Nuprl Lemma : cubes-ob
∀[X:Top]. (cat-ob(cubes(X)) ~ I:fset(ℕ) × X(I))
Proof
Definitions occuring in Statement :
cubes: cubes(X),
I_cube: A(I),
cat-ob: cat-ob(C),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubes: cubes(X),
cube-cat: CubeCat,
all: ∀x:A. B[x],
top: Top,
I_cube: A(I),
I_set: A(I)
Lemmas referenced :
sets-ob,
cube-cat_wf,
cat_ob_pair_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[X:Top]. (cat-ob(cubes(X)) \msim{} I:fset(\mBbbN{}) \mtimes{} X(I))
Date html generated:
2018_05_23-AM-08_33_13
Last ObjectModification:
2018_05_20-PM-05_46_16
Theory : cubical!type!theory
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