20 lines
648 B
Text
20 lines
648 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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Module: logic.axioms.prop_decidable
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Author: Leonardo de Moura
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Excluded middle + Hilbert implies every proposition is decidable.
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-/
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import logic.axioms.prop_complete logic.axioms.hilbert
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open decidable inhabited nonempty
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theorem decidable_inhabited [instance] (a : Prop) : inhabited (decidable a) :=
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inhabited_of_nonempty
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(or.elim (em a)
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(assume Ha, nonempty.intro (inl Ha))
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(assume Hna, nonempty.intro (inr Hna)))
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theorem prop_decidable [instance] (a : Prop) : decidable a :=
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arbitrary (decidable a)
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