29 lines
1.1 KiB
Text
29 lines
1.1 KiB
Text
/-
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Copyright (c) 2016 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, Jeremy Avigad
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The sum type, aka disjoint union.
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-/
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prelude
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import init.core
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notation α ⊕ β := sum α β
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universes u v
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variables {α : Type u} {β : Type v}
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instance sum.inhabited_left [h : inhabited α] : inhabited (α ⊕ β) :=
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⟨sum.inl (default α)⟩
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instance sum.inhabited_right [h : inhabited β] : inhabited (α ⊕ β) :=
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⟨sum.inr (default β)⟩
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instance {α : Type u} {β : Type v} [decidable_eq α] [decidable_eq β] : decidable_eq (α ⊕ β)
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| (sum.inl a) (sum.inl b) := if h : a = b then is_true (h ▸ rfl)
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else is_false (λ h', sum.no_confusion h' (λ h', absurd h' h))
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| (sum.inr a) (sum.inr b) := if h : a = b then is_true (h ▸ rfl)
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else is_false (λ h', sum.no_confusion h' (λ h', absurd h' h))
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| (sum.inr a) (sum.inl b) := is_false (λ h, sum.no_confusion h)
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| (sum.inl a) (sum.inr b) := is_false (λ h, sum.no_confusion h)
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