Nuprl Lemma : arrow_mk_functor_lemma
∀g,y,x,arrow,ob:Top. (functor(ob(a) = ob[a];arrow(u,v,f) = arrow[u;v;f]) x y g ~ arrow[x;y;g])
Proof
Definitions occuring in Statement :
functor-arrow: arrow(F),
mk-functor: mk-functor,
top: Top,
so_apply: x[s1;s2;s3],
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
mk-functor: mk-functor,
functor-arrow: arrow(F),
pi2: snd(t),
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}g,y,x,arrow,ob:Top. (functor(ob(a) = ob[a];arrow(u,v,f) = arrow[u;v;f]) x y g \msim{} arrow[x;y;g])
Date html generated:
2020_05_20-AM-07_50_56
Last ObjectModification:
2017_01_13-PM-00_41_55
Theory : small!categories
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