Nuprl Lemma : cubical-nerve-I-cube
∀[X,I:Top]. (cubical-nerve(X)(I) ~ Functor(poset-cat(I);X))
Proof
Definitions occuring in Statement :
cubical-nerve: cubical-nerve(X),
poset-cat: poset-cat(J),
I-cube: X(I),
cat-functor: Functor(C1;C2),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-nerve: cubical-nerve(X),
I-cube: X(I),
functor-ob: functor-ob(F),
pi1: fst(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,I:Top]. (cubical-nerve(X)(I) \msim{} Functor(poset-cat(I);X))
Date html generated:
2016_06_16-PM-07_02_01
Last ObjectModification:
2015_12_28-PM-04_18_36
Theory : cubical!sets
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