Nuprl Lemma : arrow_prod_lemma
∀y,x,B,A:Top. (cat-arrow(A × B) x y ~ cat-arrow(A) (fst(x)) (fst(y)) × (cat-arrow(B) (snd(x)) (snd(y))))
Proof
Definitions occuring in Statement :
product-cat: A × B,
cat-arrow: cat-arrow(C),
top: Top,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
apply: f a,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
cat-arrow: cat-arrow(C),
product-cat: A × B,
pi2: snd(t),
pi1: fst(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{}y,x,B,A:Top.
(cat-arrow(A \mtimes{} B) x y \msim{} cat-arrow(A) (fst(x)) (fst(y)) \mtimes{} (cat-arrow(B) (snd(x)) (snd(y))))
Date html generated:
2020_05_20-AM-07_54_07
Last ObjectModification:
2017_01_09-PM-00_43_24
Theory : small!categories
Home
Index