Nuprl Lemma : fibrant-type_wf
∀[X:j⊢]. (FibrantType(X) ∈ 𝕌{[i' | j']})
Proof
Definitions occuring in Statement :
fibrant-type: FibrantType(X),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fibrant-type: FibrantType(X),
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-type_wf,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. (FibrantType(X) \mmember{} \mBbbU{}\{[i' | j']\})
Date html generated:
2020_05_20-PM-05_19_42
Last ObjectModification:
2020_04_14-PM-10_38_26
Theory : cubical!type!theory
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