Nuprl Lemma : cubical-universe-ap-morph
∀[I,b,J,f,a:Top]. ((b a f) ~ csm-fibrant-type(formal-cube(I);formal-cube(J);<f>;b))
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
csm-fibrant-type: csm-fibrant-type(G;H;s;FT),
cubical-type-ap-morph: (u a f),
context-map: <rho>,
formal-cube: formal-cube(I),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type-ap-morph: (u a f),
pi2: snd(t),
cubical-universe: c𝕌,
closed-type-to-type: closed-type-to-type(T),
closed-cubical-universe: cc𝕌,
csm-fibrant-type: csm-fibrant-type(G;H;s;FT)
Lemmas referenced :
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
hypothesis,
axiomSqEquality,
inhabitedIsType,
hypothesisEquality,
sqequalHypSubstitution,
isect_memberEquality_alt,
isectElimination,
thin,
isectIsTypeImplies,
extract_by_obid
Latex:
\mforall{}[I,b,J,f,a:Top]. ((b a f) \msim{} csm-fibrant-type(formal-cube(I);formal-cube(J);<f>b))
Date html generated:
2020_05_20-PM-07_06_46
Last ObjectModification:
2020_04_25-AM-11_35_05
Theory : cubical!type!theory
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