### Nuprl Lemma : comp_product_cat_lemma

g,f,z,y,x,B,A:Top.
(cat-comp(A × B) ~ <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: a pair: <a, b> sqequal: 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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