Nuprl Lemma : functor_cat_ob_lemma
∀B,A:Top. (cat-ob(FUN(A;B)) ~ Functor(A;B))
Proof
Definitions occuring in Statement :
functor-cat: FUN(C1;C2),
cat-functor: Functor(C1;C2),
cat-ob: cat-ob(C),
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
functor-cat: FUN(C1;C2),
top: Top
Lemmas referenced :
top_wf,
cat_ob_pair_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}B,A:Top. (cat-ob(FUN(A;B)) \msim{} Functor(A;B))
Date html generated:
2020_05_20-AM-07_51_56
Last ObjectModification:
2017_01_09-PM-05_13_44
Theory : small!categories
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