311 lines
13 KiB
Text
311 lines
13 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import init.data.fin.basic init.platform
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open Nat
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def uint8Sz : Nat := 256
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structure UInt8 :=
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(val : Fin uint8Sz)
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@[extern cpp "lean::uint8_of_nat"]
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def UInt8.ofNat (n : @& Nat) : UInt8 := ⟨Fin.ofNat n⟩
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@[extern cpp "lean::uint8_to_nat"]
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def UInt8.toNat (n : UInt8) : Nat := n.val.val
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@[extern cpp inline "#1 + #2"]
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def UInt8.add (a b : UInt8) : UInt8 := ⟨a.val + b.val⟩
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@[extern cpp inline "#1 - #2"]
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def UInt8.sub (a b : UInt8) : UInt8 := ⟨a.val - b.val⟩
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@[extern cpp inline "#1 * #2"]
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def UInt8.mul (a b : UInt8) : UInt8 := ⟨a.val * b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt8.div (a b : UInt8) : UInt8 := ⟨a.val / b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 % #2"]
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def UInt8.mod (a b : UInt8) : UInt8 := ⟨a.val % b.val⟩
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@[extern cpp "lean::uint8_modn"]
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def UInt8.modn (a : UInt8) (n : @& Nat) : UInt8 := ⟨a.val %ₙ n⟩
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@[extern cpp inline "#1 & #2"]
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def UInt8.land (a b : UInt8) : UInt8 := ⟨Fin.land a.val b.val⟩
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@[extern cpp inline "#1 | #2"]
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def UInt8.lor (a b : UInt8) : UInt8 := ⟨Fin.lor a.val b.val⟩
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def UInt8.lt (a b : UInt8) : Prop := a.val < b.val
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def UInt8.le (a b : UInt8) : Prop := a.val ≤ b.val
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instance : HasZero UInt8 := ⟨UInt8.ofNat 0⟩
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instance : HasOne UInt8 := ⟨UInt8.ofNat 1⟩
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instance : HasAdd UInt8 := ⟨UInt8.add⟩
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instance : HasSub UInt8 := ⟨UInt8.sub⟩
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instance : HasMul UInt8 := ⟨UInt8.mul⟩
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instance : HasMod UInt8 := ⟨UInt8.mod⟩
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instance : HasModn UInt8 := ⟨UInt8.modn⟩
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instance : HasDiv UInt8 := ⟨UInt8.div⟩
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instance : HasLess UInt8 := ⟨UInt8.lt⟩
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instance : HasLessEq UInt8 := ⟨UInt8.le⟩
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instance : Inhabited UInt8 := ⟨0⟩
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@[extern cpp inline "#1 == #2"]
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def UInt8.decEq (a b : UInt8) : Decidable (a = b) :=
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UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
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if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt8.noConfusion h' (fun h' => absurd h' h))
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@[extern cpp inline "#1 < #2"]
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def UInt8.decLt (a b : UInt8) : Decidable (a < b) :=
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UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n < m))
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@[extern cpp inline "#1 <= #2"]
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def UInt8.decLe (a b : UInt8) : Decidable (a ≤ b) :=
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UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n <= m))
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instance : DecidableEq UInt8 := {decEq := UInt8.decEq}
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instance UInt8.hasDecidableLt (a b : UInt8) : Decidable (a < b) := UInt8.decLt a b
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instance UInt8.hasDecidableLe (a b : UInt8) : Decidable (a ≤ b) := UInt8.decLe a b
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def uint16Sz : Nat := 65536
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structure UInt16 :=
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(val : Fin uint16Sz)
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@[extern cpp "lean::uint16_of_nat"]
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def UInt16.ofNat (n : @& Nat) : UInt16 := ⟨Fin.ofNat n⟩
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@[extern cpp "lean::uint16_to_nat"]
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def UInt16.toNat (n : UInt16) : Nat := n.val.val
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@[extern cpp inline "#1 + #2"]
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def UInt16.add (a b : UInt16) : UInt16 := ⟨a.val + b.val⟩
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@[extern cpp inline "#1 - #2"]
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def UInt16.sub (a b : UInt16) : UInt16 := ⟨a.val - b.val⟩
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@[extern cpp inline "#1 * #2"]
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def UInt16.mul (a b : UInt16) : UInt16 := ⟨a.val * b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt16.div (a b : UInt16) : UInt16 := ⟨a.val / b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 % #2"]
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def UInt16.mod (a b : UInt16) : UInt16 := ⟨a.val % b.val⟩
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@[extern cpp "lean::uint16_modn"]
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def UInt16.modn (a : UInt16) (n : @& Nat) : UInt16 := ⟨a.val %ₙ n⟩
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@[extern cpp inline "#1 & #2"]
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def UInt16.land (a b : UInt16) : UInt16 := ⟨Fin.land a.val b.val⟩
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@[extern cpp inline "#1 | #2"]
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def UInt16.lor (a b : UInt16) : UInt16 := ⟨Fin.lor a.val b.val⟩
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def UInt16.lt (a b : UInt16) : Prop := a.val < b.val
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def UInt16.le (a b : UInt16) : Prop := a.val ≤ b.val
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instance : HasZero UInt16 := ⟨UInt16.ofNat 0⟩
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instance : HasOne UInt16 := ⟨UInt16.ofNat 1⟩
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instance : HasAdd UInt16 := ⟨UInt16.add⟩
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instance : HasSub UInt16 := ⟨UInt16.sub⟩
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instance : HasMul UInt16 := ⟨UInt16.mul⟩
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instance : HasMod UInt16 := ⟨UInt16.mod⟩
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instance : HasModn UInt16 := ⟨UInt16.modn⟩
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instance : HasDiv UInt16 := ⟨UInt16.div⟩
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instance : HasLess UInt16 := ⟨UInt16.lt⟩
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instance : HasLessEq UInt16 := ⟨UInt16.le⟩
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instance : Inhabited UInt16 := ⟨0⟩
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@[extern cpp inline "#1 == #2"]
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def UInt16.decEq (a b : UInt16) : Decidable (a = b) :=
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UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
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if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt16.noConfusion h' (fun h' => absurd h' h))
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@[extern cpp inline "#1 < #2"]
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def UInt16.decLt (a b : UInt16) : Decidable (a < b) :=
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UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n < m))
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@[extern cpp inline "#1 <= #2"]
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def UInt16.decLe (a b : UInt16) : Decidable (a ≤ b) :=
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UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n <= m))
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instance : DecidableEq UInt16 := {decEq := UInt16.decEq}
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instance UInt16.hasDecidableLt (a b : UInt16) : Decidable (a < b) := UInt16.decLt a b
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instance UInt16.hasDecidableLe (a b : UInt16) : Decidable (a ≤ b) := UInt16.decLe a b
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def uint32Sz : Nat := 4294967296
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structure UInt32 :=
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(val : Fin uint32Sz)
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@[extern cpp "lean::uint32_of_nat"]
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def UInt32.ofNat (n : @& Nat) : UInt32 := ⟨Fin.ofNat n⟩
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@[extern cpp "lean::uint32_to_nat"]
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def UInt32.toNat (n : UInt32) : Nat := n.val.val
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@[extern cpp inline "#1 + #2"]
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def UInt32.add (a b : UInt32) : UInt32 := ⟨a.val + b.val⟩
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@[extern cpp inline "#1 - #2"]
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def UInt32.sub (a b : UInt32) : UInt32 := ⟨a.val - b.val⟩
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@[extern cpp inline "#1 * #2"]
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def UInt32.mul (a b : UInt32) : UInt32 := ⟨a.val * b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt32.div (a b : UInt32) : UInt32 := ⟨a.val / b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 % #2"]
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def UInt32.mod (a b : UInt32) : UInt32 := ⟨a.val % b.val⟩
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@[extern cpp "lean::uint32_modn"]
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def UInt32.modn (a : UInt32) (n : @& Nat) : UInt32 := ⟨a.val %ₙ n⟩
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@[extern cpp inline "#1 & #2"]
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def UInt32.land (a b : UInt32) : UInt32 := ⟨Fin.land a.val b.val⟩
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@[extern cpp inline "#1 | #2"]
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def UInt32.lor (a b : UInt32) : UInt32 := ⟨Fin.lor a.val b.val⟩
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def UInt32.lt (a b : UInt32) : Prop := a.val < b.val
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def UInt32.le (a b : UInt32) : Prop := a.val ≤ b.val
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instance : HasZero UInt32 := ⟨UInt32.ofNat 0⟩
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instance : HasOne UInt32 := ⟨UInt32.ofNat 1⟩
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instance : HasAdd UInt32 := ⟨UInt32.add⟩
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instance : HasSub UInt32 := ⟨UInt32.sub⟩
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instance : HasMul UInt32 := ⟨UInt32.mul⟩
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instance : HasMod UInt32 := ⟨UInt32.mod⟩
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instance : HasModn UInt32 := ⟨UInt32.modn⟩
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instance : HasDiv UInt32 := ⟨UInt32.div⟩
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instance : HasLess UInt32 := ⟨UInt32.lt⟩
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instance : HasLessEq UInt32 := ⟨UInt32.le⟩
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instance : Inhabited UInt32 := ⟨0⟩
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@[extern cpp inline "#1 == #2"]
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def UInt32.decEq (a b : UInt32) : Decidable (a = b) :=
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UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
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if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt32.noConfusion h' (fun h' => absurd h' h))
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@[extern cpp inline "#1 < #2"]
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def UInt32.decLt (a b : UInt32) : Decidable (a < b) :=
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UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n < m))
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@[extern cpp inline "#1 <= #2"]
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def UInt32.decLe (a b : UInt32) : Decidable (a ≤ b) :=
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UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n <= m))
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instance : DecidableEq UInt32 := {decEq := UInt32.decEq}
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instance UInt32.hasDecidableLt (a b : UInt32) : Decidable (a < b) := UInt32.decLt a b
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instance UInt32.hasDecidableLe (a b : UInt32) : Decidable (a ≤ b) := UInt32.decLe a b
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def uint64Sz : Nat := 18446744073709551616
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structure UInt64 :=
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(val : Fin uint64Sz)
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@[extern cpp "lean::uint64_of_nat"]
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def UInt64.ofNat (n : @& Nat) : UInt64 := ⟨Fin.ofNat n⟩
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@[extern cpp "lean::uint64_to_nat"]
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def UInt64.toNat (n : UInt64) : Nat := n.val.val
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@[extern cpp inline "#1 + #2"]
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def UInt64.add (a b : UInt64) : UInt64 := ⟨a.val + b.val⟩
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@[extern cpp inline "#1 - #2"]
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def UInt64.sub (a b : UInt64) : UInt64 := ⟨a.val - b.val⟩
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@[extern cpp inline "#1 * #2"]
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def UInt64.mul (a b : UInt64) : UInt64 := ⟨a.val * b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 / #2"]
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def UInt64.div (a b : UInt64) : UInt64 := ⟨a.val / b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 % #2"]
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def UInt64.mod (a b : UInt64) : UInt64 := ⟨a.val % b.val⟩
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@[extern cpp "lean::uint64_modn"]
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def UInt64.modn (a : UInt64) (n : @& Nat) : UInt64 := ⟨a.val %ₙ n⟩
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@[extern cpp inline "#1 & #2"]
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def UInt64.land (a b : UInt64) : UInt64 := ⟨Fin.land a.val b.val⟩
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@[extern cpp inline "#1 | #2"]
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def UInt64.lor (a b : UInt64) : UInt64 := ⟨Fin.lor a.val b.val⟩
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def UInt64.lt (a b : UInt64) : Prop := a.val < b.val
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def UInt64.le (a b : UInt64) : Prop := a.val ≤ b.val
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instance : HasZero UInt64 := ⟨UInt64.ofNat 0⟩
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instance : HasOne UInt64 := ⟨UInt64.ofNat 1⟩
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instance : HasAdd UInt64 := ⟨UInt64.add⟩
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instance : HasSub UInt64 := ⟨UInt64.sub⟩
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instance : HasMul UInt64 := ⟨UInt64.mul⟩
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instance : HasMod UInt64 := ⟨UInt64.mod⟩
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instance : HasModn UInt64 := ⟨UInt64.modn⟩
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instance : HasDiv UInt64 := ⟨UInt64.div⟩
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instance : HasLess UInt64 := ⟨UInt64.lt⟩
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instance : HasLessEq UInt64 := ⟨UInt64.le⟩
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instance : Inhabited UInt64 := ⟨0⟩
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@[extern cpp inline "#1 == #2"]
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def UInt64.decEq (a b : UInt64) : Decidable (a = b) :=
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UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
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if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt64.noConfusion h' (fun h' => absurd h' h))
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@[extern cpp inline "#1 < #2"]
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def UInt64.decLt (a b : UInt64) : Decidable (a < b) :=
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UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n < m))
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@[extern cpp inline "#1 <= #2"]
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def UInt64.decLe (a b : UInt64) : Decidable (a ≤ b) :=
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UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n <= m))
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instance : DecidableEq UInt64 := {decEq := UInt64.decEq}
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instance UInt64.hasDecidableLt (a b : UInt64) : Decidable (a < b) := UInt64.decLt a b
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instance UInt64.hasDecidableLe (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
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def usizeSz : Nat := (2:Nat) ^ System.platform.nbits
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structure USize :=
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(val : Fin usizeSz)
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@[extern cpp "lean::usize_of_nat"]
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def USize.ofNat (n : @& Nat) : USize := ⟨Fin.ofNat n⟩
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@[extern cpp "lean::usize_to_nat"]
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def USize.toNat (n : USize) : Nat := n.val.val
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@[extern cpp inline "#1 + #2"]
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def USize.add (a b : USize) : USize := ⟨a.val + b.val⟩
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@[extern cpp inline "#1 - #2"]
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def USize.sub (a b : USize) : USize := ⟨a.val - b.val⟩
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@[extern cpp inline "#1 * #2"]
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def USize.mul (a b : USize) : USize := ⟨a.val * b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 / #2"]
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def USize.div (a b : USize) : USize := ⟨a.val / b.val⟩
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@[extern cpp inline "#2 == 0 ? 0 : #1 % #2"]
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def USize.mod (a b : USize) : USize := ⟨a.val % b.val⟩
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@[extern cpp "lean::usize_modn"]
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def USize.modn (a : USize) (n : @& Nat) : USize := ⟨a.val %ₙ n⟩
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@[extern cpp inline "#1 & #2"]
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def USize.land (a b : USize) : USize := ⟨Fin.land a.val b.val⟩
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@[extern cpp inline "#1 | #2"]
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def USize.lor (a b : USize) : USize := ⟨Fin.lor a.val b.val⟩
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@[extern cpp inline "#1"]
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def USize.ofUInt32 (a : UInt32) : USize := USize.ofNat (UInt32.toNat a)
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@[extern cpp inline "((lean::usize)#1)"]
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def USize.ofUInt64 (a : UInt64) : USize := USize.ofNat (UInt64.toNat a)
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-- TODO(Leo): give reference implementation for shift_left and shift_right, and define them for other UInt types
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@[extern cpp inline "#1 << #2"]
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constant USize.shift_left (a b : USize) : USize := USize.ofNat (default _)
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@[extern cpp inline "#1 >> #2"]
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constant USize.shift_right (a b : USize) : USize := USize.ofNat (default _)
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def USize.lt (a b : USize) : Prop := a.val < b.val
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def USize.le (a b : USize) : Prop := a.val ≤ b.val
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instance : HasZero USize := ⟨USize.ofNat 0⟩
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instance : HasOne USize := ⟨USize.ofNat 1⟩
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instance : HasAdd USize := ⟨USize.add⟩
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instance : HasSub USize := ⟨USize.sub⟩
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instance : HasMul USize := ⟨USize.mul⟩
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instance : HasMod USize := ⟨USize.mod⟩
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instance : HasModn USize := ⟨USize.modn⟩
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instance : HasDiv USize := ⟨USize.div⟩
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instance : HasLess USize := ⟨USize.lt⟩
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instance : HasLessEq USize := ⟨USize.le⟩
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instance : Inhabited USize := ⟨0⟩
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@[extern cpp inline "#1 == #2"]
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def USize.decEq (a b : USize) : Decidable (a = b) :=
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USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
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if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => USize.noConfusion h' (fun h' => absurd h' h))
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@[extern cpp inline "#1 < #2"]
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def USize.decLt (a b : USize) : Decidable (a < b) :=
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USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n < m))
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@[extern cpp inline "#1 <= #2"]
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def USize.decLe (a b : USize) : Decidable (a ≤ b) :=
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USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
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inferInstanceAs (Decidable (n <= m))
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instance : DecidableEq USize := {decEq := USize.decEq}
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instance USize.hasDecidableLt (a b : USize) : Decidable (a < b) := USize.decLt a b
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instance USize.hasDecidableLe (a b : USize) : Decidable (a ≤ b) := USize.decLe a b
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theorem USize.modnLt {m : Nat} : ∀ (u : USize), m > 0 → USize.toNat (u %ₙ m) < m
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| ⟨u⟩ h := Fin.modnLt u h
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