a3a99d3875
This PR adds all missing tree map lemmas about the interactions of the functions `empty`, `isEmpty`, `contains`, `size`, `insert(IfNew)` and `erase`. --------- Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
41 lines
1.2 KiB
Text
41 lines
1.2 KiB
Text
/-
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Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Paul Reichert
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-/
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import Std.Data.TreeSet.Basic
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import Std.Data.TreeSet.Lemmas
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open Std
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variable {α : Type u} {β : Type v} [Ord α]
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def mkDTreeMapSingleton (a : α) (b : β) : DTreeMap α (fun _ => β) := Id.run do
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let mut m : DTreeMap α (fun _ => β) := ∅
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m := m.insert a b
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return m
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def mkTreeMapSingleton (a : α) (b : β) : TreeMap α β := Id.run do
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let mut m : TreeMap α β := ∅
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m := m.insert a b
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return m
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def mkTreeSetSingleton (a : α) : TreeSet α := Id.run do
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let mut m : TreeSet α := ∅
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m := m.insert a
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return m
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example [TransOrd α] [LawfulEqOrd α] (a : α) (b : β) : Option β :=
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mkDTreeMapSingleton a b |>.get? a
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example [TransOrd α] [LawfulEqOrd α] (a : α) (b : β) : Option β :=
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(mkTreeMapSingleton a b)[a]?
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example [TransOrd α] (a : α) (b : β) : (mkTreeMapSingleton a b).contains a := by
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simp [mkTreeMapSingleton, Id.run]
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example [TransOrd α] (a : α) (b : β) : (mkDTreeMapSingleton a b).contains a := by
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simp [mkDTreeMapSingleton, Id.run]
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example [TransOrd α] (a : α) : (mkTreeSetSingleton a).contains a := by
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simp [mkTreeSetSingleton, Id.run]
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