0163c1aa5b
We cannot mk_dec_eq_instance everywhere in the init folder because some dec_eq instances are used to define the tactic mk_dec_eq_instance.
39 lines
1.2 KiB
Text
39 lines
1.2 KiB
Text
/-
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Copyright (c) 2014 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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import logic.connectives
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open inhabited eq.ops
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notation A ⊎ B := sum A B
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namespace sum
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notation A + B := sum A B
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namespace low_precedence_plus
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reserve infixr ` + `:25 -- conflicts with notation for addition
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infixr + := sum
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end low_precedence_plus
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variables {A B : Type}
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definition inl_ne_inr (a : A) (b : B) : inl a ≠ inr b :=
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sorry -- by contradiction
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definition inr_ne_inl (b : B) (a : A) : inr b ≠ inl a :=
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sorry -- by contradiction
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definition inl_inj {a₁ a₂ : A} : intro_left B a₁ = intro_left B a₂ → a₁ = a₂ :=
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sorry -- assume H, by injection H; assumption
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definition inr_inj {b₁ b₂ : B} : intro_right A b₁ = intro_right A b₂ → b₁ = b₂ :=
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sorry -- assume H, by injection H; assumption
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protected definition is_inhabited_left [instance] [h : inhabited A] : inhabited (A + B) :=
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inhabited.mk (inl (default A))
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protected definition is_inhabited_right [instance] [h : inhabited B] : inhabited (A + B) :=
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inhabited.mk (inr (default B))
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end sum
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