Nuprl Lemma : cubical-universe-p
∀[G:j⊢]. ∀[A:{G ⊢ _:c𝕌}]. ∀[T:{G ⊢ _}]. ((A)p ∈ {G.T ⊢ _:c𝕌})
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
csm-ap-term-p,
cubical-universe_wf,
cubical-type-cumulativity,
csm-cubical-universe,
cubical-type_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
universeIsType,
dependent_functionElimination
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A:\{G \mvdash{} \_:c\mBbbU{}\}]. \mforall{}[T:\{G \mvdash{} \_\}]. ((A)p \mmember{} \{G.T \mvdash{} \_:c\mBbbU{}\})
Date html generated:
2020_05_20-PM-07_08_59
Last ObjectModification:
2020_04_25-PM-01_41_37
Theory : cubical!type!theory
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