c039e29a3f
This PR cuts some edges from the import graph. Specifically: - `TreeMap` and `HashMap` no longer depend on `String`, so now the expensive things are all in parallel instead of partially in sequence - `Omega` no longer relies on `List` lemmas - The section of the import graph between `Init.Omega` and `Init.Data.Bitvec.Lemmas` is cleaned up a bit
81 lines
2.7 KiB
Text
81 lines
2.7 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.Vector.Lemmas
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public section
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/-!
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# Instances for `Vector`
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-/
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universe u
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namespace Vector
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open Std
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@[expose]
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protected def compareLex {α n} (cmp : α → α → Ordering) (a b : Vector α n) : Ordering :=
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Array.compareLex cmp a.toArray b.toArray
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instance {α n} [Ord α] : Ord (Vector α n) where
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compare := Vector.compareLex compare
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protected theorem compareLex_eq_compareLex_toArray {α n cmp} {a b : Vector α n} :
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Vector.compareLex cmp a b = Array.compareLex cmp a.toArray b.toArray :=
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rfl
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protected theorem compareLex_eq_compareLex_toList {α n cmp} {a b : Vector α n} :
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Vector.compareLex cmp a b = List.compareLex cmp a.toList b.toList :=
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Array.compareLex_eq_compareLex_toList
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protected theorem compare_eq_compare_toArray {α n} [Ord α] {a b : Vector α n} :
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compare a b = compare a.toArray b.toArray :=
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rfl
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protected theorem compare_eq_compare_toList {α n} [Ord α] {a b : Vector α n} :
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compare a b = compare a.toList b.toList :=
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Array.compare_eq_compare_toList
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variable {α} {cmp : α → α → Ordering}
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instance [ReflCmp cmp] {n} : ReflCmp (Vector.compareLex cmp (n := n)) where
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compare_self := ReflCmp.compare_self (cmp := Array.compareLex cmp)
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instance [LawfulEqCmp cmp] {n} : LawfulEqCmp (Vector.compareLex cmp (n := n)) where
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eq_of_compare := by simp [Vector.compareLex_eq_compareLex_toArray]
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instance [BEq α] [LawfulBEqCmp cmp] {n} : LawfulBEqCmp (Vector.compareLex cmp (n := n)) where
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compare_eq_iff_beq := by simp [Vector.compareLex_eq_compareLex_toArray,
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LawfulBEqCmp.compare_eq_iff_beq]
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instance [OrientedCmp cmp] {n} : OrientedCmp (Vector.compareLex cmp (n := n)) where
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eq_swap := OrientedCmp.eq_swap (cmp := Array.compareLex cmp)
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instance [TransCmp cmp] {n} : TransCmp (Vector.compareLex cmp (n := n)) where
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isLE_trans := TransCmp.isLE_trans (cmp := Array.compareLex cmp)
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instance [Ord α] [ReflOrd α] {n} : ReflOrd (Vector α n) :=
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inferInstanceAs <| ReflCmp (Vector.compareLex compare)
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instance [Ord α] [LawfulEqOrd α] {n} : LawfulEqOrd (Vector α n) :=
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inferInstanceAs <| LawfulEqCmp (Vector.compareLex compare)
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instance [Ord α] [BEq α] [LawfulBEqOrd α] {n} : LawfulBEqOrd (Vector α n) :=
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inferInstanceAs <| LawfulBEqCmp (Vector.compareLex compare)
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instance [Ord α] [OrientedOrd α] {n} : OrientedOrd (Vector α n) :=
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inferInstanceAs <| OrientedCmp (Vector.compareLex compare)
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instance [Ord α] [TransOrd α] {n} : TransOrd (Vector α n) :=
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inferInstanceAs <| TransCmp (Vector.compareLex compare)
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end Vector
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