Nuprl Lemma : transport-type_wf
∀[G:j⊢]. ∀[A:{G ⊢ _:c𝕌}]. (TransportType(A) ∈ 𝕌{[i'' | j'']})
Proof
Definitions occuring in Statement :
transport-type: TransportType(A),
cubical-universe: c𝕌,
cubical-term: {X ⊢ _:A},
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,
transport-type: TransportType(A),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
cubical-term_wf,
cubical-universe_wf,
subtype_rel_universe1,
path-type_wf,
cubical-term-eqcd,
cubical-fun_wf,
universe-decode_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
hypothesis,
sqequalRule,
isectEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
independent_isectElimination,
lambdaEquality_alt,
cumulativity,
universeIsType,
universeEquality,
inhabitedIsType,
lambdaFormation_alt,
functionEquality,
equalityIstype,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A:\{G \mvdash{} \_:c\mBbbU{}\}]. (TransportType(A) \mmember{} \mBbbU{}\{[i'' | j'']\})
Date html generated:
2020_05_20-PM-07_42_33
Last ObjectModification:
2020_04_30-AM-11_53_41
Theory : cubical!type!theory
Home
Index