {f : β k → β k} :
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(t.modify k f).contains k' = t.contains k' :=
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Impl.contains_modify t.wf
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theorem mem_modify {k k' : α} {f : β k → β k} :
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k' ∈ t.modify k f ↔ k' ∈ t :=
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Impl.mem_modify t.wf
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theorem size_modify {k : α} {f : β k → β k} :
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(t.modify k f).size = t.size :=
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Impl.size_modify t.wf
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|
||||
theorem get?_modify {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).get? k' =
|
||||
if h : cmp k k' = .eq then
|
||||
(cast (congrArg (Option ∘ β) (compare_eq_iff_eq.mp h)) ((t.get? k).map f))
|
||||
else
|
||||
t.get? k' :=
|
||||
Impl.get?_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get?_modify_self {k : α} {f : β k → β k} :
|
||||
(t.modify k f).get? k = (t.get? k).map f :=
|
||||
Impl.get?_modify_self t.wf
|
||||
|
||||
theorem get_modify {k k' : α} {f : β k → β k} {hc : k' ∈ t.modify k f} :
|
||||
(t.modify k f).get k' hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr heq |>.mpr <| mem_modify.mp hc
|
||||
cast (congrArg β (compare_eq_iff_eq.mp heq)) <| f (t.get k h')
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
t.get k' h' :=
|
||||
Impl.get_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get_modify_self {k : α} {f : β k → β k} {hc : k ∈ t.modify k f} :
|
||||
haveI h' : k ∈ t := mem_modify.mp hc
|
||||
(t.modify k f).get k hc = f (t.get k h') :=
|
||||
Impl.get_modify_self t.wf
|
||||
|
||||
theorem get!_modify {k k' : α} [hi : Inhabited (β k')] {f : β k → β k} :
|
||||
(t.modify k f).get! k' =
|
||||
if heq : cmp k k' = .eq then
|
||||
t.get? k |>.map f |>.map (cast (congrArg β (compare_eq_iff_eq.mp heq))) |>.get!
|
||||
else
|
||||
t.get! k' :=
|
||||
Impl.get!_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get!_modify_self {k : α} [Inhabited (β k)] {f : β k → β k} :
|
||||
(t.modify k f).get! k = ((t.get? k).map f).get! :=
|
||||
Impl.get!_modify_self t.wf
|
||||
|
||||
theorem getD_modify {k k' : α} {fallback : β k'} {f : β k → β k} :
|
||||
(t.modify k f).getD k' fallback =
|
||||
if heq : cmp k k' = .eq then
|
||||
t.get? k |>.map f |>.map (cast (congrArg β <| compare_eq_iff_eq.mp heq)) |>.getD fallback
|
||||
else
|
||||
t.getD k' fallback :=
|
||||
Impl.getD_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self {k : α} {fallback : β k} {f : β k → β k} :
|
||||
(t.modify k f).getD k fallback = ((t.get? k).map f).getD fallback :=
|
||||
Impl.getD_modify_self t.wf
|
||||
|
||||
theorem getKey?_modify {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
Impl.getKey?_modify t.wf
|
||||
|
||||
theorem getKey?_modify_self {k : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey? k = if k ∈ t then some k else none :=
|
||||
Impl.getKey?_modify_self t.wf
|
||||
|
||||
theorem getKey!_modify [Inhabited α] {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
Impl.getKey!_modify t.wf
|
||||
|
||||
theorem getKey!_modify_self [Inhabited α] {k : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey! k = if k ∈ t then k else default :=
|
||||
Impl.getKey!_modify_self t.wf
|
||||
|
||||
theorem getKey_modify [Inhabited α] {k k' : α} {f : β k → β k}
|
||||
{hc : k' ∈ t.modify k f} :
|
||||
(t.modify k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
t.getKey k' h' :=
|
||||
Impl.getKey_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self [Inhabited α] {k : α} {f : β k → β k}
|
||||
{hc : k ∈ t.modify k f} : (t.modify k f).getKey k hc = k :=
|
||||
Impl.getKey_modify_self t.wf
|
||||
|
||||
theorem getKeyD_modify {k k' fallback : α} {f : β k → β k} :
|
||||
(t.modify k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
Impl.getKeyD_modify t.wf
|
||||
|
||||
theorem getKeyD_modify_self [Inhabited α] {k fallback : α} {f : β k → β k} :
|
||||
(t.modify k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
Impl.getKeyD_modify_self t.wf
|
||||
|
||||
end Dependent
|
||||
|
||||
namespace Const
|
||||
|
||||
variable {β : Type v} {t : DTreeMap α β cmp}
|
||||
|
||||
@[simp]
|
||||
theorem isEmpty_modify {k : α} {f : β → β} :
|
||||
(modify t k f).isEmpty = t.isEmpty :=
|
||||
Impl.Const.isEmpty_modify t.wf
|
||||
|
||||
theorem contains_modify {k k' : α} {f : β → β} :
|
||||
(modify t k f).contains k' = t.contains k' :=
|
||||
Impl.Const.contains_modify t.wf
|
||||
|
||||
theorem mem_modify {k k' : α} {f : β → β} :
|
||||
k' ∈ modify t k f ↔ k' ∈ t :=
|
||||
Impl.Const.mem_modify t.wf
|
||||
|
||||
theorem size_modify {k : α} {f : β → β} :
|
||||
(modify t k f).size = t.size :=
|
||||
Impl.Const.size_modify t.wf
|
||||
|
||||
theorem get?_modify {k k' : α} {f : β → β} :
|
||||
get? (modify t k f) k' =
|
||||
if cmp k k' = .eq then
|
||||
(get? t k).map f
|
||||
else
|
||||
get? t k' :=
|
||||
Impl.Const.get?_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get?_modify_self {k : α} {f : β → β} :
|
||||
get? (modify t k f) k = (get? t k).map f :=
|
||||
Impl.Const.get?_modify_self t.wf
|
||||
|
||||
theorem get_modify {k k' : α} {f : β → β} {hc : k' ∈ modify t k f} :
|
||||
get (modify t k f) k' hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr heq |>.mpr <| mem_modify.mp hc
|
||||
f (get t k h')
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
get t k' h' :=
|
||||
Impl.Const.get_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get_modify_self {k : α} {f : β → β} {hc : k ∈ modify t k f} :
|
||||
haveI h' : k ∈ t := mem_modify.mp hc
|
||||
get (modify t k f) k hc = f (get t k h') :=
|
||||
Impl.Const.get_modify_self t.wf
|
||||
|
||||
theorem get!_modify {k k' : α} [hi : Inhabited β] {f : β → β} :
|
||||
get! (modify t k f) k' =
|
||||
if cmp k k' = .eq then
|
||||
get? t k |>.map f |>.get!
|
||||
else
|
||||
get! t k' :=
|
||||
Impl.Const.get!_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem get!_modify_self {k : α} [Inhabited β] {f : β → β} :
|
||||
get! (modify t k f) k = ((get? t k).map f).get! :=
|
||||
Impl.Const.get!_modify_self t.wf
|
||||
|
||||
theorem getD_modify {k k' : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
get? t k |>.map f |>.getD fallback
|
||||
else
|
||||
getD t k' fallback :=
|
||||
Impl.Const.getD_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self {k : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k fallback = ((get? t k).map f).getD fallback :=
|
||||
Impl.Const.getD_modify_self t.wf
|
||||
|
||||
theorem getKey?_modify {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
Impl.Const.getKey?_modify t.wf
|
||||
|
||||
theorem getKey?_modify_self {k : α} {f : β → β} :
|
||||
(modify t k f).getKey? k = if k ∈ t then some k else none :=
|
||||
Impl.Const.getKey?_modify_self t.wf
|
||||
|
||||
theorem getKey!_modify [Inhabited α] {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
Impl.Const.getKey!_modify t.wf
|
||||
|
||||
theorem getKey!_modify_self [Inhabited α] {k : α} {f : β → β} :
|
||||
(modify t k f).getKey! k = if k ∈ t then k else default :=
|
||||
Impl.Const.getKey!_modify_self t.wf
|
||||
|
||||
theorem getKey_modify [Inhabited α] {k k' : α} {f : β → β}
|
||||
{hc : k' ∈ modify t k f} :
|
||||
(modify t k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
t.getKey k' h' :=
|
||||
Impl.Const.getKey_modify t.wf
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self [Inhabited α] {k : α} {f : β → β}
|
||||
{hc : k ∈ modify t k f} : (modify t k f).getKey k hc = k :=
|
||||
Impl.Const.getKey_modify_self t.wf
|
||||
|
||||
theorem getKeyD_modify {k k' fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
Impl.Const.getKeyD_modify t.wf
|
||||
|
||||
theorem getKeyD_modify_self [Inhabited α] {k fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
Impl.Const.getKeyD_modify_self t.wf
|
||||
|
||||
end Const
|
||||
|
||||
end Modify
|
||||
|
||||
end Std.DTreeMap
|
||||
|
|
|
|||
|
|
@ -2446,4 +2446,268 @@ end Const
|
|||
|
||||
end Alter
|
||||
|
||||
section Modify
|
||||
|
||||
variable [TransCmp cmp]
|
||||
|
||||
section Dependent
|
||||
|
||||
variable [LawfulEqCmp cmp]
|
||||
|
||||
@[simp]
|
||||
theorem isEmpty_modify (h : t.WF) {k : α} {f : β k → β k} :
|
||||
(t.modify k f).isEmpty = t.isEmpty :=
|
||||
Impl.isEmpty_modify h
|
||||
|
||||
theorem contains_modify (h : t.WF) {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).contains k' = t.contains k' :=
|
||||
Impl.contains_modify h
|
||||
|
||||
theorem mem_modify (h : t.WF) {k k' : α} {f : β k → β k} :
|
||||
k' ∈ t.modify k f ↔ k' ∈ t :=
|
||||
Impl.mem_modify h
|
||||
|
||||
theorem size_modify (h : t.WF) {k : α} {f : β k → β k} :
|
||||
(t.modify k f).size = t.size :=
|
||||
Impl.size_modify h
|
||||
|
||||
theorem get?_modify (h : t.WF) {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).get? k' =
|
||||
if h : cmp k k' = .eq then
|
||||
(cast (congrArg (Option ∘ β) (compare_eq_iff_eq.mp h)) ((t.get? k).map f))
|
||||
else
|
||||
t.get? k' :=
|
||||
Impl.get?_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get?_modify_self (h : t.WF) {k : α} {f : β k → β k} :
|
||||
(t.modify k f).get? k = (t.get? k).map f :=
|
||||
Impl.get?_modify_self h
|
||||
|
||||
theorem get_modify (h : t.WF) {k k' : α} {f : β k → β k} {hc : k' ∈ t.modify k f} :
|
||||
(t.modify k f).get k' hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr h heq |>.mpr <| mem_modify h |>.mp hc
|
||||
cast (congrArg β (compare_eq_iff_eq.mp heq)) <| f (t.get k h')
|
||||
else
|
||||
haveI h' : k' ∈ t := (mem_modify h).mp hc
|
||||
t.get k' h' :=
|
||||
Impl.get_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get_modify_self (h : t.WF) {k : α} {f : β k → β k} {hc : k ∈ t.modify k f} :
|
||||
haveI h' : k ∈ t := mem_modify h |>.mp hc
|
||||
(t.modify k f).get k hc = f (t.get k h') :=
|
||||
Impl.get_modify_self h
|
||||
|
||||
theorem get!_modify (h : t.WF) {k k' : α} [hi : Inhabited (β k')] {f : β k → β k} :
|
||||
(t.modify k f).get! k' =
|
||||
if heq : cmp k k' = .eq then
|
||||
t.get? k |>.map f |>.map (cast (congrArg β (compare_eq_iff_eq.mp heq))) |>.get!
|
||||
else
|
||||
t.get! k' :=
|
||||
Impl.get!_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get!_modify_self (h : t.WF) {k : α} [Inhabited (β k)] {f : β k → β k} :
|
||||
(t.modify k f).get! k = ((t.get? k).map f).get! :=
|
||||
Impl.get!_modify_self h
|
||||
|
||||
theorem getD_modify (h : t.WF) {k k' : α} {fallback : β k'} {f : β k → β k} :
|
||||
(t.modify k f).getD k' fallback =
|
||||
if heq : cmp k k' = .eq then
|
||||
t.get? k |>.map f |>.map (cast (congrArg β <| compare_eq_iff_eq.mp heq)) |>.getD fallback
|
||||
else
|
||||
t.getD k' fallback :=
|
||||
Impl.getD_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self (h : t.WF) {k : α} {fallback : β k} {f : β k → β k} :
|
||||
(t.modify k f).getD k fallback = ((t.get? k).map f).getD fallback :=
|
||||
Impl.getD_modify_self h
|
||||
|
||||
theorem getKey?_modify (h : t.WF) {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
Impl.getKey?_modify h
|
||||
|
||||
theorem getKey?_modify_self (h : t.WF) {k : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey? k = if k ∈ t then some k else none :=
|
||||
Impl.getKey?_modify_self h
|
||||
|
||||
theorem getKey!_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
Impl.getKey!_modify h
|
||||
|
||||
theorem getKey!_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β k → β k} :
|
||||
(t.modify k f).getKey! k = if k ∈ t then k else default :=
|
||||
Impl.getKey!_modify_self h
|
||||
|
||||
theorem getKey_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β k → β k}
|
||||
{hc : k' ∈ t.modify k f} :
|
||||
(t.modify k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify h |>.mp hc
|
||||
t.getKey k' h' :=
|
||||
Impl.getKey_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β k → β k}
|
||||
{hc : k ∈ t.modify k f} : (t.modify k f).getKey k hc = k :=
|
||||
Impl.getKey_modify_self h
|
||||
|
||||
theorem getKeyD_modify (h : t.WF) {k k' fallback : α} {f : β k → β k} :
|
||||
(t.modify k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
Impl.getKeyD_modify h
|
||||
|
||||
theorem getKeyD_modify_self (h : t.WF) [Inhabited α] {k fallback : α} {f : β k → β k} :
|
||||
(t.modify k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
Impl.getKeyD_modify_self h
|
||||
|
||||
end Dependent
|
||||
|
||||
namespace Const
|
||||
|
||||
variable {β : Type v} {t : Raw α β cmp}
|
||||
|
||||
@[simp]
|
||||
theorem isEmpty_modify (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).isEmpty = t.isEmpty :=
|
||||
Impl.Const.isEmpty_modify h
|
||||
|
||||
theorem contains_modify (h : t.WF) {k k' : α} {f : β → β} :
|
||||
(modify t k f).contains k' = t.contains k' :=
|
||||
Impl.Const.contains_modify h
|
||||
|
||||
theorem mem_modify (h : t.WF) {k k' : α} {f : β → β} :
|
||||
k' ∈ modify t k f ↔ k' ∈ t :=
|
||||
Impl.Const.mem_modify h
|
||||
|
||||
theorem size_modify (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).size = t.size :=
|
||||
Impl.Const.size_modify h
|
||||
|
||||
theorem get?_modify (h : t.WF) {k k' : α} {f : β → β} :
|
||||
get? (modify t k f) k' =
|
||||
if cmp k k' = .eq then
|
||||
(get? t k).map f
|
||||
else
|
||||
get? t k' :=
|
||||
Impl.Const.get?_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get?_modify_self (h : t.WF) {k : α} {f : β → β} :
|
||||
get? (modify t k f) k = (get? t k).map f :=
|
||||
Impl.Const.get?_modify_self h
|
||||
|
||||
theorem get_modify (h : t.WF) {k k' : α} {f : β → β} {hc : k' ∈ modify t k f} :
|
||||
get (modify t k f) k' hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr h heq |>.mpr <| mem_modify h |>.mp hc
|
||||
f (get t k h')
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify h |>.mp hc
|
||||
get t k' h' :=
|
||||
Impl.Const.get_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get_modify_self (h : t.WF) {k : α} {f : β → β} {hc : k ∈ modify t k f} :
|
||||
haveI h' : k ∈ t := mem_modify h |>.mp hc
|
||||
get (modify t k f) k hc = f (get t k h') :=
|
||||
Impl.Const.get_modify_self h
|
||||
|
||||
theorem get!_modify (h : t.WF) {k k' : α} [hi : Inhabited β] {f : β → β} :
|
||||
get! (modify t k f) k' =
|
||||
if cmp k k' = .eq then
|
||||
get? t k |>.map f |>.get!
|
||||
else
|
||||
get! t k' :=
|
||||
Impl.Const.get!_modify h
|
||||
|
||||
@[simp]
|
||||
theorem get!_modify_self (h : t.WF) {k : α} [Inhabited β] {f : β → β} :
|
||||
get! (modify t k f) k = ((get? t k).map f).get! :=
|
||||
Impl.Const.get!_modify_self h
|
||||
|
||||
theorem getD_modify (h : t.WF) {k k' : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
get? t k |>.map f |>.getD fallback
|
||||
else
|
||||
getD t k' fallback :=
|
||||
Impl.Const.getD_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self (h : t.WF) {k : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k fallback = ((get? t k).map f).getD fallback :=
|
||||
Impl.Const.getD_modify_self h
|
||||
|
||||
theorem getKey?_modify (h : t.WF) {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
Impl.Const.getKey?_modify h
|
||||
|
||||
theorem getKey?_modify_self (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).getKey? k = if k ∈ t then some k else none :=
|
||||
Impl.Const.getKey?_modify_self h
|
||||
|
||||
theorem getKey!_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
Impl.Const.getKey!_modify h
|
||||
|
||||
theorem getKey!_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β → β} :
|
||||
(modify t k f).getKey! k = if k ∈ t then k else default :=
|
||||
Impl.Const.getKey!_modify_self h
|
||||
|
||||
theorem getKey_modify (h : t.WF) [Inhabited α] {k k' : α} {f : β → β}
|
||||
{hc : k' ∈ modify t k f} :
|
||||
(modify t k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify h |>.mp hc
|
||||
t.getKey k' h' :=
|
||||
Impl.Const.getKey_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self (h : t.WF) [Inhabited α] {k : α} {f : β → β}
|
||||
{hc : k ∈ modify t k f} : (modify t k f).getKey k hc = k :=
|
||||
Impl.Const.getKey_modify_self h
|
||||
|
||||
theorem getKeyD_modify (h : t.WF) {k k' fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
Impl.Const.getKeyD_modify h
|
||||
|
||||
theorem getKeyD_modify_self (h : t.WF) [Inhabited α] {k fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
Impl.Const.getKeyD_modify_self h
|
||||
|
||||
end Const
|
||||
|
||||
end Modify
|
||||
|
||||
end Std.DTreeMap.Raw
|
||||
|
|
|
|||
|
|
@ -1549,4 +1549,131 @@ theorem getKeyD_alter_self [TransCmp cmp] [Inhabited α] {k : α} {fallback : α
|
|||
|
||||
end Alter
|
||||
|
||||
section Modify
|
||||
|
||||
@[simp]
|
||||
theorem isEmpty_modify [TransCmp cmp] {k : α} {f : β → β} :
|
||||
(modify t k f).isEmpty = t.isEmpty :=
|
||||
DTreeMap.Const.isEmpty_modify
|
||||
|
||||
theorem contains_modify [TransCmp cmp] {k k' : α} {f : β → β} :
|
||||
(modify t k f).contains k' = t.contains k' :=
|
||||
DTreeMap.Const.contains_modify
|
||||
|
||||
theorem mem_modify [TransCmp cmp] {k k' : α} {f : β → β} :
|
||||
k' ∈ modify t k f ↔ k' ∈ t :=
|
||||
DTreeMap.Const.mem_modify
|
||||
|
||||
theorem size_modify [TransCmp cmp] {k : α} {f : β → β} :
|
||||
(modify t k f).size = t.size :=
|
||||
DTreeMap.Const.size_modify
|
||||
|
||||
theorem getElem?_modify [TransCmp cmp] {k k' : α} {f : β → β} :
|
||||
(modify t k f)[k']? =
|
||||
if cmp k k' = .eq then
|
||||
t[k]?.map f
|
||||
else
|
||||
t[k']? :=
|
||||
DTreeMap.Const.get?_modify
|
||||
|
||||
@[simp]
|
||||
theorem getElem?_modify_self [TransCmp cmp] {k : α} {f : β → β} :
|
||||
(modify t k f)[k]? = t[k]?.map f :=
|
||||
DTreeMap.Const.get?_modify_self
|
||||
|
||||
theorem getElem_modify [TransCmp cmp] {k k' : α} {f : β → β} {hc : k' ∈ modify t k f} :
|
||||
(modify t k f)[k']'hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr heq |>.mpr <| mem_modify.mp hc
|
||||
f (t[k]'h')
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
t[k']'h' :=
|
||||
DTreeMap.Const.get_modify
|
||||
|
||||
@[simp]
|
||||
theorem getElem_modify_self [TransCmp cmp] {k : α} {f : β → β} {hc : k ∈ modify t k f} :
|
||||
haveI h' : k ∈ t := mem_modify.mp hc
|
||||
(modify t k f)[k]'hc = f (t[k]'h') :=
|
||||
DTreeMap.Const.get_modify_self
|
||||
|
||||
theorem getElem!_modify [TransCmp cmp] {k k' : α} [hi : Inhabited β] {f : β → β} :
|
||||
(modify t k f)[k']! =
|
||||
if cmp k k' = .eq then
|
||||
t[k]? |>.map f |>.get!
|
||||
else
|
||||
t[k']! :=
|
||||
DTreeMap.Const.get!_modify
|
||||
|
||||
@[simp]
|
||||
theorem getElem!_modify_self [TransCmp cmp] {k : α} [Inhabited β] {f : β → β} :
|
||||
(modify t k f)[k]! = (t[k]?.map f).get! :=
|
||||
DTreeMap.Const.get!_modify_self
|
||||
|
||||
theorem getD_modify [TransCmp cmp] {k k' : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
t[k]?.map f |>.getD fallback
|
||||
else
|
||||
getD t k' fallback :=
|
||||
DTreeMap.Const.getD_modify
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self [TransCmp cmp] {k : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k fallback = (t[k]?.map f).getD fallback :=
|
||||
DTreeMap.Const.getD_modify_self
|
||||
|
||||
theorem getKey?_modify [TransCmp cmp] {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
DTreeMap.Const.getKey?_modify
|
||||
|
||||
theorem getKey?_modify_self [TransCmp cmp] {k : α} {f : β → β} :
|
||||
(modify t k f).getKey? k = if k ∈ t then some k else none :=
|
||||
DTreeMap.Const.getKey?_modify_self
|
||||
|
||||
theorem getKey!_modify [TransCmp cmp] [Inhabited α] {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
DTreeMap.Const.getKey!_modify
|
||||
|
||||
theorem getKey!_modify_self [TransCmp cmp] [Inhabited α] {k : α} {f : β → β} :
|
||||
(modify t k f).getKey! k = if k ∈ t then k else default :=
|
||||
DTreeMap.Const.getKey!_modify_self
|
||||
|
||||
theorem getKey_modify [TransCmp cmp] [Inhabited α] {k k' : α} {f : β → β}
|
||||
{hc : k' ∈ modify t k f} :
|
||||
(modify t k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify.mp hc
|
||||
t.getKey k' h' :=
|
||||
DTreeMap.Const.getKey_modify
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self [TransCmp cmp] [Inhabited α] {k : α} {f : β → β}
|
||||
{hc : k ∈ modify t k f} : (modify t k f).getKey k hc = k :=
|
||||
DTreeMap.Const.getKey_modify_self
|
||||
|
||||
theorem getKeyD_modify [TransCmp cmp] {k k' fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
DTreeMap.Const.getKeyD_modify
|
||||
|
||||
theorem getKeyD_modify_self [TransCmp cmp] [Inhabited α] {k fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
DTreeMap.Const.getKeyD_modify_self
|
||||
|
||||
end Modify
|
||||
|
||||
end Std.TreeMap
|
||||
|
|
|
|||
|
|
@ -1557,4 +1557,131 @@ theorem getKeyD_alter_self [TransCmp cmp] [Inhabited α] (h : t.WF) {k : α} {fa
|
|||
|
||||
end Alter
|
||||
|
||||
section Modify
|
||||
|
||||
@[simp]
|
||||
theorem isEmpty_modify [TransCmp cmp] (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).isEmpty = t.isEmpty :=
|
||||
DTreeMap.Raw.Const.isEmpty_modify h
|
||||
|
||||
theorem contains_modify [TransCmp cmp] (h : t.WF) {k k' : α} {f : β → β} :
|
||||
(modify t k f).contains k' = t.contains k' :=
|
||||
DTreeMap.Raw.Const.contains_modify h
|
||||
|
||||
theorem mem_modify [TransCmp cmp] (h : t.WF) {k k' : α} {f : β → β} :
|
||||
k' ∈ modify t k f ↔ k' ∈ t :=
|
||||
DTreeMap.Raw.Const.mem_modify h
|
||||
|
||||
theorem size_modify [TransCmp cmp] (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).size = t.size :=
|
||||
DTreeMap.Raw.Const.size_modify h
|
||||
|
||||
theorem getElem?_modify [TransCmp cmp] (h : t.WF) {k k' : α} {f : β → β} :
|
||||
(modify t k f)[k']? =
|
||||
if cmp k k' = .eq then
|
||||
t[k]?.map f
|
||||
else
|
||||
t[k']? :=
|
||||
DTreeMap.Raw.Const.get?_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getElem?_modify_self [TransCmp cmp] (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f)[k]? = t[k]?.map f :=
|
||||
DTreeMap.Raw.Const.get?_modify_self h
|
||||
|
||||
theorem getElem_modify [TransCmp cmp] (h : t.WF) {k k' : α} {f : β → β} {hc : k' ∈ modify t k f} :
|
||||
(modify t k f)[k']'hc =
|
||||
if heq : cmp k k' = .eq then
|
||||
haveI h' : k ∈ t := mem_congr h heq |>.mpr <| mem_modify h |>.mp hc
|
||||
f (t[k]'h')
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify h |>.mp hc
|
||||
t[k']'h' :=
|
||||
DTreeMap.Raw.Const.get_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getElem_modify_self [TransCmp cmp] (h : t.WF) {k : α} {f : β → β} {hc : k ∈ modify t k f} :
|
||||
haveI h' : k ∈ t := mem_modify h |>.mp hc
|
||||
(modify t k f)[k]'hc = f (t[k]'h') :=
|
||||
DTreeMap.Raw.Const.get_modify_self h
|
||||
|
||||
theorem getElem!_modify [TransCmp cmp] (h : t.WF) {k k' : α} [hi : Inhabited β] {f : β → β} :
|
||||
(modify t k f)[k']! =
|
||||
if cmp k k' = .eq then
|
||||
t[k]? |>.map f |>.get!
|
||||
else
|
||||
t[k']! :=
|
||||
DTreeMap.Raw.Const.get!_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getElem!_modify_self [TransCmp cmp] (h : t.WF) {k : α} [Inhabited β] {f : β → β} :
|
||||
(modify t k f)[k]! = (t[k]?.map f).get! :=
|
||||
DTreeMap.Raw.Const.get!_modify_self h
|
||||
|
||||
theorem getD_modify [TransCmp cmp] (h : t.WF) {k k' : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
t[k]?.map f |>.getD fallback
|
||||
else
|
||||
getD t k' fallback :=
|
||||
DTreeMap.Raw.Const.getD_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getD_modify_self [TransCmp cmp] (h : t.WF) {k : α} {fallback : β} {f : β → β} :
|
||||
getD (modify t k f) k fallback = (t[k]?.map f).getD fallback :=
|
||||
DTreeMap.Raw.Const.getD_modify_self h
|
||||
|
||||
theorem getKey?_modify [TransCmp cmp] (h : t.WF) {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey? k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then some k else none
|
||||
else
|
||||
t.getKey? k' :=
|
||||
DTreeMap.Raw.Const.getKey?_modify h
|
||||
|
||||
theorem getKey?_modify_self [TransCmp cmp] (h : t.WF) {k : α} {f : β → β} :
|
||||
(modify t k f).getKey? k = if k ∈ t then some k else none :=
|
||||
DTreeMap.Raw.Const.getKey?_modify_self h
|
||||
|
||||
theorem getKey!_modify [TransCmp cmp] (h : t.WF) [Inhabited α] {k k' : α} {f : β → β} :
|
||||
(modify t k f).getKey! k' =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else default
|
||||
else
|
||||
t.getKey! k' :=
|
||||
DTreeMap.Raw.Const.getKey!_modify h
|
||||
|
||||
theorem getKey!_modify_self [TransCmp cmp] (h : t.WF) [Inhabited α] {k : α} {f : β → β} :
|
||||
(modify t k f).getKey! k = if k ∈ t then k else default :=
|
||||
DTreeMap.Raw.Const.getKey!_modify_self h
|
||||
|
||||
theorem getKey_modify [TransCmp cmp] (h : t.WF) [Inhabited α] {k k' : α} {f : β → β}
|
||||
{hc : k' ∈ modify t k f} :
|
||||
(modify t k f).getKey k' hc =
|
||||
if cmp k k' = .eq then
|
||||
k
|
||||
else
|
||||
haveI h' : k' ∈ t := mem_modify h |>.mp hc
|
||||
t.getKey k' h' :=
|
||||
DTreeMap.Raw.Const.getKey_modify h
|
||||
|
||||
@[simp]
|
||||
theorem getKey_modify_self [TransCmp cmp] (h : t.WF) [Inhabited α] {k : α} {f : β → β}
|
||||
{hc : k ∈ modify t k f} : (modify t k f).getKey k hc = k :=
|
||||
DTreeMap.Raw.Const.getKey_modify_self h
|
||||
|
||||
theorem getKeyD_modify [TransCmp cmp] (h : t.WF) {k k' fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k' fallback =
|
||||
if cmp k k' = .eq then
|
||||
if k ∈ t then k else fallback
|
||||
else
|
||||
t.getKeyD k' fallback :=
|
||||
DTreeMap.Raw.Const.getKeyD_modify h
|
||||
|
||||
theorem getKeyD_modify_self [TransCmp cmp] (h : t.WF) [Inhabited α] {k fallback : α} {f : β → β} :
|
||||
(modify t k f).getKeyD k fallback = if k ∈ t then k else fallback :=
|
||||
DTreeMap.Raw.Const.getKeyD_modify_self h
|
||||
|
||||
end Modify
|
||||
|
||||
end Std.TreeMap.Raw
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue