This module provides slice notation for TreeMap slices and implements an iterator for those slices.

instance Std.TreeMap.instSliceableRiiSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Rii.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RiiSlice α β)

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theorem Std.TreeMap.toList_rii {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) {t : TreeMap α β cmp} : Slice.toList (Rii.Sliceable.mkSlice t *...*) = t.toList

instance Std.TreeMap.instSliceableRicSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Ric.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RicSlice α β)

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theorem Std.TreeMap.toList_ric {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {bound : α} : Slice.toList (Ric.Sliceable.mkSlice t *...=bound) = List.filter (fun (e : α × β) => (cmp e.fst bound).isLE) t.toList

instance Std.TreeMap.instSliceableRioSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Rio.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RioSlice α β)

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theorem Std.TreeMap.toList_rio {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {bound : α} : Slice.toList (Rio.Sliceable.mkSlice t *...bound) = List.filter (fun (e : α × β) => (cmp e.fst bound).isLT) t.toList

instance Std.TreeMap.instSliceableRciSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Rci.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RciSlice α β)

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theorem Std.TreeMap.toList_rci {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {bound : α} : Slice.toList (Rci.Sliceable.mkSlice t bound...*) = List.filter (fun (e : α × β) => (cmp e.fst bound).isGE) t.toList

instance Std.TreeMap.instSliceableRcoSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Rco.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RcoSlice α β)

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theorem Std.TreeMap.toList_rco {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {lowerBound upperBound : α} : Slice.toList (Rco.Sliceable.mkSlice t lowerBound...upperBound) = List.filter (fun (e : α × β) => decide ((cmp e.fst lowerBound).isGE = true ∧ (cmp e.fst upperBound).isLT = true)) t.toList

instance Std.TreeMap.instSliceableRccSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Rcc.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RccSlice α β)

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theorem Std.TreeMap.toList_rcc {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {lowerBound upperBound : α} : Slice.toList (Rcc.Sliceable.mkSlice t lowerBound...=upperBound) = List.filter (fun (e : α × β) => decide ((cmp e.fst lowerBound).isGE = true ∧ (cmp e.fst upperBound).isLE = true)) t.toList

instance Std.TreeMap.instSliceableRoiSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Roi.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RoiSlice α β)

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theorem Std.TreeMap.toList_roi {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {bound : α} : Slice.toList (Roi.Sliceable.mkSlice t bound<...*) = List.filter (fun (e : α × β) => (cmp e.fst bound).isGT) t.toList

instance Std.TreeMap.instSliceableRocSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Roc.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RocSlice α β)

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theorem Std.TreeMap.toList_roc {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {lowerBound upperBound : α} : Slice.toList (Roc.Sliceable.mkSlice t lowerBound<...=upperBound) = List.filter (fun (e : α × β) => decide ((cmp e.fst lowerBound).isGT = true ∧ (cmp e.fst upperBound).isLE = true)) t.toList

instance Std.TreeMap.instSliceableRooSlice {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) : Roo.Sliceable (TreeMap α β cmp) α (DTreeMap.Internal.Const.RooSlice α β)

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theorem Std.TreeMap.toList_roo {α : Type u} {β : Type v} (cmp : α → α → Ordering := by exact compare) [TransCmp cmp] {t : TreeMap α β cmp} {lowerBound upperBound : α} : Slice.toList (Roo.Sliceable.mkSlice t lowerBound<...upperBound) = List.filter (fun (e : α × β) => decide ((cmp e.fst lowerBound).isGT = true ∧ (cmp e.fst upperBound).isLT = true)) t.toList