2014-08-01 00:48:51 +00:00
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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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2014-08-04 02:57:29 +00:00
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import logic.connectives.basic
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2014-08-01 00:48:51 +00:00
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2014-08-15 03:12:54 +00:00
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inductive inhabited (A : Type) : Type :=
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2014-08-01 00:48:51 +00:00
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| inhabited_intro : A → inhabited A
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2014-08-15 03:12:54 +00:00
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definition inhabited_elim {A : Type} {B : Type} (H1 : inhabited A) (H2 : A → B) : B :=
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inhabited_rec H2 H1
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2014-08-15 03:12:54 +00:00
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definition inhabited_Prop [instance] : inhabited Prop :=
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inhabited_intro true
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definition inhabited_fun [instance] (A : Type) {B : Type} (H : inhabited B) : inhabited (A → B) :=
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inhabited_elim H (take b, inhabited_intro (λa, b))
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definition default (A : Type) {H : inhabited A} : A := inhabited_elim H (take a, a)
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