Nuprl Lemma : formal-cube-restriction
∀[I,f,s,A,B:Top]. (f(s) ~ s ⋅ f)
Proof
Definitions occuring in Statement :
formal-cube: formal-cube(I),
cube-set-restriction: f(s),
nh-comp: g ⋅ f,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
cube-set-restriction: f(s),
psc-restriction: f(s),
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
cube-cat: CubeCat,
all: ∀x:A. B[x]
Lemmas referenced :
Yoneda-restriction,
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,f,s,A,B:Top]. (f(s) \msim{} s \mcdot{} f)
Date html generated:
2018_05_23-AM-08_33_52
Last ObjectModification:
2018_05_20-PM-05_46_52
Theory : cubical!type!theory
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