lean2/library/data/unit.lean

-- 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.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 unit_inhabited [instance] : inhabited unit :=
inhabited_mk ⋆

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

end unit
chore(library/standard): add copyright to library files Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-06-30 18:44:47 +00:00			`-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.`
			`-- Released under Apache 2.0 license as described in the file LICENSE.`
			`-- Author: Leonardo de Moura`
refactor(library/standard): organize files into a hierarchy 2014-08-01 01:40:09 +00:00
			`import logic.classes.decidable logic.classes.inhabited`
fix(lean/library/standard): fix tests, more cleanup 2014-08-20 22:49:44 +00:00
feat(library/standard): add decidable class Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-19 19:09:47 +00:00			`using decidable`
feat(library/standard): add inhabited, and files option and unit Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-06-30 02:30:38 +00:00
feat(library/standard): add decidable class Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-19 19:09:47 +00:00			`namespace unit`
fix(lean/library/standard): fix tests, more cleanup 2014-08-20 22:49:44 +00:00
feat(library/standard): add inhabited, and files option and unit Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-06-30 02:30:38 +00:00			`inductive unit : Type :=`
feat(*): change inductive datatype syntax Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-08-22 22:46:10 +00:00			`star : unit`
refactor(library/standard/unit): make unit type similar to the one in the hott library Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-22 16:56:05 +00:00
			notation `⋆`:max := star
feat(library/standard): add inhabited, and files option and unit Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-06-30 02:30:38 +00:00
refactor(library/standard): use new coding style, rename bool.b0 and bool.b1 to bool.ff and bool.tt Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-29 02:58:57 +00:00			`theorem unit_eq (a b : unit) : a = b :=`
			`unit_rec (unit_rec (refl ⋆) b) a`
feat(library/standard): add decidable class Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-19 19:09:47 +00:00
fix(lean/library/standard): fix tests, more cleanup 2014-08-20 22:49:44 +00:00			`theorem unit_inhabited [instance] : inhabited unit :=`
feat(library/standard): port int, and reorganize a lot 2014-08-20 02:32:44 +00:00			`inhabited_mk ⋆`
feat(library/standard): add decidable class Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-19 19:09:47 +00:00
refactor(library/standard): use new coding style, rename bool.b0 and bool.b1 to bool.ff and bool.tt Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-07-29 02:58:57 +00:00			`theorem decidable_eq [instance] (a b : unit) : decidable (a = b) :=`
			`inl (unit_eq a b)`
fix(lean/library/standard): fix tests, more cleanup 2014-08-20 22:49:44 +00:00
feat(library/standard): port int, and reorganize a lot 2014-08-20 02:32:44 +00:00			`end unit`