Nuprl Lemma : formal-cube-is-rep-pre-sheaf
∀[I:Top]. (formal-cube(I) ~ rep-pre-sheaf(CubeCat;I))
Proof
Definitions occuring in Statement :
formal-cube: formal-cube(I),
cube-cat: CubeCat,
rep-pre-sheaf: rep-pre-sheaf(C;X),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
cube-cat: CubeCat,
all: ∀x:A. B[x]
Lemmas referenced :
Yoneda-is-rep-pre-sheaf,
cat_arrow_triple_lemma,
cat_comp_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
dependent_functionElimination,
hypothesis
Latex:
\mforall{}[I:Top]. (formal-cube(I) \msim{} rep-pre-sheaf(CubeCat;I))
Date html generated:
2018_05_23-AM-08_33_40
Last ObjectModification:
2018_05_20-PM-05_46_38
Theory : cubical!type!theory
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