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.
Module: data.unit
Author: Leonardo de Moura
-/
import logic.eq
namespace unit
notation `⋆` := star
protected theorem equal (a b : unit) : a = b :=
unit.rec_on a (unit.rec_on b rfl)
theorem eq_star (a : unit) : a = star :=
unit.equal a star
protected theorem subsingleton [instance] : subsingleton unit :=
subsingleton.intro (λ a b, equal a b)
protected definition is_inhabited [instance] : inhabited unit :=
inhabited.mk unit.star
protected definition has_decidable_eq [instance] : decidable_eq unit :=
take (a b : unit), decidable.inl (equal a b)
end unit