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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2014-10-05 17:50:13 +00:00
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import logic.connectives
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2014-08-01 00:48:51 +00:00
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2014-10-08 01:02:15 +00:00
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inductive inhabited [class] (A : Type) : Type :=
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2014-09-04 23:36:06 +00:00
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mk : A → inhabited A
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2014-08-01 00:48:51 +00:00
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2014-08-20 02:32:44 +00:00
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namespace inhabited
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2014-09-19 22:04:52 +00:00
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protected definition destruct {A : Type} {B : Type} (H1 : inhabited A) (H2 : A → B) : B :=
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inhabited.rec H2 H1
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2014-08-01 00:48:51 +00:00
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2014-08-20 22:49:44 +00:00
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definition Prop_inhabited [instance] : inhabited Prop :=
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mk true
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2014-08-20 22:49:44 +00:00
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definition fun_inhabited [instance] (A : Type) {B : Type} (H : inhabited B) : inhabited (A → B) :=
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2014-09-08 02:06:42 +00:00
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destruct H (λb, mk (λa, b))
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2014-09-16 18:44:50 +00:00
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definition dfun_inhabited [instance] (A : Type) {B : A → Type} (H : Πx, inhabited (B x)) :
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inhabited (Πx, B x) :=
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mk (λa, destruct (H a) (λb, b))
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2014-10-12 20:06:00 +00:00
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definition default (A : Type) [H : inhabited A] : A := destruct H (take a, a)
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2014-08-15 03:12:54 +00:00
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2014-08-20 02:32:44 +00:00
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end inhabited
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