Nuprl Lemma : functor_cat_arrow_lemma
∀G,F,B,A:Top. (cat-arrow(FUN(A;B)) F G ~ nat-trans(A;B;F;G))
Proof
Definitions occuring in Statement :
functor-cat: FUN(C1;C2),
nat-trans: nat-trans(C;D;F;G),
cat-arrow: cat-arrow(C),
top: Top,
all: ∀x:A. B[x],
apply: f a,
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_arrow_triple_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{}G,F,B,A:Top. (cat-arrow(FUN(A;B)) F G \msim{} nat-trans(A;B;F;G))
Date html generated:
2020_05_20-AM-07_51_58
Last ObjectModification:
2017_01_09-PM-05_18_32
Theory : small!categories
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