23 lines
962 B
Text
23 lines
962 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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-- Authors: Leonardo de Moura, Jeremy Avigad
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import logic.connectives.quantifiers
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inductive inhabited (A : Type) : Prop :=
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| inhabited_intro : A → inhabited A
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theorem inhabited_elim {A : Type} {B : Prop} (H1 : inhabited A) (H2 : A → B) : B :=
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inhabited_rec H2 H1
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theorem inhabited_Prop [instance] : inhabited Prop :=
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inhabited_intro true
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theorem 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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theorem inhabited_exists {A : Type} {p : A → Prop} (H : ∃x, p x) : inhabited A :=
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obtain w Hw, from H, inhabited_intro w
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