Nuprl Lemma : same-cubical-term_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u,v:{X ⊢ _:A}]. (X ⊢ u=v:A ∈ 𝕌{[i | j']})
Proof
Definitions occuring in Statement :
same-cubical-term: X ⊢ u=v:A,
cubical-term: {X ⊢ _:A},
cubical-type: {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,
same-cubical-term: X ⊢ u=v:A,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal_wf,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u,v:\{X \mvdash{} \_:A\}]. (X \mvdash{} u=v:A \mmember{} \mBbbU{}\{[i | j']\})
Date html generated:
2020_05_20-PM-03_00_00
Last ObjectModification:
2020_04_06-AM-10_44_28
Theory : cubical!type!theory
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