### 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: 2020_05_20-AM-07_54_12
Last ObjectModification: 2017_01_09-PM-00_59_51

Theory : small!categories

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