Drop `Common.Set.Interval` and `Common.Set.Partition`.

Bookshelf/Apostol/Chapter_1_11.lean

@@ -1,8 +1,6 @@
-import Mathlib.Data.Real.Basic
-
 import Common.Real.Floor
-import Common.Geometry.StepFunction
 import Common.Set.Basic
+import Mathlib.Data.Real.Basic
 
 /-! # Apostol.Chapter_1_11 -/
 

Bookshelf/Apostol/Chapter_I_03.lean

@@ -1,6 +1,5 @@
-import Mathlib.Data.Real.Basic
-
 import Common.Set
+import Mathlib.Data.Real.Basic
 
 /-! # Apostol.Chapter_I_03
 

Common/Geometry/StepFunction.lean

@@ -1,7 +1,7 @@
 import Common.Finset
 import Common.Geometry.Rectangle.Orthogonal
 import Common.List.Basic
-import Common.Set.Partition
+import Common.List.NonEmpty
 
 /-! # Common.Geometry.StepFunction
 
@@ -10,19 +10,63 @@ Characterization of step functions.
 
 namespace Geometry
 
-open Set Partition
+/--
+An interval defines a range of values, characterized by a "left" value and a
+"right" value. We require these values to be distinct; we do not support the
+notion of an empty interval.
+-/
+structure Interval (α : Type _) [LT α] where
+  left : α
+  right : α
+  h : left < right
+
+namespace Interval
+
+/--
+Computes the size of the interval.
+-/
+def size [LT α] [Sub α] (i : Interval α) : α := i.right - i.left
+
+/--
+Computes the midpoint of the interval.
+-/
+def midpoint [LT α] [Add α] [HDiv α ℝ α] (i : Interval α) : α :=
+  (i.left + i.right) / (2 : ℝ)
+
+/--
+Convert an `Interval` into a `Set.Ico`.
+-/
+def toIco [Preorder α] (i : Interval α) : Set α := Set.Ico i.left i.right
+
+/--
+Convert an `Interval` into a `Set.Ioc`.
+-/
+def toIoc [Preorder α] (i : Interval α) : Set α := Set.Ioc i.left i.right
+
+/--
+Convert an `Interval` into a `Set.Icc`.
+-/
+def toIcc [Preorder α] (i : Interval α) : Set α := Set.Icc i.left i.right
+
+/--
+Convert an `Interval` into a `Set.Ioo`.
+-/
+def toIoo [Preorder α] (i : Interval α) : Set α := Set.Ioo i.left i.right
+
+end Interval
 
 /--
 A function `f`, whose domain is a closed interval `[a, b]`, is a `StepFunction`
-if there exists a `Partition` `P = {x₀, x₁, …, xₙ}` of `[a, b]` such that `f` is
+if there exists a partition `P = {x₀, x₁, …, xₙ}` of `[a, b]` such that `f` is
 constant on each open subinterval of `P`.
 
 Instead of maintaining a function from `[a, b]` to `ℝ`, we instead maintain a
-function that maps each `Partition` index to some constant value. 
+function that maps each partition index to some constant value. 
 -/
 structure StepFunction where
-  p : Partition ℝ
-  toFun : Fin p.ivls.length → ℝ
+  ivls : List.NonEmpty (Interval ℝ)
+  connected : ∀ I ∈ ivls.toList.pairwise (·.right = ·.left), I
+  toFun : Fin ivls.length → ℝ
 
 namespace StepFunction
 
@@ -30,8 +74,8 @@ namespace StepFunction
 The ordinate set of the `StepFunction`.
 -/
 def toSet (sf : StepFunction) : Set Point :=
-  ⋃ i ∈ Finset.finRange sf.p.ivls.length,
-    let I := sf.p.ivls[i]
+  ⋃ i ∈ Finset.finRange sf.ivls.length,
+    let I := sf.ivls[i]
     Rectangle.Orthogonal.toSet
       ⟨
         {

Common/Set.lean

@@ -1,4 +1,2 @@
 import Common.Set.Basic
-import Common.Set.Interval
-import Common.Set.Partition
 import Common.Set.Peano

Common/Set/Interval.lean

@@ -1,56 +0,0 @@
-import Mathlib.Data.Real.Basic
-import Mathlib.Data.Set.Intervals.Basic
-
-/-! # Common.Set.Interval
-
-A representation of a range of values.
--/
-
-namespace Set
-
-/--
-An interval defines a range of values, characterized by a "left" value and a
-"right" value. We require these values to be distinct; we do not support the
-notion of an empty interval.
--/
-structure Interval (α : Type _) [LT α] where
-  left : α
-  right : α
-  h : left < right
-
-namespace Interval
-
-/--
-Computes the size of the interval.
--/
-def size [LT α] [Sub α] (i : Interval α) : α := i.right - i.left
-
-/--
-Computes the midpoint of the interval.
--/
-def midpoint [LT α] [Add α] [HDiv α ℝ α] (i : Interval α) : α :=
-  (i.left + i.right) / (2 : ℝ)
-
-/--
-Convert an `Interval` into a `Set.Ico`.
--/
-def toIco [Preorder α] (i : Interval α) : Set α := Set.Ico i.left i.right
-
-/--
-Convert an `Interval` into a `Set.Ioc`.
--/
-def toIoc [Preorder α] (i : Interval α) : Set α := Set.Ioc i.left i.right
-
-/--
-Convert an `Interval` into a `Set.Icc`.
--/
-def toIcc [Preorder α] (i : Interval α) : Set α := Set.Icc i.left i.right
-
-/--
-Convert an `Interval` into a `Set.Ioo`.
--/
-def toIoo [Preorder α] (i : Interval α) : Set α := Set.Ioo i.left i.right
-
-end Interval
-
-end Set

Common/Set/Partition.lean

@@ -1,37 +0,0 @@
-import Common.List.Basic
-import Common.List.NonEmpty
-import Common.Set.Interval
-
-/-! # Common.Set.Partition
-
-Additional theorems and definitions useful in the context of sets.
--/
-
-namespace Set
-
-/--
-A `Partition` is a finite subset of `[a, b]` containing points `a` and `b`.
-
-We use a `List.NonEmpty` internally to ensure the existence of at least one
-`Interval`, which cannot be empty. Thus our `Partition` can never be empty.
-The intervals are sorted via the `connected` proposition.
--/
-structure Partition (α : Type _) [LT α] where
-  ivls : List.NonEmpty (Interval α)
-  connected : ∀ I ∈ ivls.toList.pairwise (·.right = ·.left), I
-
-namespace Partition
-
-/--
-Return the left-most endpoint of the `Partition`.
--/
-def left [LT α] (p : Partition α) := p.ivls.head.left
-
-/--
-Return the right-most endpoint of the `Partition`.
--/
-def right [LT α] (p : Partition α) := p.ivls.last.right
-
-end Partition
-
-end Set