Nuprl Lemma : extension-fun_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. (extension-fun{j:l}(Gamma; A) ∈ 𝕌{[i | j'']})
Proof
Definitions occuring in Statement :
extension-fun: extension-fun{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,
extension-fun: extension-fun{i:l}(Gamma;A),
subtype_rel: A ⊆r B
Lemmas referenced :
cubical_set_wf,
cube_set_map_wf,
cubical-term_wf,
face-type_wf,
thin-context-subset,
csm-ap-type_wf,
context-subset_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-context-subset-subtype2,
constrained-cubical-term_wf,
cubical-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
lambdaEquality_alt,
cumulativity,
universeIsType,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (extension-fun\{j:l\}(Gamma; A) \mmember{} \mBbbU{}\{[i | j'']\})
Date html generated:
2020_05_20-PM-05_21_53
Last ObjectModification:
2020_04_17-AM-09_13_18
Theory : cubical!type!theory
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