Mercurial > hg > Members > tatsuki > proofsAndTypes
changeset 0:d9d5091eb899 draft default tip
Try 'and' definition on agda
author | tatsuki |
---|---|
date | Tue, 04 Mar 2014 15:04:53 +0900 |
parents | |
children | |
files | and.agda |
diffstat | 1 files changed, 38 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/and.agda Tue Mar 04 15:04:53 2014 +0900 @@ -0,0 +1,38 @@ +module and where + +postulate U : Set +postulate V : Set +postulate T : Set + +f : Set +f = U -> V + +record _x_ (U V : Set) : Set where + field + pi1 : U + pi2 : V + +postulate <_,_> : U -> V -> (U x V) + +open _x_ +postulate u : U +postulate v : V + +uv : U x V +uv = < u , v > +pair : Set +pair = U x V + + +postulate t : T + +x : T +x = t + +data _==_ {A : Set} : A -> A -> Set where + refl : {x : A} -> x == x + +lemma02 : U +lemma02 = pi1 (< u , v >) +lemma01 : (pi1 ( < u , v > )) == u +lemma01 = {!!} \ No newline at end of file