Nuprl Lemma : cubical-term_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ({X ⊢ _:A} ∈ 𝕌{[i | j']})
Proof
Definitions occuring in Statement :
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,
cubical-type: {X ⊢ _},
cubical-term: {X ⊢ _:A},
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
cubical_type_at_pair_lemma,
cubical_type_ap_morph_pair_lemma,
fset_wf,
nat_wf,
I_cube_wf,
names-hom_wf,
equal_wf,
cube-set-restriction_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
setEquality,
functionEquality,
cumulativity,
isectElimination,
hypothesisEquality,
applyEquality,
universeIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. (\{X \mvdash{} \_:A\} \mmember{} \mBbbU{}\{[i | j']\})
Date html generated:
2020_05_20-PM-01_51_13
Last ObjectModification:
2020_04_07-PM-00_18_05
Theory : cubical!type!theory
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