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