lean2/library/standard/data/unit.lean

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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
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import logic.classes.decidable logic.classes.inhabited
using decidable

namespace unit
inductive unit : Type :=
| star : unit

notation `⋆`:max := star

theorem unit_eq (a b : unit) : a = b :=
unit_rec (unit_rec (refl ⋆) b) a

theorem inhabited_unit [instance] : inhabited unit :=
inhabited_intro ⋆

theorem decidable_eq [instance] (a b : unit) : decidable (a = b) :=
inl (unit_eq a b)
end unit