Nuprl Lemma : ob_mk_functor_lemma
∀t,arrow,ob:Top. (ob(functor(ob(x) = ob[x];arrow(u,v,f) = arrow[u;v;f])) t ~ ob[t])
Proof
Definitions occuring in Statement :
functor-ob: ob(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-ob: ob(F)
,
pi1: fst(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{}t,arrow,ob:Top. (ob(functor(ob(x) = ob[x];arrow(u,v,f) = arrow[u;v;f])) t \msim{} ob[t])
Date html generated:
2017_01_19-PM-02_52_15
Last ObjectModification:
2017_01_13-PM-00_38_47
Theory : small!categories
Home
Index