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annotate boolean.agda @ 2:ca2e9f7a7898

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Add De Morgan's laws
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 13 May 2014 11:14:49 +0900
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ca2e9f7a7898 Add De Morgan's laws
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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1 open import systemT
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2 open import Relation.Binary.PropositionalEquality
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3
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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4 module boolean where
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5
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6 _and_ : Bool -> Bool -> Bool
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7 T and b = b
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8 F and _ = F
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9
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10 _or_ : Bool -> Bool -> Bool
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11 T or _ = T
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12 F or b = b
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13
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14 not : Bool -> Bool
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15 not T = F
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16 not F = T
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17
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18 De-Morgan's-laws : (a b : Bool) -> (not a) and (not b) ≡ not (a or b)
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19 De-Morgan's-laws T T = refl
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20 De-Morgan's-laws T F = refl
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21 De-Morgan's-laws F T = refl
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22 De-Morgan's-laws F F = refl