24cafcd65d
This PR provides the means to quickly provide all the order instances associated with some high-level order structure (preorder, partial order, linear preorder, linear order). This can be done via the factory functions `PreorderPackage.ofLE`, `PartialOrderPackage.ofLE`, `LinearPreorderPackage.ofLE` and `LinearOrderPackage.ofLE`.
87 lines
2.3 KiB
Text
87 lines
2.3 KiB
Text
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import Init.Data.Order.PackageFactories
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open Std
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variable {α : Type u}
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opaque X : Type := Unit
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namespace X
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#guard_msgs(error, drop warning) in
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opaque instLE : LE X := sorry
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attribute [scoped instance] instLE
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#guard_msgs(error, drop warning) in
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@[scoped instance] opaque instDecidableLE : DecidableLE X := sorry
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#guard_msgs(error, drop warning) in
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@[instance] opaque instTotal : Total (α := X) (· ≤ ·) := sorry
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#guard_msgs(error, drop warning) in
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@[instance] opaque instAntisymm : Antisymm (α := X) (· ≤ ·) := sorry
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#guard_msgs(error, drop warning) in
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@[instance] opaque instTrans : Trans (α := X) (· ≤ ·) (· ≤ ·) (· ≤ ·) := sorry
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namespace Package
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scoped instance packageOfLE : LinearOrderPackage X := .ofLE X
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example : instLE = (inferInstanceAs (PreorderPackage X)).toLE := rfl
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example : IsLinearOrder X := inferInstance
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example : LawfulOrderLT X := inferInstance
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example : LawfulOrderOrd X := inferInstance
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example : LawfulOrderMin X := inferInstance
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example : LawfulOrderMax X := inferInstance
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example : LawfulOrderLeftLeaningMin X := inferInstance
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example : LawfulOrderLeftLeaningMax X := inferInstance
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end Package
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end X
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section
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def packageWithoutSynthesizableInstances : LinearOrderPackage X := .ofLE X {
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le := X.instLE
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decidableLE := X.instDecidableLE }
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end
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section
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attribute [local instance] X.Package.packageOfLE
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def packageWithoutSynthesizableInstances' : LinearOrderPackage X := .ofLE X {
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le := X.instLE
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decidableLE := X.instDecidableLE
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}
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end
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/--
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error: could not synthesize default value for field 'lt_iff' of 'Std.Packages.PreorderOfLEArgs' using tactics
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---
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error: Failed to automatically prove that the `LE` and `LT` instances are compatible. Please ensure that a `LawfulOrderLT` instance can be synthesized or manually provide the field `lt_iff`.
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α : Type u
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inst✝² : LE α
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inst✝¹ : DecidableLE α
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inst✝ : LT α
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this✝¹ : LE α := inferInstance
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this✝ : LT α := inferInstance
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⊢ ∀ (a b : α), a < b ↔ a ≤ b ∧ ¬b ≤ a
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-/
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#guard_msgs in
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def packageOfLEOfLT1 [LE α] [DecidableLE α] [LT α] : PreorderPackage α := .ofLE α {
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le_refl := sorry
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le_trans := sorry
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}
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def packageOfLEOfLT2 [LE α] [DecidableLE α] [LT α] (h : ∀ a b : α, a < b ↔ a ≤ b ∧ ¬ b ≤ a) :
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PreorderPackage α := .ofLE α {
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lt_iff := h
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le_refl := sorry
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le_trans := sorry
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}
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