Nuprl Lemma : istype-cubical-term-closed-type
∀[X:j⊢]. ∀[T:{ * ⊢ _}]. istype({X ⊢ _:closed-type-to-type(T)})
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
closed-type-to-type: closed-type-to-type(T),
closed-cubical-type: { * ⊢ _},
cubical_set: CubicalSet,
istype: istype(T),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
closed-cubical-type: { * ⊢ _},
closed-type-to-type: closed-type-to-type(T),
cubical-term: {X ⊢ _:A},
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
cubical_type_at_pair_lemma,
cubical_type_ap_morph_pair_lemma,
fset_wf,
nat_wf,
I_cube_wf,
names-hom_wf,
cube-set-restriction_wf,
closed-cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
setIsType,
functionIsType,
universeIsType,
isectElimination,
instantiate,
hypothesisEquality,
applyEquality,
because_Cache,
equalityIstype
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[T:\{ * \mvdash{} \_\}]. istype(\{X \mvdash{} \_:closed-type-to-type(T)\})
Date html generated:
2020_05_20-PM-01_51_38
Last ObjectModification:
2020_03_20-PM-01_26_13
Theory : cubical!type!theory
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