Mercurial > hg > Members > atton > agda-proofs

annotate systemT/boolean.agda @ 77:a2e6f61d5f2b default tip

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Add modus-ponens
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Thu, 09 Feb 2017 06:32:03 +0000
parents fe247f476ecb
children
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fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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1 open import systemT
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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2 open import Relation.Binary.PropositionalEquality
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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4 module boolean where
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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5
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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6 _and_ : Bool -> Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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7 T and b = b
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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8 F and _ = F
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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parents:
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fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
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10 _or_ : Bool -> Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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11 T or _ = T
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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12 F or b = b
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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parents:
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13
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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14 not : Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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15 not T = F
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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16 not F = T
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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parents:
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17
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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18 De-Morgan's-laws : (a b : Bool) -> (not a) and (not b) ≡ not (a or b)
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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19 De-Morgan's-laws T T = refl
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
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20 De-Morgan's-laws T F = refl
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
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21 De-Morgan's-laws F T = refl
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
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22 De-Morgan's-laws F F = refl