Nuprl Lemma : cubical-universe-at
∀[I,a:Top]. (c𝕌(a) ~ A:{formal-cube(I) ⊢ _} × formal-cube(I) ⊢ CompOp(A))
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
composition-op: Gamma ⊢ CompOp(A),
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
formal-cube: formal-cube(I),
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,
cubical-universe: c𝕌,
cubical-type-at: A(a),
closed-type-to-type: closed-type-to-type(T),
closed-cubical-universe: cc𝕌,
pi1: fst(t),
fibrant-type: FibrantType(X)
Lemmas referenced :
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
axiomSqEquality,
inhabitedIsType,
hypothesisEquality,
sqequalHypSubstitution,
isect_memberEquality_alt,
isectElimination,
thin,
hypothesis,
isectIsTypeImplies,
extract_by_obid
Latex:
\mforall{}[I,a:Top]. (c\mBbbU{}(a) \msim{} A:\{formal-cube(I) \mvdash{} \_\} \mtimes{} formal-cube(I) \mvdash{} CompOp(A))
Date html generated:
2020_05_20-PM-07_07_30
Last ObjectModification:
2020_04_25-AM-11_35_37
Theory : cubical!type!theory
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