Nuprl Lemma : comp_product_cat_lemma
∀g,f,z,y,x,B,A:Top.
(cat-comp(A × B) x y z f g ~ <cat-comp(A) (fst(x)) (fst(y)) (fst(z)) (fst(f)) (fst(g))
, cat-comp(B) (snd(x)) (snd(y)) (snd(z)) (snd(f)) (snd(g))
>)
Proof
Definitions occuring in Statement :
product-cat: A × B,
cat-comp: cat-comp(C),
top: Top,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
apply: f a,
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
cat-comp: cat-comp(C),
product-cat: A × B,
pi2: snd(t),
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
introduction,
extract_by_obid
Latex:
\mforall{}g,f,z,y,x,B,A:Top.
(cat-comp(A \mtimes{} B) x y z f g \msim{} <cat-comp(A) (fst(x)) (fst(y)) (fst(z)) (fst(f)) (fst(g))
, cat-comp(B) (snd(x)) (snd(y)) (snd(z)) (snd(f)) (snd(g))
>)
Date html generated:
2017_01_10-AM-08_41_36
Last ObjectModification:
2017_01_09-PM-00_59_51
Theory : small!categories
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