Nuprl Lemma : decode-universe-term
∀[G:j⊢]. (decode(t𝕌) = c𝕌 ∈ {G ⊢' _})
Proof
Definitions occuring in Statement :
universe-term: t𝕌,
universe-decode: decode(t),
cubical-universe: c𝕌,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
universe-term: t𝕌,
member: t ∈ T,
universe-encode: encode(T;cT)
Lemmas referenced :
universe-decode-encode,
cubical-universe_wf,
univ-comp_wf,
cubical_set_wf,
csm-cubical-universe,
csm-univ-comp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
universeIsType,
Error :memTop
Latex:
\mforall{}[G:j\mvdash{}]. (decode(t\mBbbU{}) = c\mBbbU{})
Date html generated:
2020_05_20-PM-07_25_05
Last ObjectModification:
2020_04_28-PM-01_07_45
Theory : cubical!type!theory
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