lean2/library/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
import logic.core.decidable logic.core.inhabited
open decidable
inductive unit : Type :=
star : unit
namespace unit
notation `⋆`:max := star
theorem equal [protected] (a b : unit) : a = b :=
rec (rec rfl b) a
theorem eq_star (a : unit) : a = star :=
equal a star
theorem is_inhabited [protected] [instance] : inhabited unit :=
inhabited.mk ⋆
theorem has_decidable_eq [protected] [instance] : decidable_eq unit :=
take (a b : unit), inl (equal a b)
end unit