Nuprl Lemma : uabeta-type_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. G ⊢ uabeta-type(G;A;B)
Proof
Definitions occuring in Statement :
uabeta-type: uabeta-type(G;A;B),
cubical-universe: c𝕌,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uabetatype: uabetatype(G;A;B;f),
uabeta-type: uabeta-type(G;A;B),
transport-type: TransportType(A)
Lemmas referenced :
uabetatype_wf,
istype-cubical-universe-term,
cubical_set_wf,
cubical-term_wf,
cubical-universe_wf,
path-type_wf,
path-trans_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
lambdaEquality_alt,
instantiate,
dependent_functionElimination,
universeIsType,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
rename,
isect_memberEquality_alt
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. G \mvdash{} uabeta-type(G;A;B)
Date html generated:
2020_05_20-PM-07_43_07
Last ObjectModification:
2020_04_30-AM-11_46_24
Theory : cubical!type!theory
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