Nuprl Lemma : uniform-extend_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. (Gamma ⊢ Extension(A) ∈ 𝕌{[i | j'']})
Proof
Definitions occuring in Statement :
uniform-extend: uniform-extend{i:l}(Gamma; 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,
uniform-extend: uniform-extend{i:l}(Gamma; A),
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
extension-fun_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
uniform-extension-fun_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (Gamma \mvdash{} Extension(A) \mmember{} \mBbbU{}\{[i | j'']\})
Date html generated:
2020_05_20-PM-05_22_22
Last ObjectModification:
2020_04_18-PM-08_05_03
Theory : cubical!type!theory
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