Mercurial > hg > Members > atton > agda-proofs

annotate systemT/boolean.agda @ 1:fe247f476ecb

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Migrate systemT from atton/agda/systemT (13:5a81867278af)
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sun, 02 Nov 2014 09:40:54 +0900
parents
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 open import systemT
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
2 open import Relation.Binary.PropositionalEquality
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
3
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
4 module boolean where
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
5
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
6 _and_ : Bool -> Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
7 T and b = b
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
8 F and _ = F
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
9
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
10 _or_ : Bool -> Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
11 T or _ = T
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
12 F or b = b
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
13
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
14 not : Bool -> Bool
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
15 not T = F
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
16 not F = T
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
17
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
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)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
19 De-Morgan's-laws T T = refl
fe247f476ecb Migrate systemT from atton/agda/systemT (13:5a81867278af)
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
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:
diff changeset
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:
diff changeset
22 De-Morgan's-laws F F = refl