36 lines
935 B
Text
36 lines
935 B
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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Author: Leonardo de Moura, Jeremy Avigad
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-/
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prelude
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import init.datatypes init.logic
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open decidable
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universe variables u
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structure subtype {A : Type u} (p : A → Prop) :=
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tag :: (elt_of : A) (has_property : p elt_of)
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namespace subtype
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definition exists_of_subtype {A : Type u} {p : A → Prop} : { x // p x } → ∃ x, p x
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| ⟨a, h⟩ := ⟨a, h⟩
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variables {A : Type u} {p : A → Prop}
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theorem tag_irrelevant {a : A} (h1 h2 : p a) : tag a h1 = tag a h2 :=
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rfl
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protected theorem eq : ∀ {a1 a2 : {x // p x}}, elt_of a1 = elt_of a2 → a1 = a2
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| ⟨x, h1⟩ ⟨.x, h2⟩ rfl := rfl
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end subtype
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open subtype
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variables {A : Type u} {p : A → Prop}
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attribute [instance]
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protected definition subtype.is_inhabited {a : A} (h : p a) : inhabited {x // p x} :=
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⟨⟨a, h⟩⟩
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