Nuprl Lemma : cubical-type-cumulativity2
∀[X:j⊢]. ({X ⊢ _} ⊆r cubical-type{[j | i]:l}(X))
Proof
Definitions occuring in Statement :
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet
Lemmas referenced :
presheaf-type-cumulativity2,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. (\{X \mvdash{} \_\} \msubseteq{}r cubical-type\{[j | i]:l\}(X))
Date html generated:
2020_05_20-PM-01_47_08
Last ObjectModification:
2020_04_03-PM-08_23_37
Theory : cubical!type!theory
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