Nuprl Lemma : cubical-universe-cumulativity
∀[X:j⊢]. ({X ⊢ _:c𝕌} ⊆r {X ⊢ _:c𝕌'})
Proof
Definitions occuring in Statement :
cubical-universe: c𝕌,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
cubical-universe-cumulativity2,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaEquality_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
universeIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. (\{X \mvdash{} \_:c\mBbbU{}\} \msubseteq{}r \{X \mvdash{} \_:c\mBbbU{}'\})
Date html generated:
2020_05_20-PM-07_09_43
Last ObjectModification:
2020_04_25-PM-03_21_59
Theory : cubical!type!theory
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