6056dee22f
This PR adds `LawfulOrderOrd` instances for `Nat`, `Int`, and all fixed-width integer types (`Int8`, `Int16`, `Int32`, `Int64`, `ISize`, `UInt8`, `UInt16`, `UInt32`, `UInt64`, `USize`). These instances establish that the `Ord` instances for these types are compatible with their `LE` instances. Additionally, this PR adds a few missing lemmas and `grind` patterns.
115 lines
3.5 KiB
Text
115 lines
3.5 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: Markus Himmel, Paul Reichert, Robin Arnez
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-/
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module
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prelude
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public import Init.Data.Order.Ord
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public import Init.Data.Order.ClassesExtra
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public import Init.Data.UInt.Basic
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import Init.Data.UInt.Lemmas
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import Init.Data.Order.Lemmas
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public section
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/-!
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# Instances for fixed width unsigned integer types.
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-/
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set_option autoImplicit false
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set_option linter.missingDocs true
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open Std
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namespace UInt8
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instance : Ord UInt8 where
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compare x y := compareOfLessAndEq x y
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instance : TransOrd UInt8 :=
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TransOrd.compareOfLessAndEq_of_antisymm_of_trans_of_total_of_not_le
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UInt8.le_antisymm UInt8.le_trans UInt8.le_total UInt8.not_le
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instance : LawfulEqOrd UInt8 where
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eq_of_compare h := compareOfLessAndEq_eq_eq UInt8.le_refl UInt8.not_le |>.mp h
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instance : LawfulOrderOrd UInt8 where
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isLE_compare _ _ := isLE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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isGE_compare _ _ := isGE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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end UInt8
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namespace UInt16
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instance : Ord UInt16 where
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compare x y := compareOfLessAndEq x y
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instance : TransOrd UInt16 :=
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TransOrd.compareOfLessAndEq_of_antisymm_of_trans_of_total_of_not_le
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UInt16.le_antisymm UInt16.le_trans UInt16.le_total UInt16.not_le
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instance : LawfulEqOrd UInt16 where
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eq_of_compare h := compareOfLessAndEq_eq_eq UInt16.le_refl UInt16.not_le |>.mp h
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instance : LawfulOrderOrd UInt16 where
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isLE_compare _ _ := isLE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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isGE_compare _ _ := isGE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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end UInt16
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namespace UInt32
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instance : Ord UInt32 where
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compare x y := compareOfLessAndEq x y
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instance : TransOrd UInt32 :=
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TransOrd.compareOfLessAndEq_of_antisymm_of_trans_of_total_of_not_le
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UInt32.le_antisymm UInt32.le_trans UInt32.le_total UInt32.not_le
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instance : LawfulEqOrd UInt32 where
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eq_of_compare h := compareOfLessAndEq_eq_eq UInt32.le_refl UInt32.not_le |>.mp h
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instance : LawfulOrderOrd UInt32 where
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isLE_compare _ _ := isLE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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isGE_compare _ _ := isGE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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end UInt32
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namespace UInt64
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instance : Ord UInt64 where
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compare x y := compareOfLessAndEq x y
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instance : TransOrd UInt64 :=
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TransOrd.compareOfLessAndEq_of_antisymm_of_trans_of_total_of_not_le
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UInt64.le_antisymm UInt64.le_trans UInt64.le_total UInt64.not_le
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instance : LawfulEqOrd UInt64 where
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eq_of_compare h := compareOfLessAndEq_eq_eq UInt64.le_refl UInt64.not_le |>.mp h
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instance : LawfulOrderOrd UInt64 where
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isLE_compare _ _ := isLE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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isGE_compare _ _ := isGE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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end UInt64
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namespace USize
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instance : Ord USize where
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compare x y := compareOfLessAndEq x y
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instance : TransOrd USize :=
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TransOrd.compareOfLessAndEq_of_antisymm_of_trans_of_total_of_not_le
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USize.le_antisymm USize.le_trans USize.le_total USize.not_le
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instance : LawfulEqOrd USize where
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eq_of_compare h := compareOfLessAndEq_eq_eq USize.le_refl USize.not_le |>.mp h
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instance : LawfulOrderOrd USize where
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isLE_compare _ _ := isLE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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isGE_compare _ _ := isGE_compareOfLessAndEq Std.le_antisymm Std.not_le (fun _ _ => Std.le_total)
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end USize
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