23 lines
537 B
Text
23 lines
537 B
Text
-- 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: Jeremy Avigad, Floris van Doorn
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-- Empty type
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-- ----------
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import logic.core.cast
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inductive empty : Type
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namespace empty
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theorem elim [protected] (A : Type) (H : empty) : A :=
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rec (λe, A) H
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end empty
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namespace false
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theorem to_empty (H : false) : empty :=
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cast (false_elim H) true
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theorem rec_type (A : Type) (H : false) : A :=
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empty.rec (λx,A) (to_empty H)
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end false
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