Nuprl Lemma : cubical_type_wf
∀[X:j⊢]. (cubical_type{i:l}(X) ∈ 𝕌{[i'' | j']})
Proof
Definitions occuring in Statement :
cubical_type: cubical_type{i:l}(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,
cubical_set: CubicalSet,
cubical_type: cubical_type{i:l}(X),
presheaf_type: presheaf_type{i:l}(C; X),
cubes: cubes(X)
Lemmas referenced :
presheaf_type_wf,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[X:j\mvdash{}]. (cubical\_type\{i:l\}(X) \mmember{} \mBbbU{}\{[i'' | j']\})
Date html generated:
2020_05_20-PM-01_46_02
Last ObjectModification:
2020_04_03-PM-08_23_31
Theory : cubical!type!theory
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