Nuprl Lemma : id_prod_cat_lemma
∀x,B,A:Top. (cat-id(A × B) x ~ <cat-id(A) (fst(x)), cat-id(B) (snd(x))>)
Proof
Definitions occuring in Statement :
product-cat: A × B,
cat-id: cat-id(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-id: cat-id(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{}x,B,A:Top. (cat-id(A \mtimes{} B) x \msim{} <cat-id(A) (fst(x)), cat-id(B) (snd(x))>)
Date html generated:
2020_05_20-AM-07_54_10
Last ObjectModification:
2017_01_09-PM-00_46_51
Theory : small!categories
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